Structures.lua

-- Voxel world mode: detect the map's structures and pick a 3D model for
-- each -- the 3dSen idea applied to a tile map. 3dSen turns flat NES
-- scenes into 3D by classifying every graphic into a geometry archetype
-- (floor, wall, box, voxelized sprite) and building real geometry that
-- keeps the original art as its texture; this module does the same with
-- the map's tile layer as the scene description:
--
--   1. Flood-fill every connected region of solid (upright, unauthored)
--      tiles -- a house with its mailbox, the potted plant, a fence row,
--      a stretch of border forest.
--
--   2. Decide which pixels of the region's art are BACKGROUND. Tileset
--      art carries no alpha and white is a paint color (window frames,
--      wall stripes), so whiteness alone says nothing. The map does: the
--      background is the white that CONNECTS TO WALKABLE GROUND in the
--      assembled scene. Seeding a flood from the surrounding ground
--      eats the air around a fence post or a plant's leaves but cannot
--      reach an interior wall's white stripes sealed behind its dark
--      trim -- exactly the distinction a human reads.
--
--   3. Tiles whose art turned out mostly background are SPRITE-LIKE;
--      their connected clusters become per-pixel voxel OBJECTS at the
--      art's real drawn height (a 2-row plant is a 16px silhouette, a
--      fence a row of true posts with air between), thin voxel depth,
--      standing on synthesized ground. This splits mixed regions: the
--      mailbox voxelizes even where it touches the house.
--
--   4. Everything else becomes a VOLUME: each column rises to the height
--      the structure is actually DRAWN. A column's run gives its extent,
--      repetition caps it -- the border forest repeats a 2-row canopy
--      for forty rows and must be rows of 16px trees, not a monolith --
--      and columns answer to their region: the column above a doorway
--      repeats internally but adopts its 48px house. The south face
--      folds the artwork up (ChunkMesher's band rule).
--
-- data/voxel_heights.lua is the PROFILE over this: a tile authored there
-- (ledges, or a mod pinning a shape) bypasses detection entirely, the way
-- a 3dSen game profile pins a pattern to a geometry type.
--
-- Everything here is derived per map and cached; pixel access (object
-- voxelization, void detection) degrades gracefully headless -- regions
-- simply stay volumes and the geometry tests keep passing.

-- the mod namespace (see main.lua): V.require loads a sibling module
local V = ...

local Assets = require("src.render.Assets")
local Map = require("src.world.Map")
local Buildings = V.require("Buildings")
local TileShape = V.require("TileShape")
local Budget = V.require("BuildBudget")

local Structures = {}

-- must match ChunkMesher's ring (3 border blocks, in tiles)
local RING = 12

-- how far past the map body cells still get the hull. A route's ring is
-- nearly as big as its body; modelling all of it costs hundreds of
-- thousands of quads of border trees nobody walks near. Beyond this,
-- pinned cells simply are not claimed and fall through to the mesher's
-- plain box -- cheap distant scenery. (Declared up here rather than
-- beside buildCylinders because forMap's grid resolve reads it too.)
local ROUND_RING = 4

-- object-mode gates
local OBJECT_MAX_ROWS = 6          -- a prop is at most 48px of drawing
local OBJECT_MAX_QUADS = 4096      -- safety cap per cluster
local TILE_BG_RATIO = 0.20         -- art background for "sprite-like"
local CLUSTER_MIN_BG = 0.05        -- a silhouette must actually exist
local OBJECT_DEPTH = 6             -- voxel thickness of a detected prop
-- thickness of profile-pinned standees per class: a TV is a deliberate
-- object and reads better with body; `prop` doubles as the THIN pool
-- (plants, stools -- mostly silhouette); `cutout` is paper: one voxel,
-- pure profile; `post` matches the 6px the detector gives the fence
-- rows it finds on its own, so pinned and detected fences look alike;
-- `signpost` is a plate on a stick -- 2 voxels, the thinnest that still
-- shows an edge; `bike` is the same 2 for the same reason from the other
-- direction -- a bicycle drawn side-on is a LINE drawing whose negative
-- space is the drawing, and at the 5 voxels `prop` gives, the side faces
-- of neighbouring strokes close every gap in it off-axis
local PINNED_DEPTH = { billboard = 10, prop = 5, stool = 10, cutout = 1,
                       console = 10, post = 6, signpost = 2, bike = 2 }

local MAX_ROWS = 6                 -- volume height cap: 48px

local cache = {}

-- ---------------------------------------------------------------- pixels --

local atlasData = {}

local function pixels(tileset)
  local path = tileset.image
  if atlasData[path] == nil then
    local ok, data = pcall(Assets.imageData, path)
    atlasData[path] = (ok and data and data.getPixel) and data or false
  end
  return atlasData[path] or nil
end

-- tiles whose art is entirely black or transparent (interior darkness):
-- these never extrude, whatever class they resolved to
local function voidTiles(tileset)
  local data = pixels(tileset)
  if not data then return nil end
  local perRow = tileset.tilesPerRow or 16
  local iw, ih = data:getDimensions()
  local set = {}
  for t = 0, (iw / 8) * (ih / 8) - 1 do
    local ox = (t % perRow) * 8
    local oy = math.floor(t / perRow) * 8
    local void = true
    for py = 0, 7 do
      for px = 0, 7 do
        local r, g, b, a = data:getPixel(ox + px, oy + py)
        if a > 0 and math.max(r, g, b) > 0.17 then
          void = false
          break
        end
      end
      if not void then break end
    end
    if void then set[t] = true end
  end
  return set
end

-- ----------------------------------------------------------------- build --

local DIRS4 = { { 1, 0 }, { -1, 0 }, { 0, 1 }, { 0, -1 } }

local function keyOf(tx, ty)
  return (ty + 64) * 4096 + (tx + 64)
end

function Structures.forMap(map)
  local S = cache[map.id]
  if S then return S end

  local tileset = map.tileset
  local shapes = TileShape.forMap(map)
  local void = voidTiles(tileset)
  local perRow = tileset.tilesPerRow or 16

  local def = map.def
  local tw, th = def.width * 4, def.height * 4
  local x0, x1 = -RING, tw + RING - 1
  local y0, y1 = -RING, th + RING - 1

  -- resolve the whole grid once: shape + tile per key. Ring positions use
  -- the same border override the 2D renderer draws with
  -- (TileRenderer.borderBlockFor: outdoor maps ring with the solid tree
  -- wall, NOT their own borderBlock) -- a route's borderBlock is the GRASS
  -- block, and meshing that grew a 12-tile apron of tall grass past every
  -- route edge, which leaked into the neighbouring town's plaza.
  -- BLACK void fill is not a block at all: borderBlockFor answers `false`,
  -- and there is simply nothing out there to build. tileLookup then returns
  -- nil past the body and the ring keys are never written, which the whole
  -- file already copes with -- every neighbour query reaches one step
  -- outside the analysed range and reads nil for its trouble, so an absent
  -- cell is the shape "nothing" has always had here. (It used to add 1 to
  -- that `false`, which threw, failed the mesh build for every map on the
  -- route, and dropped the mode to the flat 2D path entirely.)
  local TileRenderer = require("src.render.TileRenderer")
  local borderId = TileRenderer.borderBlockFor(map)
  local borderBlk = borderId and tileset.blocks[borderId + 1] or nil
  -- TREES fill stops at ROUND_RING instead of running the full RING.
  -- Only that far out does a tree cell get carved into a hull; past it
  -- the cells fall through to the mesher's plain box, and a slab of
  -- flat-topped boxes beside the modelled wall reads as a painted-on
  -- plateau -- the wall looking like it was cut off with scissors. So
  -- the far ring is simply not built: beyond ROUND_RING tileLookup
  -- answers nil, which is the same "nothing out there" BLACK already
  -- produces and every pass below already copes with. The cut lands on
  -- the carve boundary exactly -- the 2x2-cell canopy scan starts at
  -- floor(-RING/2) and RING, ROUND_RING and the body are all multiples
  -- of 4 tiles, so no group is left half-resolved at the edge.
  --
  -- WATER and the other tilesets' own borders keep the full ring: a flat
  -- sheet of water is what water looks like from above anyway, and an
  -- interior's border is black already.
  local hullRingOnly = borderBlk and def.tileset == "OVERWORLD"
                       and (TileRenderer.voidFill or "trees") == "trees"
  local tw2, th2 = tw, th
  local function tileLookup(tx, ty)
    if tx >= 0 and ty >= 0 and tx < tw2 and ty < th2 then
      return map:tileAt(tx, ty)
    end
    if not borderBlk then return nil end
    if hullRingOnly and (tx < -ROUND_RING or ty < -ROUND_RING
                         or tx >= tw2 + ROUND_RING
                         or ty >= th2 + ROUND_RING) then
      return nil
    end
    return borderBlk[(ty % 4) * 4 + (tx % 4) + 1] or 0
  end
  local shapeAt, tileAt = {}, {}
  for ty = y0, y1 do
    for tx = x0, x1 do
      Budget.tick()
      local tile = tileLookup(tx, ty)
      if tile then
        local k = keyOf(tx, ty)
        local s = TileShape.at(map, shapes, tile, tx, ty)
        if s and void and void[tile] and not s.authored then
          s = shapes.classes.void
        end
        shapeAt[k], tileAt[k] = s, tile
      end
    end
  end

  -- ---- buildings: whole sprites voxelized band by band ----
  --
  -- Before anything else looks at this grid. A profiled building is a
  -- drawing whose bands depict DIFFERENT 3D surfaces (roof from above,
  -- facade face-on, ends sloped), and the passes below -- the door fold,
  -- the region flood, the volume builder -- all assume one drawing is one
  -- upright thing. Modelling the building first and claiming its tiles
  -- keeps every one of them off it.
  --
  -- (grassQuads live apart from objectQuads: grass renders as its own mesh
  -- AFTER the characters -- see VoxelScene -- so the southern tuft row
  -- still overdraws a walker's feet even though characters stamp over
  -- terrain.)
  S = { shapeAt = shapeAt, tileAt = tileAt, outdoor = Map.isOutdoor(def),
        hideBareRing = hullRingOnly or nil,
        runs = {}, skip = {}, ground = {}, doorFold = {}, objectQuads = {},
        grassQuads = {}, flowerQuads = {}, roundStamps = {}, figures = {},
        -- tile key -> the row a collapsed bookcase rank's box actually
        -- stands on, so a standee supported by one lands on it rather than
        -- where the drawing put it (see buildBookcases)
        bookcaseBox = {} }
  Buildings.build(S, map, pixels(tileset), perRow)

  -- Fold doors into their buildings. A door cell is WALKABLE (the player
  -- steps onto it to warp), so it resolves to ground and punches a hole in
  -- the facade: the door lies flat, the rows above it recess, and -- worse
  -- -- the hole lets the background flood into the building's interior
  -- whites, shredding it into misdetected sprite clusters. Visually the
  -- door is part of the facade, so mark the door cell's tiles structural:
  -- the fold then shows the door art standing at ground level in the
  -- building's front face. Door graphics only (the tileset's doorTiles);
  -- interior stair/mat warps stay flat.
  --
  -- A PROFILE PIN WINS over the fold. The fold is detection, and rule 1
  -- of the resolution order is that an authored tile bypasses detection
  -- -- but this used to overwrite shapeAt unconditionally, so a pin on
  -- any tile the tileset also lists in doorTiles was dead on arrival.
  -- Celadon Mansion is the case that found it: all four of its
  -- staircases are door tiles, so `stair_e` / `stair_down_w` pins there
  -- silently did nothing and the flights stayed painted on the floor.
  for cy = math.floor(y0 / 2), math.floor(y1 / 2) do
    for cx = math.floor(x0 / 2), math.floor(x1 / 2) do
      if map.doorTiles[map:cellTile(cx, cy)] then
        local northK = keyOf(cx * 2, cy * 2 - 1)
        local ns = shapeAt[northK]
        if ns and ns.art == "upright" then
          for dy = 0, 1 do
            for dx = 0, 1 do
              local dk = keyOf(cx * 2 + dx, cy * 2 + dy)
              local ds = shapeAt[dk]
              if not (ds and ds.authored) then
                shapeAt[dk] = shapes.classes.wall
                -- remembered for buildVolume: a folded doorway column
                -- answers to its REGION for height and top, not to its
                -- own drawn extent (see the door adoption there)
                S.doorFold[dk] = true
              end
            end
          end
        end
      end
    end
  end

  -- a structure cell: solid art the detector may model (authored tiles are
  -- profile-pinned and keep their authored shape)
  local function structural(k)
    local s = shapeAt[k]
    return s and s.art == "upright" and not s.authored
  end

  -- ---- cylinders: profile-pinned round graphics, one per 16x16 cell ----
  -- the flat ground tiles this map actually places, for the hull's
  -- ground matching: the ball's own drawn background picks its floor
  local groundTiles = {}
  do
    local seenG = {}
    for k, s in pairs(shapeAt) do
      if s and s.flat and s.class == "ground" then
        local t = tileAt[k]
        if t and not seenG[t] then
          seenG[t] = true
          groundTiles[#groundTiles + 1] = t
        end
      end
    end
  end
  Structures.buildCylinders(S, map, x0, x1, y0, y1, groundTiles)

  -- ---- stairs: profile-pinned cells that render as real steps ----
  Structures.buildStairs(S, map, x0, x1, y0, y1)

  -- ---- bookcases: pinned shelves collapsed to one cell of depth ----
  -- The atlas comes along so the shelf front can carry its own measured
  -- relief: the panes it seals behind its black frames sink a voxel.
  Structures.buildBookcases(S, map, x0, x1, y0, y1, pixels(tileset), perRow)

  -- ---- figures: a person drawn INTO furniture, lifted off it ----
  -- Before the region flood and the volume pass, so everything after this
  -- reads the tiles the profile says are there once the figure is gone.
  -- (Its own tiles are authored furniture or walkable floor either way, so
  -- no pass below would have claimed them -- but the repaint is what those
  -- passes should see, and this needs no pixel access to do it.)
  Structures.buildFigures(S, map, x0, x1, y0, y1)

  -- ---- mounted: a thing drawn INTO a wall band, stood proud of it ----
  -- Here for the same reason and with the same guarantee as the figures
  -- above: the repaint hands every pass below the plain panel the profile
  -- says is behind the object, so the wall band it was painted into keeps
  -- resolving as the wall it is -- without a second copy of the drawing
  -- flat on its face.
  Structures.buildMounted(S, map, x0, x1, y0, y1)

  -- ---- flood-fill regions of structural tiles ----
  local seen = {}
  local regions = {}
  for ty = y0, y1 do
    for tx = x0, x1 do
      local k = keyOf(tx, ty)
      if structural(k) and not seen[k] then
        local region = { tiles = {}, minX = tx, maxX = tx,
                         minY = ty, maxY = ty }
        local queue = { { tx, ty } }
        seen[k] = true
        while #queue > 0 do
          Budget.tick()
          local c = table.remove(queue)
          local cx, cy = c[1], c[2]
          region.tiles[#region.tiles + 1] = c
          region.minX = math.min(region.minX, cx)
          region.maxX = math.max(region.maxX, cx)
          region.minY = math.min(region.minY, cy)
          region.maxY = math.max(region.maxY, cy)
          for _, d in ipairs(DIRS4) do
            local nx, ny = cx + d[1], cy + d[2]
            if nx >= x0 and nx <= x1 and ny >= y0 and ny <= y1 then
              local nk = keyOf(nx, ny)
              if structural(nk) and not seen[nk] then
                seen[nk] = true
                queue[#queue + 1] = { nx, ny }
              end
            end
          end
        end
        regions[#regions + 1] = region
      end
    end
  end

  -- ---- model each region: carve out per-pixel objects, volume the rest --
  local data = pixels(tileset)
  for _, region in ipairs(regions) do
    local leftover = region.tiles
    if data then
      leftover = Structures.extractObjects(S, map, region, data, perRow)
    end
    if #leftover > 0 then
      Structures.buildVolume(S, map, leftover)
    end
  end

  -- ---- profile-pinned billboards (signs): forced per-pixel slabs ----
  if data then
    local seenB = {}
    for ty = y0, y1 do
      for tx = x0, x1 do
        local k = keyOf(tx, ty)
        local s = shapeAt[k]
        if s and s.art == "billboard" and not seenB[k] then
          local reg = { tiles = {}, minX = tx, maxX = tx,
                        minY = ty, maxY = ty }
          local queue = { { tx, ty } }
          seenB[k] = true
          while #queue > 0 do
            local c = table.remove(queue)
            reg.tiles[#reg.tiles + 1] = c
            reg.minX = math.min(reg.minX, c[1])
            reg.maxX = math.max(reg.maxX, c[1])
            reg.minY = math.min(reg.minY, c[2])
            reg.maxY = math.max(reg.maxY, c[2])
            for _, d in ipairs(DIRS4) do
              local nk = keyOf(c[1] + d[1], c[2] + d[2])
              local ns = shapeAt[nk]
              -- same CLASS, not just billboard art: `billboard` and
              -- `prop` are two pools precisely so touching drawings (a TV
              -- behind its console) become two standing objects instead
              -- of one stacked cutout
              if ns and ns.art == "billboard" and ns.class == s.class
                 and not seenB[nk] then
                seenB[nk] = true
                queue[#queue + 1] = { c[1] + d[1], c[2] + d[2] }
              end
            end
          end
          Structures.extractObjects(S, map, reg, data, perRow, true)
        end
      end
    end

    -- ---- profile-pinned fence posts: per-CELL standee slabs ----
    -- A fence line repeats one drawing for a dozen cells, and its art
    -- touches across cell seams. Pooled like a billboard the whole line
    -- would stand as ONE drawing-tall tower at one depth (the detector's
    -- vertical-repetition guard exists precisely to refuse that, which
    -- is why undetected fence columns fell to the volume path as boxes).
    -- Each CELL extracts alone instead: its posts stand in their own row
    -- band and the fence marches north cell by cell.
    local postCells = {}
    for ty = y0, y1 do
      for tx = x0, x1 do
        local s = shapeAt[keyOf(tx, ty)]
        if s and s.art == "post" then
          local ck = keyOf(math.floor(tx / 2), math.floor(ty / 2))
          postCells[ck] = postCells[ck] or {}
          local list = postCells[ck]
          list[#list + 1] = { tx, ty }
        end
      end
    end
    for _, tiles in pairs(postCells) do
      local reg = { tiles = tiles,
                    minX = tiles[1][1], maxX = tiles[1][1],
                    minY = tiles[1][2], maxY = tiles[1][2] }
      for _, c in ipairs(tiles) do
        reg.minX = math.min(reg.minX, c[1])
        reg.maxX = math.max(reg.maxX, c[1])
        reg.minY = math.min(reg.minY, c[2])
        reg.maxY = math.max(reg.maxY, c[2])
      end
      Structures.extractObjects(S, map, reg, data, perRow, "opaque")
    end

    -- ---- profile-pinned relief props: top-down drawings that extrude ----
    local seenR = {}
    for ty = y0, y1 do
      for tx = x0, x1 do
        local k = keyOf(tx, ty)
        local s = shapeAt[k]
        if s and s.art == "relief" and not seenR[k] then
          local reg = { tiles = {}, minX = tx, maxX = tx,
                        minY = ty, maxY = ty }
          local queue = { { tx, ty } }
          seenR[k] = true
          while #queue > 0 do
            local c = table.remove(queue)
            reg.tiles[#reg.tiles + 1] = c
            reg.minX = math.min(reg.minX, c[1])
            reg.maxX = math.max(reg.maxX, c[1])
            reg.minY = math.min(reg.minY, c[2])
            reg.maxY = math.max(reg.maxY, c[2])
            for _, d in ipairs(DIRS4) do
              local nk = keyOf(c[1] + d[1], c[2] + d[2])
              local ns = shapeAt[nk]
              if ns and ns.art == "relief" and ns.class == s.class
                 and not seenR[nk] then
                seenR[nk] = true
                queue[#queue + 1] = { c[1] + d[1], c[2] + d[2] }
              end
            end
          end
          for _, c in ipairs(reg.tiles) do
            local ck = keyOf(c[1], c[2])
            S.skip[ck] = true
            S.ground[ck] = false
          end
          Structures.buildRelief(S, map, reg, data, perRow, s.h or 5)
        end
      end
    end

    -- ---- tall grass: two standing tuft rows per tile. BODY only: the 2D
    -- renderer never draws a neighbour's ring, and standing scenery past a
    -- map's edge would poke into the map next door ----
    Structures.buildGrass(S, map, 0, tw - 1, 0, th - 1, data)

    -- ---- flowers: the animated meadow tile stands as a 1px cutout ----
    Structures.buildFlowers(S, map, tw, th, x0, x1, y0, y1, data)
  end

  -- ---- authored ground under pinned props ----
  -- The profile can name the tile a pinned prop stands on (a tileset
  -- entry's prop_ground: prop tile id -> ground tile id), overriding
  -- the neighbour vote. The cuttable bush stands on the plain grass
  -- Cut itself leaves behind, not on whatever path its neighbours
  -- happen to vote in.
  do
    local okP, prof = pcall(V.data, "voxel_heights")
    local entry = okP and type(prof) == "table" and prof.tilesets
                  and prof.tilesets[tileset.id]
    local pg = entry and entry.prop_ground
    if type(pg) == "table" then
      for k, skipped in pairs(S.skip) do
        if skipped then
          local g = pg[S.tileAt[k]]
          if g then S.ground[k] = g end
        end
      end
    end
  end

  -- unresolved claimed ground (a hull with no art match, headless
  -- cylinders): no flat neighbour to vote with, so fall back to the
  -- map's commonest ground tile
  local votes, best, bestN = {}, nil, 0
  for k, s in pairs(shapeAt) do
    if s and s.flat and s.class == "ground" then
      local t = tileAt[k]
      votes[t] = (votes[t] or 0) + 1
      if votes[t] > bestN then best, bestN = t, votes[t] end
    end
  end
  for k, g in pairs(S.ground) do
    if g == false then S.ground[k] = best end
  end

  cache[map.id] = S
  return S
end

-- ---- round scenery: outline-hulled voxel balls ----

-- Cells the profile pins as round (tree canopies -- the class keeps its
-- historical `cylinder` name in the data file) render as a VOXEL HULL cut
-- from the drawing itself. The first shipped attempt was a lathe -- the
-- per-row silhouette width revolved into a 12-segment column with the art
-- wrapped by sin(angle) -- and it read exactly like what it was: the
-- sprite pasted on a cylinder, with the wrap smearing the pixels into
-- vertical stripes. This replaces it with real voxels.
--
-- Segmentation first, silhouette-width second: the tree cell's art is a
-- ball drawn over background grass, and the background's mid greens pass
-- any brightness test (they inflated every lathe row to full width). The
-- ball's own DARKEST pixels are what bound it, so the mask is "the
-- darkest-shade outline plus everything it encloses": flood from the cell
-- border through every non-black pixel; what the flood cannot reach is
-- the tree, and the cast shadow under the canopy (dark but not enclosed)
-- floods away with the grass. Art with no closed black outline -- the
-- border tree wall is a dither of black and canopy with no drawn ring --
-- encloses nothing; there the flood passes only through the LIGHT shades
-- (the methodology doc's rule: black and dark together form the
-- boundary), and the dither mass itself becomes the mask, checker holes
-- and all, because a 4-connected flood cannot thread a diagonal checker.
--
-- Volume: each mask row is a disc. The row's span gives a center and
-- half-width, and every mask pixel's column runs that circle's chord in
-- z, quantized to whole voxels -- the front view IS the sprite, the plan
-- view is the sprite's own width profile turned in depth, and both step
-- pixel by pixel. Rows below the mask (the drawn shadow) repeat the
-- bottom row's discs down to the ground so the canopy stands on a short
-- dark foot instead of floating.
--
-- Skin: front and back faces carry the drawing per-pixel (the back reads
-- mirrored, sprite-pure); side and step faces take their column's own
-- texel, which puts the drawn outline exactly on the silhouette's rim;
-- and a fully exposed cap keeps its outline only on the rim cells while
-- the interior samples the canopy a couple of rows deeper -- painting the
-- whole cap with the outline row blacked out every dome on the first
-- attempt (the lathe hit the same bug with its top discs).
--
-- Tree walls repeat the same four tiles for hundreds of cells, so the
-- hull is built once per distinct art signature and stamped per cell.
local ROUND_SHADE = { front = 1.0, back = 0.68, side = 0.78,
                      top = 1.0, bottom = 0.55 }

-- The potted plant's ORGANIC HALF: the leaf crown (16 rows), then the
-- trunk, its root flare and the strands draping over the pot's rim (8
-- more) -- all of it stands as a slab this many voxels deep instead of
-- revolving. `depth` 5 is the thin standee pool's depth, what every other
-- interior plant already uses.
--
-- `rows` = 24 puts the slab/revolve boundary AT THE VESSEL'S RIM ROW, and
-- that placement is what makes the pot read as a pot. The first cut put
-- it at the cell seam (16), which let the root and drape rows revolve:
-- their drawn spans are 8-12 wide, so they stacked 8-12-deep discs on top
-- of the rim and the whole base read as one bulbous onion instead of a
-- flat-mouthed planter with a trunk standing out of it. Only rows 24-31
-- -- black rim edge, gold band, body, foot, the drawn flowerpot profile
-- -- are the vessel, and only they revolve.
local PLANTER_SPRAY = { rows = 24, depth = 5 }

-- `spray`, when given, caps the chord over the canvas's top `rows` rows to
-- `depth` voxels instead of revolving them.
--
-- Revolving a row turns its DRAWN WIDTH into depth, which only means
-- something when the drawing states a width to turn -- the pot's rows do
-- (a 3px stem opening to a 12px belly and closing to a 6px foot, an urn's
-- profile), and a tree canopy's do (the ball's outline is drawn). A leaf
-- crown's do NOT: the leaves are a spray that runs off all four sides of
-- its tile, so every row measures the full canvas and the revolve can only
-- produce a solid cylinder -- the "hedge column" a plant must never become,
-- with one row of texels smeared down its whole top face. Where the drawing
-- states no profile, the honest reading is the one the thin standee pools
-- exist for: the foliage stands as a per-pixel slab and keeps the airy
-- silhouette that makes it read as leaves.
-- `squash`, when given, is the PERCENT of its revolved depth every chord
-- keeps -- 100 (or nil) is the identity, 50 halves the hull front to back.
--
-- A full revolve assumes the drawing's width is also its depth, which is
-- true of a thing that really is round in plan (a hedge ball, a boulder,
-- a trash can). A TREE is round in its canopy and thin at every other
-- reading: the trunk is a stick, the crown is more air than wood, and the
-- drawing is scenery seen from one side. Revolved at full width the little
-- tree eats a whole cell of depth and reads as a boulder wearing bark, so
-- the plan stays a circle and shrinks toward an ellipse: still round in
-- section, still stepping pixel by pixel, just shallower. The chord is
-- re-centred on the mid-plane, so the model neither slides nor detaches
-- from the cells around it.
local function roundTemplate(S, map, data, cx, cy, groundTiles, N, capRows,
                             NYin, spray, baseRows, bodyRows, wellRows,
                             taperVox, squash)
  -- The canvas is NX wide and NX DEEP (a hull is round in plan, so its
  -- depth is its width) by NY tall. NX = 16 is one cell, 32 a 2x2-cell
  -- group; NY defaults to NX -- a ball -- and NY = 2 * NX is a drawing
  -- STACKED two cells high on one cell of plot (the potted plant).
  local NX = N or 16
  local NY = NYin or NX
  local N2 = NX / 2
  local perRow = map.tileset.tilesPerRow or 16
  local atlasW = map.tileset.imageWidth or 128
  local atlasH = map.tileset.imageHeight or 48

  -- cell-space art access (NX x NY, row 0 = top), anchored at cell (cx, cy)
  local function tileOf(px, py)
    return S.tileAt[keyOf(cx * 2 + math.floor(px / 8),
                          cy * 2 + math.floor(py / 8))]
  end
  local function texel(px, py)
    local tile = tileOf(px, py)
    return (tile % perRow) * 8 + px % 8,
           math.floor(tile / perRow) * 8 + py % 8
  end

  -- shade class of every canvas pixel, indexed py * NX + px
  local cls = {}
  for py = 0, NY - 1 do
    for px = 0, NX - 1 do
      local ax, ay = texel(px, py)
      local r, g, b, a = data:getPixel(ax, ay)
      cls[py * NX + px] = a == 0 and "off"
                          or Structures.shadeClass(math.min(r, g, b))
    end
  end

  -- 4-connected flood from a row band's border through `passable` classes
  local function floodOutside(passable, y0, y1)
    local out, stack = {}, {}
    local function seed(i)
      if not out[i] and passable[cls[i]] then
        out[i] = true
        stack[#stack + 1] = i
      end
    end
    for px = 0, NX - 1 do
      seed(y0 * NX + px); seed(y1 * NX + px)
    end
    for py = y0, y1 do
      seed(py * NX); seed(py * NX + NX - 1)
    end
    while #stack > 0 do
      local i = table.remove(stack)
      local px, py = i % NX, math.floor(i / NX)
      if px > 0 then seed(i - 1) end
      if px < NX - 1 then seed(i + 1) end
      if py > y0 then seed(i - NX) end
      if py < y1 then seed(i + NX) end
    end
    return out
  end

  -- The mask -- darkest-pixel outline plus its enclosure, with the dither
  -- rule as fallback -- computed per CELL BAND of NX rows.
  --
  -- A square canvas is ONE band, so this is exactly the whole-canvas rule
  -- it replaces. A STACKED canvas needs it per band because its two halves
  -- want opposite answers: the potted plant's leaf crown is a black-outlined
  -- dither drawn over floor (outline enclosure keeps it), while its pot is a
  -- solid DARK body whose base runs flush to the band's bottom edge (the
  -- enclosure flood walks in through dark and guts it, and the fallback --
  -- which the band's own `enclosed` count asks for -- keeps it). Measured on
  -- the Center plant: one flood over both bands keeps 53% of the drawing and
  -- leaves the pot a hollow black frame; per band keeps 68% and both read.
  local mask = {}
  for band = 0, NY / NX - 1 do
    local y0, y1 = band * NX, band * NX + NX - 1
    local out = floodOutside({ off = true, dark = true,
                               light = true, white = true }, y0, y1)
    local enclosed = 0
    for i = y0 * NX, (y1 + 1) * NX - 1 do
      if not out[i] then
        mask[i] = true
        if cls[i] ~= "black" then enclosed = enclosed + 1 end
      end
    end
    if enclosed < NX * NX / 8 then
      out = floodOutside({ off = true, light = true, white = true }, y0, y1)
      for i = y0 * NX, (y1 + 1) * NX - 1 do
        mask[i] = (not out[i] and cls[i] ~= "off") or nil
      end
    end
  end
  local any = nil
  for i = 0, NX * NY - 1 do any = any or mask[i] end
  if not any then return {} end

  -- a CAPPED hull (the stump): the top capRows rows of the mask are the
  -- drawn cut face -- a surface seen at an angle, not body. Strip them
  -- from the mask and remember their art span; the top-face quads below
  -- project that ellipse across the round cap.
  local capY0, capY1 = nil, nil
  if capRows and capRows > 0 then
    local top = nil
    for iy = 0, NY - 1 do
      for ix = 0, NX - 1 do
        if mask[iy * NX + ix] then top = iy break end
      end
      if top then break end
    end
    if top then
      capY0 = top
      capY1 = math.min(top + capRows - 1, NY - 2)
      for iy = capY0, capY1 do
        for ix = 0, NX - 1 do mask[iy * NX + ix] = nil end
      end
      any = nil
      for i = 0, NX * NY - 1 do any = any or mask[i] end
      if not any then return {} end
    end
  end

  -- a FLAT-BASED hull (the can): the bottom baseRows rows of the mask are
  -- the BASE circle's front arc -- the drawing's mirror of the cut face
  -- above, ground contact seen from above rather than body. A can is only
  -- round in the horizontal plane, so the drop those rows make toward the
  -- middle is DEPTH, not a narrowing of the plan: left as body they revolve
  -- into ever smaller discs and the can ends up balanced on a stem three
  -- voxels wide (which is exactly what the first build did). Strip them and
  -- the foot rule below runs the last body row's full disc straight to the
  -- floor; the rows keep their own texels there, so the front view is still
  -- the drawing, base rim and all.
  local baseArt = nil
  if baseRows and baseRows > 0 then
    local bot = nil
    for iy = NY - 1, 0, -1 do
      for ix = 0, NX - 1 do
        if mask[iy * NX + ix] then bot = iy break end
      end
      if bot then break end
    end
    if bot then
      baseArt = {}
      for iy = math.max(bot - baseRows + 1, (capY1 or -1) + 2), bot do
        for ix = 0, NX - 1 do
          local i = iy * NX + ix
          if mask[i] then baseArt[i] = true end
          mask[i] = nil
        end
      end
      any = nil
      for i = 0, NX * NY - 1 do any = any or mask[i] end
      if not any then return {} end
    end
  end

  -- The can's HEIGHT, and the one place this file departs from the drawing
  -- on purpose. Strictly un-projected, the drawing states a squat drum: cut
  -- the mouth ellipse off the top and the base circle off the bottom and
  -- barely two rows of straight side are left between them, because the GB
  -- artist spent most of a 16px cell on the opening. A real bin is TALLER
  -- than it is wide, and the flat game reads as one because the drawing is
  -- 14px tall next to a 16px player -- so the height is authored (can_height
  -- voxels) rather than measured, and the surviving body band is repeated
  -- upward to fill it, bottom row first, which continues the drawn rib
  -- rhythm instead of inventing a texel. Everything else still comes off
  -- the pixels.
  local artRow = {}
  if bodyRows and bodyRows > 0 then
    local body = {}
    for iy = 0, NY - 1 do
      for ix = 0, NX - 1 do
        if mask[iy * NX + ix] then body[#body + 1] = iy break end
      end
    end
    local nb = #body
    if nb > 0 then
      local top = body[1]
      for iy = top - 1, math.max(NY - bodyRows, 0), -1 do
        -- the LOWEST surviving body row, repeated: it is the widest and
        -- plainest reading of the material (outline, shaded flank, lit
        -- face) and stacks into a clean metal cylinder. Cycling the whole
        -- surviving band instead stacks the drawn rim arcs into a barcode
        -- of hoops, which is detail the drawing never states about the
        -- side of the can.
        local from = body[nb]
        artRow[iy] = from
        for ix = 0, NX - 1 do
          mask[iy * NX + ix] = mask[from * NX + ix]
        end
      end
    end
  end

  -- the ground the ball stands on: the drawing's own background names
  -- it. Score every flat ground tile the map places against the cell's
  -- unmasked light pixels and keep the closest -- mid-forest trees have
  -- no flat neighbour to vote with, and the commonest-ground fallback
  -- paints pale path under trees whose art sits on grass. Dark unmasked
  -- pixels (the drawn cast shadow) stay out of the score: no ground
  -- tile carries a shadow, and their darks would drag every match.
  local bg = nil
  if groundTiles and #groundTiles > 0 then
    local bestScore = nil
    for _, t in ipairs(groundTiles) do
      local ox = (t % perRow) * 8
      local oy = math.floor(t / perRow) * 8
      local score, n = 0, 0
      for py = 0, NY - 1 do
        for px = 0, NX - 1 do
          local i = py * NX + px
          local c = cls[i]
          -- a stripped base row is the OBJECT's own rim, not background:
          -- scoring its whites against the floor tiles matches paper-white
          -- ground under a can whose art stands on the gym's grey
          if not mask[i] and not (baseArt and baseArt[i])
             and (c == "light" or c == "white") then
            local ax, ay = texel(px, py)
            local r1, g1, b1 = data:getPixel(ax, ay)
            local r2, g2, b2 = data:getPixel(ox + px % 8, oy + py % 8)
            local dr, dg, db = r1 - r2, g1 - g2, b1 - b2
            score = score + dr * dr + dg * dg + db * db
            n = n + 1
          end
        end
      end
      if n > 0 then
        score = score / n
        if not bestScore or score < bestScore then bestScore, bg = score, t end
      end
    end
  end

  -- discs: per mask pixel a z chord [z0, z1), from its row's span circle.
  -- z2/z3 is an optional SECOND chord for the same pixel, which only the
  -- can's hollow mouth uses: a ring in plan needs a front wall and a back
  -- wall at the same column, and one interval cannot say that.
  local z0, z1, z2, z3, src, srcX = {}, {}, {}, {}, {}, {}
  local loRow, hiRow = {}, {}
  local yBot = nil
  for iy = 0, NY - 1 do
    local lo, hi = nil, nil
    for ix = 0, NX - 1 do
      if mask[iy * NX + ix] then
        lo = lo or ix
        hi = ix
      end
    end
    if lo then
      loRow[iy], hiRow[iy] = lo, hi
      yBot = iy
      local c = (lo + hi + 1) / 2
      local hw = (hi - lo + 1) / 2
      for ix = lo, hi do
        local i = iy * NX + ix
        if mask[i] then
          local dx = ix + 0.5 - c
          local n = 1
          if hw * hw > dx * dx then
            n = math.max(1, math.floor(2 * math.sqrt(hw * hw - dx * dx)
                                       + 0.5))
          end
          if spray and iy < spray.rows then n = math.min(n, spray.depth) end
          if squash then n = math.max(1, math.floor(n * squash / 100 + 0.5)) end
          z0[i] = math.floor(N2 - n / 2 + 0.5)
          z1[i] = z0[i] + n
          -- a row the can's body band was repeated into wears the row it
          -- was copied from, never a texel of its own
          src[i] = artRow[iy] or iy
        end
      end
    end
  end

  -- Spray-gap BACKING: the drawing's own gap pixels, one voxel deep at
  -- the slab's mid-plane. The flat crown is full of floor showing
  -- between leaves; carved as an open slab those gaps became TUNNELS --
  -- the Center couch, the man sitting on it and the void wall all read
  -- as pink/orange/black confetti INSIDE the foliage, and the sparse
  -- bottom rows (lone drawn leaf tips) floated as disconnected specks
  -- against them. The drawing itself backs every gap with its own
  -- pixels, so the hull does the same: each in-span gap below drawn
  -- foliage takes ITS OWN texel as a plate recessed behind the leaf
  -- relief. Coverage is monotone down a column, so the first backed
  -- cell always sits directly under a leaf chord -- and every chord
  -- spans the mid-plane, so no plate ever caps the crown's top: columns
  -- open to the sky stay open and the silhouette keeps its notches.
  if spray then
    for iy = 1, math.min(spray.rows, NY) - 1 do
      if loRow[iy] then
        for ix = loRow[iy], hiRow[iy] do
          local i = iy * NX + ix
          if not z0[i] then
            local covered = false
            for iy2 = 0, iy - 1 do
              if mask[iy2 * NX + ix] then covered = true break end
            end
            if covered then
              z0[i], z1[i], src[i] = N2, N2 + 1, iy
            end
          end
        end
      end
    end
  end

  -- foot: rows under the mask repeat the bottom row's discs, wearing the
  -- bottom row's (outline-dark) pixels -- except where a stripped base row
  -- DREW something at that pixel, which keeps its own texel, so a can's
  -- drawn base rim lands on the model's base instead of being painted over
  -- by the body band above it
  for iy = yBot + 1, NY - 1 do
    loRow[iy], hiRow[iy] = loRow[yBot], hiRow[yBot]
    for ix = loRow[yBot], hiRow[yBot] do
      local b = yBot * NX + ix
      if z0[b] then
        local i = iy * NX + ix
        z0[i], z1[i] = z0[b], z1[b]
        src[i] = (baseArt and baseArt[i]) and iy or yBot
      end
    end
  end

  -- the TAPER: a bin is a truncated cone, not a tube -- wide at the rim,
  -- drawn in a couple of voxels toward the base. The drawing agrees as far
  -- as it can (its own base arc pulls in to 9px from the 11px flanks), but
  -- it cannot state the whole run, so taperVox is the diameter the base
  -- loses and the rows in between interpolate. Every row keeps its plan
  -- ROUND: narrow the span, then re-cut the chords from the narrowed span,
  -- or the model comes out a cylinder with its corners shaved.
  local stepped = {}
  if taperVox and taperVox > 0 then
    local yTopRow = nil
    for iy = 0, NY - 1 do
      if loRow[iy] then yTopRow = iy break end
    end
    local span = NY - 1 - (yTopRow or 0)
    if yTopRow and span > 0 then
      for iy = yTopRow, NY - 1 do
        local inset = math.floor(taperVox / 2 * (iy - yTopRow) / span + 0.5)
        if inset > 0 and loRow[iy] then
          local lo = loRow[iy] + inset
          local hi = hiRow[iy] - inset
          if hi - lo < 1 then
            lo = math.floor((loRow[iy] + hiRow[iy]) / 2)
            hi = lo + 1
          end
          for ix = loRow[iy], hiRow[iy] do
            if ix < lo or ix > hi then
              local i = iy * NX + ix
              z0[i], z1[i], z2[i], z3[i] = nil, nil, nil, nil
            end
          end
          -- squeeze the row's ART into the narrowed span rather than
          -- clipping its ends off: the drawn outline is the last column
          -- either side, and dropping it leaves the taper's new edge
          -- wearing an interior texel -- a white chip down the rim
          for ix = lo, hi do
            srcX[iy * NX + ix] = loRow[iy]
              + math.floor((ix - lo) * (hiRow[iy] - loRow[iy])
                           / (hi - lo) + 0.5)
          end
          loRow[iy], hiRow[iy] = lo, hi
          stepped[iy] = true
          local c = (lo + hi + 1) / 2
          local hw = (hi - lo + 1) / 2
          for ix = lo, hi do
            local i = iy * NX + ix
            if z0[i] then
              local dx = ix + 0.5 - c
              local n = 1
              if hw * hw > dx * dx then
                n = math.max(1, math.floor(2 * math.sqrt(hw * hw - dx * dx)
                                           + 0.5))
              end
              if squash then
                n = math.max(1, math.floor(n * squash / 100 + 0.5))
              end
              z0[i] = math.floor(N2 - n / 2 + 0.5)
              z1[i] = z0[i] + n
            end
          end
        end
      end
    end
  end

  -- the MOUTH: a bin is open, and a solid top wearing the drawn opening
  -- only paints one. Hollow the top wellRows voxel rows -- every chord
  -- long enough to hold two walls plus a gap keeps a wall at each end and
  -- loses its middle, which is a ring in plan, so the model has a real rim
  -- to look into. The short chords at the left and right of the row ARE
  -- the ring's sides and stay solid on their own.
  local wellTop = nil
  if wellRows and wellRows > 0 then
    for iy = 0, NY - 1 do
      if loRow[iy] then wellTop = iy break end
    end
    local wall = 2
    for iy = wellTop or 0, math.min((wellTop or 0) + wellRows - 1, NY - 1) do
      if loRow[iy] then
        for ix = loRow[iy], hiRow[iy] do
          local i = iy * NX + ix
          if z0[i] and z1[i] - z0[i] > wall * 2 then
            z2[i], z3[i] = z1[i] - wall, z1[i]
            z1[i] = z0[i] + wall
          end
        end
      end
    end
  end

  -- the round cap's top row and z extent, for the stump's ring
  -- projection below
  local capTopRow, capZ0, capZ1 = nil, nil, nil
  if capY0 then
    for iy = 0, NY - 1 do
      if loRow[iy] then capTopRow = iy break end
    end
    if capTopRow then
      for ix = loRow[capTopRow], hiRow[capTopRow] do
        local i = capTopRow * NX + ix
        if z0[i] then
          -- the OUTER extent, so a hollowed row still projects the mouth
          -- across the whole opening and not just its front wall
          local back = z3[i] or z1[i]
          capZ0 = math.min(capZ0 or z0[i], z0[i])
          capZ1 = math.max(capZ1 or back, back)
        end
      end
    end
  end

  -- the art row the mouth projection puts at depth iz -- the drawn
  -- opening's north arc at the far side of the hull, its south arc at the
  -- near one. The top-face pass below reads the same mapping; this is the
  -- vertical faces inside the well asking it the same question.
  local function mouthRow(iz)
    if not (capY0 and capZ0 and capZ1) then return 0 end
    local t = capZ1 - 1 > capZ0 and (iz - capZ0) / (capZ1 - 1 - capZ0) or 0
    t = math.max(0, math.min(1, t))
    return capY0 + math.floor(t * (capY1 - capY0) + 0.5)
  end

  local function solidAt(ix, iy, iz)
    if ix < 0 or ix > NX - 1 or iy < 0 or iy > NY - 1 then return false end
    local i = iy * NX + ix
    if z0[i] == nil then return false end
    if iz >= z0[i] and iz < z1[i] then return true end
    return z2[i] ~= nil and iz >= z2[i] and iz < z3[i]
  end

  -- cap interiors sample the canopy a couple of rows below the rim,
  -- skipping outline-dark pixels
  local function deepTexel(ix, iy)
    for iy2 = iy + 2, math.min(NY - 1, iy + 4) do
      local i = iy2 * NX + ix
      if mask[i] and cls[i] ~= "black" then return texel(ix, iy2) end
    end
    return texel(ix, iy)
  end

  -- side walls read as material, not outline: walk inward past black
  -- pixels (the building extruder's de-outline rule). The silhouette's
  -- edge columns are all outline, and without this every flank of the
  -- ball paints solid black the moment the camera turns. The foot rows
  -- stay dark on purpose: their whole source row is outline-black.
  local function sideTexel(ix, iy)
    -- A foot row's SIDE keeps the last body row's material even where its
    -- FRONT wears a stripped base row (the can). The drawn base rim is
    -- front-face art; walking the de-outline inside a row that is no longer
    -- in the mask breaks at once and hands back the silhouette's own
    -- outline, which painted every flank of the can solid black.
    local r = (yBot and iy > yBot) and yBot or src[iy * NX + ix]
    -- the walk runs in ART columns, so a tapered row starts from the drawn
    -- pixel its squeezed span put here rather than from the model column
    local a = srcX[iy * NX + ix] or ix
    local dir = ix + ix < loRow[iy] + hiRow[iy] and 1 or -1
    for step = 0, 3 do
      local x2 = a + dir * step
      local i2 = r * NX + x2
      if x2 < 0 or x2 > NX - 1 or not mask[i2] then break end
      if cls[i2] ~= "black" then return texel(x2, r) end
    end
    return texel(a, r)
  end

  local quads = {}

  for iy = 0, NY - 1 do
    if loRow[iy] then
      local yB, yT = NY - 1 - iy, NY - iy

      -- front and back: the drawing per-pixel, columns merged where they
      -- share a chord plane; a run never crosses the 8px atlas tile seam
      -- (its u range must interpolate inside one tile)
      local ix = loRow[iy]
      while ix <= hiRow[iy] do
        local i = iy * NX + ix
        if z0[i] then
          local ix2 = ix
          while ix2 + 1 <= hiRow[iy] do
            local j = iy * NX + ix2 + 1
            -- src too: a can's foot row draws part of its span from the
            -- stripped base rim and the rest from the body band above it,
            -- so a run must not straddle two source rows (the u range is
            -- interpolated from one row's texels)
            if z0[j] == z0[i] and z1[j] == z1[i] and src[j] == src[i]
               and z2[j] == z2[i] and z3[j] == z3[i]
               and math.floor((ix2 + 1) / 8) == math.floor(ix / 8) then
              ix2 = ix2 + 1
            else
              break
            end
          end
          local x0, x1 = ix - N2, ix2 - N2 + 1
          -- one facing pair per chord, each face given the art row it
          -- should wear. A hollowed mouth row has two chords, and the two
          -- faces that look into the well take the drawn OPENING (via the
          -- same projection the rim does) rather than the body band: the
          -- drawing paints its mouth dark, and an inside-out white wall
          -- across the opening is the one thing that stops a bin reading
          -- as a bin.
          local function facing(za, zb, rowF, rowB)
            local zF, zB = zb - N2, za - N2
            local function pair(z, row, shade, back)
              local ax0, ay = texel(srcX[i] or ix, row)
              local ax1 = (texel(srcX[iy * NX + ix2] or ix2, row))
              local u0, u1 = (ax0 + 0.05) / atlasW, (ax1 + 0.95) / atlasW
              local v0, v1 = (ay + 0.05) / atlasH, (ay + 0.95) / atlasH
              if back then
                quads[#quads + 1] = {
                  { x1, yB, z }, { x0, yB, z }, { x0, yT, z }, { x1, yT, z },
                  uv = { { u1, v1 }, { u0, v1 }, { u0, v0 }, { u1, v0 } },
                  shade = shade,
                }
              else
                quads[#quads + 1] = {
                  { x0, yB, z }, { x1, yB, z }, { x1, yT, z }, { x0, yT, z },
                  uv = { { u0, v1 }, { u1, v1 }, { u1, v0 }, { u0, v0 } },
                  shade = shade,
                }
              end
            end
            pair(zF, rowF, ROUND_SHADE.front, false)
            pair(zB, rowB, ROUND_SHADE.back, true)
          end
          local body = src[i]
          if z2[i] then
            -- z grows toward the viewer: the low chord is the can's FAR
            -- wall, so its +z face is the inside you look across, and the
            -- near chord's -z face is the inside of the wall facing you
            facing(z0[i], z1[i], mouthRow(z1[i]), body)
            facing(z2[i], z3[i], body, mouthRow(z2[i] - 1))
          else
            facing(z0[i], z1[i], body, body)
          end
          ix = ix2 + 1
        else
          ix = ix + 1
        end
      end

      -- sides, steps, undersides: constant-texel quads over the z runs a
      -- neighbour doesn't cover
      for ix = loRow[iy], hiRow[iy] do
        local i = iy * NX + ix
        if z0[i] then
          local ax, ay = texel(srcX[i] or ix, src[i])
          local u, v = (ax + 0.5) / atlasW, (ay + 0.5) / atlasH
          local x0, x1 = ix - N2, ix - N2 + 1

          -- exposed z pieces against one neighbouring column, over each of
          -- the pixel's chords (a hollowed mouth row has two)
          local function chordPieces(nx, ny, emit, zLo, zHi)
            local iz = zLo
            while iz < zHi do
              if not solidAt(nx, ny, iz) then
                local iz2 = iz
                while iz2 + 1 < zHi and not solidAt(nx, ny, iz2 + 1) do
                  iz2 = iz2 + 1
                end
                emit(iz - N2, iz2 - N2 + 1, iz, iz2)
                iz = iz2 + 1
              else
                iz = iz + 1
              end
            end
          end
          local function pieces(nx, ny, emit)
            chordPieces(nx, ny, emit, z0[i], z1[i])
            if z2[i] then chordPieces(nx, ny, emit, z2[i], z3[i]) end
          end

          local sax, say = sideTexel(ix, iy)
          local su, sv = (sax + 0.5) / atlasW, (say + 0.5) / atlasH
          pieces(ix - 1, iy, function(zA, zB)
            quads[#quads + 1] = {
              { x0, yB, zA }, { x0, yB, zB }, { x0, yT, zB }, { x0, yT, zA },
              u = su, v = sv, shade = ROUND_SHADE.side,
            }
          end)
          pieces(ix + 1, iy, function(zA, zB)
            quads[#quads + 1] = {
              { x1, yB, zB }, { x1, yB, zA }, { x1, yT, zA }, { x1, yT, zB },
              u = su, v = sv, shade = ROUND_SHADE.side,
            }
          end)
          pieces(ix, iy - 1, function(zA, zB, izA, izB)
            local function top(za, zb, tu, tv)
              quads[#quads + 1] = {
                { x0, yT, za }, { x1, yT, za }, { x1, yT, zb }, { x0, yT, zb },
                u = tu, v = tv, shade = ROUND_SHADE.top,
              }
            end
            -- the whole hollowed band takes the projection, not just its
            -- top row: the rim ring gets the mouth's outer arcs and the
            -- floor of the well gets its middle, so looking in reads as
            -- one opening rather than a lid with a hole punched in it
            if capTopRow and capZ1
               and iy >= capTopRow and iy <= capTopRow + (wellRows or 0) then
              -- the CUT FACE (a capped hull's top): project the drawn
              -- ellipse across the round cap voxel row by voxel row --
              -- its top arc at the cap's north rim, its bottom arc at
              -- the south, the perspective the 2D art already implies
              for iz = izA, izB do
                local t = capZ1 - 1 > capZ0
                          and (iz - capZ0) / (capZ1 - 1 - capZ0) or 0
                local ry = capY0 + math.floor(t * (capY1 - capY0) + 0.5)
                local cax, cay = texel(srcX[i] or ix, ry)
                top(iz - N2, iz - N2 + 1,
                    (cax + 0.5) / atlasW, (cay + 0.5) / atlasH)
              end
            elseif izA == z0[i] and izB == z1[i] - 1 and izB - izA >= 2 then
              -- the dome cap: outline on the rim cells, canopy inside
              local du, dv = deepTexel(ix, iy)
              top(zA, zA + 1, u, v)
              top(zA + 1, zB - 1, (du + 0.5) / atlasW, (dv + 0.5) / atlasH)
              top(zB - 1, zB, u, v)
            elseif stepped[iy] then
              -- a taper STEP: the chord narrowing leaves a ring facing up
              -- at the front of the can, and wearing the lit body band it
              -- reads as a bright chip taken out of the wall. The drawing's
              -- own rim column is black, so the step wears that and the
              -- taper reads as a hoop line -- which is how the reference
              -- object is banded anyway.
              local rx = srcX[iy * NX + loRow[iy]] or loRow[iy]
              local rax, ray = texel(rx, src[i])
              top(zA, zB, (rax + 0.5) / atlasW, (ray + 0.5) / atlasH)
            else
              top(zA, zB, u, v)
            end
          end)
          if iy < NY - 1 then
            pieces(ix, iy + 1, function(zA, zB)
              quads[#quads + 1] = {
                { x0, yB, zB }, { x1, yB, zB }, { x1, yB, zA }, { x0, yB, zA },
                u = u, v = v, shade = ROUND_SHADE.bottom,
              }
            end)
          end
        end
      end
    end
  end
  return quads, bg
end

-- Hull templates dedupe GLOBALLY per (tileset, four tiles, ground set):
-- the same four-tile tree repeats for hundreds of cells on a map and
-- across every route of its tileset, so the carve runs once per distinct
-- drawing per session.  What a map keeps is a STAMP LIST -- (template,
-- cell offset) pairs the mesher expands while packing vertices -- rather
-- than materialized per-cell quad tables, which retained ~500 quads x
-- hundreds of tree cells x six Lua tables each PER MAP (the multi-GB
-- heap growth on a cross-region trek).
local roundCache = {}

function Structures.buildCylinders(S, map, x0, x1, y0, y1, groundTiles)
  local data = pixels(map.tileset)
  local tw, th = map.def.width * 4, map.def.height * 4

  -- ground-set fingerprint: the template's art-matched floor depends on
  -- which ground tiles this map places, so maps sharing a tileset but
  -- not a palette of floors carve separately
  local gsig
  do
    local g = {}
    for i, t in ipairs(groundTiles or {}) do g[i] = t end
    table.sort(g)
    gsig = table.concat(g, ",")
  end
  local tsid = tostring(map.tileset.id or map.tileset.image or "?")

  -- the stump class's drawn-ellipse height, hand-authored per tileset
  -- (the profile's stump_cap, in art rows), and the can class's three: the
  -- mouth ellipse over the top (can_cap) and the base ellipse under the
  -- bottom (can_base), both in art rows, plus the authored can_height in
  -- voxels the body band is repeated up to
  local stumpCap, canCap, canBase, canHeight, canWell, canTaper
    = 6, 9, 4, 9, 5, 4
  -- the sapling class's depth, as a PERCENT of the revolved chord
  local saplingSquash = 50
  do
    local okP, prof = pcall(V.data, "voxel_heights")
    local entry = okP and type(prof) == "table" and prof.tilesets
                  and prof.tilesets[map.tileset.id]
    if entry and type(entry.stump_cap) == "number" then
      stumpCap = entry.stump_cap
    end
    if entry and type(entry.can_cap) == "number" then
      canCap = entry.can_cap
    end
    if entry and type(entry.can_base) == "number" then
      canBase = entry.can_base
    end
    if entry and type(entry.can_height) == "number" then
      canHeight = entry.can_height
    end
    if entry and type(entry.can_well) == "number" then
      canWell = entry.can_well
    end
    if entry and type(entry.can_taper) == "number" then
      canTaper = entry.can_taper
    end
    if entry and type(entry.sapling_squash) == "number" then
      saplingSquash = entry.sapling_squash
    end
  end

  -- cells consumed by a 2x2 `canopy` group; the scan runs north to
  -- south, west to east, so an anchor always claims its partners
  -- before they are visited
  local grouped = {}
  for cy = math.floor(y0 / 2), math.floor(y1 / 2) do
    for cx = math.floor(x0 / 2), math.floor(x1 / 2) do
      Budget.tick()
      local ckey = cy * 8192 + cx
      local k = keyOf(cx * 2, cy * 2)
      local s = (not grouped[ckey]) and S.shapeAt[k] or nil
      local near = cx * 2 >= -ROUND_RING and cx * 2 < tw + ROUND_RING
               and cy * 2 >= -ROUND_RING and cy * 2 < th + ROUND_RING
      if s and s.art == "canopy" and near then
        -- ONE 32px hull over the 2x2-cell drawing. The partner cells
        -- must be round-pinned too, or the drawing is partial (a map
        -- edit, a mod's stray anchor tile) and the anchor is left
        -- alone rather than carved into a half-empty giant.
        local whole = true
        for _, d in ipairs({ { 1, 0 }, { 0, 1 }, { 1, 1 } }) do
          local ps = S.shapeAt[keyOf((cx + d[1]) * 2, (cy + d[2]) * 2)]
          if not (ps and (ps.art == "cylinder" or ps.art == "canopy")) then
            whole = false
          end
        end
        if whole then
          local ground = false
          if data then
            local ids = {}
            for dy = 0, 3 do
              for dx = 0, 3 do
                ids[#ids + 1] = S.tileAt[keyOf(cx * 2 + dx, cy * 2 + dy)]
              end
            end
            local sig = tsid .. "|g32|" .. gsig .. "|"
                        .. table.concat(ids, ":")
            local tpl = roundCache[sig]
            if not tpl then
              local tq, tbg = roundTemplate(S, map, data, cx, cy,
                                            groundTiles, 32)
              tpl = { quads = tq, bg = tbg }
              roundCache[sig] = tpl
            end
            ground = tpl.bg or false
            S.roundStamps[#S.roundStamps + 1] =
              { quads = tpl.quads, mx = cx * 16 + 16, mz = cy * 16 + 16,
                r = 16 }
          end
          for dy = 0, 3 do
            for dx = 0, 3 do
              local tk = keyOf(cx * 2 + dx, cy * 2 + dy)
              S.skip[tk] = true
              S.ground[tk] = ground
            end
          end
          grouped[ckey + 1] = true
          grouped[ckey + 8192] = true
          grouped[ckey + 8193] = true
        end
      elseif s and s.art == "planter" and near then
        -- ONE 16x32x16 hull over a drawing stacked TWO CELLS HIGH on one
        -- cell of plot: the Pokemon Centers' potted plants (a leaf crown
        -- over a flared pot, 78 placements across 13 maps).
        --
        -- The anchor is the NORTH cell -- the crown, where the canvas
        -- starts -- but the hull stands in the SOUTH cell, because that is
        -- where the pot is drawn and an object's ground contact is its
        -- plot. The crown is therefore HEIGHT, not depth: the north cell
        -- is claimed and left as floor for the crown to overhang, which is
        -- what un-projecting the 3/4 view means here. Pinning only one of
        -- the two cells leaves the drawing partial (a map edit, a mod's
        -- stray tile), so the anchor is left alone rather than carved into
        -- half a plant.
        local below = S.shapeAt[keyOf(cx * 2, (cy + 1) * 2)]
        if below and below.art == "planter" then
          local ground = false
          if data then
            local ids = {}
            for dy = 0, 3 do
              for dx = 0, 1 do
                ids[#ids + 1] = S.tileAt[keyOf(cx * 2 + dx, cy * 2 + dy)]
              end
            end
            local sig = tsid .. "|p32|" .. gsig .. "|"
                        .. table.concat(ids, ":")
            local tpl = roundCache[sig]
            if not tpl then
              local tq, tbg = roundTemplate(S, map, data, cx, cy,
                                            groundTiles, 16, nil, 32,
                                            PLANTER_SPRAY)
              tpl = { quads = tq, bg = tbg }
              roundCache[sig] = tpl
            end
            ground = tpl.bg or false
            S.roundStamps[#S.roundStamps + 1] =
              { quads = tpl.quads, mx = cx * 16 + 8,
                mz = (cy + 1) * 16 + 8 }
          end
          for dy = 0, 3 do
            for dx = 0, 1 do
              local tk = keyOf(cx * 2 + dx, cy * 2 + dy)
              S.skip[tk] = true
              S.ground[tk] = ground
            end
          end
          grouped[ckey + 8192] = true
        end
      elseif s and s.art == "cylinder" and near then
        -- a `stump`-class cell is the same hull with a cut face: its
        -- top capRows of drawing project onto the round top. A `can`-class
        -- cell is that hull cut at BOTH ends -- lid on top, base circle on
        -- the floor -- which is what a drum standing on a floor is.
        local cap = (s.class == "stump" and stumpCap)
                    or (s.class == "can" and canCap) or nil
        local base = s.class == "can" and canBase or nil
        local tall = s.class == "can" and canHeight or nil
        local well = s.class == "can" and canWell or nil
        local taper = s.class == "can" and canTaper or nil
        -- 100% is the full revolve, so it is the identity: never signed
        -- into the cache key, and never passed, by a class that has no
        -- squash of its own
        local squash = (s.class == "sapling" and saplingSquash ~= 100)
                       and saplingSquash or nil
        local ground = false
        if data then
          local sig = tsid .. (cap and ("|c" .. cap) or "")
            .. (base and ("|b" .. base) or "")
            .. (tall and ("|h" .. tall) or "")
            .. (well and ("|w" .. well) or "")
            .. (taper and ("|t" .. taper) or "")
            .. (squash and ("|q" .. squash) or "") .. "|"
            .. gsig .. "|" .. table.concat({
            S.tileAt[k], S.tileAt[keyOf(cx * 2 + 1, cy * 2)],
            S.tileAt[keyOf(cx * 2, cy * 2 + 1)],
            S.tileAt[keyOf(cx * 2 + 1, cy * 2 + 1)] }, ":")
          local tpl = roundCache[sig]
          if not tpl then
            local tq, tbg = roundTemplate(S, map, data, cx, cy,
                                          groundTiles, 16, cap, nil, nil,
                                          base, tall, well, taper, squash)
            tpl = { quads = tq, bg = tbg }
            roundCache[sig] = tpl
          end
          ground = tpl.bg or false
          S.roundStamps[#S.roundStamps + 1] =
            { quads = tpl.quads, mx = cx * 16 + 8, mz = cy * 16 + 8 }
        end
        -- headless (no pixels): no hull, but still claim the tiles so
        -- the volume path never boxes a pinned cell. Ground is the
        -- template's own art-matched tile; `false` (no match, headless)
        -- falls to the commonest-ground pass below.
        for dy = 0, 1 do
          for dx = 0, 1 do
            local tk = keyOf(cx * 2 + dx, cy * 2 + dy)
            S.skip[tk] = true
            S.ground[tk] = ground
          end
        end
      end
    end
  end
end

-- ---- relief props: top-down drawings lying on their surface ----

-- A cell pinned `relief` is a prop DRAWN FROM ABOVE (a game console on
-- the floor): standing it up would be wrong, and a solid box would carry
-- the drawn floor around it.  The drawing is segmented like any forced
-- prop (black outline; the shades touching the cluster's edge are the
-- background) and the object pixels extrude straight up a few voxels,
-- art on the top face -- a piece of the drawing pushed out of the
-- ground.  The floor the flood removed is repainted by the claimed
-- tiles' common-ground fill.
local RELIEF_SHADE = { top = 1.0, south = 0.9, north = 0.62, side = 0.75 }

function Structures.buildRelief(S, map, region, data, perRow, h)
  local atlasW = map.tileset.imageWidth or 128
  local atlasH = map.tileset.imageHeight or 48
  local bw = (region.maxX - region.minX + 1) * 8
  local bh = (region.maxY - region.minY + 1) * 8
  local member = {}
  for _, c in ipairs(region.tiles) do member[keyOf(c[1], c[2])] = true end

  local cls, srcU, srcV = {}, {}, {}
  for py = 0, bh - 1 do
    for px = 0, bw - 1 do
      local i = py * bw + px
      local k = keyOf(region.minX + math.floor(px / 8),
                      region.minY + math.floor(py / 8))
      if member[k] then
        local tile = S.tileAt[k]
        local ax = (tile % perRow) * 8 + px % 8
        local ay = math.floor(tile / perRow) * 8 + py % 8
        srcU[i], srcV[i] = ax, ay
        local r, g, b, a = data:getPixel(ax, ay)
        cls[i] = a == 0 and "off" or Structures.shadeClass(math.min(r, g, b))
      end
    end
  end

  local bg = {}
  for py = 0, bh - 1 do
    for px = 0, bw - 1 do
      if px == 0 or px == bw - 1 or py == 0 or py == bh - 1 then
        local c = cls[py * bw + px]
        if c and c ~= "black" and c ~= "off" then bg[c] = true end
      end
    end
  end

  local flooded, queue = {}, {}
  local function seed(i)
    local c = cls[i]
    if c and c ~= "black" and (c == "off" or bg[c]) and not flooded[i] then
      flooded[i] = true
      queue[#queue + 1] = i
    end
  end
  for px = 0, bw - 1 do
    seed(px)
    seed((bh - 1) * bw + px)
  end
  for py = 0, bh - 1 do
    seed(py * bw)
    seed(py * bw + bw - 1)
  end
  while #queue > 0 do
    local i = table.remove(queue)
    local px, py = i % bw, math.floor(i / bw)
    for _, d in ipairs(DIRS4) do
      local nx, ny = px + d[1], py + d[2]
      if nx >= 0 and nx < bw and ny >= 0 and ny < bh then
        seed(ny * bw + nx)
      end
    end
  end

  local function on(px, py)
    if px < 0 or px >= bw or py < 0 or py >= bh then return false end
    local i = py * bw + px
    return cls[i] ~= nil and cls[i] ~= "off" and not flooded[i]
  end

  local quads = S.objectQuads
  local wx0, wz0 = region.minX * 8, region.minY * 8
  for py = 0, bh - 1 do
    for px = 0, bw - 1 do
      if on(px, py) then
        local i = py * bw + px
        local u = (srcU[i] + 0.5) / atlasW
        local v = (srcV[i] + 0.5) / atlasH
        local x, z = wx0 + px, wz0 + py
        local function quad(c1, c2, c3, c4, shade)
          quads[#quads + 1] = { c1, c2, c3, c4, u = u, v = v, shade = shade }
        end
        quad({ x, h, z }, { x + 1, h, z }, { x + 1, h, z + 1 },
             { x, h, z + 1 }, RELIEF_SHADE.top)
        if not on(px, py + 1) then
          quad({ x, 0, z + 1 }, { x + 1, 0, z + 1 }, { x + 1, h, z + 1 },
               { x, h, z + 1 }, RELIEF_SHADE.south)
        end
        if not on(px, py - 1) then
          quad({ x + 1, 0, z }, { x, 0, z }, { x, h, z },
               { x + 1, h, z }, RELIEF_SHADE.north)
        end
        if not on(px - 1, py) then
          quad({ x, 0, z }, { x, 0, z + 1 }, { x, h, z + 1 },
               { x, h, z }, RELIEF_SHADE.side)
        end
        if not on(px + 1, py) then
          quad({ x + 1, 0, z + 1 }, { x + 1, 0, z }, { x + 1, h, z },
               { x + 1, h, z + 1 }, RELIEF_SHADE.side)
        end
      end
    end
  end
end

-- ---- bookcases: free-standing shelves collapsed to true depth ----

-- A drawn bookcase is TALL, not deep: the graphic spans two cell rows
-- because the shelf is 32px high, while the object stands one cell
-- (16px) deep.  Columns of tiles pinned `bookcase` collapse in ranks
-- (at most four drawn rows each, measured from the south): every rank
-- raises one box over its front two tile rows -- the drawing folded up
-- its south face band by band -- and its back rows become hidden floor.
-- When the row just above a rank is undetected structure (a shared trim
-- tile the profile cannot pin), the rank adopts it as its CAP: one more
-- band of height and the art its top face wears.
local BOOK_SHADE = { south = 1.0, north = 0.68, flank = 0.8, top = 0.85,
                     -- a pane's reveal: the one-voxel side of the frame
                     -- standing proud of it.  The sill catches the light
                     -- the top face does; the lintel is in shadow.
                     sill = 0.85, lintel = 0.5 }

-- A pane is a shelf opening, a glass door or an inset panel: a non-black
-- region the drawing SEALS OFF behind its own black frame.  Anything
-- wider or taller than this is a band of the front itself -- a trim
-- course, a plinth -- and stays flush.  The same number and the same
-- rule lib/Buildings.lua measures a facade's panes with, so a shelf the
-- band pipeline models and a shelf this class collapses carry the same
-- relief.
local BOOK_RECESS_MAX = 24

-- The panes of a BANK of ranks -- every rank of the same height standing
-- side by side -- as a mask over the bank's south face, plus the atlas
-- pixel each face texel comes from.  Measured over the whole bank rather
-- than per column, because a door panel drawn across two tiles is one
-- region and not two halves, and because the size test that keeps a
-- broad course flush has to see the course's real width.
--
-- `fx` runs across the bank and `fy` DOWN from its top, so the grid
-- reads like the drawing: the rank folds its tiles up band by band, the
-- southmost row lowest, and fy = 0 is the topmost drawn row.
local function bookcasePanes(map, data, perRow, run, i, j)
  if not data then return nil end
  local bands = run[i].bands
  local size = run[i].front - run[i].top + 1
  local W, H = (j - i + 1) * 8, bands * 8
  local light, srcU, srcV = {}, {}, {}
  for fy = 0, H - 1 do
    local band = bands - 1 - math.floor(fy / 8)
    local row = fy % 8
    for fx = 0, W - 1 do
      local col = run[i + math.floor(fx / 8)]
      local tile = band < size and map:tileAt(col.tx, col.front - band)
                   or col.cap
      if tile then
        local k = fy * W + fx
        local ax = (tile % perRow) * 8 + fx % 8
        local ay = math.floor(tile / perRow) * 8 + row
        srcU[k], srcV[k] = ax, ay
        local r, g, b, a = data:getPixel(ax, ay)
        light[k] = a ~= 0
          and Structures.shadeClass(math.min(r, g, b)) ~= "black"
      end
    end
  end

  -- The drawing's non-black regions, split across its black frames.  A
  -- region that reaches the face's own border is not sealed by anything
  -- -- it is a course of the front running edge to edge, the way a
  -- masonry band or a wall of siding does -- and it stays flush.  That
  -- test is what keeps this rule to shelves: `bookcase` also collapses
  -- the League's gate walls and the terraces, and their courses run off
  -- the drawing, so nothing there sinks.
  local pane, seen = {}, {}
  for k0 = 0, W * H - 1 do
    if light[k0] and not seen[k0] then
      local cells, stack = {}, { k0 }
      seen[k0] = true
      local ax0, ax1 = k0 % W, k0 % W
      local ay0, ay1 = math.floor(k0 / W), math.floor(k0 / W)
      local edge = false
      while #stack > 0 do
        local k = table.remove(stack)
        cells[#cells + 1] = k
        local cx, cy = k % W, math.floor(k / W)
        if cx < ax0 then ax0 = cx end
        if cx > ax1 then ax1 = cx end
        if cy < ay0 then ay0 = cy end
        if cy > ay1 then ay1 = cy end
        if cx == 0 or cx == W - 1 or cy == 0 or cy == H - 1 then
          edge = true
        end
        for _, d in ipairs(DIRS4) do
          local nx, ny = cx + d[1], cy + d[2]
          if nx >= 0 and nx < W and ny >= 0 and ny < H then
            local nk = ny * W + nx
            if light[nk] and not seen[nk] then
              seen[nk] = true
              stack[#stack + 1] = nk
            end
          end
        end
      end
      if not edge and ax1 - ax0 < BOOK_RECESS_MAX
         and ay1 - ay0 < BOOK_RECESS_MAX then
        for _, k in ipairs(cells) do pane[k] = true end
      end
    end
  end
  return pane, srcU, srcV, W, H
end

local function bookcaseRank(S, map, perRow, run, i, j, k, pane, srcU, srcV,
                            bankW, bankH)
  local r = run[k]
  local tx, northTy, frontTy, capTile = r.tx, r.top, r.front, r.cap
  local quads = S.objectQuads
  local atlasW = map.tileset.imageWidth or 128
  local atlasH = map.tileset.imageHeight or 48
  local function uvRect(tile)
    local ax = (tile % perRow) * 8
    local ay = math.floor(tile / perRow) * 8
    return (ax + 0.5) / atlasW, (ax + 7.5) / atlasW,
           (ay + 0.5) / atlasH, (ay + 7.5) / atlasH
  end

  local size = frontTy - northTy + 1
  local bands = r.bands
  local h = bands * 8
  local depth = math.min(2, size) * 8
  local x0, x1 = tx * 8, tx * 8 + 8
  local z1 = frontTy * 8 + 8
  local z0 = z1 - depth
  local fx0 = (k - i) * 8            -- this rank's columns within the bank

  -- does the neighbouring column continue this shelf? (flanks only cap
  -- the ends of a run of bookcases standing side by side)
  local function joined(nx)
    local ns = S.shapeAt[keyOf(nx, frontTy)]
    return ns ~= nil and ns.art == "bookcase"
  end

  local function sunk(fx, fy)
    if not pane or fx < 0 or fx >= bankW or fy < 0 or fy >= bankH then
      return false
    end
    return pane[fy * bankW + fx] == true
  end

  for band = 0, bands - 1 do
    local tile = band < size and map:tileAt(tx, frontTy - band) or capTile
    local u0, u1, v0, v1 = uvRect(tile)
    local y0, y1 = band * 8, band * 8 + 8
    local fyTop = (bands - 1 - band) * 8

    -- The south face: the drawing folded upright.  A band with no pane
    -- in it is the single quad it has always been; a band that seals
    -- one splits into per-row runs of texels, and the pane's run sinks
    -- a voxel behind the frame that stays proud around it.
    local relief = false
    if pane then
      for row = 0, 7 do
        for c = 0, 7 do
          if sunk(fx0 + c, fyTop + row) then relief = true break end
        end
        if relief then break end
      end
    end
    if not relief then
      quads[#quads + 1] = { { x0, y0, z1 }, { x1, y0, z1 },
        { x1, y1, z1 }, { x0, y1, z1 },
        uv = { { u0, v1 }, { u1, v1 }, { u1, v0 }, { u0, v0 } },
        shade = BOOK_SHADE.south }
    else
      local ax = (tile % perRow) * 8
      local ay = math.floor(tile / perRow) * 8
      for row = 0, 7 do
        local fy = fyTop + row
        local wy = y0 + 7 - row             -- the drawing's row 0 is the top
        local c = 0
        while c < 8 do
          local s = sunk(fx0 + c, fy)
          local n = 1
          while c + n < 8 and sunk(fx0 + c + n, fy) == s do n = n + 1 end
          local pz = s and z1 - 1 or z1
          local qu0 = (ax + c + 0.05) / atlasW
          local qu1 = (ax + c + n - 0.05) / atlasW
          local qv0 = (ay + row + 0.05) / atlasH
          local qv1 = (ay + row + 1 - 0.05) / atlasH
          quads[#quads + 1] = { { x0 + c, wy, pz }, { x0 + c + n, wy, pz },
            { x0 + c + n, wy + 1, pz }, { x0 + c, wy + 1, pz },
            uv = { { qu0, qv1 }, { qu1, qv1 }, { qu1, qv0 }, { qu0, qv0 } },
            shade = BOOK_SHADE.south }
          c = c + n
        end
      end
      -- the reveals: where a sunk texel meets a proud one, the frame's
      -- own one-voxel side shows.  It wears the PROUD neighbour's texel,
      -- because that is the block it belongs to.  A pane running off the
      -- bank, or off the top or bottom of the rank, needs none: the
      -- flank and top faces already close it.
      for row = 0, 7 do
        local fy = fyTop + row
        local wy = y0 + 7 - row
        for c = 0, 7 do
          if sunk(fx0 + c, fy) then
            local X = x0 + c
            local function reveal(nfx, nfy, verts, shade)
              if nfx < 0 or nfx >= bankW or nfy < 0 or nfy >= bankH then
                return
              end
              if sunk(nfx, nfy) then return end
              local nk = nfy * bankW + nfx
              if not srcU[nk] then return end
              quads[#quads + 1] = { verts[1], verts[2], verts[3], verts[4],
                u = (srcU[nk] + 0.5) / atlasW, v = (srcV[nk] + 0.5) / atlasH,
                shade = shade }
            end
            reveal(fx0 + c - 1, fy, {
              { X, wy, z1 }, { X, wy, z1 - 1 },
              { X, wy + 1, z1 - 1 }, { X, wy + 1, z1 } }, BOOK_SHADE.flank)
            reveal(fx0 + c + 1, fy, {
              { X + 1, wy, z1 - 1 }, { X + 1, wy, z1 },
              { X + 1, wy + 1, z1 }, { X + 1, wy + 1, z1 - 1 } },
              BOOK_SHADE.flank)
            reveal(fx0 + c, fy + 1, {
              { X, wy, z1 - 1 }, { X + 1, wy, z1 - 1 },
              { X + 1, wy, z1 }, { X, wy, z1 } }, BOOK_SHADE.sill)
            reveal(fx0 + c, fy - 1, {
              { X, wy + 1, z1 }, { X + 1, wy + 1, z1 },
              { X + 1, wy + 1, z1 - 1 }, { X, wy + 1, z1 - 1 } },
              BOOK_SHADE.lintel)
          end
        end
      end
    end

    quads[#quads + 1] = { { x1, y0, z0 }, { x0, y0, z0 },
      { x0, y1, z0 }, { x1, y1, z0 },
      uv = { { u0, v1 }, { u1, v1 }, { u1, v0 }, { u0, v0 } },
      shade = BOOK_SHADE.north }
    if not joined(tx - 1) then
      quads[#quads + 1] = { { x0, y0, z0 }, { x0, y0, z1 },
        { x0, y1, z1 }, { x0, y1, z0 },
        uv = { { u0, v1 }, { u1, v1 }, { u1, v0 }, { u0, v0 } },
        shade = BOOK_SHADE.flank }
    end
    if not joined(tx + 1) then
      quads[#quads + 1] = { { x1, y0, z1 }, { x1, y0, z0 },
        { x1, y1, z0 }, { x1, y1, z1 },
        uv = { { u0, v1 }, { u1, v1 }, { u1, v0 }, { u0, v0 } },
        shade = BOOK_SHADE.flank }
    end
  end

  local topTile = capTile or map:tileAt(tx, northTy)
  local u0, u1, v0, v1 = uvRect(topTile)
  for seg = 0, depth / 8 - 1 do
    local sz0 = z0 + seg * 8
    quads[#quads + 1] = { { x0, h, sz0 }, { x1, h, sz0 },
      { x1, h, sz0 + 8 }, { x0, h, sz0 + 8 },
      uv = { { u0, v0 }, { u1, v0 }, { u1, v1 }, { u0, v1 } },
      shade = BOOK_SHADE.top }
  end
end

-- The arts a `bookcase_backfill = "above"` row may inherit: terrain and
-- solid bodies only (see the note at the backfill itself).  Everything
-- absent here -- billboard, post, cylinder, grass, flower -- is a per-pixel
-- object STANDING on terrain rather than terrain.
local BACKFILL_ART = { flat = true, top = true, upright = true }

function Structures.buildBookcases(S, map, x0, x1, y0, y1, data, perRow)
  perRow = perRow or map.tileset.tilesPerRow or 16
  -- What to do with the rows a rank VACATES (see TileShape.bookcaseBackfill).
  -- Read once: it is a property of the tileset, not of the column.
  local backfill = TileShape.bookcaseBackfill(map.tileset.id)
  -- the front's measured relief: on for a shelf, off for the tilesets
  -- that borrow the collapse for masonry or machinery
  if not TileShape.bookcaseRelief(map.tileset.id) then data = nil end
  -- Ranks are collected here and emitted after the sweep: a rank's panes
  -- are measured over the whole BANK it stands in (see bookcasePanes),
  -- and the bank is only known once every column has been read.  Nothing
  -- below this loop mutates what the sweep reads, so deferring is free.
  local order, banks = {}, {}
  for tx = x0, x1 do
    local ty = y1
    while ty >= y0 do
      local s = S.shapeAt[keyOf(tx, ty)]
      if s and s.art == "bookcase" then
        -- the contiguous pinned run above this front row
        local north = ty
        while north > y0 do
          local ns = S.shapeAt[keyOf(tx, north - 1)]
          if ns and ns.art == "bookcase" then north = north - 1 else break end
        end
        -- ranks of at most four drawn rows, southmost first
        local front = ty
        while front >= north do
          local top = math.max(north, front - 3)
          -- adopt the trim row just above as the cap: either undetected
          -- structure the profile could not pin, or a row pinned `table`
          -- because the same trim tiles cap other furniture too
          local capTile = nil
          if top == north then
            local ck = keyOf(tx, north - 1)
            local cs = S.shapeAt[ck]
            if cs and not cs.flat and not S.skip[ck] and not S.runs[ck]
               and (not cs.authored or cs.class == "table") then
              capTile = S.tileAt[ck]
            end
          end
          -- The box is one cell deep, so it covers only the run's southmost
          -- rows; everything north of that is vacated.  By default a vacated
          -- row is skipped and painted with synthesized ground -- right for a
          -- shelf standing in a room.  `bookcase_backfill = "above"` hands it
          -- the cell above the run instead, shape and art, so a wall cut into
          -- a terrace has more terrace behind it rather than a trench.
          --
          -- Only BODY above backfills: a vacated row wants more of the
          -- terrace the wall is cut into, and the terrace is whatever lies
          -- flat, tops out or stands as a solid face.  A per-pixel STANDEE
          -- above -- a statue, a sign, a bush -- is an object standing ON
          -- that terrace, and copying it northward builds a second and a
          -- third of it: Indigo Plateau's avenue statues sit directly on
          -- the pilasters that collapse here, so every bird came out
          -- duplicated twice down the shaft behind itself.  A standee
          -- above means the row has no terrace to inherit, so it takes the
          -- default and is painted with synthesized ground.
          local covered = math.min(2, front - top + 1)
          local srcK = keyOf(tx, top - 1)
          local src = backfill == "above" and S.shapeAt[srcK] or nil
          if src and not BACKFILL_ART[src.art] then src = nil end
          -- Where the box ACTUALLY ends up, remembered for every row of the
          -- rank: the collapse walks the whole drawn run onto its southmost
          -- cell, so anything that has to stand ON the box has to be told
          -- where the box went.  A statue keys off the cell below its own
          -- drawing, which is the run's NORTH end -- two rows away from the
          -- box on a two-cell pilaster, which is exactly the distance the
          -- Plateau's birds floated by.
          local boxTop = front - covered + 1
          for cy = top, front do
            local tk = keyOf(tx, cy)
            S.bookcaseBox[tk] = boxTop
            if src and cy <= front - covered then
              S.shapeAt[tk] = src
              S.tileAt[tk] = S.tileAt[srcK]
            else
              S.skip[tk] = true
              S.ground[tk] = false
            end
          end
          -- ranks of the same height standing side by side are one bank
          local bands = (front - top + 1) + (capTile and 1 or 0)
          local key = top .. ":" .. front .. ":" .. bands
          local bank = banks[key]
          if not bank then
            bank = {}
            banks[key] = bank
            order[#order + 1] = key
          end
          bank[#bank + 1] = { tx = tx, top = top, front = front,
                              cap = capTile, bands = bands }
          front = top - 1
        end
        ty = north - 1
      else
        ty = ty - 1
      end
    end
  end

  -- tx ascends in the sweep above, so each bank's columns are already in
  -- order; split them into the contiguous runs that actually touch
  for _, key in ipairs(order) do
    local run = banks[key]
    local i = 1
    while i <= #run do
      local j = i
      while j < #run and run[j + 1].tx == run[j].tx + 1 do j = j + 1 end
      local pane, srcU, srcV, bankW, bankH =
        bookcasePanes(map, data, perRow, run, i, j)
      for k = i, j do
        bookcaseRank(S, map, perRow, run, i, j, k,
                     pane, srcU, srcV, bankW, bankH)
      end
      i = j + 1
    end
  end
end

-- ---- stairs: pinned cells that render as real steps ----

-- A cell the profile pins stair_e / stair_w (art "stair") becomes a
-- flight of STAIR_STEPS boxes rising evenly across the cell toward the
-- named side, each the full cell deep.  stair_down_e / stair_down_w is
-- the same flight EXCAVATED: the cell opens into a stairwell and the
-- steps descend below floor level toward the named side -- the shape a
-- staircase leading down a floor actually has.  The 2D staircase is
-- drawn from the side, so vertical faces (step fronts and stairwell
-- walls) wear the matching slice of that drawing -- the railing's
-- diagonal lands along the stepped silhouette -- while treads sample the
-- art band drawn at their own height.
--
-- stair_n / stair_down_n are the same pair of flights running INTO the
-- map rather than across it, for a staircase drawn head-on; that changes
-- the art reading enough to need its own branch below.
local STAIR_STEPS = 4

local STAIR_SHADE = { south = 1.0, north = 0.68, tread = 1.0,
                      riser = 0.82, cap = 0.78,
                      wellN = 0.9, wellS = 0.55, wellEnd = 0.15,
                      wellTread = 0.8 }

local function stairCell(S, map, data, cx, cy, s)
  local perRow = map.tileset.tilesPerRow or 16
  local atlasW = map.tileset.imageWidth or 128
  local atlasH = map.tileset.imageHeight or 48
  local quads = S.objectQuads
  local north = s.class == "stair_n" or s.class == "stair_down_n"
  local down = s.class == "stair_down_n" or s.class == "stair_down_e"
             or s.class == "stair_down_w"
  local east = s.class == "stair_e" or s.class == "stair_down_e"
  local mx, mz = cx * 16, cy * 16
  local h = s.h or 16
  local rise = h / STAIR_STEPS
  local runW = 16 / STAIR_STEPS
  local z0, z1 = mz, mz + 16

  -- cell-space art coords (16x16, row 0 the top) -> atlas uv; callers keep
  -- a quad's range inside one 8px tile so it never samples across a seam
  local function uv(px, py)
    px = math.max(0.05, math.min(15.95, px))
    py = math.max(0.05, math.min(15.95, py))
    local tile = S.tileAt[keyOf(cx * 2 + (px >= 8 and 1 or 0),
                                cy * 2 + (py >= 8 and 1 or 0))]
    return ((tile % perRow) * 8 + px % 8) / atlasW,
           (math.floor(tile / perRow) * 8 + py % 8) / atlasH
  end
  -- corners run bottom-left, bottom-right, top-right, top-left as seen
  -- from outside (the mesher's side convention); art rect in cell space
  local function face(c1, c2, c3, c4, ax0, ay0, ax1, ay1, shade)
    local u0, v0 = uv(ax0, ay0)
    local u1, v1 = uv(ax1, ay1)
    quads[#quads + 1] = { c1, c2, c3, c4,
      uv = { { u0, v1 }, { u1, v1 }, { u1, v0 }, { u0, v0 } },
      shade = shade }
  end
  -- a vertical face spanning heights [fy0, fy1] wearing art rows
  -- [ay0, ay1], emitted per 8-row art band so no quad crosses the seam
  local function banded(z, ax0, ax1, fy0, fy1, ay0, ay1, shade, flip)
    local scale = (fy1 - fy0) / math.max(ay1 - ay0, 0.001)
    for _, band in ipairs({ { ay0, math.min(8, ay1) },
                            { math.max(ay0, 8), ay1 } }) do
      local a0, a1 = band[1], band[2]
      if a1 > a0 then
        local by1 = fy1 - (a0 - ay0) * scale
        local by0 = fy1 - (a1 - ay0) * scale
        local xa, xb = mx + ax0, mx + ax1
        if flip then
          face({ xb, by0, z }, { xa, by0, z }, { xa, by1, z },
               { xb, by1, z }, ax0, a0, ax1, a1, shade)
        else
          face({ xa, by0, z }, { xb, by0, z }, { xb, by1, z },
               { xa, by1, z }, ax0, a0, ax1, a1, shade)
        end
      end
    end
  end

  -- A flight running INTO the map instead of across it.  The drawing is
  -- the same staircase seen head-on rather than from the side, and that
  -- changes which axis of the art means what: a drawn ROW is a step here,
  -- and -- because looking down a well is looking along its depth -- drawn
  -- row IS depth row, 1:1 across the cell's 16.
  --
  -- The Centers' steps state their own band table and it lands exactly:
  -- 4 white rows, 1 black, 3 grey, 1 black, 3 checker, 4 black = 16.  So
  -- an even four-step division puts a black NOSING on the southmost row of
  -- every band (15, 11, 7, 3) and leaves the rows behind it as that step's
  -- tread.  Nothing is authored but the RISE, which no head-on drawing can
  -- state; the depths, the treads and the nosings are all measured.
  --
  -- A nosing is drawn as one row because it is seen nearly edge-on, so
  -- un-projected it has real height and no depth: its row lies flat as the
  -- tread's front lip AND stands as the riser under it.  That is the one
  -- texel in the flight used twice, and using it twice is what a nosing is.
  --
  -- The well's own walls come free as well: the drawing's first and last
  -- COLUMNS are its black side walls, and its top band is the darkness the
  -- flight leaves by, which is what the far end wants to wear.
  --
  -- A flight CLIMBING away (`stair_n`) is the same reading with the sign of
  -- the rise flipped -- bands still run south to north, drawn row is still
  -- depth row, the nosing still serves twice.  Two things follow from the
  -- sign.  The risers turn around: a flight descending away from you closes
  -- its steps from below and shows you their backs, one climbing away shows
  -- you their FRONTS, so they face south.  And the drawing's black side
  -- columns stop being a well's walls and become the walls of the opening
  -- the flight climbs into: they run from each tread UP to the top of the
  -- wall band rather than down from the floor.  At the last step the flight
  -- has reached that top and there is no opening left to wall.
  --
  -- Every quad here is split at the cell's own 8px seam, in x and in rows
  -- both: `uv` resolves ONE tile per corner, and these four tiles are not
  -- neighbours in the atlas, so a quad that spans a seam interpolates
  -- between two unrelated corners of the sheet.
  if north then
    local runD = 16 / STAIR_STEPS
    local HALVES = { { 0.2, 7.9, 0, 8 }, { 8.1, 15.8, 8, 16 } }
    for i = 0, STAIR_STEPS - 1 do
      local a0 = 16 - (i + 1) * runD           -- band i, in art rows
      local a1 = a0 + runD
      local yTop = (down and -1 or 1) * (i + 1) * rise
      local ry = (down and -1 or 1) * i * rise        -- the step behind it
      local z0b, z1b = mz + a0, mz + a1

      for _, H in ipairs(HALVES) do
        local ax0, ax1, wx0, wx1 = H[1], H[2], mx + H[3], mx + H[4]

        -- the tread: the whole band, drawn row = depth row, so the nosing
        -- lies on its front lip exactly where the artist drew it
        face({ wx0, yTop, z0b }, { wx1, yTop, z0b },
             { wx1, yTop, z1b }, { wx0, yTop, z1b },
             ax0, a1, ax1, a0,
             down and STAIR_SHADE.wellTread or STAIR_SHADE.tread)

        -- the riser at that lip, one art row tall -- so it needs none of
        -- `banded`'s row splitting, and written straight keeps the geometry
        -- flush at the seam while the art stays inside its tile.  Facing
        -- north when the flight descends (the steps are closed from below,
        -- not looked at) and south when it climbs
        if down then
          face({ wx1, yTop, z1b }, { wx0, yTop, z1b },
               { wx0, ry, z1b }, { wx1, ry, z1b },
               ax1, a1 - 1, ax0, a1, STAIR_SHADE.riser)
        else
          face({ wx0, ry, z1b }, { wx1, ry, z1b },
               { wx1, yTop, z1b }, { wx0, yTop, z1b },
               ax0, a1 - 1, ax1, a1, STAIR_SHADE.riser)
        end

        -- the deep end, closing the opening this flight is cut into: from
        -- the floor of the well up to the top of the wall band beside it,
        -- in the drawing's own black top rows.  A climbing flight has no
        -- such end -- its top tread stands at the wall's own height and
        -- fills the opening
        if down and i == STAIR_STEPS - 1 then
          face({ wx1, -h, mz }, { wx0, -h, mz },
               { wx0, h, mz }, { wx1, h, mz },
               ax1, 3.9, ax0, 0.1, STAIR_SHADE.wellEnd)
        end
      end

      -- the opening's side walls beside this tread, wearing the drawing's
      -- own black edge columns -- excavation or recess, it is walled in its
      -- own texels.  Descending they run from the tread up to the floor,
      -- climbing from the tread up to the top of the wall band
      local wallTop = down and 0 or h
      local function sideWall(px, sx0, sx1, inward)
        local c
        if inward then                                  -- west wall, faces E
          c = { { px, yTop, z1b }, { px, yTop, z0b },
                { px, wallTop, z0b }, { px, wallTop, z1b } }
        else                                            -- east wall, faces W
          c = { { px, yTop, z0b }, { px, yTop, z1b },
                { px, wallTop, z1b }, { px, wallTop, z0b } }
        end
        face(c[1], c[2], c[3], c[4], sx0, a1, sx1, a0, STAIR_SHADE.wellN)
      end
      if wallTop > yTop then
        sideWall(mx, 0.1, 1.3, true)
        sideWall(mx + 16, 14.7, 15.9, false)
      end
    end
    return
  end

  for i = 0, STAIR_STEPS - 1 do
    local sx0 = east and (i * runW) or (16 - (i + 1) * runW)
    local sx1 = sx0 + runW
    local x0, x1 = mx + sx0, mx + sx1

    if down then
      -- stairwell: tread i sits (i+1) rises below the floor; the walls
      -- above it are the excavation, wearing the drawing at its depth
      local yTop = -(i + 1) * rise
      local dep = (i + 1) * rise

      face({ x0, yTop, z0 }, { x1, yTop, z0 },
           { x1, yTop, z1 }, { x0, yTop, z1 },
           sx0, dep - 1.4, sx1, dep, STAIR_SHADE.wellTread)

      -- stairwell walls above this tread: north wall faces the camera
      banded(z0, sx0, sx1, yTop, 0, 0, dep, STAIR_SHADE.wellN)
      banded(z1, sx0, sx1, yTop, 0, 0, dep, STAIR_SHADE.wellS, true)

      -- riser dropping to this tread from the shallower step
      local rx = east and x0 or x1
      local ry1 = -i * rise
      local rax = east and (sx0 + 0.1) or (sx1 - 1.3)
      if east then
        face({ rx, yTop, z0 }, { rx, yTop, z1 },
             { rx, ry1, z1 }, { rx, ry1, z0 },
             rax, i * rise, rax + 1.2, dep, STAIR_SHADE.riser)
      else
        face({ rx, yTop, z1 }, { rx, yTop, z0 },
             { rx, ry1, z0 }, { rx, ry1, z1 },
             rax, i * rise, rax + 1.2, dep, STAIR_SHADE.riser)
      end

      -- the deep end: a dark opening under the wall the flight leaves by
      if i == STAIR_STEPS - 1 then
        local px = east and (mx + 16) or mx
        local cax = east and 14.7 or 0.1
        if east then
          face({ px, -h, z1 }, { px, -h, z0 }, { px, 0, z0 }, { px, 0, z1 },
               cax, 0, cax + 1.2, 16, STAIR_SHADE.wellEnd)
        else
          face({ px, -h, z0 }, { px, -h, z1 }, { px, 0, z1 }, { px, 0, z0 },
               cax, 0, cax + 1.2, 16, STAIR_SHADE.wellEnd)
        end
      end
    else
      -- rising flight
      local yTop = (i + 1) * rise
      local py0 = 16 - yTop

      -- south + north faces: the drawn flight sliced at this step's column
      banded(z1, sx0, sx1, 0, yTop, py0, 16, STAIR_SHADE.south)
      banded(z0, sx0, sx1, 0, yTop, py0, 16, STAIR_SHADE.north, true)

      -- tread: the step's top, wearing the art band drawn at its height
      face({ x0, yTop, z0 }, { x1, yTop, z0 },
           { x1, yTop, z1 }, { x0, yTop, z1 },
           sx0, py0, sx1, py0 + 1.4, STAIR_SHADE.tread)

      -- riser: the vertical strip exposed above the previous step
      local rx = east and x0 or x1
      local ry0 = i * rise
      local rax = east and (sx0 + 0.1) or (sx1 - 1.3)
      if east then
        face({ rx, ry0, z0 }, { rx, ry0, z1 },
             { rx, yTop, z1 }, { rx, yTop, z0 },
             rax, 16 - yTop, rax + 1.2, 16 - ry0, STAIR_SHADE.riser)
      else
        face({ rx, ry0, z1 }, { rx, ry0, z0 },
             { rx, yTop, z0 }, { rx, yTop, z1 },
             rax, 16 - yTop, rax + 1.2, 16 - ry0, STAIR_SHADE.riser)
      end

      -- cap the tall end of the flight so it never shows a hole
      if i == STAIR_STEPS - 1 then
        local px = east and (mx + 16) or mx
        local cax = east and 14.7 or 0.1
        if east then
          face({ px, 0, z1 }, { px, 0, z0 }, { px, h, z0 }, { px, h, z1 },
               cax, 0, cax + 1.2, 16, STAIR_SHADE.cap)
        else
          face({ px, 0, z0 }, { px, 0, z1 }, { px, h, z1 }, { px, h, z0 },
               cax, 0, cax + 1.2, 16, STAIR_SHADE.cap)
        end
      end
    end
  end
end

function Structures.buildStairs(S, map, x0, x1, y0, y1)
  local data = pixels(map.tileset)
  for cy = math.floor(y0 / 2), math.floor(y1 / 2) do
    for cx = math.floor(x0 / 2), math.floor(x1 / 2) do
      local s = S.shapeAt[keyOf(cx * 2, cy * 2)]
      if s and s.art == "stair" then
        -- claim the cell whichever way the quads go: the mesher must not
        -- box or floor it.  A rising flight stands on the map's common
        -- floor; a stairwell IS the hole, so nothing is painted under it
        local down = s.class == "stair_down_e" or s.class == "stair_down_w"
                  or s.class == "stair_down_n"
        for dy = 0, 1 do
          for dx = 0, 1 do
            local tk = keyOf(cx * 2 + dx, cy * 2 + dy)
            S.skip[tk] = true
            if not down then S.ground[tk] = false end
          end
        end
        if data then stairCell(S, map, data, cx, cy, s) end
      end
    end
  end
end

-- ---- volume mode: per-column runs with real drawn heights ----

-- `tiles` is a list of {tx, ty} forming one region (or what is left of one
-- after object extraction); runs are column-local, heights are measured
-- per column and reconciled per region.
function Structures.buildVolume(S, map, tiles)
  local cols = {}
  for _, c in ipairs(tiles) do
    cols[c[1]] = cols[c[1]] or {}
    cols[c[1]][c[2]] = true
  end

  local runs = {}
  local heightVotes = {}
  local repeatVotes = {}
  for tx, ys in pairs(cols) do
    -- visit each contiguous vertical run in this column
    local sorted = {}
    for y in pairs(ys) do sorted[#sorted + 1] = y end
    table.sort(sorted)
    local i = 1
    while i <= #sorted do
      local north = sorted[i]
      local front = north
      while i + 1 <= #sorted and sorted[i + 1] == front + 1 do
        i = i + 1
        front = sorted[i]
      end
      i = i + 1
      local extent = front - north + 1

      -- the column's own reading: its extent, unless its tile sequence
      -- repeats -- then the repeat period is the drawn unit. Both readings
      -- cap at MAX_ROWS (a long-period repeat is still not one column of
      -- drawing).
      local unit, repeatRead = math.min(extent, MAX_ROWS), false
      if extent > 1 then
        local t0 = map:tileAt(tx, front)
        for k = 1, extent - 1 do
          if map:tileAt(tx, front - k) == t0 then
            unit = math.min(math.max(k, 2), MAX_ROWS)
            repeatRead = true
            break
          end
        end
        -- A one-row TRIM at the column's foot hides a repeat from the
        -- scan above, which anchors at the front tile: a cliff plateau
        -- ends its south edge in a rounded corner tile, the corner
        -- never recurs, and the column read its whole capped extent --
        -- a 48px fin (or a whole tent of them) sticking out of a 16px
        -- mesa on Routes 3 and 4. When the two rows directly above the
        -- front are IDENTICAL, the column is that repeat wearing a trim
        -- foot: one course plus the trim is its drawn unit. Doorway
        -- columns are untouched -- their run answers to the region
        -- (see below) before the unit matters.
        if not repeatRead and extent > 2
           and map:tileAt(tx, front - 1) == map:tileAt(tx, front - 2) then
          unit = 2
          repeatRead = true
        end
      end
      local isDoor = false
      for ty = north, front do
        if S.doorFold[keyOf(tx, ty)] then
          isDoor = true
          break
        end
      end
      local run = { front = front, north = north, extent = extent,
                    unit = unit, fromRepeat = repeatRead, door = isDoor }
      runs[#runs + 1] = { tx = tx, run = run }
      local h = unit * 8
      heightVotes[h] = (heightVotes[h] or 0) + 1
      if repeatRead then repeatVotes[h] = (repeatVotes[h] or 0) + 1 end
    end
  end

  -- region consensus: the dominant height. A column whose reading came
  -- from a repeat adopts it when taller (the column above a doorway
  -- repeats internally but belongs to a 48px house); a column that read
  -- its full extent keeps it (an attached low wing stays low).
  local modeH, modeN = 16, 0
  for h, n in pairs(heightVotes) do
    if n > modeN or (n == modeN and h > modeH) then modeH, modeN = h, n end
  end
  -- whether the region's dominant columns are flat repeats (a cliff
  -- mound's plateau) rather than drawn facades (a house's front)
  local modeRepeat = (repeatVotes[modeH] or 0) * 2 > modeN

  -- Whether this REGION's tops are a rim over a uniform body -- what every
  -- cliff mound is drawn as: a top edge, then the same rock the whole way
  -- down. The top face may then lay that rim once along its north edge and
  -- hold the body after it, instead of cycling the rim back every second
  -- tile and striping a plateau with edges it should not have.
  --
  -- Answered per column AND per region, because each catches what the
  -- other misses. A mound is one structure many columns wide, and the
  -- columns carrying its cave mouth read differently from their neighbours
  -- (their drawing ends in the mouth's own tiles): per column alone, those
  -- kept cycling while the rest held, leaving rim stubs above the doorway.
  -- But a region vote alone silences a genuine rim-over-body column that
  -- happens to stand in a region of repeating art -- three of them in the
  -- Safari Zone. A column holds if EITHER says so.
  --
  -- Art that genuinely repeats is not uniform and keeps cycling: the
  -- Safari Zone's fence alternates two tiles the whole way down, and there
  -- the repeat IS what the drawing says.
  local uniformVotes, uniformTotal = 0, 0
  for _, r in ipairs(runs) do
    local run = r.run
    if run.extent > 2 then
      uniformTotal = uniformTotal + 1
      local body = map:tileAt(r.tx, run.north + 1)
      local uniform = true
      for d = 2, run.extent - 1 do
        if map:tileAt(r.tx, run.north + d) ~= body then
          uniform = false
          break
        end
      end
      run.ownUniform = uniform
      if uniform then uniformVotes = uniformVotes + 1 end
    end
  end
  local regionUniform = uniformTotal > 0 and uniformVotes * 2 > uniformTotal
  for _, r in ipairs(runs) do
    local run = r.run
    local h = run.unit * 8
    local adopted = false
    local flatDoor = false
    if run.door then
      -- A folded doorway column answers to its region ENTIRELY. Its own
      -- reading spans the door plus everything drawn above it -- a
      -- house's full height when the door is a house's, but a 32px
      -- tower over a 16px plateau when the door is a cave mouth cut
      -- into a cliff mound (Diglett's Cave: the entrance jumped a block
      -- above the mound around it). Height and top both come from the
      -- region: the mode height, roofed like a facade when the mode
      -- columns are drawn facades, flat when they are flat repeats.
      h = modeH
      adopted = not modeRepeat
      flatDoor = modeRepeat
    elseif run.fromRepeat and modeH > h then
      h = modeH
      adopted = true
    end
    -- Outdoors, a structure's top rows are its ROOF: the drawn height
    -- splits into a vertical facade and a slope rising north to the drawn
    -- peak (the mesher builds it; hips close the exposed flanks). Repeat
    -- patterns (a border wall) stay flat-topped -- unless they adopted
    -- their region's height, which means they are part of a building (the
    -- column above a doorway) and roof with it. Total height is always
    -- the drawn height: facade + rise = extent rows * 8.
    --
    -- But only PITCHED roofs slope. Gen 1 draws two kinds: a pitched roof
    -- has distinct ridge and eaves rows (the houses' stripes), while a
    -- flat ROOFTOP (the lab, the mart) repeats one texture tile over the
    -- whole roof area -- and a rooftop tilted into a 48px ramp reads
    -- wrong instantly. Distinct top rows -> slope; repeated -> level top.
    local roofRows = 0
    if S.outdoor and (not run.fromRepeat or adopted) and h >= 16
       and not flatDoor then
      roofRows = math.min(2, math.floor(h / 8) - 1)
      if roofRows > 0 and map:tileAt(r.tx, run.north)
                         == map:tileAt(r.tx, run.north + 1) then
        roofRows = 0
      end
    end
    run.roofRows = roofRows
    run.rise = roofRows * 8
    run.peak = h
    run.h = h - run.rise               -- facade height: what sides build to
    run.topUniform = run.ownUniform or regionUniform
    for ty = run.north, run.front do
      S.runs[keyOf(r.tx, ty)] = run
    end
  end
end

-- ---- object mode: per-pixel voxelization of drawn props ----

local OBJ_SHADE = { front = 1.0, back = 0.68, side = 0.78,
                    top = 1.0, bottom = 0.55 }

-- The four GB shades, by a pixel's darkest channel.  Force-mode
-- segmentation reasons in these: black is always outline/object, the
-- other three are background only where they touch the cluster's edge.
function Structures.shadeClass(v)
  if v <= 0.25 then return "black" end
  if v <= 0.55 then return "dark" end
  if v <= 0.85 then return "light" end
  return "white"
end

-- Analyze one region's art against its surroundings, voxelize the
-- sprite-like clusters, and return the tiles that remain for volume mode.
-- `force` (profile-pinned billboards) voxelizes every tile of the region
-- unconditionally -- the pin IS the classification. `force = "opaque"`
-- (the `post` pool) keeps the decree -- every tile is a prop, aprons
-- seed the flood, validation is skipped -- but classifies pixels the way
-- the DETECTOR does (everything non-white is solid) instead of by
-- outline shade: a fence's mid browns are its body, and the outline
-- rule would strip the posts to black skeletons.
function Structures.extractObjects(S, map, region, data, perRow, force)
  local bw = (region.maxX - region.minX + 1) * 8
  local bh = (region.maxY - region.minY + 1) * 8

  local member = {}
  for _, c in ipairs(region.tiles) do member[keyOf(c[1], c[2])] = true end

  -- Image over the region bbox plus a 1px ground apron. Pixel states:
  --   solid   opaque member art (non-white, or white that survives)
  --   cand    member white: background candidate, the flood decides
  --   air     ground the flood may travel: INSIDE the bbox (the gaps
  --           between fence posts), or the SOUTH apron row. This is the
  --           direction the viewer reads background from -- a prop's
  --           white meets the ground at its feet. OUTDOORS the other
  --           aprons are barriers on purpose: a building's roof stripes
  --           touch the grass BEHIND it, and a flood allowed to walk
  --           around the sides would pour in from the north and shred the
  --           roof into misdetected sprite clusters (it did). INDOORS all
  --           four aprons seed: furniture backs onto walls and bottom-row
  --           props meet the void ring, so the south row alone often
  --           cannot reach the background at all -- and there are no
  --           roofs inside to protect.
  --   barrier everything else
  local W, H = bw + 2, bh + 2
  local state = {}
  local srcU, srcV = {}, {}
  for iy = 0, H - 1 do
    for ix = 0, W - 1 do
      Budget.tick()
      local i = iy * W + ix
      local px, py = ix - 1, iy - 1
      local tx = region.minX + math.floor(px / 8)
      local ty = region.minY + math.floor(py / 8)
      local k = keyOf(tx, ty)
      local inside = px >= 0 and px < bw and py >= 0 and py < bh
      -- a forced (pinned) prop floods from every apron even when the
      -- neighbours are solid: the pin itself declares the art a prop
      -- whose whites are background -- a monitor pinned atop its desk has
      -- no flat neighbour anywhere to seed from
      local apron = iy == H - 1
        or ((force or not S.outdoor)
            and (iy == 0 or ix == 0 or ix == W - 1))
      if inside and member[k] then
        local tile = S.tileAt[k]
        local ax = (tile % perRow) * 8 + px % 8
        local ay = math.floor(tile / perRow) * 8 + py % 8
        srcU[i], srcV[i] = ax, ay
        local r, g, b, a = data:getPixel(ax, ay)
        if a == 0 then
          state[i] = "cand"
        elseif force and force ~= "opaque" then
          state[i] = Structures.shadeClass(math.min(r, g, b))
        else
          state[i] = math.min(r, g, b) > 0.83 and "cand" or "solid"
        end
      elseif inside or apron then
        if force then
          -- a pinned prop's surroundings are background BY DECREE -- the
          -- pin declares the drawing a prop even when every neighbour is
          -- solid furniture (a vase boxed in by its table).  Ring pixels
          -- seed the flood outright; interior non-member pixels ("iair")
          -- seed it too but never drain paint whites -- only a white run
          -- reaching the RING is background white.
          state[i] = inside and "iair" or "air"
        else
          local s = S.shapeAt[k]
          state[i] = (s and s.flat and s.class ~= "void") and "air"
                     or "barrier"
        end
      else
        state[i] = "barrier"
      end
    end
  end

  -- Forced (pinned) props are segmented the way the art is authored:
  -- objects wear a BLACK OUTLINE, and the background is whatever shades
  -- actually touch the cluster's edge -- the white floor around a TV,
  -- the grey tabletop around a vase.  Only those shades flood; the
  -- outline, its interior, the drawing's paint whites and anything they
  -- enclose all survive as the object.
  --
  -- The `cutout` pool is STRICTER, per the pure-profile contract: mid
  -- shades are always background (a drawn cast shadow must not ring the
  -- object in brown), and whites flood only along white runs from the
  -- edge -- a background white sheet drains away, but paint whites the
  -- flood could only reach through grey are the object.
  if force and force ~= "opaque" then
    local strict = false
    do
      local fs = S.shapeAt[keyOf(region.tiles[1][1], region.tiles[1][2])]
      strict = fs ~= nil and fs.class == "cutout"
    end
    -- The rim vote reads the shades on the DRAWING'S OWN bounding box, so a
    -- prop whose body reaches its own edge votes itself out. The Center's
    -- potted plants are the case: the pot's olive base is drawn flush on the
    -- bottom row of the block, so "dark" came back as background and every
    -- dark pixel in the whole plant drained with it -- the pots rendered as
    -- hollow black frames while the 2D art has solid olive bodies.
    --
    -- Where the vote misreads the art, the profile can name the background
    -- shades outright (a tileset entry's prop_bg). Keyed BY TILE rather than
    -- per tileset, because the answer is per drawing: the healing consoles'
    -- screens really do stand on a dark wall band and really do need dark
    -- voted out, and the PC really does need light kept.
    local bg = {}
    do
      local named = TileShape.propBg(map.tileset.id)
      if named then
        for _, c in ipairs(region.tiles) do
          local rule = named[S.tileAt[keyOf(c[1], c[2])]]
          if rule then
            for shadeName in pairs(rule) do bg[shadeName] = true end
            break
          end
        end
      end
    end
    if not next(bg) then
      for iy = 0, H - 1 do
        for ix = 0, W - 1 do
          local px, py = ix - 1, iy - 1
          local edge = px == 0 or px == bw - 1 or py == 0 or py == bh - 1
          local st = state[iy * W + ix]
          if edge and (st == "dark" or st == "light" or st == "white") then
            bg[st] = true
          end
        end
      end
      if not (bg.dark or bg.light or bg.white) then bg.white = true end
    end
    for i, st in pairs(state) do
      if strict then
        if st == "dark" or st == "light" then
          state[i] = "cand"
        elseif st == "white" then
          state[i] = "wcand"
        elseif st == "black" then
          state[i] = "solid"
        end
      elseif st == "dark" or st == "light" or st == "white" then
        state[i] = bg[st] and "cand" or "solid"
      elseif st == "black" then
        state[i] = "solid"
      end
    end
  end

  -- flood background in from the ground at the structure's feet
  local flooded = {}
  local queue = {}
  for i, st in pairs(state) do
    if st == "air" or st == "iair" then
      flooded[i] = true
      queue[#queue + 1] = i
    end
  end
  while #queue > 0 do
    Budget.tick()
    local i = table.remove(queue)
    local ix, iy = i % W, math.floor(i / W)
    for _, d in ipairs(DIRS4) do
      local nx, ny = ix + d[1], iy + d[2]
      if nx >= 0 and nx < W and ny >= 0 and ny < H then
        local ni = ny * W + nx
        if not flooded[ni] then
          local ns = state[ni]
          -- "wcand" (a strict cutout's white) drains only along a white
          -- run that reaches the RING: entered from the outer apron or
          -- from another flooded white, never through grey or through
          -- interior air
          if ns == "cand" or ns == "air" or ns == "iair"
             or (ns == "wcand"
                 and (state[i] == "air" or state[i] == "wcand")) then
            flooded[ni] = true
            queue[#queue + 1] = ni
          end
        end
      end
    end
  end

  -- per-tile background ratio -> sprite-like tiles (a pinned billboard is
  -- sprite-like by decree)
  local sprite = {}
  for _, c in ipairs(region.tiles) do
    Budget.tick()
    if force then
      sprite[keyOf(c[1], c[2])] = true
    else
      local bx = (c[1] - region.minX) * 8
      local by = (c[2] - region.minY) * 8
      local bg = 0
      for py = 0, 7 do
        for px = 0, 7 do
          if flooded[(by + py + 1) * W + (bx + px + 1)] then bg = bg + 1 end
        end
      end
      if bg / 64 >= TILE_BG_RATIO then sprite[keyOf(c[1], c[2])] = true end
    end
  end

  -- cluster sprite-like tiles; validate each cluster as one prop
  local leftover, claimed = {}, {}
  local clusterSeen = {}
  for _, c in ipairs(region.tiles) do
    local k = keyOf(c[1], c[2])
    if sprite[k] and not clusterSeen[k] then
      local cluster = { tiles = {}, minX = c[1], maxX = c[1],
                        minY = c[2], maxY = c[2] }
      local queue2 = { c }
      clusterSeen[k] = true
      while #queue2 > 0 do
        local cc = table.remove(queue2)
        cluster.tiles[#cluster.tiles + 1] = cc
        cluster.minX = math.min(cluster.minX, cc[1])
        cluster.maxX = math.max(cluster.maxX, cc[1])
        cluster.minY = math.min(cluster.minY, cc[2])
        cluster.maxY = math.max(cluster.maxY, cc[2])
        for _, d in ipairs(DIRS4) do
          local nk = keyOf(cc[1] + d[1], cc[2] + d[2])
          if sprite[nk] and not clusterSeen[nk] then
            clusterSeen[nk] = true
            queue2[#queue2 + 1] = { cc[1] + d[1], cc[2] + d[2] }
          end
        end
      end
      if Structures.buildObject(S, map, region, cluster,
                                state, flooded, srcU, srcV, W, force) then
        for _, cc in ipairs(cluster.tiles) do
          claimed[keyOf(cc[1], cc[2])] = true
        end
      end
    end
  end

  for _, c in ipairs(region.tiles) do
    if not claimed[keyOf(c[1], c[2])] then leftover[#leftover + 1] = c end
  end
  return leftover
end

-- One sprite-like cluster -> a per-pixel voxel prism, or false when it
-- fails validation (too tall, vertically repeating, too big) and should
-- stay part of the volume.
function Structures.buildObject(S, map, region, cluster,
                                state, flooded, srcU, srcV, W, force)
  local rows = cluster.maxY - cluster.minY + 1
  if not force then
    if rows > OBJECT_MAX_ROWS then return false end

    -- a prop stands ON the ground: somewhere the cluster must meet flat
    -- ground to its south. A cluster carved out of a structure's middle
    -- (roof rows whose whites leaked) fails this and stays in the volume.
    -- Indoors any side will do -- furniture backs onto walls and bottom-row
    -- props meet the void ring, so south alone is too strict.
    local dirs = S.outdoor and { { 0, 1 } } or DIRS4
    local touchesGround = false
    for _, c in ipairs(cluster.tiles) do
      for _, d in ipairs(dirs) do
        local ss = S.shapeAt[keyOf(c[1] + d[1], c[2] + d[2])]
        if ss and ss.flat and ss.class ~= "void" then
          touchesGround = true
          break
        end
      end
      if touchesGround then break end
    end
    if not touchesGround then return false end

    -- a vertically repeating cluster (tree wall edge) is scenery, not a
    -- prop
    local cols = {}
    for _, c in ipairs(cluster.tiles) do
      cols[c[1]] = cols[c[1]] or {}
      cols[c[1]][c[2]] = true
    end
    for tx, ys in pairs(cols) do
      local front = nil
      for y in pairs(ys) do front = math.max(front or y, y) end
      local extent = 0
      while ys[front - extent] do extent = extent + 1 end
      if extent > 1 then
        local t0 = map:tileAt(tx, front)
        for k = 1, extent - 1 do
          if map:tileAt(tx, front - k) == t0 then return false end
        end
      end
    end
  end

  local memberC = {}
  for _, c in ipairs(cluster.tiles) do memberC[keyOf(c[1], c[2])] = true end

  -- solid pixels of this cluster (art minus flooded background)
  local solidPx, count, bgCount = {}, 0, 0
  local bw = (cluster.maxX - cluster.minX + 1) * 8
  local bh = (cluster.maxY - cluster.minY + 1) * 8
  for _, c in ipairs(cluster.tiles) do
    local rx = (c[1] - region.minX) * 8
    local ry = (c[2] - region.minY) * 8
    for py = 0, 7 do
      Budget.tick()
      for px = 0, 7 do
        local i = (ry + py + 1) * W + (rx + px + 1)
        local on = state[i] ~= nil and state[i] ~= "air"
                   and state[i] ~= "iair" and state[i] ~= "barrier"
                   and not flooded[i]
        if on then
          local lx = (c[1] - cluster.minX) * 8 + px
          local ly = (c[2] - cluster.minY) * 8 + py
          solidPx[ly * bw + lx] = i
          count = count + 1
        else
          bgCount = bgCount + 1
        end
      end
    end
  end
  if count == 0 or count > OBJECT_MAX_QUADS then return false end
  if not force and bgCount / (count + bgCount) < CLUSTER_MIN_BG then
    return false
  end

  -- geometry: each solid pixel is one voxel column deep enough to read as
  -- a body, standing at the cluster's south row, base on the ground plane
  local depth = OBJECT_DEPTH
  if force then
    local cs = S.shapeAt[keyOf(cluster.tiles[1][1], cluster.tiles[1][2])]
    depth = (cs and PINNED_DEPTH[cs.class]) or PINNED_DEPTH.billboard
  end
  local wx0 = cluster.minX * 8

  -- A pinned prop drawn directly above an authored box stands ON it -- a
  -- monitor on its desk, a flower pot on the table.  The prism rises from
  -- the box's top with its feet on the box's north row, and the claimed
  -- tiles keep rendering as that box (wearing its plain art) instead of
  -- punching a floor-level hole through it.
  --
  -- Only when the prop's OWN CELL IS BLOCKED, though.  "Is something
  -- drawn above me?" is not the same question as "am I standing on it":
  -- a chair drawn against the north side of a table is above the table's
  -- trim row too, and it was being lifted onto the tabletop -- three
  -- chairs standing on the furniture in Cinnabar's trade room and
  -- Fuchsia's meeting room, with the claimed cells re-tiled as tabletop
  -- so the table marched two rows north with them.  The world already
  -- knows which is which: a thing that sits ON furniture occupies a
  -- blocked cell (you cannot walk through the gym statue, Red's plant,
  -- the PC), while a seat you walk up to is in a walkable one.
  --
  -- FENCE POSTS (the `post` pool, force == "opaque") never take the lift
  -- at all. A post stands in the ground by definition -- it is not a
  -- thing set down on top of something -- and its cell is blocked like
  -- any other post, so the test above cannot tell it apart. Lavender
  -- Town is where it showed: pinning the cliff's slope chain gave the
  -- posts along the cliff edge an authored 16px box to their south, and
  -- they were hoisted to stand on the clifftop instead of the path.
  local baseY, support, supportRow = 0, nil, nil
  if force and force ~= "opaque" then
    local belowK = keyOf(cluster.minX, cluster.maxY + 1)
    local bs = S.shapeAt[belowK]
    local blocked = not map:isWalkableCell(math.floor(cluster.minX / 2),
                                           math.floor(cluster.maxY / 2))
    -- `bookcase` supports as well as `upright`.  A prop drawn above an
    -- authored box stands ON it whatever art the box renders with, and a
    -- stacked box is still a box: the Plateau's gate pilasters carry a
    -- statue on 48 of their tops, and collapsing the pilaster to a stacked
    -- run made every one of them fail this test and drop to ground level.
    -- A `building` claim supports too, when it carries a height: a
    -- Buildings template that names `support` is furniture modelled in
    -- full with a standee left standing on it (Red's dining table under
    -- its potted plant), and the height it states is the model's top
    -- plane.  A plain claim stays at h = 0 and supports nothing.
    if blocked and bs and bs.authored and (bs.h or 0) > 0
       and (bs.art == "upright" or bs.art == "bookcase"
            or bs.class == "building") then
      baseY, support = bs.h, bs
      -- A bookcase support has MOVED: the collapse walks the whole drawn
      -- run onto its southmost cell, and the cell tested above is the run's
      -- north end.  On the Plateau's two-cell pilasters that is a full cell
      -- away, and the bird stood at the right HEIGHT over open ground with
      -- its pillar behind it -- floating.  Stand it on the box's own north
      -- row instead of one row south of its drawing.
      supportRow = S.bookcaseBox[belowK]
    end
  end
  local atlasW = map.tileset.imageWidth or 128
  local atlasH = map.tileset.imageHeight or 48
  local quads = S.objectQuads

  local function at(lx, ly)
    if lx < 0 or lx >= bw or ly < 0 or ly >= bh then return nil end
    return solidPx[ly * bw + lx]
  end

  -- Connected components: one cluster can hold several OBJECTS -- two
  -- stools stacked in adjacent cells, a loose leaf beside a vase.  Each
  -- component stands on its own feet (base on the ground or the support
  -- box, never floating at its bbox height) in the depth band of the
  -- tile row its lowest pixel is drawn in, so stacked drawings become
  -- separate standees in their own cells instead of one tower.
  -- 8-connectivity keeps diagonal strokes whole.
  local comp, comps = {}, {}
  for ly = 0, bh - 1 do
    Budget.tick()
    for lx = 0, bw - 1 do
      local idx = ly * bw + lx
      if solidPx[idx] and not comp[idx] then
        local c = { lowY = ly, n = 0 }
        comps[#comps + 1] = c
        local stack = { idx }
        comp[idx] = c
        while #stack > 0 do
          local p = table.remove(stack)
          local px, py = p % bw, math.floor(p / bw)
          c.n = c.n + 1
          if py > c.lowY then c.lowY = py end
          for dy = -1, 1 do
            for dx = -1, 1 do
              local nx, ny = px + dx, py + dy
              if (dx ~= 0 or dy ~= 0) and nx >= 0 and nx < bw
                 and ny >= 0 and ny < bh then
                local ni = ny * bw + nx
                if solidPx[ni] and not comp[ni] then
                  comp[ni] = c
                  stack[#stack + 1] = ni
                end
              end
            end
          end
        end
      end
    end
  end
  for _, c in ipairs(comps) do
    c.z0 = supportRow and (supportRow * 8 + (8 - depth) / 2)
           or (cluster.minY * 8 + math.floor(c.lowY / 8) * 8
               + (support and 8 or 0) + (8 - depth) / 2)
    c.z1 = c.z0 + depth
  end

  -- A `cutout` or `console` pin is ONE object by contract: keep only
  -- the largest connected drawing.  Loose black scraps -- a cast
  -- shadow's drawn edge, a seam, the vertical rules the surrounding
  -- furniture draws down its own edges -- are background even though
  -- black pixels always survive the shade flood, and this is what
  -- removes them.  Every other pool may hold several objects per
  -- cluster (two stools side by side, a leaf beside a vase), so this
  -- cannot be the default.
  if force then
    local cs = S.shapeAt[keyOf(cluster.tiles[1][1], cluster.tiles[1][2])]
    if cs and (cs.class == "cutout" or cs.class == "console")
       and #comps > 1 then
      local biggest = comps[1]
      for _, c in ipairs(comps) do
        if c.n > biggest.n then biggest = c end
      end
      for idx, c in pairs(comp) do
        if c ~= biggest then solidPx[idx] = nil end
      end
    end
  end

  for ly = 0, bh - 1 do
    Budget.tick()
    for lx = 0, bw - 1 do
      local i = at(lx, ly)
      if i then
        local c = comp[ly * bw + lx]
        local z0, z1 = c.z0, c.z1
        local x, y = wx0 + lx, baseY + c.lowY - ly
        local u = (srcU[i] + 0.5) / atlasW
        local v = (srcV[i] + 0.5) / atlasH
        local function quad(c1, c2, c3, c4, shade)
          quads[#quads + 1] = { c1, c2, c3, c4, u = u, v = v, shade = shade }
        end
        quad({ x, y, z1 }, { x + 1, y, z1 }, { x + 1, y + 1, z1 },
             { x, y + 1, z1 }, OBJ_SHADE.front)
        quad({ x + 1, y, z0 }, { x, y, z0 }, { x, y + 1, z0 },
             { x + 1, y + 1, z0 }, OBJ_SHADE.back)
        if not at(lx, ly - 1) then
          quad({ x, y + 1, z0 }, { x + 1, y + 1, z0 }, { x + 1, y + 1, z1 },
               { x, y + 1, z1 }, OBJ_SHADE.top)
        end
        if y > baseY and not at(lx, ly + 1) then
          quad({ x, y, z1 }, { x + 1, y, z1 }, { x + 1, y, z0 },
               { x, y, z0 }, OBJ_SHADE.bottom)
        end
        if not at(lx - 1, ly) then
          quad({ x, y, z0 }, { x, y, z1 }, { x, y + 1, z1 },
               { x, y + 1, z0 }, OBJ_SHADE.side)
        end
        if not at(lx + 1, ly) then
          quad({ x + 1, y, z1 }, { x + 1, y, z0 }, { x + 1, y + 1, z0 },
               { x + 1, y + 1, z1 }, OBJ_SHADE.side)
        end
      end
    end
  end

  -- the ground the prop stands on: the commonest flat tile touching the
  -- cluster, painted under every cluster tile (the art that was there is
  -- now standing up as the object)
  local votes, best, bestN = {}, nil, 0
  for _, c in ipairs(cluster.tiles) do
    for _, d in ipairs(DIRS4) do
      local nk = keyOf(c[1] + d[1], c[2] + d[2])
      local ns = S.shapeAt[nk]
      if ns and ns.flat and ns.class ~= "void" and not memberC[nk] then
        local t = S.tileAt[nk]
        votes[t] = (votes[t] or 0) + 1
        if votes[t] > bestN then best, bestN = t, votes[t] end
      end
    end
  end
  for _, c in ipairs(cluster.tiles) do
    local k = keyOf(c[1], c[2])
    if support and (support.class == "wall" or support.class == "cliff"
                    or support.art == "bookcase"
                    or support.class == "building") then
      -- a figure drawn above a FULL-HEIGHT block (the gym statue on its
      -- plinth) is a statue on a pillar with ONE cell of footprint: the
      -- block below already carries the whole base, so the drawn cell
      -- becomes synthesized floor rather than a second block marching
      -- the base backwards. Furniture supports (a monitor on its desk)
      -- keep the box-extension below -- their drawn cell is the
      -- furniture's own upper rows, and floor there would amputate it.
      --
      -- STRUCTURE, not height, decides which: `cliff` and `bookcase` are
      -- full-height blocks like `wall` and belong here, while `desk` is
      -- 24px and still furniture.  The Plateau's statues on stacked
      -- pilasters found this -- taking the furniture branch turned each
      -- statue's own two rows into a 32px box wearing the pilaster's art,
      -- so every one of them stood inside a slab of its own plinth.
      -- A `building` support belongs here too: the template's stamped
      -- model already carries every surface under the standee (that is
      -- what its `support` height asserts), so a box here would stand
      -- INSIDE the modelled tabletop.  Its stamp pre-painted the floor
      -- under these tiles, which the `or` keeps when no flat tile
      -- touches a cluster ringed by its own furniture.
      S.skip[k] = true
      S.ground[k] = best or S.ground[k]
    elseif support then
      -- the claimed tile keeps rendering as the box the prop stands on,
      -- wearing the art its own ROW would have without the drawing (the
      -- trim row stays trim); only when the whole row is the prop does
      -- it fall back to the row below
      S.shapeAt[k] = support
      local src = keyOf(c[1], cluster.maxY + 1)
      for dx = 1, 3 do
        for _, sx in ipairs({ c[1] - dx, c[1] + dx }) do
          local nk = keyOf(sx, c[2])
          local ns = S.shapeAt[nk]
          if not memberC[nk] and ns and ns.authored
             and ns.class == support.class then
            src = nk
            break
          end
        end
        if src ~= keyOf(c[1], cluster.maxY + 1) then break end
      end
      S.tileAt[k] = S.tileAt[src]
    else
      S.skip[k] = true
      S.ground[k] = best
    end
  end
  return true
end

-- ---- authored masks with a body ----

-- One authored mask emitted as a per-pixel voxel slab in WORLD space --
-- the treatment every solid standee in this file gets, driven by a hand
-- drawn silhouette instead of a flood.
--
-- The caller owns placement entirely, because placement is the whole
-- difference between the two things that use this: `x0` is the world x of
-- the mask's west edge, `yOf(ly)` the world y a drawn row lands at, and
-- `bandOf(ly)` its z span.  A bicycle hung on a wall keeps its drawn
-- elevation and juts south of the band; a cash register stands on the
-- counter's top plane and sits inside its own cell.
--
-- `bandOf` is per ROW rather than per object so one drawing can hold parts
-- of different thickness (the register's receipt curl over its body).
-- Where the band CHANGES between two stacked rows the lower row still gets
-- its top face: without that the body would be open along the strip the
-- thinner part does not cover, and you would see into the machine.
--
-- `omit` is a rect of the mask this pass does NOT extrude, because it is
-- not a face at all -- maskPlate lays it flat instead.  It leaves the mask
-- for good here, neighbours included, so the extrusion closes up around
-- the notch exactly as if the drawing had never filled it.
local function maskSlab(quads, m, perRow, atlasW, atlasH, x0, yOf, bandOf,
                        yFloor, omit)
  local bw, bh = m.w * 8, m.h * 8

  local function at(lx, ly)
    if lx < 0 or lx >= bw or ly < 0 or ly >= bh then return false end
    if omit and lx >= omit.x0 and lx <= omit.x1
       and ly >= omit.r0 and ly <= omit.r1 then return false end
    return m.mask[ly * bw + lx] or false
  end

  for ly = 0, bh - 1 do
    Budget.tick()
    local z0, z1 = bandOf(ly)
    local pz0, pz1 = bandOf(ly - 1)
    local capped = (pz0 ~= z0 or pz1 ~= z1)
    for lx = 0, bw - 1 do
      if at(lx, ly) then
        local tile = m.tiles[math.floor(ly / 8) * m.w
                             + math.floor(lx / 8) + 1]
        local u = ((tile % perRow) * 8 + lx % 8 + 0.5) / atlasW
        local v = (math.floor(tile / perRow) * 8 + ly % 8 + 0.5) / atlasH
        local x, y = x0 + lx, yOf(ly)
        local function quad(c1, c2, c3, c4, shade)
          quads[#quads + 1] = { c1, c2, c3, c4, u = u, v = v, shade = shade }
        end
        quad({ x, y, z1 }, { x + 1, y, z1 }, { x + 1, y + 1, z1 },
             { x, y + 1, z1 }, OBJ_SHADE.front)
        quad({ x + 1, y, z0 }, { x, y, z0 }, { x, y + 1, z0 },
             { x + 1, y + 1, z0 }, OBJ_SHADE.back)
        if capped or not at(lx, ly - 1) then
          quad({ x, y + 1, z0 }, { x + 1, y + 1, z0 }, { x + 1, y + 1, z1 },
               { x, y + 1, z1 }, OBJ_SHADE.top)
        end
        if y > yFloor and not at(lx, ly + 1) then
          quad({ x, y, z1 }, { x + 1, y, z1 }, { x + 1, y, z0 },
               { x, y, z0 }, OBJ_SHADE.bottom)
        end
        if not at(lx - 1, ly) then
          quad({ x, y, z0 }, { x, y, z1 }, { x, y + 1, z1 },
               { x, y + 1, z0 }, OBJ_SHADE.side)
        end
        if not at(lx + 1, ly) then
          quad({ x + 1, y, z1 }, { x + 1, y, z0 }, { x + 1, y + 1, z0 },
               { x + 1, y + 1, z1 }, OBJ_SHADE.side)
        end
      end
    end
  end
end

-- The other half of the same drawing: a rect of the mask that is a
-- TOP-VIEW surface, laid HORIZONTAL instead of extruded.
--
-- This is the methodology's band classification at rect granularity, and
-- the reason the register is not a box.  A GB cell packs several facings,
-- and the register's keypad is drawn from ABOVE -- its keys lie on the
-- machine's deck, sealed behind their own black border inside the outer
-- silhouette.  Extruding it stands that surface on end and paints the keys
-- up the machine's face, which is the extruded-picture failure exactly.
--
-- So the rect lands one voxel proud of what maskSlab left below it, at `y`,
-- one voxel thick, filling the body's whole depth band (`z0`, `D`).
--
-- The rect STRETCHES over that band rather than laying its rows 1:1: it is
-- the machine's whole deck, so it has to reach the machine's whole depth,
-- and the alternative -- panel at the front, bare deck behind -- leaves a
-- strip of the base band's top showing through where the keys should be.
-- Sampled at the voxel's CENTRE, the same rule Stage 1 samples the atlas
-- with, so a band scales by whole voxels and nothing blurs: at 8 rows over
-- 12 voxels every second drawn row doubles.  The one place in the model
-- where a texel is not 1:1 with a drawn pixel, and the reason `depth` is an
-- authored number again.  No bottom faces: it rests on the box.
local function maskPlate(quads, m, perRow, atlasW, atlasH, x0, r, y, z0, D)
  local bw, bh = m.w * 8, m.h * 8
  local rows = r.r1 - r.r0 + 1

  -- depth voxel -> the drawn row it wears
  local function rowAt(k)
    if k < 0 or k >= D then return nil end
    return r.r0 + math.min(rows - 1, math.floor((k + 0.5) * rows / D))
  end

  local function at(lx, k)
    local ly = rowAt(k)
    if not ly or lx < r.x0 or lx > r.x1 then return false end
    return m.mask[ly * bw + lx] or false
  end

  -- The plate's rim, in the two directions the drawing treats differently.
  -- ACROSS the rows the neighbour is the extrusion standing BESIDE the
  -- notch (the register's display unit), which is tall and covers the
  -- plate's edge, so that face must not be drawn twice.  ALONG them the
  -- neighbour is the extrusion BELOW it (the base band, whose own front
  -- face stops one voxel short), so the plate's front lip is exposed and
  -- is the deck's own front edge.
  local function beside(lx, ly)
    if lx < 0 or lx >= bw or ly < 0 or ly >= bh then return false end
    return m.mask[ly * bw + lx] or false
  end

  for k = 0, D - 1 do
    Budget.tick()
    local ly, z = rowAt(k), z0 + k
    for lx = r.x0, r.x1 do
      if at(lx, k) then
        local tile = m.tiles[math.floor(ly / 8) * m.w
                             + math.floor(lx / 8) + 1]
        local u = ((tile % perRow) * 8 + lx % 8 + 0.5) / atlasW
        local v = (math.floor(tile / perRow) * 8 + ly % 8 + 0.5) / atlasH
        local x = x0 + lx
        local function quad(c1, c2, c3, c4, shade)
          quads[#quads + 1] = { c1, c2, c3, c4, u = u, v = v, shade = shade }
        end
        quad({ x, y + 1, z }, { x + 1, y + 1, z }, { x + 1, y + 1, z + 1 },
             { x, y + 1, z + 1 }, OBJ_SHADE.top)
        if not at(lx, k + 1) then
          quad({ x, y, z + 1 }, { x + 1, y, z + 1 }, { x + 1, y + 1, z + 1 },
               { x, y + 1, z + 1 }, OBJ_SHADE.front)
        end
        if not at(lx, k - 1) then
          quad({ x + 1, y, z }, { x, y, z }, { x, y + 1, z },
               { x + 1, y + 1, z }, OBJ_SHADE.back)
        end
        if not beside(lx - 1, ly) then
          quad({ x, y, z }, { x, y, z + 1 }, { x, y + 1, z + 1 },
               { x, y + 1, z }, OBJ_SHADE.side)
        end
        if not beside(lx + 1, ly) then
          quad({ x + 1, y, z + 1 }, { x + 1, y, z }, { x + 1, y + 1, z },
               { x + 1, y + 1, z + 1 }, OBJ_SHADE.side)
        end
      end
    end
  end
end

-- An AUTHORED solid standing on furniture, given as plan layers instead of
-- extruded from the drawing (see TileShape's `model`).  The one thing it
-- shares with the mask paths is that nothing here is a colour: each layer
-- names the atlas texels its top and its sides wear, and every quad below
-- samples one of them, so the Centers' bell is painted out of the counter's
-- own pixels and recolours with it.
--
-- Placement is by CELL, not by drawn row.  A model exists because the
-- drawing was too small to un-project, so its drawn row says nothing about
-- depth worth keeping -- what says something is which piece of furniture it
-- is on and which end of it a person reaches: the solid is centred on the
-- mask's own columns and pushed to the SOUTH edge of the support cell, the
-- face the aisle is on, less the entry's `inset` -- the one number here
-- taste can move, because flush against the counter's own front lip is a
-- real position and so is a couple of voxels back from it.
local function maskModel(quads, m, perRow, atlasW, atlasH, xMid, zSouth, y0)
  local function uvOf(t)
    local tile, row, col = t[1], t[2], t[3] or 0
    return ((tile % perRow) * 8 + col + 0.5) / atlasW,
           (math.floor(tile / perRow) * 8 + row + 0.5) / atlasH
  end

  for k, L in ipairs(m) do
    local u, v = uvOf(L.side)
    local ut, vt = uvOf(L.top)
    local above = m[k + 1]
    local x0 = xMid - math.floor(L.w / 2)
    local z0 = zSouth - L.d
    local function solid(layer, dx, dz)
      if not layer or dx < 0 or dx >= layer.w or dz < 0 or dz >= layer.d then
        return false
      end
      return layer.cells[dz * layer.w + dx] or false
    end
    for dz = 0, L.d - 1 do
      for dx = 0, L.w - 1 do
        if solid(L, dx, dz) then
          local x, y, z = x0 + dx, y0 + k - 1, z0 + dz
          local function quad(c1, c2, c3, c4, uu, vv, shade)
            quads[#quads + 1] = { c1, c2, c3, c4, u = uu, v = vv,
                                  shade = shade }
          end
          -- a layer's own plan is what closes it: a face is drawn wherever
          -- the neighbouring cell of this layer is empty, and the top
          -- wherever the layer ABOVE does not stand on it.  Nothing needs a
          -- bottom -- layer 1 rests on the furniture and the rest rest on
          -- each other.
          if not solid(above, dx, dz) then
            quad({ x, y + 1, z }, { x + 1, y + 1, z }, { x + 1, y + 1, z + 1 },
                 { x, y + 1, z + 1 }, ut, vt, OBJ_SHADE.top)
          end
          if not solid(L, dx, dz + 1) then
            quad({ x, y, z + 1 }, { x + 1, y, z + 1 },
                 { x + 1, y + 1, z + 1 }, { x, y + 1, z + 1 }, u, v,
                 OBJ_SHADE.front)
          end
          if not solid(L, dx, dz - 1) then
            quad({ x + 1, y, z }, { x, y, z }, { x, y + 1, z },
                 { x + 1, y + 1, z }, u, v, OBJ_SHADE.back)
          end
          if not solid(L, dx - 1, dz) then
            quad({ x, y, z }, { x, y, z + 1 }, { x, y + 1, z + 1 },
                 { x, y + 1, z }, u, v, OBJ_SHADE.side)
          end
          if not solid(L, dx + 1, dz) then
            quad({ x + 1, y, z + 1 }, { x + 1, y, z }, { x + 1, y + 1, z },
                 { x + 1, y + 1, z + 1 }, u, v, OBJ_SHADE.side)
          end
        end
      end
    end
  end
end

-- ---- figures: a thing drawn INTO furniture, cut out and stood up ----

-- One authored figure at one matched position.
--
-- The mask IS the classification: no flood, no shade segmentation, no
-- validation gate.  Every automatic route in this file asks the art where
-- the object ends, and a figure painted into its own furniture has no
-- answer to give -- so the profile answers instead, and this only has to
-- believe it.  Which also means figures build HEADLESS: unlike every
-- other standee here, nothing below reads a pixel.
--
-- A PERSON is a SPRITE, not a prop, and an entry that states no `depth`
-- gets exactly the treatment SpriteBillboards gives a character: one flat
-- plane of the drawing's own pixels, no thickness, standing at its feet
-- and leaned back by the camera's pitch at draw time so it always reads
-- face-on -- because that is what the artwork is.  A seated man drawn
-- face-on is a 2D icon like every other Gen 1 figure; extruding him into
-- a slab reconstructs a body nobody drew (the ten-voxel version read as a
-- wedge of furniture, and even one voxel showed an edge the sprites never
-- show).
--
-- So the card's quads are emitted in its OWN LOCAL SPACE -- x from the
-- mask's west edge, y from his feet, all at z = 0 -- and the placement
-- (`wx`, `wz`, `y`) rides along for VoxelScene to build the lean matrix
-- from.  One quad per pixel rather than one alpha-keyed texture: the
-- tileset atlas has no alpha to key on, and per-pixel quads cut the exact
-- same silhouette straight out of the live atlas, so every palette bake
-- (SGB, RED++ per-tile groups, a mod's own art) textures him for free.
--
-- An entry that DOES state a `depth` is not a person, and takes the other
-- branch: a per-pixel voxel slab in world space (maskSlab above), standing
-- on the same furniture the card would have stood on.  The Marts' cash
-- register is why -- a machine set down on a counter is a box seen from
-- the front, and a card of it is the billboard failure the standee pools
-- exist to avoid.  It keeps the card's anchoring exactly: its feet on the
-- support's top plane, and its body in the 8px depth band of the tile row
-- its lowest pixel is drawn in, which is where a character card would
-- have pivoted.  So the machine sits at the FRONT of the counter cell it
-- is drawn low in, and never leans into the aisle behind it.
local function buildFigure(S, map, fig, tx, ty, perRow)
  local bw, bh = fig.w * 8, fig.h * 8

  local function at(lx, ly)
    if lx < 0 or lx >= bw or ly < 0 or ly >= bh then return false end
    return fig.mask[ly * bw + lx] or false
  end

  -- his feet and his west edge: the card's own origin
  local lowY, minX = 0, bw - 1
  for ly = 0, bh - 1 do
    for lx = 0, bw - 1 do
      if at(lx, ly) then
        if ly > lowY then lowY = ly end
        if lx < minX then minX = lx end
      end
    end
  end

  -- He stands ON the furniture he was drawn into -- the same lift a pinned
  -- prop above a pinned box takes (see buildObject), and gated the same
  -- way: a thing set down on furniture occupies a BLOCKED cell, while a
  -- seat you merely walk up to is in a walkable one.  The row under his
  -- card is SCANNED for the tallest authored upright rather than read at
  -- its west corner: the corner tile can be furniture that is not his
  -- seat (the couch's raised backrest column stands there, `top` art and
  -- taller than the cushion he actually sits on).
  local baseY = 0
  local blocked = not map:isWalkableCell(math.floor(tx / 2),
                                         math.floor((ty + fig.h - 1) / 2))
  if blocked then
    for dx = 0, fig.w - 1 do
      local bs = S.shapeAt[keyOf(tx + dx, ty + fig.h)]
      if bs and bs.authored and bs.art == "upright"
         and (bs.h or 0) > baseY then
        baseY = bs.h
      end
    end
  end

  local atlasW = map.tileset.imageWidth or 128
  local atlasH = map.tileset.imageHeight or 48

  if fig.model then
    -- An authored solid: centred on the mask's own columns, standing on
    -- the furniture's top plane at the front of its cell.
    local maxX = minX
    for ly = 0, bh - 1 do
      for lx = 0, bw - 1 do
        if at(lx, ly) and lx > maxX then maxX = lx end
      end
    end
    local xMid = tx * 8 + math.floor((minX + maxX + 1) / 2)
    local zSouth = (math.floor((ty + fig.h - 1) / 2) + 1) * 16 - (fig.inset or 0)
    maskModel(S.objectQuads, fig.model, perRow, atlasW, atlasH,
              xMid, zSouth, baseY)
  elseif fig.depth then
    -- An OBJECT: the standee slab, standing on the FRONT edge of the tile
    -- row its feet are drawn in -- the south face of the 8px band a
    -- character card would have pivoted in.  It is anchored there and
    -- grows NORTH rather than being centred, so that `depth` is free to
    -- exceed the 8px band without the machine ever creeping toward the
    -- aisle: a till drawn low on a counter is at the counter's front, and
    -- a deeper one just eats more of the bare top behind it.  (At the
    -- 8 the band itself is, the two rules agree.)
    --
    -- `thin` caps the top rows to their own thickness, centred in the
    -- body's depth -- the register's receipt curl leaves the arm's top
    -- face by a slot in the middle of it, not flush with its front.
    local south = ty * 8 + math.floor(lowY / 8) * 8 + 8
    local function bandOf(ly)
      local z0 = south - fig.depth
      if fig.thin and ly < fig.thin.rows then
        local m = math.floor((fig.depth - fig.thin.depth) / 2)
        return z0 + m, z0 + m + fig.thin.depth
      end
      return z0, south
    end
    local function yOf(ly) return baseY + lowY - ly end
    maskSlab(S.objectQuads, fig, perRow, atlasW, atlasH, tx * 8,
             yOf, bandOf, baseY, fig.flat)
    if fig.flat then
      -- The top-view rect lands on the plane its own BOTTOM row would
      -- have stood at -- which is the top of whatever the extrusion left
      -- under it (the register's base band), so the keys lie on the deck
      -- and never float.
      --
      -- In depth it fills the body's whole band, STRETCHED to it: the rect
      -- is the machine's deck, so it reaches as deep as the machine does,
      -- and its last drawn row stays the deck's front edge directly over
      -- the fascia below it -- an object drawn LOW on a surface is drawn
      -- NEAR its front.
      maskPlate(S.objectQuads, fig, perRow, atlasW, atlasH, tx * 8,
                fig.flat, yOf(fig.flat.r1), south - fig.depth, fig.depth)
    end
  else
    local quads = {}
    for ly = 0, bh - 1 do
      Budget.tick()
      for lx = 0, bw - 1 do
        if at(lx, ly) then
          local tile = fig.tiles[math.floor(ly / 8) * fig.w
                                 + math.floor(lx / 8) + 1]
          local u = ((tile % perRow) * 8 + lx % 8 + 0.5) / atlasW
          local v = (math.floor(tile / perRow) * 8 + ly % 8 + 0.5) / atlasH
          local x, y = lx - minX, lowY - ly
          quads[#quads + 1] = { { x, y, 0 }, { x + 1, y, 0 },
                                { x + 1, y + 1, 0 }, { x, y + 1, 0 },
                                u = u, v = v, shade = 1 }
        end
      end
    end

    -- Where the card stands.  `wz` is the MIDDLE of the tile row his feet
    -- are drawn in, which is the same convention a character card uses
    -- (its feet plane sits at its cell's middle) -- so he sorts against
    -- the couch and against a player walking past exactly the way an NPC
    -- standing there would.
    S.figures[#S.figures + 1] = {
      quads = quads,
      wx = tx * 8 + minX,
      wz = ty * 8 + math.floor(lowY / 8) * 8 + 4,
      y = baseY,
    }
  end

  -- What each covered tile wears now that he is off it.  Only the ART
  -- changes: the couch tiles keep their `counter` box (they ARE the
  -- couch) and the floor tiles he overhung stay flat floor -- the
  -- profile just names the version of each drawing without him in it,
  -- so nothing has to be synthesized or repainted from a neighbour vote.
  for i = 1, #fig.tiles do
    local dx, dy = (i - 1) % fig.w, math.floor((i - 1) / fig.w)
    S.tileAt[keyOf(tx + dx, ty + dy)] = fig.under[i]
  end
end

-- Every authored figure, wherever the map draws it.
--
-- Matched by TILE PATTERN rather than by coordinates: one blockset entry
-- places this couch once in each of the eleven Pokemon Centers (and the
-- Celadon Hotel), so the pattern finds all of them without the profile
-- naming a single map or cell.  The repaint above replaces the pattern's
-- own tiles, so a match can never fire twice on the same drawing.
function Structures.buildFigures(S, map, x0, x1, y0, y1)
  local figures = TileShape.figures(map.tileset.id)
  if not figures then return end
  local perRow = map.tileset.tilesPerRow or 16
  for _, fig in ipairs(figures) do
    for ty = y0, y1 - fig.h + 1 do
      for tx = x0, x1 - fig.w + 1 do
        Budget.tick()
        local hit = true
        for i = 1, #fig.tiles do
          local dx, dy = (i - 1) % fig.w, math.floor((i - 1) / fig.w)
          if S.tileAt[keyOf(tx + dx, ty + dy)] ~= fig.tiles[i] then
            hit = false
            break
          end
        end
        if hit then buildFigure(S, map, fig, tx, ty, perRow) end
      end
    end
  end
end

-- ---- mounted: a thing drawn INTO a wall band, stood proud of it ----

-- One authored mounted object at one matched position.
--
-- Same authoring premise as a figure -- the mask IS the classification,
-- because a drawing painted onto the wall it hangs on has no background
-- margin for a flood to enter by, and here the wall's own #555 stripes
-- are a flood boundary as well, so a silhouette comes back striped.
-- Like a figure it therefore builds HEADLESS: nothing below reads a
-- pixel.
--
-- But a mounted object is an OBJECT, so it is built the way every other
-- standee here is -- a per-pixel voxel slab wearing the drawing's own
-- texels, quads emitted in world space -- and not as a sprite card:
--
--   ELEVATION is the drawn one.  A figure stands on its own feet; this
--   keeps the row it is painted in, because the band it is painted into
--   is a measured 16px face rising off the floor.  So drawn row `ly`
--   becomes world y = (band height - 1) - ly, and a bicycle whose wheels
--   are drawn on the band's bottom row lands on the floor while one hung
--   clear of it stays hung.
--   DEPTH juts SOUTH of the band's own face (z0 at the drawing's south
--   edge), so the object stands in front of the wall rather than inside
--   it.  It overhangs the walkable cell in front, which is what a bicycle
--   leaning on a wall does; nothing about collision changes.
local function buildMountedAt(S, map, m, tx, ty, perRow)
  local bh = m.h * 8
  local z0 = (ty + m.h) * 8
  local z1 = z0 + (m.depth or 2)

  maskSlab(S.objectQuads, m, perRow, map.tileset.imageWidth or 128,
           map.tileset.imageHeight or 48, tx * 8,
           function(ly) return (bh - 1) - ly end,
           function() return z0, z1 end, 0)

  -- What the band wears now that the object is off it: the plain panel
  -- the artist drew everywhere else along the same wall.  Only the ART
  -- changes -- these tiles keep the `wall` box they always resolved to,
  -- because they ARE the wall.
  for i = 1, #m.tiles do
    local dx, dy = (i - 1) % m.w, math.floor((i - 1) / m.w)
    S.tileAt[keyOf(tx + dx, ty + dy)] = m.under[i]
  end
end

-- Every authored mounted object, wherever the map draws it.  Matched by
-- TILE PATTERN like a figure, and for the same reason -- one blockset
-- entry can place the same drawing in several rooms -- and the repaint
-- above replaces the pattern's own tiles, so a match never fires twice
-- on one drawing.
function Structures.buildMounted(S, map, x0, x1, y0, y1)
  local list = TileShape.mounted(map.tileset.id)
  if not list then return end
  local perRow = map.tileset.tilesPerRow or 16
  for _, m in ipairs(list) do
    for ty = y0, y1 - m.h + 1 do
      for tx = x0, x1 - m.w + 1 do
        Budget.tick()
        local hit = true
        for i = 1, #m.tiles do
          local dx, dy = (i - 1) % m.w, math.floor((i - 1) / m.w)
          if S.tileAt[keyOf(tx + dx, ty + dy)] ~= m.tiles[i] then
            hit = false
            break
          end
        end
        if hit then buildMountedAt(S, map, m, tx, ty, perRow) end
      end
    end
  end
end

-- ---- tall grass ----

-- ---- closing a standee's sides ----
--
-- The grass tufts and the flowers are both built the same way: each row of
-- the 8x8 drawing becomes a horizontal RUN of lit pixels, stood up as a
-- front face and a back face one voxel apart, with a lid on top. What that
-- leaves open is the two ENDS of every run -- so the slab was a pair of
-- billboards rather than a solid, and from any angle off square you looked
-- in through the edge and straight out the other side. At the low cameras
-- this mod has grown (1ST, 3RD, the battle's floor-level seat) that is
-- most of the time.
--
-- A wall goes on an end only where the pixel beyond it is actually clear,
-- which for a run's end it is by construction -- except where two runs on
-- the same row meet across a gap of nothing, which cannot happen, and at
-- the tile's border, where the neighbouring tile's own standee may or may
-- not continue the shape. The border is closed anyway: tufts sit on their
-- own half-cells with a gap between them, so an open border edge is a hole
-- in the open, not a seam with anything.
--
-- Each wall samples ONE texel at its centre -- the end pixel it is closing
-- off -- so it wears that pixel's own colour, which is the nearest coloured
-- pixel to the surface being filled. Sampling a single texel is also what
-- carries the animation: when a frame keys that pixel out, the wall's own
-- fragments discard with the faces either side of it, so a swaying tuft
-- never leaves a wall standing where its blade no longer is.
-- `everyPixel` is for a standee whose silhouette ANIMATES. The mesh is
-- built once, over the UNION of every frame's mask, and each frame is cut
-- out again in texture space -- so a run that is six pixels wide in the
-- union may be two pixels wide in the frame on screen, and the four pixels
-- that dropped out took the union's end walls with them. What is left
-- exposed is an interior boundary, which had no wall because in the union
-- it was not a boundary at all. That is the gap that survived closing the
-- run ends: the first frame looked solid and every other frame did not.
--
-- So an animated standee gets a wall on BOTH sides of EVERY pixel. A wall
-- between two lit pixels is enclosed by the front and back faces and never
-- seen; the moment its neighbour is keyed out it becomes the edge, already
-- in place and already wearing the right colour. Each is inset a hair into
-- its own pixel so the two that meet at a boundary are not coplanar -- the
-- voxel pass draws with culling off, and two quads in the same plane would
-- z-fight rather than politely take turns.
local SIDE_INSET = 0.03

local function sideQuads(quads, ix, ix2, yBot, yTop, zB, zF,
                         ax0, ay0, atlasW, atlasH, py, lit, everyPixel)
  local function texel(px)
    return (ax0 + px + 0.5) / atlasW, (ay0 + py + 0.5) / atlasH
  end
  local function left(px, at)
    local u, v = texel(px)
    quads[#quads + 1] = {                 -- facing -X
      { at, yBot, zB }, { at, yBot, zF },
      { at, yTop, zF }, { at, yTop, zB },
      uv = { { u, v }, { u, v }, { u, v }, { u, v } },
      shade = OBJ_SHADE.side,
    }
  end
  local function right(px, at)
    local u, v = texel(px)
    quads[#quads + 1] = {                 -- facing +X
      { at, yBot, zF }, { at, yBot, zB },
      { at, yTop, zB }, { at, yTop, zF },
      uv = { { u, v }, { u, v }, { u, v }, { u, v } },
      shade = OBJ_SHADE.side,
    }
  end
  if everyPixel then
    for px = ix, ix2 do
      left(px, px + SIDE_INSET)
      right(px, px + 1 - SIDE_INSET)
    end
    return
  end
  if not lit(ix - 1, py) then left(ix, ix) end
  if not lit(ix2 + 1, py) then right(ix2, ix2 + 1) end
end

-- A tall-grass CELL is four tufts: 2x2 tiles, and each 8x8 tile is one
-- whole clump of grass. Each tile stands as its own thin per-pixel slab
-- at ITS OWN depth -- the cell's north tile row in the north half of the
-- cell, the south row in the south half -- over the flat grass base the
-- tile already renders. So the player walks BETWEEN the two rows, and
-- the southern row occludes their feet the way the 2D grass overdraw
-- did. Transparency respected: only the tuft strokes stand. Runs of
-- adjacent pixels merge into single quads, and one template per grass
-- tile id is stamped across the map (grass comes in fields).
--
-- One tile is ONE standing piece, full height. The first cut split each
-- tile again into its top and bottom four art rows and stood those at
-- two different depths, which cut every blade that runs down the tile
-- clean in half -- the two halves ended up 4px tall and 4px apart in
-- depth, so a clump read as two stubs rather than one tuft.
local GRASS_THICK = 2

local function grassTemplate(map, data, tileId)
  local perRow = map.tileset.tilesPerRow or 16
  local atlasW = map.tileset.imageWidth or 128
  local atlasH = map.tileset.imageHeight or 48
  local ax0 = (tileId % perRow) * 8
  local ay0 = math.floor(tileId / perRow) * 8

  local function opaque(px, py)
    if px < 0 or px > 7 or py < 0 or py > 7 then return false end
    local r, g, b, a = data:getPixel(ax0 + px, ay0 + py)
    return a > 0 and math.min(r, g, b) <= 0.83
  end

  local quads = {}
  -- the slab stands across the middle of its own tile, so the two tile
  -- rows of a cell are half a cell apart in depth
  local zMid = 4
  local zB, zF = zMid - GRASS_THICK / 2, zMid + GRASS_THICK / 2
  for iy = 0, 7 do
    local yTop = 8 - iy
    local yBot = yTop - 1
    local ix = 0
    while ix < 8 do
      if opaque(ix, iy) then
        local ix2 = ix
        while ix2 + 1 < 8 and opaque(ix2 + 1, iy) do
          ix2 = ix2 + 1
        end
        local u0 = (ax0 + ix + 0.05) / atlasW
        local u1 = (ax0 + ix2 + 0.95) / atlasW
        local v0 = (ay0 + iy + 0.05) / atlasH
        local v1 = (ay0 + iy + 0.95) / atlasH
        quads[#quads + 1] = {           -- front
          { ix, yBot, zF }, { ix2 + 1, yBot, zF },
          { ix2 + 1, yTop, zF }, { ix, yTop, zF },
          uv = { { u0, v1 }, { u1, v1 }, { u1, v0 }, { u0, v0 } },
          shade = 1,
        }
        quads[#quads + 1] = {           -- back
          { ix2 + 1, yBot, zB }, { ix, yBot, zB },
          { ix, yTop, zB }, { ix2 + 1, yTop, zB },
          uv = { { u1, v1 }, { u0, v1 }, { u0, v0 }, { u1, v0 } },
          shade = 0.68,
        }
        -- blade tips: a top strip where the row above is clear
        if not opaque(ix, iy - 1) then
          quads[#quads + 1] = {
            { ix, yTop, zB }, { ix2 + 1, yTop, zB },
            { ix2 + 1, yTop, zF }, { ix, yTop, zF },
            uv = { { u0, v0 }, { u1, v0 }, { u1, v0 }, { u0, v0 } },
            shade = 1,
          }
        end
        -- and underneath, where a blade ends in mid-air over the ground
        if not opaque(ix, iy + 1) then
          quads[#quads + 1] = {
            { ix, yBot, zF }, { ix2 + 1, yBot, zF },
            { ix2 + 1, yBot, zB }, { ix, yBot, zB },
            uv = { { u0, v1 }, { u1, v1 }, { u1, v1 }, { u0, v1 } },
            shade = OBJ_SHADE.bottom,
          }
        end
        -- and the run's two end walls, which is what makes a blade a solid
        -- thing rather than two billboards you can see between (sideQuads
        -- above argues it, and why each wall wears its end pixel's colour)
        sideQuads(quads, ix, ix2, yBot, yTop, zB, zF,
                  ax0, ay0, atlasW, atlasH, iy, opaque)
        ix = ix2 + 1
      else
        ix = ix + 1
      end
    end
  end
  return quads
end

function Structures.buildGrass(S, map, x0, x1, y0, y1, data)
  local templates = {}
  local quads = S.grassQuads
  for ty = y0, y1 do
    for tx = x0, x1 do
      Budget.tick()
      local k = keyOf(tx, ty)
      local s = S.shapeAt[k]
      -- tufts only where the CELL is tall grass by the engine's own rule
      -- (isGrassCell: the cell's collision tile). The grass GRAPHIC also
      -- appears as decorative filler inside ordinary ground blocks, and a
      -- tile-level test sprouted tufts all over town plazas.
      if s and s.art == "grass"
         and map:isGrassCell(math.floor(tx / 2), math.floor(ty / 2)) then
        local tileId = S.tileAt[k]
        local tpl = templates[tileId]
        if not tpl then
          tpl = grassTemplate(map, data, tileId)
          templates[tileId] = tpl
        end
        local wx, wz = tx * 8, ty * 8
        -- Stable diagonal phase per tuft. Both ends of every quad receive
        -- the same value, so a gust bends the slab without shearing it.
        local sway = wx * 0.050 + wz * 0.031
        for _, q in ipairs(tpl) do
          quads[#quads + 1] = {
            { q[1][1] + wx, q[1][2], q[1][3] + wz },
            { q[2][1] + wx, q[2][2], q[2][3] + wz },
            { q[3][1] + wx, q[3][2], q[3][3] + wz },
            { q[4][1] + wx, q[4][2], q[4][3] + wz },
            uv = q.uv, shade = q.shade, sway = sway,
            cx = wx + 4, cz = wz + 4,
          }
        end

        -- Sparse wind-borne leaf. It reuses one opaque grass texel and is
        -- animated entirely on the GPU, so no per-frame Lua particles exist.
        if #tpl > 0 and ((tx * 13 + ty * 7) % 11 == 0) then
          local src = tpl[1]
          local uv = src.uv and src.uv[1] or { src.u, src.v }
          local lx = wx + 2 + ((tx * 5 + ty * 3) % 5)
          local lz = wz + 4
          local ly, size = 9 + ((tx + ty) % 3), 1.25
          quads[#quads + 1] = {
            { lx - size, ly,        lz }, { lx + size, ly,        lz },
            { lx + size, ly + size, lz }, { lx - size, ly + size, lz },
            uv = { uv, uv, uv, uv }, shade = 1, sway = sway + 0.73,
            cx = lx, cz = lz, leaf = true,
          }
        end

        -- Rarer one-pixel firefly. Geometry exists all day, but the shader
        -- gives it zero glow outside outdoor night.
        if #tpl > 0 and ((tx * 17 + ty * 11) % 29 == 0) then
          local src = tpl[1]
          local uv = src.uv and src.uv[1] or { src.u, src.v }
          local fx = wx + 2 + ((tx * 3 + ty * 5) % 5)
          local fz = wz + 4
          local fy, half = 9 + ((tx + ty) % 4), 0.5
          quads[#quads + 1] = {
            { fx - half, fy,     fz }, { fx + half, fy,     fz },
            { fx + half, fy + 1, fz }, { fx - half, fy + 1, fz },
            uv = { uv, uv, uv, uv }, shade = 1, sway = sway + 1.37,
            cx = fx, cz = fz, firefly = true,
          }
        end
      end
    end
  end
end

-- ---- flowers ----

-- The animated flower tile stands up as a billboard ONE VOXEL deep, cut
-- to the drawing's darkest tones PLUS everything they enclose -- the
-- round-scenery hull's rule: flood the tile border through every
-- non-dark pixel, and what the flood cannot reach is the flower, its
-- pale petal insides included. The mesh is static and the flower is
-- not, so the geometry spans the UNION of that mask over the base art
-- and every animation frame, and TerrainAtlas rewrites the tile's slot
-- each step with only the CURRENT frame's mask opaque -- the rest keyed
-- to alpha, which the voxel shader discards. The standing silhouette
-- trims itself frame by frame in texture space; the sway animates
-- without a vertex moving, off the same engine clock as the flat path.
--
-- The ground beneath is synthesized from the commonest flat neighbour,
-- like the ground under a detected prop: the tile's own slot no longer
-- holds art anyone can draw flat.
local FLOWER_THICK = 1

local function flowerFrames(tileset, tileId)
  local out = {}
  local ok, declared = pcall(function()
    if tileset.animatedTiles then return tileset.animatedTiles end
    local TileRenderer = require("src.render.TileRenderer")
    return TileRenderer.defaultAnimatedTiles(tileset)
  end)
  if not ok then return out end
  for _, spec in ipairs(type(declared) == "table" and declared or {}) do
    if spec.kind == "frames" and spec.tile == tileId then
      for _, path in pairs(spec.images or {}) do
        local okF, frame = pcall(Assets.imageData, path)
        if okF and frame then out[#out + 1] = frame end
      end
    end
  end
  return out
end

local function flowerTemplate(map, data, tileId)
  local tileset = map.tileset
  local perRow = tileset.tilesPerRow or 16
  local atlasW = tileset.imageWidth or 128
  local atlasH = tileset.imageHeight or 48
  local ax0 = (tileId % perRow) * 8
  local ay0 = math.floor(tileId / perRow) * 8

  -- per image: dark tones, then the border flood that finds what they
  -- enclose. Each image closes over ITS OWN outline before the union --
  -- a pocket two frames only enclose together is not part of either.
  local dark = {}
  local function markMask(img, ox, oy)
    local d, reach, stack = {}, {}, {}
    for py = 0, 7 do
      for px = 0, 7 do
        local r, g, b, a = img:getPixel(ox + px, oy + py)
        if a > 0 and math.min(r, g, b) <= 0.5 then
          d[py * 8 + px] = true
        end
      end
    end
    for i = 0, 7 do
      for _, s in ipairs({ i, 56 + i, i * 8, i * 8 + 7 }) do
        if not d[s] and not reach[s] then
          reach[s] = true
          stack[#stack + 1] = s
        end
      end
    end
    while #stack > 0 do
      local p = table.remove(stack)
      local px, py = p % 8, math.floor(p / 8)
      for _, dir in ipairs(DIRS4) do
        local nx, ny = px + dir[1], py + dir[2]
        if nx >= 0 and nx < 8 and ny >= 0 and ny < 8 then
          local ni = ny * 8 + nx
          if not d[ni] and not reach[ni] then
            reach[ni] = true
            stack[#stack + 1] = ni
          end
        end
      end
    end
    for i = 0, 63 do
      if d[i] or not reach[i] then dark[i] = true end
    end
  end
  markMask(data, ax0, ay0)
  for _, frame in ipairs(flowerFrames(tileset, tileId)) do
    pcall(markMask, frame, 0, 0)
  end

  local function on(px, py)
    if px < 0 or px > 7 or py < 0 or py > 7 then return false end
    return dark[py * 8 + px] == true
  end

  local quads = {}
  local zB = 4 - FLOWER_THICK / 2      -- one slab at the tile's middle
  local zF = zB + FLOWER_THICK
  for py = 0, 7 do
    Budget.tick()
    local yTop, yBot = 8 - py, 7 - py
    local ix = 0
    while ix < 8 do
      if on(ix, py) then
        local ix2 = ix
        while ix2 + 1 < 8 and on(ix2 + 1, py) do ix2 = ix2 + 1 end
        local u0 = (ax0 + ix + 0.05) / atlasW
        local u1 = (ax0 + ix2 + 0.95) / atlasW
        local v0 = (ay0 + py + 0.05) / atlasH
        local v1 = (ay0 + py + 0.95) / atlasH
        quads[#quads + 1] = {           -- front
          { ix, yBot, zF }, { ix2 + 1, yBot, zF },
          { ix2 + 1, yTop, zF }, { ix, yTop, zF },
          uv = { { u0, v1 }, { u1, v1 }, { u1, v0 }, { u0, v0 } },
          shade = OBJ_SHADE.front,
        }
        quads[#quads + 1] = {           -- back
          { ix2 + 1, yBot, zB }, { ix, yBot, zB },
          { ix, yTop, zB }, { ix2 + 1, yTop, zB },
          uv = { { u1, v1 }, { u0, v1 }, { u0, v0 }, { u1, v0 } },
          shade = OBJ_SHADE.back,
        }
        -- ------- the shell, closed on all four remaining faces
        --
        -- A flower SWAYS: the geometry spans the union of every animation
        -- frame's mask and each frame is cut back out of it in texture
        -- space (see the header). So "is there a pixel next door" has two
        -- different answers -- one in the union this mesh was built from,
        -- and one in the frame actually on screen -- and only the second
        -- decides what is exposed.
        --
        -- Closing the union's own edges is therefore not enough, and was
        -- the bug the first cut of this shipped: the base frame looked
        -- solid and every other frame still had gaps, because a pixel that
        -- drops out of a frame takes the union's wall with it and leaves an
        -- interior boundary that never had one.
        --
        -- So every pixel gets a cap on all four of its remaining faces,
        -- whatever its neighbours do. A cap between two lit pixels sits
        -- inside the slab, enclosed by the front and back faces, and is
        -- never seen; the moment its neighbour is keyed out it IS the edge,
        -- already there and already wearing the right colour. Each samples
        -- its own pixel's texel, so it appears and vanishes with the pixel
        -- it belongs to rather than with the one it is closing off.
        --
        -- Inset a hair into its own pixel, because the voxel pass draws
        -- with culling off: the two caps that meet at a boundary would be
        -- coplanar and z-fight rather than politely take turns.
        for px = ix, ix2 do
          local tu = (ax0 + px + 0.5) / atlasW
          local tv = (ay0 + py + 0.5) / atlasH
          local xa, xb = px, px + 1
          local yT = yTop - SIDE_INSET
          local yB = yBot + SIDE_INSET
          quads[#quads + 1] = {           -- the pixel's own lid
            { xa, yT, zB }, { xb, yT, zB }, { xb, yT, zF }, { xa, yT, zF },
            uv = { { tu, tv }, { tu, tv }, { tu, tv }, { tu, tv } },
            shade = OBJ_SHADE.top,
          }
          quads[#quads + 1] = {           -- and its floor
            { xa, yB, zF }, { xb, yB, zF }, { xb, yB, zB }, { xa, yB, zB },
            uv = { { tu, tv }, { tu, tv }, { tu, tv }, { tu, tv } },
            shade = OBJ_SHADE.bottom,
          }
        end
        sideQuads(quads, ix, ix2, yBot, yTop, zB, zF,
                  ax0, ay0, atlasW, atlasH, py, on, true)
        ix = ix2 + 1
      else
        ix = ix + 1
      end
    end
  end
  return quads
end

function Structures.buildFlowers(S, map, tw, th, x0, x1, y0, y1, data)
  local templates = {}
  -- flowerQuads, not objectQuads: flowers sit on WALKABLE cells, so
  -- their mesh draws after the characters with the character pull
  -- (ChunkMesher's flower mesh) -- terrain-baked they lose the depth
  -- fight against the pulled card whenever the player stands among them
  local quads = S.flowerQuads
  for ty = y0, y1 do
    for tx = x0, x1 do
      Budget.tick()
      local k = keyOf(tx, ty)
      local s = S.shapeAt[k]
      if s and s.art == "flower" then
        -- the tile's atlas slot carries only the standing cutout now, so
        -- EVERY flower position -- ring included -- paints synthesized
        -- ground instead of its own art: the commonest flat neighbour
        -- that is not itself a flower, else the map's commonest ground
        -- (forMap's end-of-build vote resolves the `false`)
        S.skip[k] = true
        local votes, best, bestN = {}, nil, 0
        for _, d in ipairs(DIRS4) do
          local nk = keyOf(tx + d[1], ty + d[2])
          local ns = S.shapeAt[nk]
          if ns and ns.flat and ns.class ~= "void"
             and ns.class ~= "flower" then
            local t = S.tileAt[nk]
            votes[t] = (votes[t] or 0) + 1
            if votes[t] > bestN then best, bestN = t, votes[t] end
          end
        end
        S.ground[k] = best or false

        -- standee BODY only, like grass: standing scenery past a map's
        -- edge would poke into the map next door
        if tx >= 0 and ty >= 0 and tx < tw and ty < th then
          local tileId = S.tileAt[k]
          local tpl = templates[tileId]
          if not tpl then
            tpl = flowerTemplate(map, data, tileId)
            templates[tileId] = tpl
          end
          local wx, wz = tx * 8, ty * 8
          for _, q in ipairs(tpl) do
            quads[#quads + 1] = {
              { q[1][1] + wx, q[1][2], q[1][3] + wz },
              { q[2][1] + wx, q[2][2], q[2][3] + wz },
              { q[3][1] + wx, q[3][2], q[3][3] + wz },
              { q[4][1] + wx, q[4][2], q[4][3] + wz },
              uv = q.uv, shade = q.shade,
            }
          end
        end
      end
    end
  end
end

-- Drop one map's analysis (Cut changed the block layer) or everything.
-- Hull templates key on art content (tileset + tiles), which a block edit
-- cannot change, so only the full drop clears them (atlas reload).
function Structures.invalidate(mapId)
  if mapId then
    cache[mapId] = nil
  else
    cache = {}
    atlasData = {}
    roundCache = {}
    Buildings.invalidate()
  end
end

Assets.register(function() Structures.invalidate() end)

return Structures