Tooling

Tools/Terrain/internal/dt/dt.go

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+// Package dt is the exact Euclidean distance transform, with a feature index and an optional cylinder.
+//
+// It lives on its own because three different things need it and two of them are nowhere near the coast:
+// the coastal pass writes every one of its processes as "how far is this cell from the waterline and which
+// stretch of shore does it belong to"; the region partitioner dilates the land mask to decide which
+// landmasses are close enough to be solved together; and the template classifier dissolves the decorative
+// stroke an artist drew by handing each of its pixels to the nearest pixel that means something.
+//
+// Exact, not a chamfer approximation: Felzenszwalb and Huttenlocher's transform is two 1-D passes and O(n)
+// whatever the radius, so there is nothing to buy by approximating, and a chamfer's 2 % anisotropy would
+// show up directly as a shelf wider along the grid axes than across them.
+package dt
+
+import (
+	"math"
+
+	"salty/terrain/internal/field"
+)
+
+// Transform returns, for every cell, the squared distance in cells to the nearest seed cell and the flat
+// index of that seed. A column pass finds the nearest seed in each column; a row pass takes the lower
+// envelope of the parabolas those distances define.
+//
+// With wrapX the row pass is periodic, so the left and right edges of the grid are neighbours. That is what
+// a planet needs: a landmass straddling the seam is one landmass, and the shelf in front of it is one shelf.
+//
+// Cells in a column with no seed at all are given a cost above any real distance rather than an infinity, so
+// the envelope arithmetic never sees a NaN; they are then never chosen unless the grid has no seeds
+// anywhere, in which case every near index comes back -1.
+func Transform(seed []bool, w, h int, wrapX bool) (d2 []float32, near []int32) {
+	return transform(seed, w, h, wrapX, true)
+}
+
+// Distance2 is Transform without the feature index, for a caller that only wants "how far".
+//
+// It is a separate entry point rather than a nil argument because the saving is the point: at planet scale
+// the index and the column scratch it needs are two more arrays of four bytes a cell, which is most of a
+// gigabyte for an answer nobody reads. The region partitioner only asks whether a cell is within a margin
+// of land.
+func Distance2(seed []bool, w, h int, wrapX bool) []float32 {
+	d2, _ := transform(seed, w, h, wrapX, false)
+	return d2
+}
+
+func transform(seed []bool, w, h int, wrapX, wantNear bool) (d2 []float32, near []int32) {
+	d2 = make([]float32, w*h)
+	if wantNear {
+		near = make([]int32, w*h)
+	}
+
+	bigF := float64(w*w+h*h) * 4 // above any achievable dx² + dy²
+	bigD := float32(math.Sqrt(bigF))
+
+	colD := make([]float32, w*h) // distance in cells to the nearest seed in this column
+	var colN []int32             // that seed's row, or -1; only needed for the feature index
+	if wantNear {
+		colN = make([]int32, w*h)
+	}
+
+	field.Rows(w, func(x0, x1 int) {
+		for x := x0; x < x1; x++ {
+			best := -1
+			for y := 0; y < h; y++ {
+				i := y*w + x
+				if seed[i] {
+					best = y
+				}
+				if best < 0 {
+					colD[i] = bigD
+					if wantNear {
+						colN[i] = -1
+					}
+				} else {
+					colD[i] = float32(y - best)
+					if wantNear {
+						colN[i] = int32(best)
+					}
+				}
+			}
+			best = -1
+			for y := h - 1; y >= 0; y-- {
+				i := y*w + x
+				if seed[i] {
+					best = y
+				}
+				if best >= 0 {
+					if d := float32(best - y); d < colD[i] {
+						colD[i] = d
+						if wantNear {
+							colN[i] = int32(best)
+						}
+					}
+				}
+			}
+		}
+	})
+
+	// The row pass. On a cylinder the row is laid out three times - one turn to the left, the row itself,
+	// one turn to the right - and the answer is read out of the middle copy. From a cell in the middle copy
+	// the three images of any column sit at offsets d, d-w and d+w, whose smallest absolute value is the
+	// cyclic distance, so the envelope returns exactly the wrapped answer with no special cases in it.
+	span := w
+	off := 0
+	if wrapX {
+		span = 3 * w
+		off = w
+	}
+	field.Rows(h, func(y0, y1 int) {
+		f := make([]float64, span)
+		v := make([]int, span)
+		z := make([]float64, span+1)
+		for y := y0; y < y1; y++ {
+			row := y * w
+			for j := 0; j < span; j++ {
+				d := float64(colD[row+srcX(j, off, w)])
+				f[j] = d * d
+			}
+			k := 0
+			v[0] = 0
+			z[0] = math.Inf(-1)
+			z[1] = math.Inf(1)
+			for q := 1; q < span; q++ {
+				s := intersect(f, v[k], q)
+				for s <= z[k] {
+					k--
+					s = intersect(f, v[k], q)
+				}
+				k++
+				v[k] = q
+				z[k] = s
+				z[k+1] = math.Inf(1)
+			}
+			k = 0
+			for q := 0; q < span; q++ {
+				for z[k+1] < float64(q) {
+					k++
+				}
+				if q < off || q >= off+w {
+					continue // a replica column; only the middle copy is the answer
+				}
+				dx := float64(q - v[k])
+				o := row + q - off
+				d2[o] = float32(dx*dx + f[v[k]])
+				if !wantNear {
+					continue
+				}
+				sx := srcX(v[k], off, w)
+				if n := colN[row+sx]; n < 0 {
+					near[o] = -1
+				} else {
+					near[o] = n*int32(w) + int32(sx)
+				}
+			}
+		}
+	})
+	return d2, near
+}
+
+// srcX maps a column of the (possibly replicated) row back to a real column.
+func srcX(j, off, w int) int {
+	x := j - off
+	for x < 0 {
+		x += w
+	}
+	for x >= w {
+		x -= w
+	}
+	return x
+}
+
+// intersect is where the parabolas rooted at p and q cross.
+func intersect(f []float64, p, q int) float64 {
+	return ((f[q] + float64(q*q)) - (f[p] + float64(p*p))) / float64(2*q-2*p)
+}