UnrealPrototyping/Tools/Terrain/internal/coast/distance.go

package coast

import (
	"math"

	"salty/terrain/internal/field"
)

// The coast is a *distance*, not a line. Every coastal process is written in terms of how far a cell is from
// the waterline and which stretch of waterline it belongs to: the shelf deepens with distance offshore, the
// surf planes the land within a reach of it, sediment settles in the shallows behind it, and shelter is a
// property of a stretch of shore that every cell near it inherits. So the first thing the pass builds is an
// exact signed distance field with a feature index, and everything after it is a lookup.
//
// Exact, not a chamfer approximation: Felzenszwalb & 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 that is wider along the grid axes than across them.

// edt returns, for every cell, the squared distance in cells to the nearest seed cell and the 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.
//
// 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 map has no seeds anywhere,
// which the caller checks for.
func edt(seed []bool, w, h int) (d2 []float32, near []int32) {
	d2 = make([]float32, w*h)
	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
	colN := make([]int32, w*h)   // that seed's row, or -1

	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], colN[i] = bigD, -1
				} else {
					colD[i], colN[i] = float32(y-best), 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], colN[i] = d, int32(best)
					}
				}
			}
		}
	})

	field.Rows(h, func(y0, y1 int) {
		f := make([]float64, w)
		v := make([]int, w)
		z := make([]float64, w+1)
		for y := y0; y < y1; y++ {
			row := y * w
			for x := 0; x < w; x++ {
				d := float64(colD[row+x])
				f[x] = d * d
			}
			k := 0
			v[0] = 0
			z[0] = math.Inf(-1)
			z[1] = math.Inf(1)
			for q := 1; q < w; 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 < w; q++ {
				for z[k+1] < float64(q) {
					k++
				}
				dx := float64(q - v[k])
				d2[row+q] = float32(dx*dx + f[v[k]])
				if n := colN[row+v[k]]; n < 0 {
					near[row+q] = -1
				} else {
					near[row+q] = n*int32(w) + int32(v[k])
				}
			}
		}
	})
	return d2, near
}

// 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)
}

// Geometry is the coastline as the rest of the pass sees it.
type Geometry struct {
	W, H  int
	CellM float64

	// Dist is metres to the waterline: positive inland, negative offshore.
	Dist *field.Field

	// Ref is, for every cell, the waterline cell whose stretch of shore it belongs to. A land cell takes the
	// sea cell nearest to it, which is on the waterline by construction; a sea cell takes the waterline cell
	// nearest to the land cell nearest to it, which is the stretch of shore facing it. Every per-shore
	// quantity — shelter, shelf width, the backshore relief — is computed once on the waterline and read
	// everywhere else through this.
	Ref []int32

	// Waterline is the sea cells that touch land, in row-major order so anything iterating them is
	// deterministic.
	Waterline []int32

	// ShoreM is the length of the land/sea boundary in metres, counted as boundary edges. It overestimates a
	// diagonal coast by about 4/pi, as any edge-counted perimeter does.
	ShoreM float64
}

// Measure builds the signed distance field and the shore reference from a land/sea mask.
func Measure(sea []bool, w, h int, cellM float64) *Geometry {
	anySea, anyLand := false, false
	land := make([]bool, len(sea))
	for i, s := range sea {
		land[i] = !s
		if s {
			anySea = true
		} else {
			anyLand = true
		}
	}
	g := &Geometry{W: w, H: h, CellM: cellM, Dist: field.New(w, h, cellM), Ref: make([]int32, w*h)}
	for i := range g.Ref {
		g.Ref[i] = -1
	}
	if !anySea || !anyLand {
		return g // an all-land or all-sea map has no coast; every pass below is a no-op on it
	}

	d2Sea, nearSea := edt(sea, w, h)    // for a land cell: how far to water, and where
	d2Land, nearLand := edt(land, w, h) // for a sea cell: how far to land, and where

	for i := range sea {
		if sea[i] {
			g.Dist.Data[i] = float32(-math.Sqrt(float64(d2Land[i])) * cellM)
		} else {
			g.Dist.Data[i] = float32(math.Sqrt(float64(d2Sea[i])) * cellM)
		}
	}

	// The waterline: sea cells with land in the eight-neighbourhood, which is d2Land of 1 or 2.
	for i := range sea {
		if sea[i] && d2Land[i] <= 2.001 {
			g.Waterline = append(g.Waterline, int32(i))
		}
	}

	for i := range sea {
		if sea[i] {
			if l := nearLand[i]; l >= 0 {
				g.Ref[i] = nearSea[l]
			}
		} else {
			g.Ref[i] = nearSea[i]
		}
	}

	// Perimeter by boundary edges, which is what a shoreline length means on a grid.
	edges := 0
	for y := 0; y < h; y++ {
		for x := 0; x < w; x++ {
			i := y*w + x
			if x+1 < w && sea[i] != sea[i+1] {
				edges++
			}
			if y+1 < h && sea[i] != sea[i+w] {
				edges++
			}
		}
	}
	g.ShoreM = float64(edges) * cellM
	return g
}