Added: Initial world generation tool

Tools/Terrain/internal/thermal/thermal_test.go

@@ -0,0 +1,73 @@
+package thermal
+
+import (
+	"math"
+	"testing"
+)
+
+// TestConeIsCutToRepose is the property the whole hillslope story rests on: after enough passes nothing may
+// stand steeper than the angle of repose. A cone is the worst case, because every cell on it is steep.
+func TestConeIsCutToRepose(t *testing.T) {
+	const (
+		w, h  = 101, 101
+		cellM = 10.0
+		deg   = 33.0
+	)
+	talus := TalusFromDegrees(deg)
+	field := make([]float32, w*h)
+	for y := 0; y < h; y++ {
+		for x := 0; x < w; x++ {
+			// A steep cone: 60 m of fall per 10 m cell at the flanks, far beyond repose.
+			d := math.Hypot(float64(x-w/2), float64(y-h/2))
+			field[y*w+x] = float32(math.Max(0, 600-6*d*cellM))
+		}
+	}
+	before := maxSlope(field, w, h, cellM)
+	scratch := make([]float32, w*h)
+
+	volBefore := sum(field)
+	Apply(field, w, h, cellM, talus, 400, nil, scratch)
+	volAfter := sum(field)
+
+	after := maxSlope(field, w, h, cellM)
+	t.Logf("max slope %.1f deg -> %.1f deg (repose %.1f)", degOf(before), degOf(after), deg)
+	if degOf(after) > deg+2 {
+		t.Errorf("after 400 passes the steepest slope is %.1f deg, want no more than %.1f", degOf(after), deg+2)
+	}
+	if rel := math.Abs(volAfter-volBefore) / volBefore; rel > 1e-4 {
+		t.Errorf("mass changed by %.4f%%; thermal weathering must conserve it", rel*100)
+	}
+}
+
+func sum(a []float32) float64 {
+	var s float64
+	for _, v := range a {
+		s += float64(v)
+	}
+	return s
+}
+
+func degOf(slope float64) float64 { return math.Atan(slope) * 180 / math.Pi }
+
+func maxSlope(a []float32, w, h int, cellM float64) float64 {
+	worst := 0.0
+	for y := 0; y < h; y++ {
+		for x := 0; x < w; x++ {
+			i := y*w + x
+			for k := 0; k < 8; k++ {
+				nx, ny := x+dx8[k], y+dy8[k]
+				if nx < 0 || ny < 0 || nx >= w || ny >= h {
+					continue
+				}
+				d := cellM
+				if dx8[k] != 0 && dy8[k] != 0 {
+					d = cellM * math.Sqrt2
+				}
+				if s := float64(a[i]-a[ny*w+nx]) / d; s > worst {
+					worst = s
+				}
+			}
+		}
+	}
+	return worst
+}