spline

2026-07-05 20:53:59 +02:00
parent eab050e291
commit b4712ff5c6
3 changed files with 223 additions and 0 deletions
@@ -50,6 +50,10 @@ func lerp(part, from, to float64) float64 {
 	return from + part*(to-from)
 }

+func lerp32(part, from, to float32) float32 {
+	return from + part*(to-from)
+}
+
 func (n PerlinNoise) Sample(x, y, z float64, yamp, ymin float64) (v float64) {
 	var h1, h2, h3 uint8
 	var t1, t2, t3 float64
@@ -0,0 +1,209 @@
+package gen
+
+type Spline interface {
+	Sample(t []float32) float32
+}
+
+type FixedSpline struct {
+	Val float32
+}
+
+func (s FixedSpline) Sample(t []float32) float32 {
+	return s.Val
+}
+
+type SubSpline struct {
+	Loc, Der float32
+	Val      Spline
+}
+type SplineA struct {
+	TargetIndex int
+	Points      []SubSpline
+}
+
+func ternery[T any](a bool, b T, c T) T {
+	if a {
+		return b
+	}
+	return c
+}
+
+func (s SplineA) Sample(in []float32) float32 {
+	f := in[s.TargetIndex]
+
+	i := 0
+	for _, p := range s.Points {
+		if f <= p.Loc {
+			break
+		}
+		i++
+	}
+	if i == 0 || i == len(s.Points) {
+		if i != 0 {
+			i--
+		}
+		v := s.Points[i].Val.Sample(in)
+		return v + s.Points[i].Der*(f-s.Points[i].Loc)
+	}
+	s1 := s.Points[i-1]
+	s2 := s.Points[i]
+	g := s.Points[i-1].Loc
+	h := s.Points[i].Loc
+	k := (f - g) / (h - g)
+	l := s.Points[i-1].Der
+	m := s.Points[i].Der
+	n := s1.Val.Sample(in)
+	o := s2.Val.Sample(in)
+	p := l*(h-g) - (o - n)
+	q := -m*(h-g) + (o - n)
+	r := lerp32(k, n, o) + k*(1.0-k)*lerp32(k, p, q)
+	return r
+}
+
+const (
+	splineIndexContinentalNess = iota
+	splineIndexErosion
+	splineIndexWeirdness
+)
+
+func getOffsetValue(weirdness float32, continentalness float32) float32 {
+	f0 := 1.0 - (1.0-continentalness)*0.5
+	f1 := 0.5 * (1.0 - continentalness)
+	f2 := (weirdness + 1.17) * 0.46082947
+	off := f2*f0 - f1
+	if weirdness < -0.7 {
+		if off > -0.2222 {
+			return off
+		}
+		return -0.2222
+	}
+	if off > 0 {
+		return off
+	}
+	return 0
+
+}
+
+func createSpline38219(f float32, bl bool) Spline {
+	s := SplineA{
+		TargetIndex: splineIndexWeirdness,
+		Points:      nil,
+	}
+	i := getOffsetValue(-1.0, f)
+	k := getOffsetValue(1.0, f)
+	l := 1.0 - (1.0-f)*0.5
+	u := 0.5 * (1.0 - f)
+	l = u/(0.46082947*l) - 1.17
+
+	if -0.65 < l && l < 1.0 {
+		u = getOffsetValue(-0.65, f)
+		p := getOffsetValue(-0.75, f)
+		q := (p - i) * 4.0
+		r := getOffsetValue(l, f)
+		z := (k - r) / (1.0 - l)
+
+		s.Points = append(s.Points, SubSpline{-1.0, q, FixedSpline{i}})
+		s.Points = append(s.Points, SubSpline{-0.75, 0, FixedSpline{p}})
+		s.Points = append(s.Points, SubSpline{-0.65, 0, FixedSpline{u}})
+		s.Points = append(s.Points, SubSpline{l - 0.01, 0, FixedSpline{r}})
+		s.Points = append(s.Points, SubSpline{l, z, FixedSpline{r}})
+		s.Points = append(s.Points, SubSpline{1.0, z, FixedSpline{k}})
+	} else {
+		u = (k - i) * 0.5
+		if bl {
+			s.Points = append(s.Points, SubSpline{-1.0, 0, FixedSpline{ternery(i > 0.2, i, 0.2)}})
+			s.Points = append(s.Points, SubSpline{0.0, u, FixedSpline{lerp32(0.5, i, k)}})
+		} else {
+			s.Points = append(s.Points, SubSpline{-1.0, u, FixedSpline{i}})
+		}
+		s.Points = append(s.Points, SubSpline{1.0, u, FixedSpline{k}})
+	}
+	return s
+}
+
+func createFlatOffsetSpline(f, g, h, i, j, k float32) Spline {
+	l := 0.5 * (g - f)
+	if l < k {
+		l = k
+	}
+	m := 5.0 * (h - g)
+	n := m
+	if l < m {
+		n = l
+	}
+
+	return SplineA{
+		TargetIndex: splineIndexWeirdness,
+		Points: []SubSpline{
+			{-1, l, FixedSpline{f}},
+			{-0.4, n, FixedSpline{g}},
+			{0, m, FixedSpline{h}},
+			{0.4, 2.0 * (i - h), FixedSpline{i}},
+			{1, 0.7 * (j - i), FixedSpline{j}},
+		},
+	}
+}
+
+func landSpline(f, g, h, i, j, k float32, bl bool) Spline {
+	s1 := createSpline38219(lerp32(i, 0.6, 1.5), bl)
+	s2 := createSpline38219(lerp32(i, 0.6, 1.0), bl)
+	s3 := createSpline38219(i, bl)
+	ih := 0.5 * i
+	s4 := createFlatOffsetSpline(f-0.15, ih, ih, ih, i*0.6, 0.5)
+	s5 := createFlatOffsetSpline(f, j*i, g*i, ih, i*0.6, 0.5)
+	s6 := createFlatOffsetSpline(f, j, j, g, h, 0.5)
+	s7 := createFlatOffsetSpline(f, j, j, g, h, 0.5)
+	s8 := SplineA{
+		TargetIndex: splineIndexWeirdness,
+		Points: []SubSpline{
+			{-1, 0, FixedSpline{f}},
+			{-0.4, 0, s6},
+			{0, 0, FixedSpline{h + 0.07}},
+		},
+	}
+	s9 := createFlatOffsetSpline(-0.02, k, k, g, h, 0)
+	s := SplineA{
+		TargetIndex: splineIndexErosion,
+		Points: []SubSpline{
+			{-0.85, 0, s1},
+			{-0.7, 0, s2},
+			{-0.4, 0, s3},
+			{-0.35, 0, s4},
+			{-0.1, 0, s5},
+			{0.2, 0, s6},
+		},
+	}
+	if bl {
+		s.Points = append(s.Points, SubSpline{0.4, 0, s7})
+		s.Points = append(s.Points, SubSpline{0.45, 0, s8})
+		s.Points = append(s.Points, SubSpline{0.55, 0, s8})
+		s.Points = append(s.Points, SubSpline{0.58, 0, s7})
+	}
+	s.Points = append(s.Points, SubSpline{0.7, 0, s9})
+	return s
+}
+
+func CreateBiomeDepthSpline() Spline {
+	sp1 := landSpline(-0.15, 0.00, 0.0, 0.1, 0.00, -0.03, false)
+	sp2 := landSpline(-0.10, 0.03, 0.1, 0.1, 0.01, -0.03, false)
+	sp3 := landSpline(-0.10, 0.03, 0.1, 0.7, 0.01, -0.03, true)
+	sp4 := landSpline(-0.05, 0.03, 0.1, 1.0, 0.01, 0.01, true)
+
+	return SplineA{
+		TargetIndex: splineIndexContinentalNess,
+		Points: []SubSpline{
+			{Loc: -1.10, Val: FixedSpline{Val: 0.044}, Der: 0.0},
+			{Loc: -1.02, Val: FixedSpline{Val: -0.2222}, Der: 0.0},
+			{Loc: -0.51, Val: FixedSpline{Val: -0.2222}, Der: 0.0},
+			{Loc: -0.44, Val: FixedSpline{Val: -0.12}, Der: 0.0},
+			{Loc: -0.18, Val: FixedSpline{Val: -0.12}, Der: 0.0},
+			{Loc: -0.16, Val: sp1, Der: 0.0},
+			{Loc: -0.15, Val: sp1, Der: 0.0},
+			{Loc: -0.10, Val: sp2, Der: 0.0},
+			{Loc: 0.25, Val: sp3, Der: 0.0},
+			{Loc: 1.00, Val: sp4, Der: 0.0},
+		},
+	}
+}
+
+var BiomeDepthSpline = CreateBiomeDepthSpline()
@@ -0,0 +1,10 @@
+package gen
+
+import "testing"
+
+func TestSpline(t *testing.T) {
+	v := BiomeDepthSpline.Sample([]float32{0.236413047, 0.220234469, 0.139604524, -0.339296669})
+	if v != 0.025035858154296875 {
+		t.Errorf("bad value: %f", v)
+	}
+}