a7bb9496ae
Vanilla-faithful overworld generator (final_density + multi-noise biomes), full connection lifecycle (status/login/configuration/play), chunk streaming, creative block editing, and the protocol/nbt/registry infrastructure.
46 lines
1.5 KiB
Go
46 lines
1.5 KiB
Go
package worldgen
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// CubicSpline is Minecraft's cubic spline over a coordinate density function.
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// Each point's value is itself a density function (often a constant or a nested
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// spline), enabling multi-dimensional terrain shaping.
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type CubicSpline struct {
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coordinate DensityFunction
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locations []float32
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values []DensityFunction
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derivatives []float32
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}
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func (s *CubicSpline) Compute(c FunctionContext) float64 {
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t := float32(s.coordinate.Compute(c))
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n := len(s.locations)
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// Below the first point or above the last: linear extrapolation.
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if t < s.locations[0] {
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return float64(extend(s.values[0].Compute(c), s.derivatives[0], s.locations[0], t))
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}
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if t >= s.locations[n-1] {
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return float64(extend(s.values[n-1].Compute(c), s.derivatives[n-1], s.locations[n-1], t))
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}
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// Find the segment [i, i+1] containing t.
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i := 0
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for i < n-1 && s.locations[i+1] <= t {
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i++
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}
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loc0, loc1 := s.locations[i], s.locations[i+1]
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d0, d1 := s.derivatives[i], s.derivatives[i+1]
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p0 := float32(s.values[i].Compute(c))
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p1 := float32(s.values[i+1].Compute(c))
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k := (t - loc0) / (loc1 - loc0)
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l := d0*(loc1-loc0) - (p1 - p0)
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m := -d1*(loc1-loc0) + (p1 - p0)
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return float64(lerp32(k, p0, p1) + k*(1-k)*lerp32(k, l, m))
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}
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// extend linearly extrapolates a point's value beyond the spline's range.
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func extend(value float64, derivative, loc, t float32) float32 {
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return float32(value) + derivative*(t-loc)
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}
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func lerp32(t, a, b float32) float32 { return a + t*(b-a) }
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