78 lines
2.0 KiB
Go
78 lines
2.0 KiB
Go
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package ltp
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import (
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"math"
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"sync"
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)
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// 分段 Chebyshev 缓存的覆盖与精度：最短周期项 157.87 年，200 年段 16 阶误差远小于 1e-12 rad。
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const (
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basisStart = -10200.0
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basisSpan = 200.0
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basisSegs = 102
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basisDegree = 16
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)
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type basisSeg struct {
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once sync.Once
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// 6 个分量（x 的 3 个、z 的 3 个）各 basisDegree+1 个系数，c0 已减半。
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c [6][basisDegree + 1]float64
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}
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var basisTable [basisSegs]basisSeg
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// EclipticBasisExact 历元平黄道在 J2000 平赤道下的正交基：x 指向平春分点，z 为黄道极 / exact basis of the mean ecliptic of date.
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func EclipticBasisExact(epj float64) (x, y, z Vector3) {
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z = EclipticPole(epj)
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x, _ = Normalize(Cross(EquatorPole(epj), z))
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return x, Cross(z, x), z
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}
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// EclipticBasis 同 EclipticBasisExact，覆盖区间内用分段 Chebyshev 近似（差 < 1e-12 rad），区间外精确计算 / cached form of EclipticBasisExact.
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func EclipticBasis(epj float64) (x, y, z Vector3) {
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u := (epj - basisStart) / basisSpan
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i := int(math.Floor(u))
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if i < 0 || i >= basisSegs {
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return EclipticBasisExact(epj)
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}
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seg := &basisTable[i]
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seg.once.Do(func() { seg.fit(basisStart + float64(i)*basisSpan) })
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s := 2*(u-float64(i)) - 1
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var v [6]float64
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for k := range v {
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v[k] = clenshaw(&seg.c[k], s)
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}
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x = Vector3{v[0], v[1], v[2]}
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z = Vector3{v[3], v[4], v[5]}
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return x, Cross(z, x), z
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}
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func (seg *basisSeg) fit(start float64) {
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const n = basisDegree + 1
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var f [n][6]float64
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for j := 0; j < n; j++ {
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s := math.Cos(math.Pi * (float64(j) + 0.5) / n)
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x, _, z := EclipticBasisExact(start + (s+1)/2*basisSpan)
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f[j] = [6]float64{x[0], x[1], x[2], z[0], z[1], z[2]}
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}
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for k := 0; k < 6; k++ {
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for m := 0; m < n; m++ {
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sum := 0.0
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for j := 0; j < n; j++ {
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sum += f[j][k] * math.Cos(math.Pi*float64(m)*(float64(j)+0.5)/n)
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}
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seg.c[k][m] = 2 * sum / n
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}
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seg.c[k][0] /= 2
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}
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}
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func clenshaw(c *[basisDegree + 1]float64, s float64) float64 {
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b1, b2 := 0.0, 0.0
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for m := basisDegree; m >= 1; m-- {
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b1, b2 = 2*s*b1-b2+c[m], b1
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}
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return s*b1 - b2 + c[0]
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}
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