98 lines
2.5 KiB
Go
98 lines
2.5 KiB
Go
// FittingBezier
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/*
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------------------------------------------------------
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作者 : Black Ghost
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日期 : 2018-12-23
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版本 : 0.0.0
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------------------------------------------------------
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Bezier曲线拟合控制点
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理论：
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给定控制点集(xi, yi), i=0,1,...,N
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则Bezier曲线可以表示为：
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| N
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|x(t) = Sum xi*B_(i,N)(t)
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| i=0
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| N
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|y(t) = Sum yi*B_(i,N)(t)
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| i=0
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其中，
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B_(i,N)(t)为Bernstein多项式：
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N-i
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B_(i,N)(t) = C *t^i*(1-t)^(N-i)
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N
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0 <= t <= 1
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参考：John H. Mathews and Kurtis D. Fink. Numerical
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methods using MATLAB, 4th ed. Pearson
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Education, 2004. ss 5.5
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------------------------------------------------------
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输入 :
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XY 数据对，nx2，x-y
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输出 :
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sol 解，(N+1)x2，x(t)-y(t)
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err 解出标志：false-未解出或达到边界；
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true-全部解出
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------------------------------------------------------
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*/
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package goNum
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//BernsteinPoly Bernstein Polynomial
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func BernsteinPoly(i, N int) Matrix {
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cni := Cnm(N, i)
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sol := ZeroMatrix(N+1, 1)
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soltemp := ZeroMatrix(N+1, 1)
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soltemp.Data[0] = 1.0
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soltemp.Data[1] = -1.0 //1-t
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//(1-t)^(N-i)
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if N-i > 1 {
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for j := 2; j < N-i+1; j++ {
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for k := j; k > 0; k-- {
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soltemp.Data[k] = soltemp.Data[k] - soltemp.Data[k-1]
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}
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}
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}
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//(1-t)^(N-i) * t^i
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for j := N; j >= i; j-- {
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sol.Data[j] = float64(cni) * soltemp.Data[j-i]
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}
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return sol
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}
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// FittingBezier Bezier曲线拟合控制点
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func FittingBezier(XY Matrix) (Matrix, bool) {
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/*
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Bezier曲线拟合控制点
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输入 :
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XY 数据对，nx2，x-y
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输出 :
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sol 解，(N+1)x2，x(t)-y(t)
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err 解出标志：false-未解出或达到边界；
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true-全部解出
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*/
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//判断维数
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if XY.Columns < 2 {
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panic("Error in goNum.FittingBezier: At least 2 columns of XY needed")
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}
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n := XY.Rows - 1 //N-1
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sol := ZeroMatrix(n+1, 2)
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var err bool = false
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//计算
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for i := 0; i < n+1; i++ { //n+1项BernsteinPoly
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soltemp := BernsteinPoly(i, n)
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xi := XY.GetFromMatrix(i, 0)
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yi := XY.GetFromMatrix(i, 1)
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for j := 0; j < n+1; j++ { //n次BernsteinPoly
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sol.SetMatrix(j, 0, sol.GetFromMatrix(j, 0)+xi*soltemp.Data[j])
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sol.SetMatrix(j, 1, sol.GetFromMatrix(j, 1)+yi*soltemp.Data[j])
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}
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}
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err = true
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return sol, err
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}
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