fixed dependencies

vendor/github.com/nuknal/goNum/FittingBezier.go

@@ -0,0 +1,97 @@
+// FittingBezier
+/*
+------------------------------------------------------
+作者   : Black Ghost
+日期   : 2018-12-23
+版本   : 0.0.0
+------------------------------------------------------
+    Bezier曲线拟合控制点
+理论：
+    给定控制点集(xi, yi), i=0,1,...,N
+    则Bezier曲线可以表示为：
+    |        N
+    |x(t) = Sum xi*B_(i,N)(t)
+    |       i=0
+    |
+    |        N
+    |y(t) = Sum yi*B_(i,N)(t)
+    |       i=0
+    其中，
+    B_(i,N)(t)为Bernstein多项式：
+                  N-i
+    B_(i,N)(t) = C   *t^i*(1-t)^(N-i)
+                  N
+    0 <= t <= 1
+
+    参考：John H. Mathews and Kurtis D. Fink. Numerical
+         methods using MATLAB, 4th ed. Pearson
+         Education, 2004. ss 5.5
+------------------------------------------------------
+输入   :
+    XY      数据对，nx2，x-y
+输出   :
+    sol     解，(N+1)x2，x(t)-y(t)
+    err     解出标志：false-未解出或达到边界；
+                     true-全部解出
+------------------------------------------------------
+*/
+
+package goNum
+
+//BernsteinPoly Bernstein Polynomial
+func BernsteinPoly(i, N int) Matrix {
+	cni := Cnm(N, i)
+	sol := ZeroMatrix(N+1, 1)
+	soltemp := ZeroMatrix(N+1, 1)
+
+	soltemp.Data[0] = 1.0
+	soltemp.Data[1] = -1.0 //1-t
+	//(1-t)^(N-i)
+	if N-i > 1 {
+		for j := 2; j < N-i+1; j++ {
+			for k := j; k > 0; k-- {
+				soltemp.Data[k] = soltemp.Data[k] - soltemp.Data[k-1]
+			}
+		}
+	}
+	//(1-t)^(N-i) * t^i
+	for j := N; j >= i; j-- {
+		sol.Data[j] = float64(cni) * soltemp.Data[j-i]
+	}
+
+	return sol
+}
+
+// FittingBezier Bezier曲线拟合控制点
+func FittingBezier(XY Matrix) (Matrix, bool) {
+	/*
+		Bezier曲线拟合控制点
+		输入   :
+		    XY      数据对，nx2，x-y
+		输出   :
+		    sol     解，(N+1)x2，x(t)-y(t)
+		    err     解出标志：false-未解出或达到边界；
+		                     true-全部解出
+	*/
+	//判断维数
+	if XY.Columns < 2 {
+		panic("Error in goNum.FittingBezier: At least 2 columns of XY needed")
+	}
+	n := XY.Rows - 1 //N-1
+	sol := ZeroMatrix(n+1, 2)
+	var err bool = false
+
+	//计算
+	for i := 0; i < n+1; i++ { //n+1项BernsteinPoly
+		soltemp := BernsteinPoly(i, n)
+		xi := XY.GetFromMatrix(i, 0)
+		yi := XY.GetFromMatrix(i, 1)
+		for j := 0; j < n+1; j++ { //n次BernsteinPoly
+			sol.SetMatrix(j, 0, sol.GetFromMatrix(j, 0)+xi*soltemp.Data[j])
+			sol.SetMatrix(j, 1, sol.GetFromMatrix(j, 1)+yi*soltemp.Data[j])
+		}
+	}
+
+	err = true
+	return sol, err
+}