b样条曲线C语言代码-样条曲线算法实现代码-曲线拟合-曲线平滑-样条曲线计算-二次样条曲线-三次样条曲线

#include <stdio.h> #include<stdlib.h> #include"b_spline.h" /* 计算最终b样条平滑时生成的点数. num_points:输入的散点数量. degree:b样条曲线的阶次，可选2次或者3次 num_div:两点之间细分的线段数量. */ int cal_b_spline_points_num(int num_points,int degree, int num_div) { int num; num = (num_points +2-degree) *num_div+ 1; return num; } /* 生成多个控制点之间的b样条的曲线. p_array:三个点或者四个点组成的数组，数据排布格式为x0,y0,z0,x1,y1,z1,...,xn,yn,zn. degree:样条曲线的阶次，可选二次或者三次. num_div : 两点之间细分线段的数量. dims：坐标点的维度数，可以是二维或者三维. results:保存计算结果的缓冲区,数据排布格式为x0,y0,z0,x1,y1,z1.....xn,yn,zn '*/ void b_spline(float* p_array, int degree, int num_div, int dims, float* results) { float scale = 1.0f / num_div; float t, t1, t2, t3, b0, b1, b2, b3; if (degree == 2) { for (int i = 0; i <= num_div; i++) { t = i * scale; t1 = t; t2 = t1 * t; b0 = 0.5 * (t2 - 2 * t1 + 1); b1 = 0.5*(-2*t2+2*t1+1); b2 = 0.5 * t2; for (int j = 0; j < dims; j++) { results[i * dims + j] = p_array[j] * b0 + p_array[dims+j] * b1 + p_array[2*dims+j] * b2; } } } else { for (int i = 0; i <= num_div; i++) { t = i * scale; t1 = t; t2 = t1 * t; t3 = t2 * t; b0 =(-t3+3*t2-3*t1+1)/6.0; b1 =(3*t3-6*t2+4)/6.0; b2 =(-3*t3+3*t2+3*t1+1)/6.0; b3 =t3/6.0; for (int j = 0; j < dims; j++) { results[i * dims + j] = p_array[j] * b0 + p_array[dims+j] * b1 + p_array[2*dims+j] * b2+p_array[3*dims+j]*b3; } } } } /* 通过一系列散点生成b样条平滑曲线. p_array : 曲线散点序列，数组形状为(N, 2), 或者(N, 3), 点的坐标是二维坐标(x, y)或三维坐标(x, y, z).例如，散点输入为 [[1, 2, 3], [2, 1, 1], ...] . num_points:输入散的点数量. degree:样条曲线的阶次. num_div : 两散点之间划分的线段数量，数值越大，线段越多，曲线越平滑. dims：坐标点的维度数，可以是二维或者三维. results:保存计算结果的缓冲区,数据排布格式为x0,y0,z0,x1,y1,z1.....xn,yn,zn. */ void b_spline_curve(float* p_array, int num_points, int degree, int num_div, int dims, float* results) { float* points = (float*)malloc(sizeof(float) * (num_points+2) * dims); if (degree == 2) { for (int i = 0; i < dims; i++) { points[i] = p_array[i]; } float* q = &points[dims]; int m = num_points * dims; for (int i = 0; i < m; i++) { *q= p_array[i]; q++; } for (int i = 0; i < dims; i++) { q[i] = p_array[(num_points - 1) * dims + i]; } } else { for (int i = 0; i < dims; i++) { points[i] = 2 * p_array[i] - p_array[dims+i]; } float* q = &points[dims]; int m = num_points * dims; for (int i = 0; i < m; i++) { *q = p_array[i]; q++; } for (int i = 0; i < dims; i++) { q[i] = 2 * p_array[(num_points - 1) * dims + i] - p_array[(num_points - 2) * dims + i]; } } int num_seg = num_points+2-degree; for (int i = 0; i <num_seg; i++) { int j = i * dims; int offset = i * num_div * dims; b_spline(&points[j],degree,num_div,dims,&results[offset]); } free(points); }