曲线生成 | 图解B样条曲线生成原理(附ROS C++/Python/Matlab仿真)

#include <vector>
#include <iostream>

// 定义B样条控制点
std::vector<double> control_points = {
    0.0, 0.0, 0.0,
    1.0, 0.0, 0.0,
    1.0, 1.0, 0.0,
    0.0, 1.0, 0.0
};

// 生成B样条曲线的函数
std::vector<double> generate_b_spline(int num_control_points, double step_size) {
    std::vector<double> knots = {0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0}; // 一维B样条的knots向量
    std::vector<double> result;

    // 迭代生成曲线上的点
    for (double t = knots[0]; t < knots[7]; t += step_size) {
        double point[3] = {0.0, 0.0, 0.0};
        for (int i = 0; i < num_control_points; ++i) {
            double N = calc_basis_function(t, i, knots); // 计算基函数的值
            for (int j = 0; j < 3; ++j) {
                point[j] += N * control_points[i * 3 + j];
            }
        }
        result.push_back(point[0]);
        result.push_back(point[1]);
        result.push_back(point[2]);
    }

    return result;
}

// 计算B样条基函数的函数
double calc_basis_function(double u, int i, const std::vector<double>& knots) {
    // 基函数的计算逻辑...
    // 此处省略具体实现，应根据B样条基函数的定义进行计算
    return 0.0; // 示例返回值
}

int main() {
    std::vector<double> b_spline_points = generate_b_spline(4, 0.1);
    for (size_t i = 0; i < b_spline_points.size(); i += 3) {
        std::cout << "Point: (" << b_spline_points[i] << ", " << b_spline_points[i+1] << ", " << b_spline_points[i+2] << ")" << std::endl;
    }
    return 0;
}