理论篇

代码篇：

opencv环境配置
注意！注意！注意！
配置结束后运行环境切换为如下再运行：

#include <iostream>
#include <cmath>#include <opencv2/opencv.hpp>using namespace std;double a_max = 1.5; // 最大加速度
double v_max = 6.0; // 最大速度
double J = 1; // 最大速度
double T4 = 2.0;double T1 = a_max / J;
double T3 = T1; 
double T5 = T3;
double T7 = T5;double T2 = v_max / a_max - T1; 
double T6 = T2;double t1 = T1;
double t2 = t1 + T2;
double t3 = t2 + T3;
double t4 = t3 + T4;
double t5 = t4 + T5;
double t6 = t5 + T6;
double t7 = t6 + T7;double a1 = J * T1;//该段最后时刻的速度
double a2 = a_max;
double a3 = 0;
double a4 = 0;
double a5 = a_max - J * T5;
double a6 = -a_max;
double a7 = 0;double v1 = 0.5 * J * pow(T1, 2);//该段最后时刻的速度
double v2 = v1 + J * T1 * T2;
double v3 = v2 + 0.5 * J * pow(T1, 2);
double v4 = v3;
double v5 = v4 - 0.5 * J * pow(T5, 2);
double v6 = v5 - J * T5 * T6;
double v7 = v6 - 0.5 * J * pow(T5, 2);double S1 = J * pow(T1, 3) / 6.0;
double S2 = S1 + v1 * T2 + J * T1 * pow(T2, 2) * 0.5;
double S3 = S2 + v2 * T3 + J * T1 * pow(T3, 2) * 0.5 - J * pow(T3, 3) / 6;
double S4 = S3 + v3 * T4;
double S5 = S4 + v4 * T5 - J * pow(T5, 3) / 6;
double S6 = S5 + v5 * T6 - J * T1 * pow(T6, 2) * 0.5;
double S7 = S6 + v6 * T7 - J * T1 * pow(T7, 2) * 0.5 + J * pow(T7, 3) / 6;double VelocityCurve(double t) {double temp = 0;if (t < 0 || t >= t7) {return 0;}else if (t < t1) {return 0.5 * J * pow(t, 2);}else if (t < t2) {temp = t - t1;return v1 + J * T1 * temp;}else if (t < t3) {temp = t - t2;return v2 + J * T1 * temp - 0.5 * J * pow(temp, 2);}else if (t < t4) {temp = t - t3;return v3;}else if (t < t5) {//std::cout << "t5时刻的具体时间： " << t << "    ";temp = t - t4;return v4 - 0.5 * J * pow(temp, 2);}else if (t < t6) {//std::cout << "t6时刻的具体时间： " << t << "    ";std::cout << "ssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss： " << t << "    ";temp = t - t5;return v5 - J * T5 * temp;}else if (t < t7) {//std::cout << "t7时刻的具体时间： " << t << "    ";temp = t - t6;return v6 - J * T5 * temp + 0.5 * J * pow(temp, 2);}
}double PathCurve(double t) {double temp = 0;if (t < 0) {return 0;}else if (t >= t7) {return S7;}else if (t < t1) {return J * pow(t, 3) / 6.0;}else if (t < t2) {temp = t - t1;return S1 + v1 * temp + J * T1 * pow(temp, 2) * 0.5;}else if (t < t3) {temp = t - t2;return S2 + v2 * temp + J * T1 * pow(temp, 2) * 0.5 - J * pow(temp, 3) / 6;}else if (t < t4) {temp = t - t3;return S3 + v3 * temp;}else if (t < t5) {std::cout << "t5时刻的具体时间： " << t << std::endl;temp = t - t4;return S4 + v4 * temp - J * pow(temp, 3) / 6;}else if (t < t6) {std::cout << "t6时刻的具体时间： " << t << std::endl;temp = t - t5;return S5 + v5 * temp - J * T1 * pow(temp, 2) * 0.5;}else if (t < t7) {std::cout << "t7时刻的具体时间： " << t << std::endl;temp = t - t6;return S6 + v6 * temp - J * T1 * pow(temp, 2) * 0.5 + J * pow(temp, 3) / 6;}
}int main() {double tf = 16.0; // 总时间cv::Mat canvas(400, 400, CV_8UC3, cv::Scalar(255, 255, 255)); // 创建一个300x300像素的画布// 显示第一个圆cv::line(canvas, cv::Point(0, 0), cv::Point(0, 400), cv::Scalar(255, 0, 0), 2);//y周  (x,y)cv::line(canvas, cv::Point(0, 0), cv::Point(400, 0), cv::Scalar(255, 0, 0), 2);//x周  (x,y)bool flag = false;double last_st = 0, last_t = 0;int kx = 30, ky = 10;for (double t = 0.0; t <= tf; t += 0.1) {//double s_t = PathCurve(t);double s_t = VelocityCurve(t);if (!flag) {cv::circle(canvas, cv::Point(t * kx, s_t * ky), 2, cv::Scalar(0, 0, 255), -1);}else {cv::circle(canvas, cv::Point(t * kx, s_t * ky), 2, cv::Scalar(0, 0, 255), -1);cv::line(canvas, cv::Point(last_t * kx, last_st * ky), cv::Point(t * kx, s_t * ky), cv::Scalar(255, 0, 0), 1);//y周  (x,y)}last_st = s_t;last_st = t;std::cout <<t<< "时刻的位置 = " << s_t << std::endl;}cout << "t5:" << t5 << endl;cout << "t6:" << t6 << endl;cout << "t7:" << t7 << endl;// 创建镜像图像矩阵  cv::Mat mirror_img;cv::flip(canvas, mirror_img, 0);  // 水平镜像，flipCode=1  // 显示原始图像和镜像图像  //cv::imshow("Original Image", canvas);cv::imshow("Image", mirror_img);//cv::waitKey(0);cv::waitKey(); // 等待10秒return 0;
}

运行结果：