c++实现三次bezier曲线动画

三次贝塞尔曲线是一种平滑的曲线，由4个控制点定义，其中第一个和第四个点是曲线的端点，第二个和第三个点是控制点。在C++中实现三次贝塞尔曲线动画的步骤如下：

1. 定义4个点，包括起点、终点和两个控制点。

const int NUM_POINTS = 4;
const int START_X = 50, START_Y = 50;
const int END_X = 400, END_Y = 400;
const int CONTROL1_X = 100, CONTROL1_Y = 200;
const int CONTROL2_X = 300, CONTROL2_Y = 300;

2. 使用循环计算曲线上的点，并将其保存在数组中。

const int NUM_SEGMENTS = 100;
int curvePoints[NUM_SEGMENTS][2];

for (int i = 0; i < NUM_SEGMENTS; i++) {
  float t = (float)i / (float)(NUM_SEGMENTS-1);
  float oneMinusT = 1.0 - t;
  float oneMinusTSquared = oneMinusT * oneMinusT;
  float oneMinusTCubed = oneMinusTSquared * oneMinusT;
  float tSquared = t * t;
  float tCubed = tSquared * t;

  float x = oneMinusTCubed * START_X +
            3 * oneMinusTSquared * t * CONTROL1_X +
            3 * oneMinusT * tSquared * CONTROL2_X +
            tCubed * END_X;

  float y = oneMinusTCubed * START_Y +
            3 * oneMinusTSquared * t * CONTROL1_Y +
            3 * oneMinusT * tSquared * CONTROL2_Y +
            tCubed * END_Y;

  curvePoints[i][0] = (int)x;
  curvePoints[i][1] = (int)y;
}

3. 在循环中将曲线上的点绘制到屏幕上。

for (int i = 0; i < NUM_SEGMENTS-1; i++) {
  int x1 = curvePoints[i][0], y1 = curvePoints[i][1];
  int x2 = curvePoints[i+1][0], y2 = curvePoints[i+1][1];
  line(x1, y1, x2, y2);
}

完整的代码示例如下：

#include <graphics.h>

const int NUM_POINTS = 4;
const int START_X = 50, START_Y = 50;
const int END_X = 400, END_Y = 400;
const int CONTROL1_X = 100, CONTROL1_Y = 200;
const int CONTROL2_X = 300, CONTROL2_Y = 300;

const int NUM_SEGMENTS = 100;
int curvePoints[NUM_SEGMENTS][2];

int main() {
  initwindow(500, 500);

  // 计算曲线上的点
  for (int i = 0; i < NUM_SEGMENTS; i++) {
    float t = (float)i / (float)(NUM_SEGMENTS-1);
    float oneMinusT = 1.0 - t;
    float oneMinusTSquared = oneMinusT * oneMinusT;
    float oneMinusTCubed = oneMinusTSquared * oneMinusT;
    float tSquared = t * t;
    float tCubed = tSquared * t;

    float x = oneMinusTCubed * START_X +
              3 * oneMinusTSquared * t * CONTROL1_X +
              3 * oneMinusT * tSquared * CONTROL2_X +
              tCubed * END_X;

    float y = oneMinusTCubed * START_Y +
              3 * oneMinusTSquared * t * CONTROL1_Y +
              3 * oneMinusT * tSquared * CONTROL2_Y +
              tCubed * END_Y;

    curvePoints[i][0] = (int)x;
    curvePoints[i][1] = (int)y;
  }

  // 绘制曲线
  for (int i = 0; i < NUM_SEGMENTS-1; i++) {
    int x1 = curvePoints[i][0], y1 = curvePoints[i][1];
    int x2 = curvePoints[i+1][0], y2 = curvePoints[i+1][1];
    line(x1, y1, x2, y2);
  }

  getch();
  closegraph();
  return 0;
}