二维，三维坐标旋转算法(公式）

本文是有关二维，三维坐标旋转算法笔记。

１．二维坐标旋转。二维坐标旋转公式图下：

void Rotate2(double x1, double y1, double alpha, double& x2, double& y2) { x2 = x1 * cos(alpha) - y1 * sin(alpha); y2 = x1 * sin(alpha) + y1 * cos(alpha); }

２．三维坐标旋转

在处理三维坐标旋转时，使用标准的数学公式是沒有问题的。但是把二维坐标旋转调用三次，也能够实现三维坐标的旋转，而且有易读易懂，処理速度快的长处。

void Rotate3(double x1, double y1, double z1, double alphaX,double alphaY,double alphaZ, double& x2, double& y2, double& z2) { //Z Axis Rotation double x3 = x1 * cos(alphaZ) - y1 * sin(alphaZ); double y3 = x1 * sin(alphaZ) + y1 * cos(alphaZ); double z3 = z1; //Y Axis Rotation double z4 = z3 * cos(alphaY) - x3 * sin(alphaY); double x4 = z3 * sin(alphaY) + x3 * cos(alphaY); double y4 = y3; //X Axis Rotation y2 = y4 * cos(alphaX) - z4 * sin(alphaX); z2 = y4 * sin(alphaX) + z4 * cos(alphaX); x2 = x4; }