2D 欧几里得矢量旋转 [英] 2D Euclidean vector rotations

问题描述

我有一个欧几里得向量 a 位于坐标 (0, 1).我想将 a 围绕原点旋转 90 度(顺时针):(0, 0).

I have a euclidean vector a sitting at the coordinates (0, 1). I want to rotate a by 90 degrees (clockwise) around the origin: (0, 0).

如果我对它的工作原理有正确的理解，旋转后的结果 (x, y) 坐标应该是 (1, 0).如果我将它旋转 45 度(仍然是顺时针)，我会期望得到的坐标是 (0.707, 0.707).

If I have a proper understanding of how this should work, the resultant (x, y) coordinates after the rotation should be (1, 0). If I were to rotate it by 45 degrees (still clockwise) instead, I would have expected the resultant coordinates to be (0.707, 0.707).

theta = deg2rad(angle);

cs = cos(theta);
sn = sin(theta);

x = x * cs - y * sn;
y = x * sn + y * cs;

使用上述代码，angle 值为 90.0 度，结果坐标为:(-1, 1).我真是太糊涂了.以下链接中的示例肯定代表上面显示的相同公式吗?

Using the above code, with an angle value of 90.0 degrees, the resultant coordinates are: (-1, 1). And I am so damn confused. The examples seen in the following links represent the same formula shown above surely?

我做错了什么?还是我误解了矢量是如何旋转的?

What have I done wrong? Or have I misunderstood how a vector is to be rotated?

推荐答案

你应该从函数中删除变量:

you should remove the vars from the function:

x = x * cs - y * sn; // now x is something different than original vector x
y = x * sn + y * cs;

创建新坐标变为，避免在到达第二行之前计算x:

create new coordinates becomes, to avoid calculation of x before it reaches the second line:

px = x * cs - y * sn; 
py = x * sn + y * cs;

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