如何围绕某个点旋转顶点? [英] How to rotate a vertex around a certain point?

问题描述

假设您在二维空间中有两个点，您需要将其中一个点旋转 X 度，另一个点作为中心.

Imagine you have two points in 2d space and you need to rotate one of these points by X degrees with the other point acting as a center.

float distX = Math.abs( centerX -point2X );
float distY = Math.abs( centerY -point2Y );

float dist = FloatMath.sqrt( distX*distX + distY*distY );

到目前为止，我只是找到了两点之间的距离……我应该从哪里开始有任何想法?

So far I just got to finding the distance between the two points... any ideas where should I go from that?

推荐答案

最简单的方法是组合三个转换:

The easiest approach is to compose three transformations:

1. 将第 1 点带到原点的翻译
2. 绕原点旋转所需的角度
3. 将第 1 点带回其原始位置的翻译

当你把这一切都搞定后，你会得到以下转换(其中 x 是所需的旋转角度，以弧度为单位):

When you work this all out, you end up with the following transformation (where x is the desired angle of rotation in radians):

newX = centerX + (point2x-centerX)*Math.cos(x) - (point2y-centerY)*Math.sin(x);

newY = centerY + (point2x-centerX)*Math.sin(x) + (point2y-centerY)*Math.cos(x);

请注意，这假设角度 x 对于顺时针旋转为负(所谓的 坐标系的标准或右手方向).如果情况并非如此，则您需要反转涉及 sin(x) 的术语的符号.

Note that this makes the assumption that the angle x is negative for clockwise rotation (the so-called standard or right-hand orientation for the coordinate system). If that's not the case, then you would need to reverse the sign on the terms involving sin(x).

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