如何围绕任意点旋转一组2D形状 [英] How to rotate a group of 2D shapes around an arbitrary point

问题描述

我正在做一个身体类，它持有一堆2D形状在一起，形成一个单一的可移动，可旋转的身体。

and i'm making a 'Body' class which holds a bunch of 2D shapes together to form a single moveable, rotatable body.

我需要知道的是如何旋转每个单独的形状，使其看起来像整个身体旋转，而不是每个形状做它自己的旋转它的中心。
我不能只改变每个形状的旋转中心到同一点，因为这将导致他们的位置也受到影响。

What i need to know is how i can rotate each individual shape in a way that makes it look like the whole body is rotating, not each shape doing it's own rotation around it's center. I can't just change each shapes center of rotation to the same point, as this would cause their placement to be affected also.

因此，我需要找到一种使用 body center 重新定位和重新旋转每个单独形状的方程

Therefore i need to find some kind of equation that uses the bodies center to re-position and re-rotate each individual shape in a body in a way that keeps the Body figure undeformed?

如何做到这一点？

推荐答案

我假设你用笛卡尔坐标（x，y）表示点，并且你喜欢向量的基本概念。

I'll assume you're representing points in Cartesian coordinates (x,y) and that you're comfortable with the basic idea of vectors.

以给定角度θ旋转单个点;围绕原点（0,0），我们将其转换如下：

To rotate a single point by a given angle θ around the origin (0,0), we transform it like so:

x'= x cos（θ） - y sin（θ）

y'= x sin（θ）+ y cos（θ）

x' = x cos(θ) - y sin(θ)
y' = x sin(θ) + y cos(θ)

或以矢量矩阵形式：

X' = M （θ） X

X' = M(θ) X

要旋转 X 点点 B ，请执行以下操作：

To rotate the point X around a point B, do this:

X' = B M （<θ>）（ X B ）

;关于其中心 B ，只需将每个形状的中心旋转θ约b b，并且围绕其自己的中心旋转每个形状θ， （您可以按任何顺序执行这些步骤）。

To rotate the whole Body by θ about its center B, just rotate each shape's center by θ about B, and rotate each shape about its own center by θ (you can do those steps in any order).

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