旋转后查找点的新坐标 [英] Find new coordinates of a point after rotation

问题描述

假设我有一个尺寸为w * h的矩形，并且让该矩形内的任意位置(x，y)处有一个任意点，现在我将该矩形旋转到X度，那么该任意位置的新位置是什么旋转后指向.

Suppose i have a rectangle of dimension w*h , and let there is an arbitrary point inside this rectangle at position (x,y) , now i rotate this rectangle to X degree, What will be the new position of that arbitrary point after rotation..

推荐答案

新坐标(x'，y')是标准旋转公式的结果:

The new coordinate (x',y') is a result of the standard rotation formula:

y' = y*cos(a) - x*sin(a)
x' = y*sin(a) + x*cos(a)

其中，a是顺时针旋转的角度.假设(x，y)是相对于旋转中心给出的.换句话说，(0,0)是旋转中心.

where a is the angle of a clockwise rotation. This assumes the (x,y) is given with respect to the center of rotation. In other words, (0,0) is the center of rotation.

大多数sin/cos函数要求角度以弧度为单位.在这种情况下，如果X以度为单位，请使用以下转换公式:

Most sin/cos functions require the angle to be in radians. In that case, use this conversion formula if X is in degrees:

a = X * pi / 180

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