如何计算具有 4 个点 (x1,y1,.,x4,y4) 的矩形在顺时针方向上的旋转角度，使其笔直或 0 度

Question

给定一个多边形（倾斜矩形），它代表一个单词区域，其中 4 个点按顺时针方向排列，如何识别旋转角度以使其在视角中为 0 度以使文本歪斜？

Answer 1

I guess the rectangle looks like this?!

The red angle, let's call it alpha , is your rotation angle. Let's say the top left point is named A and top right is called B . The line from A to B is the hypotenuse of the red triangle which is as long as the width of the rectangle. The opposite cathetus is the right side of the red triangle which is as long as the difference between the y coordinates of A and B .

The sine function is defined as the opposite cathetus divided by the hyptenuse.

sin(alpha) = (y_A-y_B)/width -> alpha = sin^-1((y_A-y_B)/width)

# I guess the coordinates are stored in a list (x1,y1,...,x4,y4) called coords
y_A = coords[1]
y_B = coords[3]

op_cath = y_A - y_B

import math
alpha = math.asin(op_cath/width)

To get the new coordinates (rotation).

# new coordinates of A
x_A = x_A*math.cos(alpha)-y_A*math.sin(alpha)
y_A = x_A*math.sin(alpha)+y_A*math.cos(alpha)

# repeat for each point

( https://math.stackexchange.com/questions/2581058/rotating-rectangle-by-its-center )