math - Rotate point about another point in degrees python

Question

If you had a point (in 2d), how could you rotate that point by degrees around the other point (the origin) in python?

You might, for example, tilt the first point around the origin by 10 degrees.

Basically you have one point PointA and origin that it rotates around. The code could look something like this:

PointA=(200,300)
origin=(100,100)

NewPointA=rotate(origin,PointA,10) #The rotate function rotates it by 10 degrees

Answer 1

The following rotate function performs a rotation of the point point by the angle angle (counterclockwise, in radians) around origin, in the Cartesian plane, with the usual axis conventions: x increasing from left to right, y increasing vertically upwards. All points are represented as length-2 tuples of the form (x_coord, y_coord).

import math

def rotate(origin, point, angle):
    """
    Rotate a point counterclockwise by a given angle around a given origin.

    The angle should be given in radians.
    """
    ox, oy = origin
    px, py = point

    qx = ox + math.cos(angle) * (px - ox) - math.sin(angle) * (py - oy)
    qy = oy + math.sin(angle) * (px - ox) + math.cos(angle) * (py - oy)
    return qx, qy

If your angle is specified in degrees, you can convert it to radians first using math.radians. For a clockwise rotation, negate the angle.

Example: rotating the point (3, 4) around an origin of (2, 2) counterclockwise by an angle of 10 degrees:

>>> point = (3, 4)
>>> origin = (2, 2)
>>> rotate(origin, point, math.radians(10))
(2.6375113976783475, 4.143263683691346)

Note that there's some obvious repeated calculation in the rotate function: math.cos(angle) and math.sin(angle) are each computed twice, as are px - ox and py - oy. I leave it to you to factor that out if necessary.