from math import radians, cos, sin

import numpy as np


def combine(*transformations):
    result = transformations[0]
    for transformation in transformations[1:]:
        result = np.dot(result, transformation)

    return result


def identity():
    return np.identity(3)


def rotation(angle):
    a = radians(-angle)
    i = identity()
    i[0, 0] = cos(a)
    i[0, 1] = -sin(a)
    i[1, 0] = sin(a)
    i[1, 1] = cos(a)
    return i


def scaling(sx, sy):
    i = identity()
    i[0, 0] = sx
    i[1, 1] = sy
    return i


def translation(dx, dy):
    i = identity()
    i[0, 2] = dx
    i[1, 2] = dy
    return i


def shear(k):
    i = identity()
    i[0, 1] = k
    return i