Affine Transformation

affine_transformation.py

import numpy as np

def produce_transformation(tuples,tuples_t):
	"""
	Given points in some 2d space, and points in a transformed
	2d space, produces function to tranform one space to other.

	tuples : points in original space (list of x,y tuples)
	tuples_t : corresponding points in transformed space (")
	"""
	x = np.array(tuples)
	X = np.kron(np.eye(2),np.hstack([x,np.ones(x.shape[0])[:,None]]))
	X_inv = np.dot(np.linalg.inv(np.dot(X.T,X)),X.T)
	x_prime = np.concatenate(zip(*tuples_t))[:,None]
	a = np.dot(X_inv,x_prime)
	def f(tuples):
		x = np.array(tuples)
		X = np.kron(np.eye(2),np.hstack([x,np.ones(x.shape[0])[:,None]]))
		x_prime = np.squeeze(np.dot(X,a))
		return zip(x_prime[0:len(tuples)],x_prime[len(tuples):])
	return f