The Python affine6p lib to estimate affine transformation parameters between two sets of 2D points


Keywords
calculate affine transformation six parameters
License
MIT
Install
pip install affine6p==1.0.0

Documentation

affine6p

The Python affine6p lib is to estimate affine transformation parameters between two sets of 2D points.:

| x' |   | a  b  p | | x |
| y' | = | c  d  q | | y |
| 1  |   | 0  0  1 | | 1 |
Example transformation

When the sets are more than three points, the lib estimate parameters with the least squares method.

In making this lib, I used a lot of ideas in nudged lib. Ref: https://github.com/axelpale/nudged-py

Install

Use pip:

pip install affine6p

Usage

You have lists of points for the original and converted of the transformation function to be estimated:

import affine6p
origin = [[0,0], [1,0], [0,1], [1,1]]
convert = [[0,0], [1,0], [0,1], [1,1.1]]
trans = affine6p.estimate(origin, convert)
trans.get_matrix()
# [[1.0, 0.0, 0.0],
# [0.050000000000000044, 1.05, -0.02499999999999991],
# [0, 0, 1]]
affine6p.estimate_error(trans, origin, convert)
# 0.025000000000000022

When the number of origin is 1, assume the following relationship:

a = d = 1 and b = c = 0

When the number of origin is 2, assume the following relationship as described in estimate_helmert.:

a = d and b = -c

You can access Transform class members.:

trans.a() # params[0]
trans.b() # params[1]
trans.c() # params[2]
trans.d() # params[3]
trans.p() # params[4]
trans.q() # params[5]
trans.get_matrix() # [[a, b, p], [c, d, q], [0, 0, 1]]
trans.get_rotation_x() # math.atan2(-b, a)
trans.get_rotation_y() # math.atan2(c, d)
trans.get_scale_x() # sqrt(a*a + b*b)
trans.get_scale_y() # sqrt(c*c + d*d)
trans.get_scale() # sqrt((scale_x*scale_x+scale_y*scale_y)*0.5)
trans.get_translation() # [p, q]
trans.params # [a, b, c, d, p, q]

You can apply transform or rotate to 2D point or points. The rotate means p = q = 0.:

trans.transform([0, 0])
trans.transform([[0, 0], [1, 1]])
point = [0, 0]
trans.transform_inv(point)
trans.rotate(point)
trans.rotate_inv(point)