affine6p 1.0.0

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

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 |

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)