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

Project description

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)

Project details


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Filename, size & hash SHA256 hash help File type Python version Upload date
affine6p-1.0.0-py2.py3-none-any.whl (5.9 kB) Copy SHA256 hash SHA256 Wheel py2.py3 Jul 21, 2018
affine6p-1.0.0.tar.gz (4.1 kB) Copy SHA256 hash SHA256 Source None Jul 21, 2018

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