petyr 0.0.3

2D Affine and Projective Transformations

petyr

Affine and Projective transformations for Python 3. Fast and chainable operations.

Install

pip3 install petyr

from petyr import Affine

Applying Transformation

p = np.array([[0,0],[1,0],[1,1],[0,1]])
rotate_and_move = Affine().rotate(90).translate(2,1)
print(rotate_and_move)

Affine(
[[ 0. -1.  2.]
 [ 1.  0.  1.]
 [ 0.  0.  1.]])

q = rotate_and_move * p
print(q)

[[2. 1.]
 [2. 2.]
 [1. 2.]
 [1. 1.]]

Finding Transformation

Affine.from_points(p,q)

Affine(
[[-0. -1.  2.]
 [ 1.  0.  1.]
 [ 0.  0.  1.]])

Basic Operations

Translation

at = Affine()
at.translate(1, 3)

Affine(
[[1. 0. 1.]
 [0. 1. 3.]
 [0. 0. 1.]])

Scaling

at = Affine()
at.scale(1.05, 2)

Affine(
[[1.05 0.   0.  ]
 [0.   2.   0.  ]
 [0.   0.   1.  ]])

Rotation

at = Affine()
at.rotate(45, degrees=True)

Affine(
[[ 0.707 -0.707  0.   ]
 [ 0.707  0.707  0.   ]
 [ 0.     0.     1.   ]])

Shearing

at = Affine()
at.shear(10, 45)

Affine(
[[1.    0.176 0.   ]
 [1.    1.    0.   ]
 [0.    0.    1.   ]])

Inversion

at = Affine()
at.rotate(90).scale(2)
at_inv = at.invert()
at * at_inv

Affine(
[[1. 0. 0.]
 [0. 1. 0.]
 [0. 0. 1.]])

Operation Chaining

Mutiple operations can be chained together.

at = Affine()
at.scale(2,2).rotate(90)
at.shear(10, 0).translate(-3, 4)

Affine(
[[ 0.353 -2.    -3.   ]
 [ 2.     0.     4.   ]
 [ 0.     0.     1.   ]])

Multiple transforms can be multiplied together.

a = Affine()
a.translate(2,3)
b = Affine()
b.scale(4,5)
a * b

Affine(
[[4. 0. 2.]
 [0. 5. 3.]
 [0. 0. 1.]])

TODO

• Implement Affine.Projective class.
• Extend from_points method to projective transform.