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Create Transformations2D.py (#2310)

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* Create Transformations2D.py

* Update Transformations2D.py

* Drop numpy and add type hints and doctests

* Rename Transformations2D.py to transformations_2d.py

Co-authored-by: Christian Clauss <cclauss@me.com>
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Yukti Khosla 2020-08-15 21:49:33 +05:30 committed by GitHub
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linear_algebra/src/transformations_2d.py Normal file
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"""
2D Transformations are regularly used in Linear Algebra.
I have added the codes for reflection, projection, scaling and rotation 2D matrices.
scaling(5) = [[5.0, 0.0], [0.0, 5.0]]
rotation(45) = [[0.5253219888177297, -0.8509035245341184],
[0.8509035245341184, 0.5253219888177297]]
projection(45) = [[0.27596319193541496, 0.446998331800279],
[0.446998331800279, 0.7240368080645851]]
reflection(45) = [[0.05064397763545947, 0.893996663600558],
[0.893996663600558, 0.7018070490682369]]
"""
from math import cos, sin
from typing import List
def scaling(scaling_factor: float) -> List[List[float]]:
"""
>>> scaling(5)
[[5.0, 0.0], [0.0, 5.0]]
"""
scaling_factor = float(scaling_factor)
return [[scaling_factor * int(x == y) for x in range(2)] for y in range(2)]
def rotation(angle: float) -> List[List[float]]:
"""
>>> rotation(45) # doctest: +NORMALIZE_WHITESPACE
[[0.5253219888177297, -0.8509035245341184],
[0.8509035245341184, 0.5253219888177297]]
"""
c, s = cos(angle), sin(angle)
return [[c, -s], [s, c]]
def projection(angle: float) -> List[List[float]]:
"""
>>> projection(45) # doctest: +NORMALIZE_WHITESPACE
[[0.27596319193541496, 0.446998331800279],
[0.446998331800279, 0.7240368080645851]]
"""
c, s = cos(angle), sin(angle)
cs = c * s
return [[c * c, cs], [cs, s * s]]
def reflection(angle: float) -> List[List[float]]:
"""
>>> reflection(45) # doctest: +NORMALIZE_WHITESPACE
[[0.05064397763545947, 0.893996663600558],
[0.893996663600558, 0.7018070490682369]]
"""
c, s = cos(angle), sin(angle)
cs = c * s
return [[2 * c - 1, 2 * cs], [2 * cs, 2 * s - 1]]
print(f" {scaling(5) = }")
print(f" {rotation(45) = }")
print(f"{projection(45) = }")
print(f"{reflection(45) = }")