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63 lines
1.8 KiB
Python
63 lines
1.8 KiB
Python
"""
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2D Transformations are regularly used in Linear Algebra.
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I have added the codes for reflection, projection, scaling and rotation 2D matrices.
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scaling(5) = [[5.0, 0.0], [0.0, 5.0]]
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rotation(45) = [[0.5253219888177297, -0.8509035245341184],
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[0.8509035245341184, 0.5253219888177297]]
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projection(45) = [[0.27596319193541496, 0.446998331800279],
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[0.446998331800279, 0.7240368080645851]]
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reflection(45) = [[0.05064397763545947, 0.893996663600558],
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[0.893996663600558, 0.7018070490682369]]
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"""
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from math import cos, sin
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def scaling(scaling_factor: float) -> list[list[float]]:
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"""
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>>> scaling(5)
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[[5.0, 0.0], [0.0, 5.0]]
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"""
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scaling_factor = float(scaling_factor)
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return [[scaling_factor * int(x == y) for x in range(2)] for y in range(2)]
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def rotation(angle: float) -> list[list[float]]:
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"""
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>>> rotation(45) # doctest: +NORMALIZE_WHITESPACE
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[[0.5253219888177297, -0.8509035245341184],
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[0.8509035245341184, 0.5253219888177297]]
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"""
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c, s = cos(angle), sin(angle)
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return [[c, -s], [s, c]]
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def projection(angle: float) -> list[list[float]]:
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"""
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>>> projection(45) # doctest: +NORMALIZE_WHITESPACE
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[[0.27596319193541496, 0.446998331800279],
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[0.446998331800279, 0.7240368080645851]]
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"""
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c, s = cos(angle), sin(angle)
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cs = c * s
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return [[c * c, cs], [cs, s * s]]
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def reflection(angle: float) -> list[list[float]]:
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"""
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>>> reflection(45) # doctest: +NORMALIZE_WHITESPACE
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[[0.05064397763545947, 0.893996663600558],
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[0.893996663600558, 0.7018070490682369]]
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"""
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c, s = cos(angle), sin(angle)
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cs = c * s
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return [[2 * c - 1, 2 * cs], [2 * cs, 2 * s - 1]]
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print(f" {scaling(5) = }")
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print(f" {rotation(45) = }")
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print(f"{projection(45) = }")
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print(f"{reflection(45) = }")
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