projection & 3Drot
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@@ -120,6 +120,64 @@ def matmul(A: Matrix, B: Matrix) -> Matrix:
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return result
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def rot_3D(angle: float, axis: str) -> list[list[float]]:
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"""Berechnet die 3D-Rotationsmatrix für einen gegebenen Winkel und eine Achse.
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Die Rotationsmatrizen lauten:
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Rotation um die x-Achse:
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R_x(θ) = [[1, 0, 0],
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[0, cos(θ), -sin(θ)],
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[0, sin(θ), cos(θ)]]
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Rotation um die y-Achse:
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R_y(θ) = [[ cos(θ), 0, sin(θ)],
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[ 0, 1, 0],
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[-sin(θ), 0, cos(θ)]]
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Rotation um die z-Achse:
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R_z(θ) = [[cos(θ), -sin(θ), 0],
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[sin(θ), cos(θ), 0],
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[ 0, 0, 1]]
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Args:
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angle (float): Der Rotationswinkel in Bogenmaß (Radians).
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axis (str): Die Rotationsachse ('x', 'y' oder 'z').
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Returns:
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list[list[float]]: Die 3x3-Rotationsmatrix als geschachtelte Liste.
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Raises:
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ValueError: Wenn ein ungültiger Achsenwert übergeben wird.
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"""
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cos_a = math.cos(angle)
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sin_a = math.sin(angle)
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if axis == "x":
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return [[1.0, 0.0, 0.0], [0.0, cos_a, -sin_a], [0.0, sin_a, cos_a]]
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elif axis == "y":
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return [[cos_a, 0.0, sin_a], [0.0, 1.0, 0.0], [-sin_a, 0.0, cos_a]]
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elif axis == "z":
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return [[cos_a, -sin_a, 0.0], [sin_a, cos_a, 0.0], [0.0, 0.0, 1.0]]
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else:
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raise ValueError(
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f"Ungültige Achse '{axis}'. Gültige Achsen sind 'x', 'y' oder 'z'."
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)
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def project_ortho(point: tuple[float, float, float], scale: float = 1) -> tuple[float, float]:
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"""Projiziert einen 3D-Punkt (x, y, z) orthogonal auf eine 2D-Fläche (x, y),
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indem die z-Koordinate ignoriert und der Punkt mit scale multipliziert wird.
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Args:
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point (tuple[float, float, float]): Der 3D-Punkt als (x, y, z).
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scale (float, optional): Skalierungsfaktor für die Ausgabe. Standard ist 1.
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Returns:
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tuple[float, float]: Der 2D-Punkt als (x * scale, y * scale).
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"""
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x, y, _ = point
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return (x * scale, y * scale)
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if __name__ == "__main__":
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# Test für rot_2D (z. B. Rotation um 90 Grad = pi / 2)
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theta = math.pi / 2
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Whitespace-only changes.
@@ -0,0 +1,16 @@
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import pytest
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from matrixmania.compute import project_ortho
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def test_project_ortho_default_scale():
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# Test ohne Angabe von scale (Standardwert = 1)
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point = (1.0, 2.0, 3.0)
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result = project_ortho(point)
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assert result == (1.0, 2.0)
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def test_project_ortho_with_scale():
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# Test mit scale = 100
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point = (1.0, 2.0, 3.0)
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result = project_ortho(point, scale=100)
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assert result == (100.0, 200.0)
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@@ -0,0 +1,32 @@
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import math
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import pytest
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from matrixmania.compute import rot_3D
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def test_rot_3D_x_axis():
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# Test bei 0 Radian (Identitätsmatrix)
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res = rot_3D(0.0, "x")
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assert res == [[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]]
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# Test bei 90 Grad (PI / 2)
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res_90 = rot_3D(math.pi / 2, "x")
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assert pytest.approx(res_90[1][1]) == 0.0
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assert pytest.approx(res_90[1][2]) == -1.0
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assert pytest.approx(res_90[2][1]) == 1.0
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assert pytest.approx(res_90[2][2]) == 0.0
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def test_rot_3D_y_axis():
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res = rot_3D(0.0, "y")
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assert res == [[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]]
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def test_rot_3D_z_axis():
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res = rot_3D(0.0, "z")
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assert res == [[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]]
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def test_rot_3D_invalid_axis():
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# Prüft, ob bei ungültiger Achse ein ValueError geworfen wird
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with pytest.raises(ValueError):
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rot_3D(1.0, "w")
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