48 lines
1.4 KiB
Python
48 lines
1.4 KiB
Python
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import numpy as np
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from math import cos, sin
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def create_rx(unit_axis: np.ndarray) -> np.ndarray:
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(a, b, c) = unit_axis.tolist()
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d = (b ** 2 + c ** 2) ** 0.5
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return np.array(
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[[1, 0, 0, 0], [0, c / d, -b / d, 0], [0, b / d, c / d, 0], [0, 0, 0, 1]]
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)
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def create_ry(unit_axis: np.ndarray) -> np.ndarray:
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(a, b, c) = unit_axis.tolist()
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d = (b ** 2 + c ** 2) ** 0.5
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return np.array([[d, 0, -a, 0], [0, 1, 0, 0], [a, 0, d, 0], [0, 0, 0, 1]])
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def create_rz(angel: float) -> np.ndarray:
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return np.array(
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[
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[cos(angel), -sin(angel), 0, 0],
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[sin(angel), cos(angel), 0, 0],
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[0, 0, 1, 0],
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[0, 0, 0, 1],
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]
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)
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def create_t(axis: np.ndarray) -> np.ndarray:
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(x1, y1, z1) = axis.tolist()
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return np.array([[1, 0, 0, -x1], [0, 1, 0, -y1], [0, 0, 1, -z1], [0, 0, 0, 1]])
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def rotation(angel: float, axis: np.ndarray, points: np.ndarray):
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# 依据《计算机图形学》第4版 9.28公式
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unit_axis = axis / np.linalg.norm(axis)
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rz = create_rz(angel)
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rx = create_rx(unit_axis)
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ry = create_ry(unit_axis)
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t = create_t(axis)
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t_i = np.linalg.inv(t)
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rx_i = np.linalg.inv(rx)
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ry_i = np.linalg.inv(ry)
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r_transform = t_i.dot(rx_i.dot(ry_i.dot(rz.dot(ry.dot(rx.dot(t))))))
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expand_point = np.concatenate((points, np.ones((points.shape[0], 1))), axis=1)
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return r_transform.dot(expand_point.T)
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