完成旋转矩阵。

Signed-off-by: facat <facat@facat.com>

.gitignore

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+.idea
+__pycache__

main.py

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+import math
+from transformation import rotation
+import numpy as np
+
+if __name__ == "__main__":
+    t = rotation(
+        45 / 180 * math.pi, np.array([0, 0, 1]), np.array([[1, 1, 0], [2, 3, 4]])
+    )
+    print(t)

transformation.py

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