add bezier curve calculation by numpy as an exercise

exploration/np_bezier.py

@@ -0,0 +1,153 @@
+# Copyright (c) 2024, Manfred Moitzi
+# License: MIT License
+from __future__ import annotations
+from typing import Sequence, Iterable, Iterator
+import time
+
+import numpy as np
+from ezdxf.math import Bezier3P, Vec3, UVec, Bezier4P
+
+
+class NumpyQuadraticBezier:
+    def __init__(self, control_points: Iterable[UVec]) -> None:
+        cpts = np.array(Vec3.list(control_points), dtype=np.double)
+        assert cpts.shape[0] == 3
+        # first control point is (0, 0, 0)
+        offset = cpts[0].copy()
+        cpts -= offset
+        self._cpts = cpts
+        self._offset = offset
+
+    def points(self, params: Sequence[float]) -> Iterator[Vec3]:
+        # 1st control point is always (0, 0, 0) => a = 0
+        t = np.array(params, dtype=np.double)
+        b = t * 2.0 * (1.0 - t)
+        c = t * t
+        return self._eval(Vec3(self._offset), b, c)
+
+    def tangents(self, params: Sequence[float]) -> Iterator[Vec3]:
+        # 1st control point is always (0, 0, 0) => a = 0
+        t = np.array(params, dtype=np.double)
+        b = t * -4.0 + 2.0
+        c = t * 2.0
+        return self._eval(Vec3(), b, c)
+
+    def _eval(self, offset: Vec3, b, c) -> Iterator[Vec3]:
+        _, cp1, cp2 = self._cpts
+        x = b * cp1[0] + c * cp2[0]
+        y = b * cp1[1] + c * cp2[1]
+        z = b * cp1[2] + c * cp2[2]
+        return (offset + xyz for xyz in np.column_stack((x, y, z)))
+
+
+class NumpyCubicBezier:
+    def __init__(self, control_points: Iterable[UVec]) -> None:
+        cpts = np.array(Vec3.list(control_points), dtype=np.double)
+        assert cpts.shape[0] == 4
+        # first control point is (0, 0, 0)
+        offset = cpts[0].copy()
+        cpts -= offset
+        self._cpts = cpts
+        self._offset = offset
+
+    def points(self, params: Sequence[float]) -> Iterator[Vec3]:
+        # 1st control point is always (0, 0, 0) => a = 0
+        t = np.array(params, dtype=np.double)
+        t2 = t * t
+        _1_minus_t = 1.0 - t
+        _1_minus_t_square = _1_minus_t * _1_minus_t
+        b = 3.0 * _1_minus_t_square * t
+        c = 3.0 * _1_minus_t * t2
+        d = t2 * t
+        return self._eval(Vec3(self._offset), b, c, d)
+
+    def tangents(self, params: Sequence[float]) -> Iterator[Vec3]:
+        # 1st control point is always (0, 0, 0) => a = 0
+        t = np.array(params, dtype=np.double)
+        _3t = t * 3.0
+        d = t * _3t
+        b = 3.0 * (1.0 - 4.0 * t + d)
+        c = _3t * (2.0 - _3t)
+        return self._eval(Vec3(), b, c, d)
+
+    def _eval(self, offset: Vec3, b, c, d) -> Iterator[Vec3]:
+        _, cp1, cp2, cp3 = self._cpts
+        x = b * cp1[0] + c * cp2[0] + d * cp3[0]
+        y = b * cp1[1] + c * cp2[1] + d * cp3[1]
+        z = b * cp1[2] + c * cp2[2] + d * cp3[2]
+        return (offset + xyz for xyz in np.column_stack((x, y, z)))
+
+
+def compare_quad_curves():
+    print("\nQuadratic Bèzier Curve")
+    cpts = [(1, 2, 3), (4, 3, 1), (5, 6, 7)]
+    c0 = NumpyQuadraticBezier(cpts)
+    c1 = Bezier3P(cpts)
+    execute(c0, c1)
+
+
+def compare_cubic_curves():
+    print("\nCubic Bèzier Curve")
+    cpts = [(1, 2, 3), (4, 3, 1), (5, 6, 7), (3, 4, 8)]
+    c0 = NumpyCubicBezier(cpts)
+    c1 = Bezier4P(cpts)
+    execute(c0, c1)
+
+
+def execute(c0, c1):
+    params = [0.5, 0.6, 0.7]
+    print("Points Calculation")
+    print("Numpy:   ", list(c0.points(params)))
+    print("Cython:  ", [c1.point(t) for t in params])
+
+    print("\n1st Derivative Calculation")
+    print("Numpy:  ", list(c0.tangents(params)))
+    print("Cython: ", [c1.tangent(t) for t in params])
+
+
+def profile():
+    print("\nQuadratic Bèzier Curve")
+    cpts = [(1, 2, 3), (4, 3, 1), (5, 6, 7)]
+    curve = NumpyQuadraticBezier(cpts)
+    params = np.linspace(0.1, 0.9, 100)
+    count = 10_000
+
+    t0 = time.perf_counter()
+    profile_numpy(count, curve, params)
+    print(f"Numpy:  {time.perf_counter() - t0}")
+
+    curve = Bezier3P(cpts)
+    t0 = time.perf_counter()
+    profile_cython(count, curve, params)
+    print(f"Cython: {time.perf_counter() - t0}")
+
+    print("\nCubic Bèzier Curve")
+    cpts = [(1, 2, 3), (4, 3, 1), (5, 6, 7), (3, 4, 8)]
+    curve = NumpyCubicBezier(cpts)
+
+    t0 = time.perf_counter()
+    profile_numpy(count, curve, params)
+    print(f"Numpy:  {time.perf_counter() - t0}")
+
+    curve = Bezier4P(cpts)
+    t0 = time.perf_counter()
+    profile_cython(count, curve, params)
+    print(f"Cython: {time.perf_counter() - t0}")
+
+
+def profile_numpy(count, curve, params):
+    for _ in range(count):
+        list(curve.points(params))
+        list(curve.tangents(params))
+
+
+def profile_cython(count, curve, params):
+    for _ in range(count):
+        [curve.point(t) for t in params]
+        [curve.tangent(t) for t in params]
+
+
+if __name__ == "__main__":
+    compare_quad_curves()
+    compare_cubic_curves()
+    profile()