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# 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()
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