41 lines
1.2 KiB
Python
41 lines
1.2 KiB
Python
# Copyright (c) 2020-2024, Manfred Moitzi
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# License: MIT License
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from __future__ import annotations
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from typing import Iterable
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import numpy as np
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from ezdxf.math import Vec3
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class CSpline:
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"""
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In numerical analysis, a cubic Hermite spline or cubic Hermite interpolator
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is a spline where each piece is a third-degree polynomial specified in
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Hermite form, that is, by its values and first derivatives at the end points
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of the corresponding domain interval.
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Source: https://en.wikipedia.org/wiki/Cubic_Hermite_spline
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"""
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# https://de.wikipedia.org/wiki/Kubisch_Hermitescher_Spline
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def __init__(self, p0: Vec3, p1: Vec3, m0: Vec3, m1: Vec3):
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self.p0 = p0
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self.p1 = p1
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self.m0 = m0
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self.m1 = m1
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def point(self, t: float) -> Vec3:
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t2 = t * t
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t3 = t2 * t
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h00 = t3 * 2.0 - t2 * 3.0 + 1.0
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h10 = -t3 * 2.0 + t2 * 3.0
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h01 = t3 - t2 * 2.0 + t
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h11 = t3 - t2
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return self.p0 * h00 + self.p1 * h10 + self.m0 * h01 + self.m1 * h11
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def approximate(csplines: Iterable[CSpline], count) -> Iterable[Vec3]:
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for cspline in csplines:
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for t in np.linspace(0.0, 1.0, count):
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yield cspline.point(t)
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