refactor: excel parse

server/venv/lib/python3.9/site-packages/ezdxf/math/cspline.py

@@ -0,0 +1,40 @@
+# Copyright (c) 2020-2024, Manfred Moitzi
+# License: MIT License
+from __future__ import annotations
+from typing import Iterable
+import numpy as np
+
+from ezdxf.math import Vec3
+
+
+class CSpline:
+    """
+    In numerical analysis, a cubic Hermite spline or cubic Hermite interpolator
+    is a spline where each piece is a third-degree polynomial specified in
+    Hermite form, that is, by its values and first derivatives at the end points
+    of the corresponding domain interval.
+
+    Source: https://en.wikipedia.org/wiki/Cubic_Hermite_spline
+    """
+
+    # https://de.wikipedia.org/wiki/Kubisch_Hermitescher_Spline
+    def __init__(self, p0: Vec3, p1: Vec3, m0: Vec3, m1: Vec3):
+        self.p0 = p0
+        self.p1 = p1
+        self.m0 = m0
+        self.m1 = m1
+
+    def point(self, t: float) -> Vec3:
+        t2 = t * t
+        t3 = t2 * t
+        h00 = t3 * 2.0 - t2 * 3.0 + 1.0
+        h10 = -t3 * 2.0 + t2 * 3.0
+        h01 = t3 - t2 * 2.0 + t
+        h11 = t3 - t2
+        return self.p0 * h00 + self.p1 * h10 + self.m0 * h01 + self.m1 * h11
+
+
+def approximate(csplines: Iterable[CSpline], count) -> Iterable[Vec3]:
+    for cspline in csplines:
+        for t in np.linspace(0.0, 1.0, count):
+            yield cspline.point(t)