Spatial Pythagorean-Hodograph B-Spline curves and 3D point data interpolation

被引：18

作者：

Albrecht, Gudrun ^{[1
]}

Beccari, Carolina Vittoria ^{[2
]}

Romani, Lucia ^{[2
]}

机构：

[1] Univ Nacl Colombia, Sede Medellin, Escuela Matemat, Carrera 65 59A-110, Medellin, Colombia

[2] Univ Bologna, Dept Math, Pzza Porta San Donato 5, I-40127 Bologna, Italy

来源：

COMPUTER AIDED GEOMETRIC DESIGN | 2020年 / 80卷

关键词：

Non-uniform B-Spline; Space curve; Pythagorean-Hodograph; Interpolation; Fairness measure; Pipe surface; ROTATION-MINIMIZING FRAMES; C-2 HERMITE INTERPOLATION;

D O I：

10.1016/j.cagd.2020.101868

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

This article deals with the spatial counterpart of the recently introduced class of planar Pythagorean-Hodograph (PH) B-Spline curves. Spatial Pythagorean-Hodograph B-Spline curves are odd-degree, non-uniform, parametric spatial B-Spline curves whose arc length is a B-Spline function of the curve parameter and can thus be computed explicitly without numerical quadrature. After giving a general definition for this new class of curves, we exploit quaternion algebra to provide an elegant description of their coordinate components and useful formulae for the construction of their control polygon. We hence consider the interpolation of spatial point data by clamped and closed PH B-Spline curves of arbitrary odd degree and discuss how degree-(2n + 1), C-n-continuous PH B-Spline curves can be computed by optimizing several scale-invariant fairness measures with interpolation constraints. (C) 2020 Elsevier B.V. All rights reserved.

引用

页数：22

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