Rational C1 cubic Powell-Sabin B-splines with application to representation of ruled surfaces

被引：0

作者：

Groselj, Jan ^{[1
,2
]}

Praprotnik, Ada Sadl ^{[1
]}

机构：

[1] Univ Ljubljana, Fac Math & Phys, Jadranska 19, Ljubljana 1000, Slovenia

[2] Inst Math Phys & Mech, Jadranska 19, Ljubljana 1000, Slovenia

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2025年 / 457卷

关键词：

Splines on triangulations; Rational Powell-Sabin splines; B-splines; Ruled surfaces; NORMALIZED BASIS;

D O I：

10.1016/j.cam.2024.116292

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper defines rational C 1 cubic Powell-Sabin splines and analyses their basic properties. A rational B-spline basis is established and an algorithm for determining the corresponding control points and weights by using the blossoming operator is presented. The capability of the introduced splines to represent rational cubic triangular B & eacute;zier patches and quadratic NURPS is discussed and explicit conversion formulas are provided. Moreover, the application of the rational C 1 cubic Powell-Sabin splines to representation of ruled surfaces is studied, showing that the cubic splines can give smoother parametrizations than the NURPS.

引用

页数：14

共 33 条

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[32] Superconvergent C1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^1$$\end{document} cubic spline quasi-interpolants on Powell-Sabin partitions
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[33] A construction of edge B-spline functions for a C1 polynomial spline on two triangles and its application to Argyris type splines
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