NURBS approximation of surface / surface intersection curves
type: Item
instance of: scholarly article
title: NURBS approximation of surface / surface intersection curves
zbMATH Open document ID: 0831.65014
DOI: 10.1007/BF02519033
author: Chandrajit L. Bajaj
author: Guo-Liang Xu
published in: Advances in Computational Mathematics
publication date: 1995-09-26T00:00:00Z
review text: To compute parametric representations for non-parametric algebraic intersection curves requires approximation. In this paper, the authors present algorithms to construct a piecewise rational \(B\)-spline approximation to a space curve, which comes from the intersection of two implicitly defined surfaces, or the intersection of two parametric defined surfaces. At singular points, the authors use the classical Newton power series factorization to determine the distinct branches of the space intersection curve. In addition to singular points, the authors obtain an adaptive selection of regular points about which the curve approximation yields a small number of curve segments yet achieves \(C^k\)-continuity between segments. Details of the implementation of these algorithm and approximation error bounds are also provided.
Mathematics Subject Classification ID: 65D17
Mathematics Subject Classification ID: 65D18
zbMATH DE Number: 784482
zbMATH Keywords: implicit algebraic surfaces
zbMATH Keywords: parametric algebraic surfaces
zbMATH Keywords: algebraic intersection curves
zbMATH Keywords: algorithms
zbMATH Keywords: piecewise rational \(B\)-spline approximation
reviewed by: José L. Fernández Muñiz
describes a project that uses: GANITH
MaRDI profile type: Publication
cites work: Algebraic surface design with Hermite interpolation
cites work: Q4332138
cites work: Tracing surface intersections
cites work: A practical guide to splines
cites work: Q4091004
cites work: Q4041056
cites work: On computing the intersection of a pair of algebraic surfaces
cites work: Geometric continuity
cites work: Q4729233
cites work: Computing frames along a trajectory
cites work: Convergence of a surface/surface intersection algorithm
cites work: On determining start points for a surface/surface intersection algorithm
cites work: Curve and surface constructions using rational B-splines
cites work: Geometric Hermite approximation of surface patch intersection curves
cites work: Polar forms for geometrically continuous spline curves of arbitrary degree
description: scientific article; zbMATH DE number 784482