Shape determination of planar uniform cubic B-spline segments
type: Item
instance of: scholarly article
title: Shape determination of planar uniform cubic B-spline segments
zbMATH Open document ID: 0708.65015
DOI: 10.1016/0010-4485(90)90108-O
author: D. S. Meek
author: D. J. Walton
published in: CAD. Computer-Aided Design
publication date: 1990-01-01T00:00:00Z
review text: A parametric uniform cubic B-spline curve in the plane is determined by four control vertices. The authors investigate how the movement of any control vertex affects the shape of the curve segments. \textit{C. Y. Wang} [ibid. 13, 199-206 (1981)] gave conditions on the coefficients of the cubic polynomials such that the corresponding cubic B-spline segment has a corner or cusp, one inflection point, two inflection points, or forms a loop. In this paper, simpler conditions are developed which make it possible to divide the plane into regions such that placing an appropriate control vertex in one of the regions will cause the cubic B-spline segments to have a particular feature according to the above classification.
Mathematics Subject Classification ID: 65D17
Mathematics Subject Classification ID: 65D07
zbMATH DE Number: 4164005
zbMATH Keywords: computer-aided design
zbMATH Keywords: parametric uniform cubic B-spline curve
zbMATH Keywords: control vertices
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4164005