Piecewise polynomial spaces and geometric continuity of curves
type: Item
instance of: scholarly article
title: Piecewise polynomial spaces and geometric continuity of curves
zbMATH Open document ID: 0638.65010
DOI: 10.1007/BF01396765
published in: Numerische Mathematik
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/133321
review text: We say that a curve has geometric continuity if its Frenet frame is continuous. The curve has arc-length continuity of order k if it is k time continuously differentiable in the arc-length parametrization. In this paper we introduce spaces of piecewise polynomials which can be used to model space curves with geometric on arc-length continuity. We show that the basic theoretical properties of ordinary spline functions also hold for these spaces. These results extend and unify recent work on Beta-splines and Nu-splines, which are used as a design tool in computer- aided geometric design of free form curves and surfaces.
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 53A04
zbMATH DE Number: 4041140
zbMATH Keywords: Frenet frame
zbMATH Keywords: arc-length continuity
zbMATH Keywords: piecewise polynomials
zbMATH Keywords: spline functions
zbMATH Keywords: beta-splines and nu-splines
zbMATH Keywords: computer-aided geometric design
zbMATH Keywords: free form curves
zbMATH Keywords: surfaces
zbMATH Keywords: parametric representation
zbMATH Keywords: curvatures
zbMATH Keywords: variation diminishing
zbMATH Keywords: shape preservations
zbMATH Keywords: total positivity
author: Nira Dyn
author: Charles A. Micchelli
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4041140