Smooth closed surfaces with discrete triangular interpolants
type: Item
instance of: scholarly article
title: Smooth closed surfaces with discrete triangular interpolants
zbMATH Open document ID: 0585.65004
DOI: 10.1016/S0167-8396(85)80004-2
published in: Computer Aided Geometric Design
publication date: 1985-01-01T00:00:00Z
review text: When using discrete interpolants which involve cross boundary derivatives in an attempt to form \(C^ 1\) surfaces, an impossibility is found if the surface contains more connections that can be achieved in the domain. The usual solution is to relax the \(C^ 1\) continuity of an interpolant to ''visually \(C^ 1\)'' (see \textit{G. Farin}, Comput. Graphics Image Process. 20, 272-282 (1982; Zbl 0541.65006)). The author develops a method of forming smooth closed surfaces from a discrete triangular interpolant; the only constraint on the scheme is that the data define a unique tangent plane at each vertex where several triangles meet. Some examples with the list of needed calculations and pictures are given.
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 41A63
Mathematics Subject Classification ID: 53A05
zbMATH DE Number: 3938419
zbMATH Keywords: smooth interpolation
zbMATH Keywords: visual continuity
zbMATH Keywords: smooth closed surfaces
zbMATH Keywords: discrete triangular interpolant
author: Gary J. Herron
reviewed by: Antonio de Castro
MaRDI profile type: Publication
cites work: Smooth interpolation in triangles
cites work: Q4194439
cites work: Surfaces in computer aided geometric design: A survey with new results
cites work: A construction for visualC1 continuity of polynomial surface patches
cites work: Q4178157
cites work: A Characterization of Certain $C^1 $ Discrete Triangular Interpolants
Recommended article: Q4017051
Recommended article: Q4938384
Recommended article: On the approximation of a smooth surface with a triangulated mesh
Recommended article: Q4664933
Recommended article: A smooth surface interpolation to 3D triangulations.
Recommended article: Q4483810
Recommended article: Parametrization and smooth approximation of surface triangulations
Recommended article: Interpolation on a triangulated 3D surface
Recommended article: Smooth parametric surface approximations to discrete data
description: scientific article; zbMATH DE number 3938419