How to morph tilings injectively
type: Item
instance of: scholarly article
title: How to morph tilings injectively
zbMATH Open document ID: 0946.52010
DOI: 10.1016/S0377-0427(98)00202-7
author: Michael S. Floater
author: Craig Gotsman
published in: Journal of Computational and Applied Mathematics
publication date: 2000-10-08T00:00:00Z
review text: The continuous transformation of a geometric configuration into another (analogous to a homotopy) is called \textit{morphing}. Here the authors discuss morphing a (finite) tiling by convex polygons (in the plane) to a \textit{compatible} tiling. Since linear interpolation may produce degenerate tilings, they propose a \textit{convex} morph: Each (interior) vertex is represented as a convex combination of its neighbours which is used for interpolation (by solving the resulting linear system). This leads to a valid morph if the boundary of the tiling is convex and remains unchanged, and to a morph preserving starshape (at least) when distinct boundaries are morphed using polar coordinates. Some examples are given.
Mathematics Subject Classification ID: 52C20
Mathematics Subject Classification ID: 65D18
Mathematics Subject Classification ID: 52B55
Mathematics Subject Classification ID: 52A99
Mathematics Subject Classification ID: 57Q99
zbMATH DE Number: 1331085
zbMATH Keywords: morphing
zbMATH Keywords: triangulations
zbMATH Keywords: tilings
zbMATH Keywords: polygons
zbMATH Keywords: convex combinations
MaRDI profile type: Publication
cites work: On compatible triangulations of simple polygons
cites work: Parametrization and smooth approximation of surface triangulations
cites work: Q3992847
cites work: Convex Representations of Graphs
cites work: How to Draw a Graph
cites work: Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
description: scientific article; zbMATH DE number 1331085