Towards compatible triangulations

Authors:
Oswin Aichholzer;Franz Aurenhammer;Ferran Hurtado;Hannes Krasser
Affiliations:
Institute for Theoretical Computer Science, Graz University of Technology, Innfeldgasse 16 B, 8010 Graz, Austria;Institute for Theoretical Computer Science, Graz University of Technology, Innfeldgasse 16 B, 8010 Graz, Austria;Departament de Matemática Aplicada II, Universitat Politécnica de Catalunya, Barcelona, Spain;Institute for Theoretical Computer Science, Graz University of Technology, Innfeldgasse 16 B, 8010 Graz, Austria
Venue:
Theoretical Computer Science - Computing and combinatorics
Year:
2003

Citing 7
Cited 3

Joint triangulations and triangulation maps

SCG '87 Proceedings of the third annual symposium on Computational geometry
Feature-based image metamorphosis

SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
On compatible triangulations of simple polygons

Computational Geometry: Theory and Applications
How to morph tilings injectively

Journal of Computational and Applied Mathematics
Enumerating order types for small sets with applications

SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Shape Blending Using the Star-Skeleton Representation

IEEE Computer Graphics and Applications
Reducing Simple Polygons to Triangles - A Proof for an Improved Conjecture

ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming

Compatible triangulations and point partitions by series-triangular graphs

Computational Geometry: Theory and Applications
Compatible triangulations and point partitions by series-triangular graphs

Computational Geometry: Theory and Applications
Mixed-Integer Models for Nonseparable Piecewise-Linear Optimization: Unifying Framework and Extensions

Operations Research

Quantified Score

Hi-index	0.00

Visualization

Abstract

We state the following conjecture: any two planar n-point sets that agree on the number of convex hull points can be triangulated in a compatible manner, i.e., such that the resulting two triangulations are topologically equivalent. We first describe a class of point sets which can be triangulated compatibly with any other set (that satisfies the obvious size and shape restrictions). The conjecture is then proved true for point sets with at most three interior points. Finally, we demonstrate that adding a small number of extraneous points (the number of interior points minus three) always allows for compatible triangulations. The linear bound extends to point sets of arbitrary size and shape.