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BIT Numerical Mathematics

, Volume 30, Issue 4, pp 570–582

# On the minimality of polygon triangulation

• Chiuyuan Chen
• Ruei-Chuan Chang
Part I Computer Science

## Abstract

The problem of triangulating a polygon using the minimum number of triangles is treated. We show that the minimum number of triangles required to partition a simplen-gon is equal ton+2wd − 2, wherew is the number of holes andd is the maximum number of independent degenerate triangles of then-gon. We also propose an algorithm for constructing the minimum triangulation of a simple hole-freen-gon. The algorithm takesO(nlog2n+DK2) time, whereD is the maximum number of vertices lying on the same line in then-gon andK is the number of minimally degenerate triangles of then-gon.

## CR subjects classifications

G.1.6 I.1.2 I.3.5

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## Copyright information

© BIT Foundations 1990

## Authors and Affiliations

• Chiuyuan Chen
• 1
• 2
• 3
• Ruei-Chuan Chang
• 1
• 2
• 3
1. 1.Institute of Computer Science and Information EngineeringNational Chiao Tung UniversityHsinchuTaiwan, 30050 Republic of China
2. 2.Institute of Computer and Information ScienceNational Chiao Tung UniversityHsinchuTaiwan, 30050 Republic of China
3. 3.Institute of Information ScienceAcademia Sinica NankangTaipeiTaiwan, 11529 Republic of China