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Construction of a Realistic, Whole-Body, Three-Dimensional Equine Skeletal Model using Computed Tomography Data

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Published on: February 25, 2021

Weighted straight skeletons in the plane.

Therese Biedl¹, Martin Held², Stefan Huber³

¹David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, Ontario N2L 1A2, Canada.

Computational Geometry : Theory and Applications

|February 5, 2015

Summary

This study explores weighted straight skeletons, revealing they can be non-planar and cyclic. A linear-time algorithm is presented for strictly convex polygons, offering a new construction method.

Keywords:

Ambiguity Characterization Generalization Positive and negative weights Straight skeleton

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Area of Science:

Computational Geometry
Graph Theory
Combinatorics

Background:

Straight skeletons are fundamental geometric structures with applications in computer graphics and mesh generation.
Existing definitions can be ambiguous, necessitating a rigorous approach.
Weighted variations introduce complexity and alter structural properties.

Purpose of the Study:

To provide a comprehensive investigation of weighted straight skeletons.
To clarify ambiguities in their procedural definition.
To analyze their geometric, graph-theoretical, and combinatorial properties.

Main Methods:

Formal geometric and combinatorial analysis.
Exploration of the roof model and face topology.
Case analysis for connectivity and planarity.
Development of a non-procedural construction algorithm.

Main Results:

Weighted straight skeletons can be non-planar and contain cycles.
Conditions for connectivity are identified.
A linear-time construction algorithm is derived for strictly convex polygons with arbitrary weights.
Restrictions are discussed for preserving unweighted skeleton behavior.

Conclusions:

The study clarifies the complex nature of weighted straight skeletons.
New insights into their structure and properties are provided.
Efficient algorithms are developed for specific polygon classes, advancing computational geometry.