On incremental rendering of silhouette maps of a polyhedral scene

Alon Efrat, Leonidas J. Guibas, Olaf A. Hall-Holt, Li Zhang

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

We consider the problem of incrementally rendering a polyhedral scene while the viewpoint is moving. In practical situations the number of geometric primitives to be rendered can be as large as many millions. It is sometimes advantageous to render only the silhouettes of the objects, rather than the objects themselves. Such an approach is regularly used for example in the domain of non-photorealistic rendering, where the rendering of silhouette edges plays a key role. The difficult part in efficiently implementing a kinetic approach to this problem is to realize when the rendered silhouette undergoes a combinatorial change. In this paper, we obtain bounds on several problems involving the number of these events for a collection of k objects, with a total of n edges. We assume that our objects are convex polytopes, and that the viewpoint is moving along a straight line, or along an algebraic curve of bounded low degree. We also study the special case when the scene is a polyhedral terrain, and present improved bounds for this case. In addition to bounding the number events, we also obtain algorithms that compute all the changes occurring during a linear motion both for general scenes and for terrains.

Original languageEnglish (US)
Pages (from-to)129-138
Number of pages10
JournalComputational Geometry: Theory and Applications
Volume38
Issue number3
DOIs
StatePublished - Oct 2007

Fingerprint

Silhouette
Rendering
Kinetics
Polyhedral Terrains
Non-photorealistic Rendering
Convex Polytopes
Algebraic curve
Straight Line
Motion
Object
Rendering (computer graphics)

Keywords

  • Incremental rendering
  • Silhouette arrangements
  • Visibility graphs

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Computer Science Applications
  • Computational Mathematics
  • Control and Optimization
  • Geometry and Topology

Cite this

On incremental rendering of silhouette maps of a polyhedral scene. / Efrat, Alon; Guibas, Leonidas J.; Hall-Holt, Olaf A.; Zhang, Li.

In: Computational Geometry: Theory and Applications, Vol. 38, No. 3, 10.2007, p. 129-138.

Research output: Contribution to journalArticle

Efrat, Alon ; Guibas, Leonidas J. ; Hall-Holt, Olaf A. ; Zhang, Li. / On incremental rendering of silhouette maps of a polyhedral scene. In: Computational Geometry: Theory and Applications. 2007 ; Vol. 38, No. 3. pp. 129-138.
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