### 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 language | English (US) |
---|---|

Pages (from-to) | 129-138 |

Number of pages | 10 |

Journal | Computational Geometry: Theory and Applications |

Volume | 38 |

Issue number | 3 |

DOIs | |

State | Published - Oct 2007 |

### Fingerprint

### 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

*Computational Geometry: Theory and Applications*,

*38*(3), 129-138. https://doi.org/10.1016/j.comgeo.2006.12.003

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

Research output: Contribution to journal › Article

*Computational Geometry: Theory and Applications*, vol. 38, no. 3, pp. 129-138. https://doi.org/10.1016/j.comgeo.2006.12.003

}

TY - JOUR

T1 - On incremental rendering of silhouette maps of a polyhedral scene

AU - Efrat, Alon

AU - Guibas, Leonidas J.

AU - Hall-Holt, Olaf A.

AU - Zhang, Li

PY - 2007/10

Y1 - 2007/10

N2 - 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.

AB - 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.

KW - Incremental rendering

KW - Silhouette arrangements

KW - Visibility graphs

UR - http://www.scopus.com/inward/record.url?scp=34547987024&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34547987024&partnerID=8YFLogxK

U2 - 10.1016/j.comgeo.2006.12.003

DO - 10.1016/j.comgeo.2006.12.003

M3 - Article

AN - SCOPUS:34547987024

VL - 38

SP - 129

EP - 138

JO - Computational Geometry: Theory and Applications

JF - Computational Geometry: Theory and Applications

SN - 0925-7721

IS - 3

ER -