Visibility problems for polyhedral terrains
Journal of Symbolic Computation
Hidden surface removal with respect to a moving view point
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
View-dependent simplification of arbitrary polygonal environments
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
The common exterior of convex polygons in the plane
Computational Geometry: Theory and Applications
Efficient perspective-accurate silhouette computation
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Data structures for mobile data
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
On incremental rendering of silhouette maps of polyhedral scene
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Efficient perspective-accurate silhouette computation and applications
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Shadow algorithms for computer graphics
SIGGRAPH '77 Proceedings of the 4th annual conference on Computer graphics and interactive techniques
On the Number of Views of Polyhedral Scenes
JCDCG '00 Revised Papers from the Japanese Conference on Discrete and Computational Geometry
Output Sensitive Extraction of Silhouettes from Polygonal Geometry
PG '99 Proceedings of the 7th Pacific Conference on Computer Graphics and Applications
On the Size of the 3D Visibility Skeleton: Experimental Results
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Line transversals of convex polyhedra in R3
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
On the complexity of umbra and penumbra
Computational Geometry: Theory and Applications
On the complexity of sets of free lines and line segments among balls in three dimensions
Proceedings of the twenty-sixth annual symposium on Computational geometry
Line Transversals of Convex Polyhedra in $\mathbb{R}^3$
SIAM Journal on Computing
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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.