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We study the problem of visibility in polyhedral terrains in the presence of multiple viewpoints. We consider a triangulated terrain with m > 1 viewpoints (or guards) located on the terrain surface. A point on the terrain is considered visible if it has an unobstructed line of sight to at least one viewpoint. We study several natural and fundamental visibility structures: (1) the visibility map, which is a partition of the terrain into visible and invisible regions; (2) the colored visibility map, which is a partition of the terrain into regions whose points have exactly the same visible viewpoints; and (3) the Voronoi visibility map, which is a partition of the terrain into regions whose points have the same closest visible viewpoint. We study the complexity of each structure for both 1.5D and 2.5D terrains, and provide efficient algorithms to construct them. Our algorithm for the visibility map in 2.5D terrains improves on the only existing algorithm in this setting. To the best of our knowledge, the other structures have not been studied before. [ABSTRACT FROM AUTHOR]

A novel parallelization of the Lepp-bisection algorithm for triangulation refinement on multicore systems is presented. Randomization and wise use of the memory hierarchy are shown to highly improve algorithm performance. Given a list of selected triangles to be refined, random selection of candidates together with pre-fetching of Lepp-submeshes lead to a scalable and efficient multi-core parallel implementation. The quality of the refinement is shown to be preserved. [ABSTRACT FROM AUTHOR]

No abstract received. [ABSTRACT FROM AUTHOR]

We show how to construct a stable hierarchical basis for piecewise quadratic C1 continuous splines defined on Powell–Sabin triangulations. We prove that this hierarchical basis is well suited for compressing surfaces. Our compression method does not require the construction of wavelets which are usually expensive to compute, but instead we use a stable quasi-interpolation scheme that achieves optimal approximation order. Numerical experiments demonstrate the high compression rate of the algorithm. [ABSTRACT FROM AUTHOR]