Proceedings of the twelfth annual symposium on Computational geometry
MAPS: multiresolution adaptive parameterization of surfaces
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Semantic Reasoning for Scene Interpretation
Cognitive Vision
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Frequently, data in scientific computing is in its abstract form a finite point set in space, and it is often useful or required to compute what one might call the ``shape'''' of the set. For that purpose, this thesis deals with the formal notion of the family of alpha shapes of a finite point set in three-dimensional space. Each shape is a well-defined polytope, derived from the Delaunay triangulation of the point set, with a real parameter controlling the desired level of detail. Algorithms and data structures are presented that construct and store the entire family of shapes, with a quadratic time and space complexity, in the worst case. Implementations of the algorithms are discussed, with an emphasis on the robust construction of three-dimensional Delaunay triangulations. A general-purpose programming technique, called Simulation of Simplicity, is used to cope with degenerate input data. This method relieves the programmer from the task of providing a consistent treatment for every single special case that can occur. The programs that use the technique tend to be considerably smaller and more robust than others.