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During the last years the concept of multi-resolution modeling has gained special attention in many fields of computer graphics and geometric modeling. In this paper we generalize powerful multi-resolution techniques to arbitrary triangle meshes without requiring subdivision connectivity. Our major observation is that the hierarchy of nested spaces which is(More)
The decimation of highly detailed meshes has emerged as an important issue in many computer graphics related fields. A whole library of different algorithms has been proposed in the literature. By carefully investigating such algorithms, we can derive a generic structure for mesh reduction schemes which is analogous to a class of greedy-algorithms for(More)
Due to their simplicity triangle meshes are used to represent surfaces in many applications. Since the number of triangles often goes beyond the capabilities of computer graphics hardware, a large variety of mesh simplification algorithms has been proposed in the last years. In this paper we identify major requirements for the practical usability of general(More)
In a broad range of computer graphics applications the representation of geometric shape is based on triangle meshes. General purpose data structures for polygonal meshes typically provide fast access to geometric objects (e.g. points) and topologic entities (e.g. neighborhood relation) but the memory requirements are rather high due to the many special(More)
Due to their simplicity, triangle meshes are used to represent geometric objects in many applications. Since the number of triangles often goes beyond the capabilities of computer graphics hardware and the transmission time of such data is often inappropriately high, a large variety of mesh simplification algorithms has been proposed in the last years. In(More)
Ray tracing is a well known rendering technique for producing high quality photorealistic pictures. Parametric surfaces are being used extensively in geometric modeling and require fast and robust methods for computing the intersetions of rays with these surfaces. In this paper, we review two recent intersections methods and discuss their problems.(More)