Mesh Simplification Using the Edge Attributes
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Mesh Simplification Using the Edge Attributes Il Dong Yun School of Electronics and Information Engineering, Hankuk University of F. S., Yongin 449-791, Korea Email: [email protected]
Kyowoong Choo Motorola Korea Design Center, Seoul 135-766, Korea Email: [email protected]
Sang Uk Lee School of Electrical Engineering, Seoul National University, Seoul 151-742, Korea Email: [email protected] Received 14 November 2001 and in revised form 15 February 2002 This paper presents a novel technique for simplifying a triangulated surface at different levels of resolution. While most existing algorithms, based on iterative vertex decimation, employ the distance for error metric, the proposed algorithm utilizes an edge criterion for removing a vertex. An interior angle of a vertex is defined as the maximum value of all possible angles formed by combinations of edges connected to a vertex. Since the surface curvature examined with the interior angle provides more information for decision of vertex removal than the conventional distance measure, the proposed algorithm can approximate the surface with less computation. The height of a triangle, which is formed by the pair of edges, is also used for an additional constraint. The computational complexity can thus be greatly alleviated to logarithmic scale from the exponential scale required for the conventional algorithms, while yielding the comparable error level. Keywords and phrases: LOD, level of detail, mesh simplification, multiresolution.
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INTRODUCTION
Detailed mesh data models, obtained from range scanning systems, are too dense for practical applications. Transmission and storage requirements of such 3D graphic models are very demanding, due to the large amounts of data [1]. While rendering performance is continually improving, further improvement in performance could be possible by adapting the complexity of a model to its contribution to the rendered image. The ideal solution will efficiently determine the coarsest model, while retaining the perceptual image qualities. One common heuristic technique is to author several versions of a model at various level of detail (LOD); a detailed triangle mesh is used when the object is close to the viewer, and coarser approximations are substituted as the viewing distance increases. The LOD assigns multiple models varying in resolution for an object. Thus, virtual reality (VR) machines can render objects in a virtual world according to their proper resolution, without displaying all the polygons in full detail. The multiresolution modeling, motivated by such requirements, approximates high-density models nearly indistinguishably with fewer faces for rendering efficiency [2].
This is accomplished by iteratively removing vertices from original faces that will not significantly degrade the global shape of the model. The distance from the original surface to the reformed one usually represents the error caused by removing each vertex. Most existing algorithms mainly differ in their order of choosing a vertex for removal. However, he
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