A quasi-Monte Carlo method for computing areas of point-sampled surfaces |
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Authors: | Yu-Shen Liu [Author Vitae] Jun-Hai Yong [Author Vitae] |
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Affiliation: | a School of Software, Tsinghua University, Beijing 100084, People's Republic of China b Department of Computer Science and Technology, Tsinghua University, Beijing 100084, People's Republic of China c The University of Hong Kong, Hong Kong, China |
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Abstract: | A novel and efficient quasi-Monte Carlo method for computing the area of a point-sampled surface with associated surface normal for each point is presented. Our method operates directly on the point cloud without any surface reconstruction procedure. Using the Cauchy-Crofton formula, the area of the point-sampled surface is calculated by counting the number of intersection points between the point cloud and a set of uniformly distributed lines generated with low-discrepancy sequences. Based on a clustering technique, we also propose an effective algorithm for computing the intersection points of a line with the point-sampled surface. By testing on a number of point-based models, experiments suggest that our method is more robust and more efficient than those conventional approaches based on surface reconstruction. |
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Keywords: | Point-sampled surfaces Area Quasi-Monte Carlo methods Intersection |
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