Determining an Optimal Penetration Among Weighted Regions in Two and Three Dimensions |
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Authors: | Danny Z Chen Ovidiu Daescu Xiaobo Hu Xiaodong Wu Jinhui Xu |
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Institution: | (1) Department of Computer Science and Engineering, University of Notre Dame, Notre Dame, IN 46556, USA |
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Abstract: | We present efficient algorithms for solving the problem of computing an optimal penetration (a ray or a semi-ray) among weighted regions in 2-D and 3-D spaces. This problem finds applications in several areas, such as radiation therapy, geological exploration, and environmental engineering. Our algorithms are based on a combination of geometric techniques and optimization methods. Our geometric analysis shows that the d-D (d = 2, 3) optimal penetration problem can be reduced to solving O(n
2(d–1)) instances of certain special types of non-linear optimization problems, where n is the total number of vertices of the regions. We also give implementation results of our 2-D algorithms. |
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Keywords: | optimal penetration geometric techniques optimization weighted region |
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