| T. S. Tan, Optimal two-dimensional triangulations, Ph.D. thesis, University of Illinois, Urbana-Champaign, Illinois, 1993. 81 |
....But dynamic programming is not always the most eOEcient method. For instance, the min max angle problem (nd a triangulation that minimizes the largest angle in all of its triangles) for a simple polygon can be solved by dynamic programming in O(n 3 ) time and O(n 2 ) space. Tan showed in [30] how this problem can be solved in O(n 2 log(n) time and O(n) space by using edge insertion techniques. There are other interesting problems that can be solved by dynamic programming and whose structures are identical to the one described above. Two famous examples are computing the optimal ....
T.-S. Tan. "Optimal Two-Dimensional Triangulations". Department of Computer Science, University of Illinois at Urbana-Champaign (1993).
....output(T ) The algorithm can be made to function for the lower and higher dimensional versions of the problem. In 4D, the major difficulty is the fact that a guaranteed method of making a Delaunay triangulation conform to an arbitrary polyhedral surface is presently an unsolved problem [58]: it is easy to make the edges of a surface conform but a surface may not be present in a triangulation even if its edges are. 6.2 Arrangements Recall from Section 5.2 that a sub arrangement is a description of the way the space inside some bounding region is divided by a set of planes into a set ....
....have run time of the same order as the number of tetrahedra in the triangulation, which is at most O(n 2 ) 1] Recall from Section 6.5. 3 that the best known algorithm for conforming triangulation in 2D for a graph with n e edges adds O(n 2 e n) new points in O(n 2 e n n 2 ) time [58]. A 2D conforming operation for each 2 face is sufficient for 3D conforming. The author knows of no polynomial time conforming algorithm for delete obtuse. Perhaps the best results yet for small angle conforming triangulation are those of [59] which do not consider Delaunay triangulation. Since no ....
T-S. Tan. Optimal two-dimensional triangulations. PhD thesis, University of Illinois at Urbana-Champaign, 1993. BIBLIOGRAPHY 69
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T. S. Tan, Optimal two-dimensional triangulations, Ph.D. thesis, University of Illinois, Urbana-Champaign, Illinois, 1993. 81
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T. S. Tan, Optimal two-dimensional triangulations, Ph.D. thesis, University of Illinois, Urbana-Champaign, Illinois, 1993. 81
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