We investigate how to define a triangulated ruled surface interpolating two polygonal directrices that will meet a variety of optimization objectives which originate from many CAD/CAM and geometric modeling applications. This optimal triangulation problem is formulated as a combinatorial search problem whose search space however has the size tightly factorial to the numbers of points on the two directrices. To tackle this bound, we introduce a novel computational tool called multilayer directed graph and establish an equivalence between the optimal triangulation and the single-source shortest path problem on the graph. Well known graph search algorithms such as the Dijkstra’s are then employed to solve the single-source shortest path problem, which effectively solves the optimal triangulation problem in time, where and are the numbers of vertices on the two directrices respectively. Numerous experimental examples are provided to demonstrate the usefulness of the proposed optimal triangulation problem in a variety of engineering applications.
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December 2005
Special Issue Papers
Optimal Boundary Triangulations of an Interpolating Ruled Surface
Charlie C. L. Wang
,
Charlie C. L. Wang
Department of Automation and Computer-Aided Engineering,
cwang@acae.cuhk.edu.hk
Chinese University of Hong Kong
, Shatin, N.T., Hong Kong, People’s Republic of China
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Kai Tang
Kai Tang
Department of Mechanical Engineering,
mektang@ust.hk
Hong Kong University of Science and Technology
, Clear Water Bay, KLN, ong Kong, People’s Republic of China
Search for other works by this author on:
Charlie C. L. Wang
Department of Automation and Computer-Aided Engineering,
Chinese University of Hong Kong
, Shatin, N.T., Hong Kong, People’s Republic of Chinacwang@acae.cuhk.edu.hk
Kai Tang
Department of Mechanical Engineering,
Hong Kong University of Science and Technology
, Clear Water Bay, KLN, ong Kong, People’s Republic of Chinamektang@ust.hk
J. Comput. Inf. Sci. Eng. Dec 2005, 5(4): 291-301 (11 pages)
Published Online: February 22, 2005
Article history
Received:
November 25, 2004
Revised:
February 22, 2005
Citation
Wang, C. C. L., and Tang, K. (February 22, 2005). "Optimal Boundary Triangulations of an Interpolating Ruled Surface." ASME. J. Comput. Inf. Sci. Eng. December 2005; 5(4): 291–301. https://doi.org/10.1115/1.2052850
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