Optimal Triangulation

Author(s):  
Tiow-Seng Tan
1999 ◽  
Vol 14 (1-3) ◽  
pp. 49-65 ◽  
Author(s):  
Paul S. Heckbert ◽  
Michael Garland

2005 ◽  
Vol 5 (4) ◽  
pp. 291-301 ◽  
Author(s):  
Charlie C. L. Wang ◽  
Kai Tang

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 O(mn) time, where n and m 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.


2000 ◽  
Vol 17 (8) ◽  
pp. 767-787 ◽  
Author(s):  
Martin Bertram ◽  
James C. Barnes ◽  
Bernd Hamann ◽  
Kenneth I. Joy ◽  
Helmut Pottmann ◽  
...  

2014 ◽  
Vol 3 (2) ◽  
Author(s):  
Sead H Mašović ◽  
Muzafer H Saračević

2012 ◽  
Vol 229-231 ◽  
pp. 2294-2297
Author(s):  
Zi Ming Xiong ◽  
Gang Wan

In this paper, we propose an approach to automatic great-scene 3D reconstruction based on UAV sequence images. In this method, Harris feature point and SIFT feature vector is used to distill image feature, achieving images match; quasi-perspective projection model and factorization is employed to calibrate the uncalibrated image sequences automatically; Efficient suboptimal solutions to the optimal triangulation is plied to obtain the coordinate of 3D points; quasi-dense diffusing algorithm is bestowed to make 3D point denseness; the algorithm of bundle adjustment is taken to improve the precision of 3D points; the approach of Possion surface reconstruction is used to make 3D points gridded. This paper introduces the theory and technology of computer vision into great-scene 3D reconstruction, provides a new way for the construction of 3D scene, and provides a new thinking for the appliance of UAV sequence images.


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