Constant-time all-pairs geodesic distance query on triangle meshes

Proceedings - I3D 2012: ACM SIGGRAPH Symposium on Interactive 3D Graphics and Games

Volumn , Issue , 2012, Pages 31-38

  Xin, Shi Qing ^a   Ying, Xiang ^a   He, Ying ^a  

^a NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

Author keywords

all pairs geodesic distance query; constant time algorithm; discrete exponential map; discrete geodesics; geodesic distance field

Indexed keywords

CONSTANT TIME ALGORITHMS; DISCRETE GEODESIC; EXPONENTIAL MAP; GEODESIC DISTANCE FIELD; GEODESIC DISTANCES;

ALGORITHMS; INTERACTIVE COMPUTER GRAPHICS; MANGANESE COMPOUNDS; THREE DIMENSIONAL;

GEODESY;

EID: 84859863446     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/2159616.2159622     Document Type: Conference Paper

References (35)

1. AGARWAL, P. K., ARONOV, B., O'ROURKE, J., AND SCHEVON, C. A. 1997. Star unfolding of a polytope with applications. SIAM J. Comput. 26, 6, 1689-1713.
2. BARBEHENN, M. 1998. A note on the complexity of Dijkstra's algorithm for graphs with weighted vertices. IEEE Trans. Comput. 47, 2, 263.
3. BASWANA, S., HARIHARAN, R., AND SEN, S. 2003. Maintaining all-pairs approximate shortest paths under deletion of edges. In SODA '03, 394-403.
4. CHEN, J., AND HAN, Y. 1990. Shortest paths on a polyhedron. In SCG '90, 360-369.
5. CHOI, J., SELLEN, J., AND YAP, C.-K. 1994. Approximate euclidean shortest path in 3-space. In SCG '94, 41-48.
6. CLARKSON, K. 1987. Approximation algorithms for shortest path motion planning. In STOC '87, 56-65.
7. COOK IV, A. F., AND WENK, C. 2009. Shortest path problems on a polyhedral surface. In WADS '09, 156-167.
8. DIJKSTRA, E. 1959. A note on two problems in connexion with graphs. Numerische Mathematik 1, 1, 269-271.
9. DOR, D., HALPERIN, S., AND ZWICK, U. 2000. All-pairs almost shortest paths. SIAM J. Comput. 29, 1740-1759.
10. HUANG, Q.-X., ADAMS, B., WICKE, M., AND GUIBAS, L. J. 2008. Non-rigid registration under isometric deformations. In SGP '08, 1449-1457.
11. KANAI, T., AND SUZUKI, H. 2000. Approximate shortest path on polyhedral surface based on selective refinement of the discrete graph and its applications. In GMP '00, 241-250.
12. KIMMEL, R., AND SETHIAN, J. A. 1998. Computing geodesic paths on manifolds. In Proc. Natl. Acad. Sci. USA, 8431-8435.
13. LEE, H., TONG, Y., AND DESBRUN, M. 2005. Geodesics-based one-to-one parameterization of 3d triangle meshes. IEEE Multi-Media 12, 27-33.
14. MITCHELL, J. S. B., MOUNT, D. M., AND PAPADIMITRIOU, C. H. 1987. The discrete geodesic problem. SIAM J. Comput. 16, 4, 647-668.
15. MITCHELL, J. S. B. 2004. New results on shortest paths in three dimensions. In SCG '04, 124-133.
16. OSADA, R., FUNKHOUSER, T., CHAZELLE, B., AND DOBKIN, D. 2002. Shape distributions. ACM Trans. Graph. 21, 807-832.
17. PAPADIMITRIOU, C. H. 1985. An algorithm for shortest-path motion in three dimensions. IPL 20, 259-263.
18. PEYRÉ, G., AND COHEN, L. D. 2006. Geodesic remeshing using front propagation. Int. J. Comput. Vision 69, 1, 145-156.
19. POLTHIER, K., AND SCHMIES, M. 1999. Geodesic flow on polyhedral surfaces. In Proceedings of Eurographics-IEEE Symposium on Scientific Visualization '99, 179-188.
20. SANDER, P. V., WOOD, Z. J., GORTLER, S. J., SNYDER, J., AND HOPPE, H. 2003. Multi-chart geometry images. In SGP '03.
21. SCHMIDT, R., GRIMM, C., AND WYVILL, B. 2006. Interactive decal compositing with discrete exponential maps. ACM Trans. Graph. 25 (July), 605-613.
22. SCHREIBER, Y., AND SHARIR, M. 2006. An optimal-time algorithm for shortest paths on a convex polytope in three dimensions. In SCG '06, 30-39.
23. SHARIR, M., AND SCHORR, A. 1986. On shortest paths in polyhedral spaces. SIAM J. Comput. 15, 1, 193-215.
24. SPIRA, A., AND KIMMEL, R. 2002. Geodesic curvature flow on parametric surfaces. In Curve and Surface Design, 365-373.
25. SURAZHSKY, V., SURAZHSKY, T., KIRSANOV, D., GORTLER, S. J., AND HOPPE, H. 2005. Fast exact and approximate geodesics on meshes. ACM Trans. Graph. 24, 3, 553-560.
26. WEBER, O., DEVIR, Y. S., BRONSTEIN, A. M., BRONSTEIN, M. M., AND KIMMEL, R. 2008. Parallel algorithms for approximation of distance maps on parametric surfaces. ACM Trans. Graph. 27, 4.
27. XIA, J., GARCIA, I., HE, Y., XIN, S.-Q., AND PATOW, G. 2011. Editable polycube map for gpu-based subdivision surfaces. In Symposium on Interactive 3D Graphics and Games, 151-158.
28. XIN, S.-Q., AND WANG, G.-J. 2009. Improving Chen and Han's algorithm on the discrete geodesic problem. ACM Trans. Graph. 28, 4, 1-8.
29. XIN, S.-Q., AND WANG, G.-J. 2010. Applying the improved Chen and Han's algorithm to different versions of shortest path problems on a polyhedral surface. CAD 42, 942-951.
30. XIN, S.-Q., YING, X., AND HE, Y. 2011. Efficiently computing geodesic offsets on triangle meshes by the extended xin-wang algorithm. Computer Aided Design 43, 1468-1476.
31. XIN, S.-Q., HE, Y., AND FU, C.-W. 2012. Efficiently computing exact geodesic loops within finite steps. IEEE Transactions on Visualization and Computer Graphics (TVCG), to appear.
32. ZELINKA, S., AND GARLAND, M. 2004. Similarity-based surface modelling using geodesic fans. In SGP '04, 204-213.
33. ZHOU, K., SYNDER, J., GUO, B., AND SHUM, H.-Y. 2004. Isocharts: stretch-driven mesh parameterization using spectral analysis. In SGP '04, 45-54.
34. ZWICK, U. 1998. All pairs shortest paths in weighted directed graphs - exact and almost exact algorithms. In FOCS '98, 310-319.
35. ZWICK, U. 2002. All pairs shortest paths using bridging sets and rectangular matrix multiplication. J. ACM 49, 289-317.