Efficiently computing geodesic offsets on triangle meshes by the extended XinWang algorithm

CAD Computer Aided Design

Volumn 43, Issue 11, 2011, Pages 1468-1476

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

^a NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

Author keywords

Discrete geodesics; Exact algorithm; Geodesic distance field; Geodesic offsets

Indexed keywords

ASYMPTOTIC TIME COMPLEXITY; COMPLICATED GEOMETRY; DIFFERENTIAL GEOMETRY; DISCRETE GEODESIC; EXACT ALGORITHM; EXACT ALGORITHMS; GEODESIC DISTANCE FIELD; GEODESIC OFFSETS; LARGE-SCALE MODELS; NC-MACHINING; PIECEWISE LINEAR; SOLID-MODELING; SPACE COMPLEXITY; TOOLPATHS; TRIANGLE MESH; UNDERLYING SURFACE;

ALGORITHMS; COMPUTER AIDED DESIGN; COMPUTER GRAPHICS; CURVE FITTING; DATA STRUCTURES; GEODESY; INDUSTRIAL APPLICATIONS; MACHINE DESIGN; PIECEWISE LINEAR TECHNIQUES; ROBOT PROGRAMMING;

TREES (MATHEMATICS);

EID: 80054698964     PISSN: 00104485     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cad.2011.08.027     Document Type: Article

References (38)

1. J.R. Rossignac, and A.A.G. Requicha Offsetting operations in solid modelling Computer Aided Geometric Design 3 1986 129 148
2. Forsyth M. Shelling and offsetting bodies. In: Proceedings of the third ACM symposium on solid modeling and applications. SMA'95. 1995. p. 37381.
3. T. Lozano-Perez, and M. Wesley An algorithm for planning collision free paths amongst polyhedral obstacles Communications of the ACM 25 9 1979 560 570 (Pubitemid 10424755)
4. K. Marciniak Geometric modeling for numerically controlled machining 1991 Oxford University Press
5. B.K. Choi, and R. Jerard Sculptured surface machiningtheory and applications 1998 Kluwer Academic Publishers
6. K.I. Kim, and K. Kim A new machine strategy for sculptured surfaces using offset surface International Journal of Production Research 33 6 1995 1683 1697
7. N.M. Patrikalakis, and L. Bardis Offsets of curves on rational b-spline surfaces Engineering with Computers 5 1 1989 39 46
8. A. Hatna, R.J. Grieve, and P. Broomhead Offsetting 3D contours on parametric surfaces The International Journal of Advanced Manufacturing Technology 16 3 2000 189 195 (Pubitemid 30566148)
9. L.A. Piegl, and W. Tiller Computing offsets of NURBS curves and surfaces Computer-Aided Design 31 2 1999 147 156
10. V.D. Holla, K.G. Shastry, and B.G. Prakash Offset of curves on tessellated surfaces Computer-Aided Design 35 12 2003 1099 1108
11. Chen Z, Chen Y, Liang F. A new offset approach for curves on triangle mesh surfaces. In: Technology and innovation conference 2006. 2006. p. 2028.
12. Bommes D, Kobbelt L. Accurate computation of geodesic distance fields for polygonal curves on triangle meshes. In: VMV'07. 2007. p. 15160.
13. J.S.B. Mitchell, D.M. Mount, and C.H. Papadimitriou The discrete geodesic problem SIAM Journal on Computing 16 4 1987 647 668
14. S.-Q. Xin, and G.-J. Wang Improving Chen and Han's algorithm on the discrete geodesic problem ACM Transactions on Graphics 28 2009 104:1104:8
15. M. Sharir, and A. Schorr On shortest paths in polyhedral spaces SIAM Journal on Computing 15 1 1986 193 215
16. Chen J, Han Y. Shortest paths on a polyhedron. In: SCG'90: proceedings of the sixth annual symposium on computational geometry. 1990. p. 3609.
17. V. Surazhsky, T. Surazhsky, D. Kirsanov, S.J. Gortler, and H. Hoppe Fast exact and approximate geodesics on meshes ACM Transactions on Graphics 24 3 2005 553 560
18. R 3. In: SODA'95: proceedings of the sixth annual ACMSIAM symposium on discrete algorithms. 1995. p. 44756.
19. Varadarajan KR, Agarwal PK. Approximating shortest paths on a nonconvex polyhedron. In: IEEE symposium on foundations of computer science. 1997. p. 18291.
20. P.K. Agarwal, S. Har-Peled, M. Sharir, and K.R. Varadarajan Approximating shortest paths on a convex polytope in three dimensions Journal of the ACM 44 4 1997 567 584 (Pubitemid 127617704)
21. Lanthier M, Maheshwari A, Sack J-R. Approximating weighted shortest paths on polyhedral surfaces. In: SCG'97: proceedings of the thirteenth annual symposium on computational geometry. 1997. p. 4856.
22. M. Barbehenn A note on the complexity of Dijkstra's algorithm for graphs with weighted vertices IEEE Transactions on Computers 47 2 1998 263 (Pubitemid 128737459)
23. R. Kimmel, and J.A. Sethian Computing geodesic paths on manifolds Proceedings of the National Academy of Sciences USA 1998 8431 8435 (Pubitemid 28350504)
24. S. Har-Peled Approximate shortest paths and geodesic diameter on a convex polytope in three dimensions Discrete & Computational Geometry 21 2 1999 217 231
25. Agarwal PK, Har-Peled S, Karia M. Computing approximate shortest paths on convex polytopes. In: Symposium on computational geometry. 2000. p. 2709.
26. A. Spira, and R. Kimmel Geodesic curvature flow on parametric surfaces Curve and surface design 2002 365 373
27. Aleksandrov L, Maheshwari A, Sack J-R. An improved approximation algorithm for computing geometric shortest paths. In: The 14th international symposium on fundamentals of computation theory. 2003. p. 24657.
28. C.H. Papadimitriou An algorithm for shortest-path motion in three dimensions Information Processing Letters 20 5 1985 259 263
29. Clarkson K. Approximation algorithms for shortest path motion planning. In: Proceedings of the nineteenth annual ACM symposium on theory of computing. 1987. p. 5665. (Pubitemid 18643391)
30. Choi J, Sellen J, Yap C-K. Approximate Euclidean shortest path in 3-space. In: Proceedings of the tenth annual symposium on computational geometry. 1994. p. 418.
31. K. Polthier, and M. Schmies Mathematical visualization 1998 Springer Verlag [Chapter] Straightest geodesics on polyhedral surfaces, p. 391
32. Polthier K, Schmies M. Geodesic flow on polyhedral surfaces. In: Proceedings of eurographics-IEEE symposium on scientific visualization'99. 1999. p. 17988.
33. S.-Q. Xin, and G.-J. Wang Efficiently determining a locally exact shortest path on polyhedral surfaces Computer-Aided Design 39 12 2007 1081 1090 (Pubitemid 350166328)
34. Xin S-Q, He Y, Fu C-W. Efficiently computing exact geodesic loops within finite steps. IEEE Transactions on Visualization and Computer Graphics, vol. 99. Los Alamitos, CA, USA: IEEE Computer Society, 2011 [in press].
35. B. Pham Offset curves and surfaces: a brief survey Computer-Aided Design 24 4 1992 223 229
36. G. Elber, I.-K. Lee, and M.S. Kim Comparing offset curve approximation methods IEEE Computer Graphics and Applications 17 3 1997 62 71 (Pubitemid 127571471)
37. T. Maekawa An overview of offset curves and surfaces Computer-Aided Design 31 3 1999 165 173
38. E.W. Dijkstra A note on two problems in connexion with graphs Numerische Mathematik 1 1959 269 271