Duplex fitting of zero-level and offset surfaces

CAD Computer Aided Design

Volumn 41, Issue 4, 2009, Pages 268-281

  Liu, Shengjun ^a,b   Wang, Charlie C L ^a  

^a CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

^b CENTRAL SOUTH UNIVERSITY   (China)

Author keywords

CAD CAM; Hollowed model; Implicit surface; Offset surface; Surface reconstruction

Indexed keywords

ADAPTIVE SLICING; CAD/CAM; COARSE TO FINES; COMPACTLY SUPPORTED RADIAL BASIS FUNCTIONS; COMPUTATIONAL PROCEDURES; EXISTING METHODS; HIERARCHICAL METHODS; HOLLOWED MODEL; IMPLICIT FUNCTIONS; IMPLICIT SURFACE; LARGE PARTS; MISSING DATUM; OFFSET SURFACE; POINT SETS; SCATTERED DATUM;

CONCURRENT ENGINEERING; JOB ANALYSIS; RADIAL BASIS FUNCTION NETWORKS; RAPID PROTOTYPING; RESTORATION;

SURFACE RECONSTRUCTION;

EID: 64249115156     PISSN: 00104485     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cad.2008.10.008     Document Type: Article

References (48)

1. Ohtake Y., Belyaev A., Alexa M., Turk G., and Seidel H. Multi-level partition of unity implicits. ACM Transaction on Graphics 22 3 (2003) 463-470
2. Ohtake Y., Belyaev A., and Seidel H. 3D scattered data interpolation and approximation with multilevel compactly supported RBFs. Graphical Models 67 (2005) 150-165
3. Rossignac J.R., and Requicha A.A.G. Offsetting operations in solid modelling. Computer Aided Geometry Design 3 2 (1986) 129-148
4. Varadhan G, Manocha D. Accurate minkowski sum approximation of polyhedral models. In: Proceedings of pacific graphics conference 2004. p. 392-401
5. Forsyth M. Shelling and offsetting bodies. In: Proceedings of the ACM symposium on solid modeling and applications. 1995. p. 373-81
6. Qu X., and Stucker B. A 3d surface offset method for stl-format models. Rapid Prototyping Journal 9 3 (2003) 133-141
7. Lien JM, Amato NM. Approximate convex decomposition of polyhedra. In: Proceedings of the ACM symposium on solid and physical modeling. 2007. p. 121-31
8. Cohen J, Varshney A, Manocha D, Turk G, Weber H, Agarwal P. et al. Simplification envelopes. In: Proceedings of ACM SIGGRAPH. 1996. p. 119-28
9. Breen DE, Mauch S. Generating shaded offset surfaces with distance, closest-point and color volumes. In: Proceedings of the international workshop on volume graphics. 1999. p. 307-20
10. Breen D.E., Mauch S., and Whitaker R.T. 3D scan conversion of CSG models into distance volumes. Proceedings of the 1998 IEEE symposium on Volume visualization (1998), ACM Press, New York (USA) 7-14
11. Chen Y, Wang H, Rosen DW, Rossignac J. Filleting and rounding using a point-based method. In: DETC'05 proceedings. 2005
12. Chen Y, Wang H, Rosen DW, Rossignac J. A Point-based offsetting method of polygonal meshes. Technical report. 2005
13. Huang J., and Crawfis R. Adaptively represented complete distance fields. Geometric modeling for scientific visualization (2002)
14. Huang J, Li Y, Crawfis R, Lu SC, Liou SY. A complete distance field representation. In: Proceedings of the conference on visualization'01. 2001. p. 247-54
15. Pavic D, Kobbelt L. High-resolution volumetric computation of offset surfaces with feature presentation. In: Proceedings of eurographics 2008
16. Hoppe H, Derose T, Duchamp T, Mcdonald J, Stuetzle W. Surface reconstruction from unorganized points. In: Proceedings of ACM SIGGRAPH. 1992. p. 71-8
17. Curless B, Levoy M. A volumetric method for building complex models from range images. In: Proceedings of SIGGRAPH 1996. p. 303-12
18. Whitaker R. A level-set approach to 3d reconstruction from range data. In: Proceedings of IJCV 1998. p. 203-31
19. Carr J, Beatson R, Cherrie H, Mitchel T, Fright W, Mccallum B. et al. Reconstruction and representation of 3D objects with radial basis functions. In: Proceedings of ACM SIGGRAPH 2001. p. 67-76
20. Davis J, Marschner SR, Garr M, Levoy M. Filling holes in complex surfaces using volumetric diffusion. In: First international symposium on 3d data processing, visualization, and transmission. 2002. p. 428-38
21. Ohtake Y, Belyaev A, Seidel H. 3D scattered data approximation with adaptive compactly supported radial basis functions. In: Proceedings of the shape modeling international. 2004. p. 31-9
22. Turk G., and O'brien J. Modelling with implicit surfaces that interpolate. ACM Transaction on Graphics 21 4 (2004) 855-873
23. Sethian J.A. Level set methods and fast marching methods. second ed. (1999), Cambridge University Press, Cambridge
24. Turk G, Brien JO. Shape transformation using variational implicit surfaces. In: Proceedings of ACM SIGGRAPH 1999. p. 335-342
25. Frisken SF, Perry RN, Rockwood A, Jones TR. Adaptively sampled distance fields: A general representation of shape for computer graphics. In: Proceedings of ACM SIGGRAPH 2000. p. 249-54
26. Zhao H., and Osher S. Visualization, analysis and shape reconstruction of unorganized data sets. In: Osher S., and Paragios N. (Eds). Geometric level set methods in imaging, vision and graphics (2002), Springer, Berlin
27. Dinh HQ, Slabaugh G, Turk G. Reconstructing surfaces using anisotropic basis functions. In: International conference on computer vision. 2001. p. 606-13
28. Dinh H.Q., Turk G., and Slabaugh G. Reconstructing surfaces by volumetric regularization. IEEE Transactions on Pattern Analysis and Machine Intelligence 24 10 (2002) 1358-1371
29. Morse BS, Yoo TS, Rheingans P, Chen DT, Subramanian KR. Interpolating implicit surfaces from scattered surface data using compactly supported radial basis functions. In: Shape modeling international 2001. 2001. p. 89-98
30. Alexa M, Behr J, Cohen-Or D, Fleishman S, Levin D, Silva CT. Point set surfaces. In: Proceedings of IEEE visualization 2001. p. 21-8
31. Amenta N., and Kil Y. Defining point-set surfaces. ACM Transactions on Graphics 23 3 (2004) 264-270
32. Levin D. Mesh-independent surface interpolation. Geometric modeling for scientific visualization (2003), Springer, Berlin
33. In: Bloomenthal J. (Ed). Introduction to implicit surfaces (1997), Morgan Kaufmann, Los Altos
34. Dyn N., Levin D., and Rappa S. Numerical procedures for global surface fitting of scattered data by radial functions. SIAM Journal on Scientific and Statistical Computing 7 (1986) 639-659
35. Schaback R. Creating surfaces from scattered data using radial basis functions. In: Daehlen M., Lyche T., and Schumaker L. (Eds). Mathematical methods for curve and surfaces (1995), Vanderbilt University Press, Nashville 477-496
36. Wu Z. Multivariate compactly supported positive definite radial functions. Advances in Computational Mathematics 49 (1995) 283-292
37. Wendland H. Piecewise polynomial, positive definite and compactly supported radial basis functions of minimal degree. Advances in Computational Mathematics 4 (1995) 389-396
38. Kojekine N., Hagiwara I., and Savchenko V. Software tools using CSRBFs for processing scattered data. Computers and Graphics 27 2 (2003) 309-317
39. Goldman R. Curvature formulas for implicit curves and surfaces. Computer Aided Geometric Design 22 (2005) 632-658
40. Kulkarni P., and Dutta D. An accurate slicing procedure for layered manufacturing. Computer Aided Design 28 9 (1996) 683-697
41. Yang P., and Qian X. Adaptive slicing of moving least squares surfaces: Toward direct manufacturing from point cloud data. ASME Transactions Journal of Computing and Information Science in Engineering 8 3 (2008)
42. Cignoni P., Rocchini C., and Scopigno R. Metro: Measuring error on simplified surfaces. Computer Graphics Forum 17 2 (1998) 167-174
43. Lorensen W.E., and Cline H.E. Marching cubes: A high resolution 3D surface construction algorithm. Computer Graphics 21 3 (1987) 163-169
44. Bloomenthal J. An implicit surface polygonizer. Graphics Gems IV 1 (1994) 324-349
45. Jones T.R., Durand F., and Desbrun M. Non-iterative, feature-preserving mesh smoothing. ACM Transaction on Graphics 21 3 (2003) 943-949
46. Buatois L, Caumon G, Levy B. Concurrent number cruncher - A GPU implementation of a general sparse linear solver. International Journal of Parallel, Emergent and Distributed Systems; 2008 [in press]
47. Marching squares. http://www.polytech.unice.fr/~lingrand/MarchingCubes/algo.html#squar
48. SolidWorks. http://www.solidworks.com