Constructing medial axis transform of extruded and revolved 3D objects with free-form boundaries

CAD Computer Aided Design

Volumn 37, Issue 13, 2005, Pages 1370-1387

  Ramanathan, M ^a,b   Gurumoorthy, B ^a  

^a INDIAN INSTITUTE OF SCIENCE   (India)

^b TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

Free form boundaries; Medial axis transform; Skeleton; Voronoi diagram

Indexed keywords

ALGORITHMS; COMPUTATIONAL GEOMETRY; FINITE ELEMENT METHOD; IMAGE ANALYSIS; MATHEMATICAL TRANSFORMATIONS; THREE DIMENSIONAL; TOPOLOGY;

FREE FORM BOUNDARIES; MEDIAL AXIS TRANSFORM; SKELETON; VORONOI DIAGRAM;

COMPUTER AIDED DESIGN;

EID: 22944433814     PISSN: 00104485     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cad.2005.01.006     Document Type: Article

References (30)

1. H. Blum A transformation for extracting new descriptors of shape W. Dunn Models for the perception of speech and visual form 1967 MIT Press Cambridge 362 381
2. H. Blum Biological shape and visual science (Part I) J Theor Biol 38 1973 205 287
3. G.S. Baja, and E. Thiel (3-4)-Weighted skeleton decomposition for pattern representation and description Pattern Recognit 27 8 1994 1039 1049
4. U. Montanari Continuous skeletons from digitized images J Assoc Comput Mach 16 4 October 1969 534 549
5. H.N. Gursoy, and N.M. Patrikalakis An automatic coarse and finite surface mesh generation scheme based on medial axis transform: part 1 algorithms Eng Comput 8 1992 121 137
6. C.G. Armstrong Modeling requirements for finite element analysis Comput Aided Des 26 7 July 1994 573 578
7. Ramanathan M. Medial axis transform for the prediction of shrinkage and distortion in Castings, MSc Thesis, Department of Mechanical Engineering, Indian Institute of Science, Bangalore, India.
8. J. O'Rourke Computational geometry in C 1993 Cambridge University Press Cambridge
9. J.M. Reddy, and G.M. Turkiyyah Computation of 3D skeletons using generalized delaunay triangulation technique Comput Aided Des 27 9 1995 677 694
10. S. Gelston, and D. Dutta Boundary surface recovery from skeleton curves and surfaces Comput Aided Geometric Des 12 1995 27 51
11. Wolter FE. Cut locus and medial axis in global shape interrogation and representation, design laboratory Memorandum 92-2, Department of Ocean Engineering, MIT, 1992.
12. D.J. Sheehy, C.G. Armstrong, and D.J. Robinson Shape description by medial surface construction IEEE Trans Visualization Comput Graphics 2 1 1996 62 72
13. G.M. Turkiyyah, D.W. Storti, M. Ganter, H. Chen, and M. Vimawala An accelerated triangulation method for computing skeletons of free-form solid models Comput Aided Des 29 1 1997 5 19
14. R. Farouki, and R. Ramamurthy Specified-precision computation of curve/curve bisectors Int J Comput Geometry Appl 8 5-6 1998 599 617
15. E.C. Sherbrooke, N.M. Patrikalakis, and E. Brisson Computation of the medial axis transform of 3-D polyhedra Proceedings of the solid modeling and applications'95 1995 pp. 187-199
16. E.C. Sherbrooke, N.M. Patrikalakis, and E. Brisson An algorithm for medial axis transform of 3-D polyhedral solids IEEE Trans Visualization Comput Graphics 2 1 1996 44 61
17. Culver T, Keyser J, Manocha D. Accurate computation of the medial axis of a polyhedron, in Proceedings of the symposium on solid modeling and applications, Ann Arbor, Michigan, 1999, pp. 179-190.
18. D. Dutta, and C.M. Hoffmann On the skeleton of simple CSG objects J Mech Des Trans ASME 115 1993 87 94
19. G. Elber, and M. Kim The bisector surface of rational space curves ACM Trans Graphics 17 1 January 1998 32 39
20. G. Elber, and M. Kim Computing rational bisectors IEEE Comput Graphics Appl 1999 76 81
21. G. Elber, and M. Kim Rational bisectors of CSG primitives Proceedings of the symposium on solid modeling and applications 1999 Ann Arbor Michigan pp. 159-166
22. D. Lavender, A. Bowyer, J. Davenport, A. Wallis, and J. Woodwark Voronoi diagrams of set theoretic solid models IEEE Comput Graphics Appl September 1992 69 77
23. Y.G. Lee, and K. Lee Computing the medial surface of a 3-D boundary representation model Adv Eng Software 28 1997 593 605
24. M. Etzion, and Ari Rappoport Computing Voronoi skeletons of a 3-D polyhedron by space subdivision Comput Geometry Theory Appl 21 2002 87 120
25. J.J. Chou Voronoi diagrams for planar shapes IEEE Comput Graphics Appl 1995 52 59
26. H. Blum, and R.N. Nagel Shape description using weighted symmetric axis features Pattern Recognit 10 1978 167 180
27. M. Ramanathan, and B. Gurumoorthy Constructing medial axis transform of planar domains with curved boundaries Comput Aided Des 35 7 2003 619 632
28. B.K. Choi, and C.S. Jun Ball-end cutter interference avoidance in NC machining of sculptured surfaces Comput Aided Des 21 6 1989 371 378
29. D.F. Rogers, and J.A. Adams Mathematical elements for computer graphics 1990 McGraw-Hill Publishing Company New York
30. M.P. do Carmo Differential geometry of curves and surfaces 1976 Prentice-Hall, Inc. Englewoods Cliffs, NJ