In the framework of Virtual CMM [1], virtual parts are proposed to be constructed as triangulated surface models. This paper presents a novel surface reconstruction method to the creation of virtual parts. It is based on the idea of identification and sculpting of concave regions of a Delaunay triangulation of the sample data. The proposed algorithm is capable of handling the reconstruction of surfaces with or without boundaries from unorganized points. Comparisons with other Delaunay-based algorithms show that it is more efficient in that it can optimally adapt to the geometric complexity of the sampled object. To validate the proposed algorithm, some detailed illustrations are given.
1.
Yau, H. T., and Kuo, C. C., 2002, “Virtual CMM and Virtual Part for Intelligent Dimensional Inspection,” 2002 Japan-USA Symposium on Flexible Automation, pp. 1289–1296.
2.
Hoppe, H., DeRose, T., Duchamp, McDonald, T., J., and Stuetzle, W., 1992, “Surface Reconstruction from Unorganized Points,” Proc. SIGGRAPH ’92, pp. 71–78.
3.
Amenta, N., Bern, M., and Kamvysselis, M., 1998, “A New Voronoi-based Surface Reconstruction Algorithm,” Proc. SIGGRAPH ’98, pp. 415–421.
4.
Amenta
, N.
, and Bern
, M.
, 1999
, “Surface Reconstruction by Voronoi Filtering
,” Discrete Comput. Geom.
, 22
, pp. 481
–504
.5.
Amenta, N., Choi, S., and Kolluri, R. V., 2001, “The Power Crust,” Proc. 6th ACM Sympos. on Solid modeling and applications, pp. 249–266.
6.
Amenta
, N.
, Choi
, S.
, and Kolluri
, R. K.
, 2001, “The Power Crust, Unions of Balls, and the Medial Axis Transform,” Computational Geometry: Theory and Applications, 19(2–3), pp. 127–153.7.
Dey
, T. K.
, Giesen
, J.
, Leekha
, N.
, and Wenger
, R.
, 2001, “Detecting Boundaries for Surface Reconstruction Using Co-cones,” Intl. J. Comput. Graphics & CAD/CAM, 16, pp. 141–159.8.
Dey, T. K., and Giesen, J., 2001, “Detecting Undersampling in Surface Reconstruction,” Proc. 17th ACM Sympos. on Comput. Geom, pp. 257–63.
9.
Dey, T. K., Giesen, J., Goswami, S., Hudson, J., Wenger, R., and Zhao, W., 2001, “Undersampling and Oversampling in Sample Based Shape Modeling,” Proc. IEEE Visualization 2001, pp. 83–90.
10.
Boissonnat
, J. D.
, 1984
, “Geometric Structures for Three-dimensional Shape Representation
,” ACM Trans. Graph.
, 3
(4
), pp. 266
–286
.11.
Edelsbrunner
, H.
, Kirkpatrick
, D. G.
, and Seidel
, R.
, 1983
, “On the Shape of a Set of Points in the Plane
,” IEEE Trans. Inf. Theory
, IT-29
, pp. 551
–559
.12.
Edelsbrunner, H., 1992, “Weighted Alpha Shapes,” Technical Report UIUCDCS-R-92-1760, Department of Computer Science, University of Illinois, Urbana-Champagne, IL.
13.
Edelsbrunner
, H.
, and Mucke
, E. P.
, 1994
, “Three-dimensional Alpha Shapes
,” ACM Trans. Graphics
, 13
(1
), pp. 43
–72
.14.
Bernardini
, F.
, Mittleman
, J.
, Rushmeier
, H.
, Silva
, C.
, and Taubin
, G.
, 1999
, “The Ball-Pivoting Algorithm for Surface Reconstruction
,” IEEE Trans. Vis. Comput. Graph.
, 5
(4
), pp. 349
–359
.15.
Petitjean
, S.
, and Boyer
, E.
, 2001, “Regular and Non-regular Point Sets: Properties and Reconstruction,” Comput. Geom. Theory Appl., 19, pp. 101–126.16.
Huang
, J.
, and Menq
, C. H.
, 2002
, “Combinatorial Manifold Mesh Reconstruction and Optimization from Unorganized Points with Arbitrary Topology
,” Comput.-Aided Des.
, 34
(2
), pp. 149
–165
.17.
Bajaj, C., Bernardini, F., and Xu, G., 1995, “Automatic Reconstruction of Surfaces and Scalar Fields from 3D Scans,” Proc. SIGGRAPH ’95, pp. 109–118.
18.
Bajaj, C., Bernardini, F., Chen, J., and Schikore, D., 1997, “Triangulation-based 3D Reconstruction Methods,” Proc. 13th ACM Sympos. on Comput. Geom., pp. 484–484.
19.
Bajaj
, C.
, Bernardini
, F.
, and Xu
, G.
, 1997
, “Reconstruction of Surfaces and Surfaces-on-Surfaces from Unorganized Three-Dimensional Data
,” Algorithmica
, 19
, pp. 243
–261
.20.
Bernardini
, F.
, Bajaj
, C.
, Chen
, J.
, and Schikore
, D.
, 1999, “Automatic Reconstruction of 3D CAD Models from Digital Scans,” Int. J. on Comp. Geom. and Appl., 9(4–5), pp. 327–370.21.
Curless, B., and Levoy, M., 1996, “A Volumetric Method for Building Complex Models from Range Images,” Proc. SIGGRAPH ’96, pp. 303–312.
22.
Boissonnat, J-D., and Cazals, F., 2000, “Smooth Surface Reconstruction via Natural Neighbor Interpolation of Distance Functions,” Proc. 16th. ACM Sympos. on Comput. Geom, pp. 223–232.
23.
Bentley
, L.
, 1975
, “Multidimensional Binary Search Trees Used for Associative Searching
,” Commun. ACM
, 18
(9
), pp. 509
–517
.24.
Edelsbrunner
, H.
, and Guoy
, D.
, 2002, “Sink-insertion for Mesh Improvement,” Int. J. Found. Comput. Sci., 13, pp. 223–242.25.
Yau
, H. T.
, Kuo
, C. C.
, and Yeh
, C. H.
, 2002
, “Extension of Surface Reconstruction Algorithm to the Global Stitching and Repairing of STL Models
,” Comput.-Aided Des.
, 35
(5
), pp. 477
–486
.26.
Jun
, C. S.
, Kim
, D. S.
, and Park
, S.
, 2002
, “A New Curve-based Approach to Polyhedral Machining
,” Comput.-Aided Des.
, 34
(5
), pp. 379
–389
.27.
Aurenhammer
, F.
, 1991
, “Voronoi Diagrams—A Survey of a Fundamental Geometric Data Structure
,” ACM Comput. Surv.
, 23
(3
), pp. 345
–405
.28.
http://www.cgal.org/
29.
Boissonnat, J. D., Devillers, O., Teillaud, M., and Yvinec, M., 2000, “Triangulations in CGAL,” Proc. 14th ACM Sympos. On Comput. Geom., pp. 11–18.
30.
Bro¨nnimann, H., Burnikel, C., and Pion S., 1998, “Interval Arithmetic Yields Efficient Dynamic Filters for Computational Geometry,” Proc. 14th. ACM Sympos. on Comput. Geom., pp. 165–174.
31.
Devillers, O., 1998, “Improved Incremental Randomized Delaunay Triangulation,” Proc. 14th ACM Sympos. Comput. on Geom., pp. 106–115.
32.
http://www.cs.utexas.edu/users/amenta/powercrust/welcome.html
33.
http://www.cis.ohio-state.edu/∼tamaldey/cocone.html
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