Computer graphics processing and selective visual display system – Computer graphics processing – Three-dimension
Reexamination Certificate
2005-10-18
2005-10-18
Wong, Don (Department: 2821)
Computer graphics processing and selective visual display system
Computer graphics processing
Three-dimension
C382S133000
Reexamination Certificate
active
06956568
ABSTRACT:
Umbilics of two surfaces are compared and it is determined from this comparison whether the suspect surface is a copy of the original surface based on the comparison. Comparing umbilics includes determining whether locations of the umbilics of the suspect surface match within a specified margin umbilics of the original surface, and determining whether pattern types of umbilics of the suspect surface match pattern types of corresponding umbilics of the original surface. A “weak” test may be performed, in which corresponding points on the two surfaces are compared, wherein the comparison of umbilics is performed if corresponding points of the two surfaces are located within a specified margin of each other. The points may be gridpoints on wireframes, which in turn may be based on lines of curvature of the surfaces. Comparing umbilics is performed if it is determined that each surface has at least one umbilic. Further still, an “intermediate” test may be performed which includes, for each surface, computing the principal directions of lines of curvature at each grid point. The computed directions of lines of curvature for corresponding gridpoints on the surfaces are compared. A determination is made as to whether the suspect surface is a copy of the original surface, based on the comparison.
REFERENCES:
patent: 5238860 (1993-08-01), Sawada et al.
patent: 6148114 (2000-11-01), Han
patent: 6636623 (2003-10-01), Nelson et al.
patent: 2003/0031352 (2003-02-01), Nelson et al.
patent: 2003/0135846 (2003-07-01), Jayaram et al.
Abrams, S.L., et al., “The Geometric Modeling and Interrogation System Praxiteles,”Journal of Ship Production, 11: 117-132 (1995).
Abrams, S.L., et al., “Efficient and reliable methods for rounded-interval arithmetic,”Computer-Aided Design, 30(8): 657-665 (1998).
Asano, T., et al., “Practical Use of Bucketing Techniques in Computational Geometry.” InComputational Geometry, G.T. Toussaint, editor (North Holland: Elsevier Science Publishers B.V.), pp. 153-195 (1985).
Benedens, O., “Geometry-Based Watermaking of 3D Models,”IEEE Computer Graphics and Applications, 46-55 (1999, Jan./Feb.).
Borgefors, G., “Distance Transformations in Arbitrary Dimensions,”Computer Vision, Graphics, and Image Processing, 27:321-345 (1984).
Cormen, T.H., “Sorting in Linear Time.” InIntroduction to Algorithms, MIT Press, (NY: McGraw Hill), pp. 180-184 (1990).
Crandall, S.H., et al., “Dynamical Properties of a Rigid Body.” InDynamics of Mechanical and Electromechanical Systems, Stephen H. Crandall, editor (NY: McGraw-Hill Inc.), pp. 170-175 (1968).
Fornaro, C., and Sanna, A., “Public key watermarking for authentication of CSG models,”Computer-Aided Design, 32: 727-735 (2000).
Hilbert, D., and Cohn-Vossen, S., “Ansch Au Liche Geometrie” [“Geometry and the Imagination”], (NY: Chelsea Publishing Company), pp. 202-203 (1952).
Hu, C.-Y., “Towards Robust Interval Solid Modeling of Curved Objects.” Unpublished PhD thesis, Massachusetts Institute of Technology, Cambridge, MA. (1995).
Hu, Chun-Yi, et al., “Robust interval algorithm for surface intersections,”Computer-Aided Design, 29(9): 617-627 (1997).
Hu, Chun-Yi, et al., “Robust interval algorithm for curve intersections,”Computer-Aided Design, 28(6/7): 495-506 (1996).
Kanai, S., et al., “Digital Watermarking for 3D Polygons using Multiresolution Wavelet Decomposition.” InProceedings of the Sixth IFIP WG5. 2/GI International Workshop on Geometric Modelling: Fundamentals and Applications(Tokyo), pp. 296-307 (1998).
Maekawa, T., “Robust Computational Methods for Shape Interrogation.” Unpublished PhD thesis, Massachusetts Institute of Technology, Cambridge, MA. (1993).
Maekawa, T. and Patrikalakis, N.M., “Computation of singularities and intersections of offsets of planar curvers,”Computer Aided Geometric Design, 10: 407-429 (1993).
Maekawa, T., and Patrikalakis, N.M., “Interrogation of differential geometry properties for design and manufacture,”The Visual Computer, 10: 216-237 (1994).
Maekawa, T., et al., “Umbilics and lines of curvature for shape interrogation,”Computer Aided Geometric Design, 13: 133-161 (1996).
Mortenson, M.E.,Geometric Modeling, (NY: John Wiley & Sons) (1985).
Ohbuchi, R., et al., “Watermarking Three-Dimensional Polygonal Models Through Geometric and Topological Modifications,”IEEE Journal on Selected Areas in Communications, 16(4): 551-560 (1998).
Ohbuchi, R., et al., “A Shape-Preserving Data Embedding Algorithm for NURBD Curves and Surfaces.” InProceedings of Computer Graphics International, CGI '99, pp. 180-187 (1999).
Patrikalakis, N.M., and Bardis, L., “Localization of Rational B-Spline Surfaces,”Engineering with Computers, 7: 237-252 (1991).
Pegna, J. and Wolter, F.-E., “Surface Curve Design by Orthogonal Projection of Space Curves Onto Free-Form Surfaces,”Journal of Medical Design, 118: 45-52 (1996).
Praun, E., et al., “Robust Mesh Watermarking,”Computer Graphics Proceedings, Annual Conference Series, 49-56 (1999).
Sherbrooke, E.C., and Patrikalakis, N.M., “Computation of the solutions of nonlinear polynomial systems,”Computer Aided Geometric Design, 10: 379-405 (1993).
Yeo, B.-L., and Yeung, M.M., “watermarking 3D Objects for Verification,”IEEE Computer Graphics and Applications, pp. 36-45 (1999, Jan./Feb.).
Zhou, J., et al., “Computation of Stationary Points of Distance Fuctions,”Engineering with Computers, 9: 231-246 (1993).
Maekawa Takashi
Masuda Hiroshi
Patrikalakis Nicholas M.
Wolter Franz-Erich
Cao Huedung X.
Massachussetts Institute of Technology
LandOfFree
Shape-intrinsic watermarks for 3-D solids does not yet have a rating. At this time, there are no reviews or comments for this patent.
If you have personal experience with Shape-intrinsic watermarks for 3-D solids, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Shape-intrinsic watermarks for 3-D solids will most certainly appreciate the feedback.
Profile ID: LFUS-PAI-O-3450493