Solid-modeling system using topology directed subdivision for de

Details Solid-modeling system using topology directed subdivision for de Solid-modeling system using topology directed subdivision for de

1989-02-09

1989-12-26

Gruber, Felix D.

Boots, shoes, and leggings

364522, G06F 1560, G06F 1572

Patent

active

048902420

ABSTRACT:
A system for topology directed subdivision of a pair of surfaces to identify intersecting portions thereof includes the steps of obtaining a pair of surfaces from a main pool of surface representations and performing a mutual point exclusion test to determine if the surfaces may have an intersection. For those pairs of surfaces possibly having an intersection, the transversality of the surface is checked. If tranversal, the intersection set is computed. For those pairs which are not transversal, recursive subdivision is performed until transversality is established or until a flatness criteria is met. A parallel processing system including a master processor and a plurality of slave processors performs the subdivision operation on the surfaces in a parallel fashion.

REFERENCES:
patent: 4451895 (1984-05-01), Sliwkowski
patent: 4459655 (1984-07-01), Willemin
patent: 4491906 (1985-01-01), Kishi et al.
patent: 4549275 (1985-10-01), Sukonick
patent: 4618924 (1986-10-01), Hinds
patent: 4698766 (1987-10-01), Entwistle et al.
Bjorck, Ake, et al., "Numerical Methods for Computing Angles Between Subspaces," Mathematics of Computation, vol. 27, No. 123, Jun., 1973, pp. 579-594.
Casale, Malcolm, et al., "An Overview of Analytical Solid Modeling," IEEE CG&A, Feb., 1985, pp. 45-56.
Catmull, E., "A Subdivision Algorithm for Computer Display of Curved Surfaces," University of Utah Com. Sci. Dept., UTEC-CSC-74-133, (1974).
Cohen, Elaine, et al., "Discrete B-Splines and Subdivision Techniques in Computer-Aided Geometric Design and Computer Graphics," Computer Graphics and Image Processing, vol. 14, 1980, pp. 87-111.
Comba, Paul, "A Procedure for Detecting Intersections of Three-Dimensional Objects," Journal of the ACM, vol. 15, Jul., 1968, pp. 354-366.
De Boor, Carl, "On Calculating with B-Splines," Journal of Approximation Theory, vol. 6, 1972, pp. 50-62.
Farouki, Rida, et al., "A Hierarchy of Geometric Forms," IEEE CG&A, May, 1985, pp. 51-78.
Houghton, Elizabeth, et al., "Implementation of a Divide-and-Conquer Method for Intersection of Parametric Surfaces," Computer Aided Geometric Design, vol. 2, 1985, pp. 173-183.
Lane, Jeffrey, et al., "A Generalized Scan Line Algorithm for the Computer Display of Parametrically Defined Surfaces," Computer Graphics and Image Processing, vol. 11, 1979, pp. 290-297.
Lane, Jeffrey, et al., "A Theoretical Development for the Computer Generation and Display of Piecewise Polynomial Surfaces," Transactions on Pattern Analysis and Machine Intelligence, vol. PAMI-2, No. 1, Jan., 1980, pp. 35-46.
Lee, Randy, et al., "Intersection of Parametric Surfaces and a Plane," IEEE CG&A, Aug., 1984, pp. 48-51.
Levin, Joshua, "A Parametric Algorithm for Drawing Pictures of Solid Objects Composed of Quadric Surfaces," Comm. of the ACM, vol. 19, No. 10, Oct., 1976, pp. 555-563.
Levin, Joshua, "Mathematical Models for Determining the Intersections of Quadric Surfaces," Computer Graphics and Imaging Processing, vol. 11, 1979, pp. 73-87.
Lozano-Perez, Tomas, et al., "An Algorithm for Planning Collision-Free Paths Among Polyhedral Obstacles," Comm. of the ACM, vol. 22, No. 10, Oct., 1979, pp. 560-570.
Meagher, Donald, "Geometric Modeling Using Octree Encoding," Computer Graphics and Image Processing, vol. 19, 1982, pp. 129-147.
Morgan, Alexander, "A Method for Computing All Solutions to Systems of Polynomial Equations," ACM Transactions on Mathematical Software, vol. 9, No. 1, Mar., 1983, pp. 1-17.
Mudur et al., "Interval Method for Processing Geometric Objects," IEEE CG&A, Feb., 1984, pp. 7-17.
Peng, Q. S., "An Algorithm for Finding the Intersection Lines Between Two B-Spline Surfaces," CAD, vol. 16, No. 4, Jul., 1984, pp. 191-196.
Requicha, A. A., et al., "Solid Modeling: Current Status and Research Directions," IEEE CG&A, Oct., 1983, pp. 25-37.
Sarraga, Ramon, "Algebraic Methods for Intersections of Quadric Surfaces in GMSOLID," Computer Vision, Graphics and Image Processing, vol. 22, 1983, pp. 222-238.
Segal, Mark, et al., "Consistent Calculations for Solid Modeling," Proc. of the Symposium on Computational Geometry, Jun., 1985, pp. 29-38.
Sinha, Pradeep, et al.,

Affiliated with

Also associated with

Rating

Solid-modeling system using topology directed subdivision for de does not yet have a rating. At this time, there are no reviews or comments for this patent.

If you have personal experience with Solid-modeling system using topology directed subdivision for de, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Solid-modeling system using topology directed subdivision for de will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFUS-PAI-O-1580650