Abstract
We present efficient and accurate algorithms for Boolean combinations of solids composed of sculptured models. The boundary of each solid is represented as a collection of trimmed spline surfaces and a connectivity graph. Based on algorithms for trapezoidation of polygons, partitioning of polygons using polygonal chains, surface intersection of high degree spline surfaces and ray-shooting, the boundaries of the resulting solids and its connectivity graph after the Boolean operation are computed. We also present accurate representations of the intersection curves and boundary of the resulting solids. The resulting boundaries are used for interactive display and walkthrough applications. The system has been used to convert parts of a submarine storage and handling system model represented as more than 2, 000 CSG trees. The B-rep consists of more than 30, 000 trimmed spline surfaces and is displayed at interactive rates on the Pixel-Planes 5 graphics system.
Chapter PDF
References
S.S. Abi-Ezzi and L.A. Shirman. Tessellation of curved surfaces under highly varying transformations. Proceedings of Eurographics’91, pages 385–97, 1991.
C.L. Bajaj and A. Royappa. Triangulation and display of rational parametric surfaces. In Proceedings of Visualization’9j, pages 69–76, IEEE Computer Society, Los Alamitos, CA, 1994.
E. Cohen. Some mathematical tools for a modeler’s workbench. IEEE Computer Graphics and Applications, 3 (7): 63–66, 1983.
G. Farin. Curves and Surfaces for Computer Aided Geometric Design: A Practical Guide. Academic Press Inc., 1993.
C.M. Hoffmann. Geometric and Solid Modeling. Morgan Kaufmann, San Mateo, California, 1989.
M.E. Hohmeyer. A surface intersection algorithm based on loop detection. International Journal of Computational Geometry and Applications 1(4):473–490, 1991. Special issue on Solid Modeling.
S. Krishnan and D. Manocha. An efficient surface intersection algorithm based on the lower dimensional formulation. Technical Report TR94–062, Department of Computer Science, University of North Carolina, 1994.
S. Kumar and D. Manocha. Efficient rendering of trimmed NURBS surfaces. Computer-Aided Design, pages 509–521, 1995.
S. Kumar, D. Manocha, and A. Lastra. Interactive display of large scale NURBS models. In Proc. of ACM Interactive 3D Graphics Conference, pages 51–58, 1995.
S. Krishnan, A. Narkhede, and D. Manocha. Boole: A system to compute boolean combinations of sculptured solids. Technical Report TR95–008, Department of Computer Science, University of North Carolina, 1995.
W.L. Luken and Fuhua Cheng. Rendering trimmed NURB surfaces. Computer science research report 18669(81711), IBM Research Division, 1993.
D. Manocha. Solving polynomial systems for curve, surface and solid modeling. In ACM/SIGGRAPH Symposium on Solid Modeling, pages 169–178, 1993.
A. Rockwood, K. Heaton, and T. Davis. Real-time rendering of trimmed surfaces. In Proceedings of ACM Siggraph, pages 107–17, 1989.
A.A.G. Requicha. and J.R. Rossignac. Solid modeling and beyond. IEEE Computer Graphics and Applications, pages 31–44, September 1992.
M. Segal. Using tolerances to guarantee valid polyhedral modeling results. In Proceedings of ACM Siggraph, pages 105–114, 1990.
R. Seidel. Linear programming and convex hulls made easy. In Proc. 6th Ann. ACM Conf. on Computational Geometry, pages 211–215, Berkeley, California, 1990.
R. Seidel. A simple and fast randomized algorithm for computing trapezoidal decompositions and for triangulating polygons. Computational Geometry Theory 6 Applications, 1 (1): 51–64, 1991.
T.W. Sederberg and T. Nishita. Geometric hermite approximation of surface patch intersection curves. Computer Aided Geometric Design, 8: 97–114, 1991.
W. Tiller. Rational B-splines for curve and surface representation. IEEE Computer Graphics and Applications, 3 (6): 61–69, 1983.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1997 IFIP International Federation for Information Processing
About this chapter
Cite this chapter
Krishnan, S., Kumar, S., Manocha, D. (1997). Representation, Boundary Computation and Fast Display of CSG Models with NURBS Primitives. In: Pratt, M.J., Sriram, R.D., Wozny, M.J. (eds) Product Modeling for Computer Integrated Design and Manufacture. IFIP Advances in Information and Communication Technology. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-35187-2_29
Download citation
DOI: https://doi.org/10.1007/978-0-387-35187-2_29
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-5041-2887-2
Online ISBN: 978-0-387-35187-2
eBook Packages: Springer Book Archive