Accurate solid modeling using polyhedral approximations
- 1 May 1988
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Computer Graphics and Applications
- Vol. 8 (3) , 14-28
- https://doi.org/10.1109/38.510
Abstract
Although curved-surface solid modeling systems achieve a higher level of accuracy than faceted systems, they also introduce a host of topological, geometric, and numerical complications. A method for calculating accurate boundary representations of solid models is introduced that reduces the impact of these complications. The method uses a pair of bounding polyhedral approximations to enclose the boundary of each object. A structural analysis automatically determines where to make adaptive refinements to the polyhedrons to assure the topological validity of the results. Potential singularities are localized. The implementation is an experimental extension to the Geometric Design Processor (GDP) solid modeling system.Keywords
This publication has 24 references indexed in Scilit:
- Algebraic Geometry for Computer-Aided Geometric DesignIEEE Computer Graphics and Applications, 1986
- Comparison of three curve intersection algorithmsComputer-Aided Design, 1986
- Intersection of parametric surfaces by means of look-up tablesIEEE Computer Graphics and Applications, 1983
- An algorithm and data structure for 3D object synthesis using surface patch intersectionsACM SIGGRAPH Computer Graphics, 1982
- GRIN: Interactive Graphics for Modeling SolidsIBM Journal of Research and Development, 1981
- Introduction to Numerical AnalysisPublished by Springer Nature ,1980
- A Theoretical Development for the Computer Generation and Display of Piecewise Polynomial SurfacesPublished by Institute of Electrical and Electronics Engineers (IEEE) ,1980
- A surface display algorithmComputer-Aided Design, 1978
- A data-structure for the elimination of hidden surfaces by patch subdivisionComputer-Aided Design, 1975
- A modified Newton method for the solution of ill-conditioned systems of nonlinear equations with application to multiple shootingNumerische Mathematik, 1974