Analysis of quadric-surface-based solid models

The author discusses data representations and analytical tools commonly used in solid modelers for three analysis operations: boundary evaluation, image generation, and mechanical property calculation. The methods described are generally applicable to solid models bounded by quadric surfaces (e.g. planes, cylinders, spheres, and cones). Only methods applicable to constructive solid geometry or boundary representation modelers are considered. The author concludes with a review of ongoing research into other analysis operations appropriate for solid modeling representations.<<ETX>>

[1]  Herbert B. Voelcker,et al.  Graphical simulation & automatic verification of NC machining programs , 1986, Proceedings. 1986 IEEE International Conference on Robotics and Automation.

[2]  Joshua Z. Levin.  Mathematical models for determining the intersections of quadric surfaces , 1979 .

[3]  Alan E. Middleditch,et al.  Set-Theoretic Volume Model Evaluation and Picture-Plane Coherence , 1984, IEEE Computer Graphics and Applications.

[4]  Renato Perucchio,et al.  Toward automatic finite element analysis , 1987 .

[5]  Peter R. Atherton,et al.  A scan-line hidden surface removal procedure for constructive solid geometry , 1983, SIGGRAPH.

[6]  Mark S. Shephard,et al.  Finite Element Mesh Generation for Use with Solid Modeling and Adaptive Analysis , 1984 .

[7]  Brown,et al.  PADL-2: A Technical Summary , 1982, IEEE Computer Graphics and Applications.

[8]  Joshua Levin,et al.  A parametric algorithm for drawing pictures of solid objects composed of quadric surfaces , 1976, CACM.

[9]  A. Robson,et al.  Solid Analytical Geometry and Determinants , 1930 .

[10]  Scott D. Roth,et al.  Ray casting for modeling solids , 1982, Comput. Graph. Image Process..

[11]  James R. Miller,et al.  Sculptured Surfaces in Solid Models: Issues and Alternative Approaches , 1986, IEEE Computer Graphics and Applications.

[12]  R. Nagel,et al.  3-D Visual simulation , 1971 .

[13]  Robert B. Tilove,et al.  Set Membership Classification: A Unified Approach to Geometric Intersection Problems , 1980, IEEE Transactions on Computers.

[14]  Ramon F. Sarraga,et al.  Algebraic methods for intersections of quadric surfaces in GMSOLID , 1983, Comput. Vis. Graph. Image Process..

[15]  Peter R. Wilson,et al.  Conic Representations for Shape Description , 1987, IEEE Computer Graphics and Applications.

[16]  Joshua Zev Levin.  Quisp: a computer processor for the design and display of quadric-surface bodies , 1980 .

[17]  Aristides A. G. Requicha,et al.  Mathematical Foundations of Constructive Solid Geometry: General Topology of Closed Regular Sets , 1978 .

[18]  Herbert B. Voelcker,et al.  An introduction to MPL - A new machining process/Programming language , 1986, Proceedings. 1986 IEEE International Conference on Robotics and Automation.

[19]  J. Schwartz,et al.  Precise Implementation of Cad Primitives using Rational Parameterizations of Standard Surfaces , 1984 .

[20]  James D. Foley,et al.  Fundamentals of interactive computer graphics , 1982 .

[21]  Tony C. Woo,et al.  AN ALGORITHM FOR GENERATING SOLID ELEMENTS IN OBJECTS WITH HOLES , 1984 .

[22]  Ronald Goldman.  Two Approaches to a Computer Model for Quadric Surfaces , 1983, IEEE Computer Graphics and Applications.

[23]  Alan de Pennington,et al.  Automatic finite-element mesh generation from geometric models—A point-based approach , 1984, TOGS.

[24]  SatoHiroyuki,et al.  Fast image generation of construcitve solid geometry using a cellular array processor , 1985 .

[25]  C. H. Edwards,et al.  Calculus and Analytic Geometry , 1982 .

[26]  James R. Miller,et al.  Geometric approaches to nonplanar quadric surface intersection curves , 1987, TOGS.

[27]  Hiroyuki Sato,et al.  Fast image generation of construcitve solid geometry using a cellular array processor , 1985, SIGGRAPH '85.

[28]  Willem F. Bronsvoort,et al.  Two methods for improving the efficiency of ray casting in solid modelling , 1984 .

[29]  Wayne Tiller,et al.  Rational B-Splines for Curve and Surface Representation , 1983, IEEE Computer Graphics and Applications.

[30]  Aristides A. G. Requicha,et al.  Algorithms for computing the volume and other integral properties of solids. I. known methods and open issues , 1982, CACM.

[31]  Donald P. Greenberg,et al.  Improved Computational Methods for Ray Tracing , 1984, TOGS.

[32]  James E. Bobrow,et al.  NC machine tool path generation from CSG part representations , 1985 .

[33]  Burkard Wordenweber,et al.  Finite-Element Analysis for the Naive User , 1984 .

[34]  A.A.G. Requicha,et al.  Boolean operations in solid modeling: Boundary evaluation and merging algorithms , 1985, Proceedings of the IEEE.

[35]  Aristides A. G. Requicha,et al.  Depth-Buffering Display Techniques for Constructive Solid Geometry , 1986, IEEE Computer Graphics and Applications.

[36]  ARISTIDES A. G. REQUICHA,et al.  Representations for Rigid Solids: Theory, Methods, and Systems , 1980, CSUR.

[37]  Michael J. Bailey,et al.  The Vectorization of a Ray-Tracing Algorithm for Improved Execution Speed , 1985, IEEE Computer Graphics and Applications.

[38]  Aristides A. G. Requicha,et al.  Algorithms for computing the volume and other integral properties of solids. II. A family of algorithms based on representation conversion and cellular approximation , 1982, CACM.

[39]  H. Timmer,et al.  Computation of global geometric properties of solid objects , 1980 .