Abstract
Geometric modelling of physical solid objects is rapidly becoming a well-established interdisciplinary field, whose importance for robotics and automation is widely acknowledged both in academia and industry. The scientific literature in the field has increased dramatically, the first two textbooks that address solid modelling have been published [Mortenson 1985, Mäntylä 1988], solid modelling systems offered by many vendors are being used industrially in increasing numbers, and market projections for the technology are bright [Brown 1986, Marks 1986]. The fundamental concepts of solid modelling, as well as the state of the art in the early 1980s are described in [Requicha & Voelcker 1982, 1983]. The present paper assesses the progress in solid modelling and its applications over the last five years. The literature citations below are meant to be representative rather than exhaustive.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
F. Arbab, “Examples of geometric reasoning with Oar”, Computer Science Dept., University of Southern California, 1988.
D. Ayala, P. Brunei, R. Juan, and I. Navazo, “Object representation by means of nonminimal division quadtrees and octrees”, ACM Trans. on Graphics, Vol. 4, No. 1, pp. 41–59, January 1985.
C. Bajaj and M.-S. Kim, “Generation of configuration space obstacles I: The case of a moving sphere”, IEEE J. Robotics and Automation, Vol. 4, No. 1, pp. 94–99, February 1988.
C. L. Bajaj, C. M. Hoffmann, J. E. Hopcroft, and R. E. Lynch, “Tracing surface intersections”, Tech. Rept. CSD-TR-728, Computer Science Dept., Purdue University, December 1987.
R. E. Barnhill, G. Farin, M. Jordan and B. R. Piper, “Surface/surface intersection”, Computer Aided Geometric Design, Vol. 4, No. 1–2, pp. 3–16, July 1987.
A. H. Barr, “Global and local deformations of solid primitives”, ACM Computer Graphics, Vol. 18, No. 3, pp. 21–30, July 1984. (Proc. SIGGRAPH ’84.)
J. E. Bobrow, “NC machine tool path generation from CSG part representations”, Computer-Aided Design, Vol. 17, No. 2, pp. 69–76, March 1985.
V. J. Brown, “Market status and trends in solid modeling”, Proc. Solid Modeling ’86, Boston, MA, October 20–22, 1986.
B. Brüderlin, “Constructing three-dimensional geometric objects defined by constraints”, Proc. 1986 ACM Workshop on Interactive 3D Graphics, Chapel Hill, NC, October 23–24, 1986, pp. 111–129.
W. C Burkett, “PDDI approach to dimensioning and tolerancing a solid model”, Report P-85-ASPP-02, CAM-I, Inc., Arlington, TX, July 10, 1985.
S. A. Cameron, “Modelling solids in motion”, Ph.D. Dissertation, Univ. of Edinburgh, 1984.
S. A. Cameron and R. K. Culley, “Determining the minimum translational distance between two convex polyhedra”, Proc. 1986 IEEE Intl. Conf. on Robotics and Automation, San Francisco, CA, pp. 591–596, April 7–10, 1986.
J. Canny, “Collision detection for moving polyhedra”, IEEE Trans. on Pattern Analysis and Machine Intelligence, Vol. PAMI-8, No. 2, pp. 200–209, March 1986.
I. Carlbom, I. Chakravarty, and D. Vanderschel, “A hierarchical data structure for representing the spatial decomposition of 3-D objects”, IEEE Computer Graphics and Applications, Vol. 5, No. 4, pp. 24–31, April 1985.
J. C. Cavendish, D. A. Field, and W. H. Frey, “An approach to automatic three-dimensional finite element mesh generation, Intl. Journal Numerical Methods in Engineering, Vol. 21, pp. 329–347,1985.
S. C. Chan and H. B. Voelcker, “An introduction to MPL — A new machining process/programming language”, Proc. 1986 IEEE Intl. Conf. on Robotics and Automation, San Francisco, CA, pp. 333–344, April 7–10,1986.
G. A. Crocker and W. F. Reinke, “Boundary evaluation of non-convex primitives to produce parametric trimmed surfaces”, ACM Computer Graphics, Vol 21, No. 4, pp. 129–136, July 1987. (Proc. SIGGRAPH ’87.)
R. K. Culley and K. G. Kempf, “A collision detection algorithm based on velocity and distance bounds”, Proc. 1986 IEEE Intl. Conf. on Robotics and Automation, San Francisco, CA, pp. 1064–1069, April 7–10, 1986.
M. R. Cutkosky, J. M. Tenenbaum and D. Müller, “Features in process-based design”, ASME Computers in Engineering Conf., San Francisco, CA, August 1–3, 1988.
E. Dombre, A. Fournier, C. Quaro, and P. Borrel, “Trends in CAD/CAM systems for robotics”, Proc. 1986 IEEE Intl. Conf. on Robotics and Automation, San Francisco, CA, pp. 1913–1918, April 7–10, 1986.
B. R. Donald, “Robot motion planning with uncertainty in the geometric model of the robot and environment: a formal framework for error detection and recovery”, Proc. 1986 IEEE Intl. Conf. on Robotics and Automation, San Francisco, CA, April 7–10, 1986, pp. 1588–1593.
B. Dufay and C Laugier, “Geometrical reasoning in automatic grasping and contact analysis, in T. M. R. Ellis and O. Semenkov, Eds., Advances in CAD/CAM. Amsterdam: North-Holland, 1983, pp. 473–482. (Proc. Prolamat ’82.)
H. F. Durrant-Whyte, “Uncertain geometry in robotics”, IEEE J. Robotics and Automation, Vol. 4, No. 1, pp. 23–31, February 1988.
H. Edelsbrunner and E. P. Mucke, “Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms”, Rept. UIUCDCS-R-87–1393, Computer Science Dept., Univ. Illinois at Urbana, December 1987.
R. C. Evans, G. Koppelman and V. T. Rajan, “Shaping geometric objects by cumulative translational sweeps”, IBM J. Research and Development, Vol. 31, No. 3, pp. 343–360, May 1987.
R. T. Farouki, “Exact offset procedures for simple solids”, Computer-Aided Geometric Design, Vol. 2, pp. 257–279, 1985.
R. T. Farouki, “The characterization of parametric surface sections”, Computer Vision, Graphics, and Image Processing, Vol. 33, No. 2, pp. 209–236, February 1986.
R. T. Farouki, “Computational issues in solid boundary evaluation”, IBM Res. Rept. No. RC--12454, January 1987.
R. T. Farouki, “Trimmed surface algorithms for the evaluation and interrogation of solid boundary representations”, IBM J. Research and Development, Vol. 31, No. 3, pp. 314–334, May 1987.
R. T. Farouki and V. T. Rajan, “On the numerical condition of algebraic curves and surfaces 1. Implicit equations”, Rept. RC 13263, IBM T. J. Watson Research Center, Yorktown Heights, NY, November 1987.
I. D. Faux and M. J. Pratt, Computational Geometry for Design and Manufacture. Chichester, U.K.: Ellis Horwood, Ltd., 1979.
B. Faverjon, “Obstacle avoidance using an octree in the configuration space of a manipulator”, Proc. IEEE Intl. Conf. on Robotics, Atlanta, GA, pp. 504–512, March 13–15, 1984.
B. Faverjon, “Object level programming of industrial robots”, Proc. 1986 IEEE Intl. Conf. on Robotics and Automation, San Francisco, CA, pp. 1406–1412, April 7–10, 1986.
D. J. Filip and M. S. Pickett, “Decomposing simple outlines into constructive geometry binary trees”, Report GMR-4593, Computer Science Dept., General Motors Research Labs., February 1984.
D. Filip, R. Magedson and R. Markot, “Surface algorithms using bounds on derivatives”, Computer Aided Geometric Design, Vol. 3, No. 4, pp. 295–311, December 1986.
A. D. Fleming, “Analysis of uncertainties in a structure of parts”, University of Edinburgh, U.K., 1986.
E. G. Gilbert, D. W. Johnson and S. S. Keerthi, “A fast procedure for Computing the distance between complex objects in three-dimensional space”, IEEE J. Robotics and Automation, Vol. 4, No. 2, pp. 193–203, April 1988.
P. K. Ghosh and S. P. Mudur, “Theoretical framework for shape representation and analysis”, in R. A. Earnshaw, Ed., Fundamental Algorithms for Computer Graphics. Berlin: Springer-Verlag, 1985, pp. 949–993.
J. Gjovaag, personal communication, 1987.
J. Goldfeather, J. P. M. Hultquist and Henry Fuchs, “Fast constructive solid geometry display in the Pixel-Powers graphic system”, ACM Computer Graphics, Vol. 20, No. 4, pp. 107–116, August 1986. (Proc. SIGGRAPH ’86.)
L. J. Guibas and R. Seidel, “Computing convolutions by reciprocal search”, Proc. ACM Symp. on Computational Geometry, Yorktown Heights, NY, 1986.
O. Gunther, “Efficient stuctures for geometric data management”, Ph.D. Dissertation, Univ. California at Berkeley, Memo. No. UCB/ERL M87/77, November 1987.
V. Hayward, “Fast collision detection scheme by recursive decomposition of a manipulator workspace”, Proc. 1986 IEEE Intl. Conf. on Robotics and Automation, San Francisco, CA, pp. 1044–1049, April 7–10, 1986.
M. R. Henderson, “Extraction of feature information from three dimensional CAD data”, Ph.D. Dissertation, Purdue University, May 1984.
M. R. Henderson, “Extraction and organization of form features”, Proc. Prolamat ’85, Paris, France, June 11–13, 1985, pp. 131–141.
C. Hoffman and J. Hopcroft, “Automatic surface generation in computer aided design”, Visual Computer, Vol. 1, pp. 91–100, 1985.
C. Hoffman and J. Hopcroft, “Quadratic blending surfaces”,Computer-Aided Design, Vol. 18, No. 6, pp. 301–306, July/August 1986.
C. Hoffman and J. Hopcroft, “Simulation of physical systems from geometric models”, IEEE J. Robotics and Automation, Vol. RA-3, No. 3, pp. 194–206, June 1987.
C. M. Hoffmann, J. E. Hopcroft and M. S. Karasick, “Robust set operations on polyhedral solids”, Rept. CSD-TR-723, Computer Science Dept., Purdue Univ., November 1987.
C. M. Hoffmann, J. E. Hopcroft and M. S. Karasick, “Towards implementing robust geometric computations”, Rept. CSD-TR-729, Computer Science Dept., Purdue Univ., December 1987.
T. van Hook, “Real time shaded NC milling display”, ACM Computer Graphics, Vol. 20, No. 4, pp. 15–20, August 1986.
M. L. Hornick and B. Ravani, “Computer-aided off-line planning and programming of robot motion”, Intl. Journal of Robotics Research, Vol. 4, No. 4, pp. 18–31, Winter 1986.
E. G. Houghton, R. F. Emnett, J. D. Factor, and C. L. Sabharwal, “Implementation of a divide-and-conquer method for intersection of parametric surfaces”, Computer-Aided Geometric Design, Vol. 2, No. 1–3, pp. 173–183, 1985.
R. Jayaraman and V. Srinivasan, “ Geometric tolerancing: I. Virtual boundary requirements; and II. Conditional tolerances”, to appear in IBM J. Research and Development, 1988.
R. H. Johnson et al., “Dimensioning and tolerancing final report”, Report R-84-GM-02.2, CAM-I, Inc., Arlington, TX, May 1985.
G. Kedem and J. L. Ellis, “Computer structures for curve-solid classification in geometric modelling”, Tech. Memo. No. 51, Production Automation Project, Univ. of Rochester, May 1984.
A. Kela, R. Perucchio, and H. B. Voelcker, “Toward automatic finite element analysis”, ASME Computers in Mechanical Engineering (CIME), Vol. 5, No. 1, July 1986.
F. Kimura, H. Suzuki, and L. Wingard, “A uniform approach to dimensioning and tolerancing in product modelling”, in K. Bö, I. Estensen, P. Falster and A. E. Warman Eds., Computer Applications in Production and Engineering. Amsterdam: North Holland, 1987. (Proc. CAPE ’86.)
H. Ko and K. Lee, “Automatic assembling procedure generation from mating conditions”, Computer-Aided Design, Vol. 19, No. 1, pp. 3–10, January/February 1987.
A. Koutsou, “A spatial reasoning system for parts mating operations”, University of Edinburgh, October 1984.
D. H. Laidlaw, W. B. Trumbore and J. F. Hughes, “Constructive solid geometry for polyhedral objects”, ACM Computer Graphics, Vol. 20, No. 4, pp. 161–170, July 1986. (Proc. SIGGRAPH ’86.)
Y. T. Lee, A. de Pennington, and N. K. Shaw, “Automatic finite-element mesh generation from geometric models — A point-based approach”, ACM Trans. on Graphics, Vol. 3, No. 4, pp. 287–311, October 1984.
K. Lee and D. C. Gossard, A hierarchical data structure for representing assemblies: Part I”, Computer-Aided Design, Vol. 17, No. 1, pp. 15–19, January/February 1985.
K. Lee and G. Andrews, “Inference of the positions of components in an assembly: Part 2”, Computer-Aided Design, Vol. 17, No. 1, pp. 20–24, January/February 1985.
S. Lien and J. T. Kajiya, “A symbolic method for calculating the integral properties of arbitrary nonconvex polyhedra”, IEEE Computer Graphics and Applications, Vol. 4, No. 10, pp. 35–41, October 1984.
W. C Lin and K. S. Fu, “A syntactic approach to 3-D object representation”, IEEE Trans. Pattern Analyis and Machine Intelligence, vol. PAMI-6, no. 3, pp. 351–364, May 1984.
T. Lozano-Pérez, “A simple motion-planning algorithm for general robot manipulators”, IEEE J. Robotics and Automation, Vol. RA-3, No. 3, pp. 224–238, June 1987.
S. C. Luby, J. R. Dixon and M. K. Simmons, “Creating and using a CAD features data base”, ASME Computers in Mechanical Engineering (CIME), Vol. 5, No. 3, pp. 25–33, November 1986.
M. Mäntylä, “Boolean operations of 2-manifolds through vertex neighborhood classification”, ACM Trans. on Graphics, Vol. 5, No. 1, pp. 1–29, January 1986.
M. Mäntylä, An Introduction to Solid Modeling. Rockville, Maryland: Computer Science Press, 1988.
P. Marks, “Solid modeling paybacks”, Proc. Solid Modeling ’86, Boston, MA, October 20–22, 1986.
D. J. Meagher, “The Solids EngineTM: A processor for interactive solid modeling”, Proc. Nicograph ’84, Tokyo, Japan, November 1984.
K. Melhorn, Data Structures and Algorithms, Vol. 3. New York: Springer Verlag, 1984.
A. E. Middleditch and K. H. Sears, “Blend surfaces for set theoretic volume modelling systems”, ACM Computer Graphics, Vol. 19, No. 3, pp. 161–170, July 1985. (Proc. SIGGRAPH ’85).
V. J. Milenkovic, “Verifiable implementations of geometric algorithms using finite precision arithmetic”, Proc. Intl. Workshop on Geometric Reasoning, Oxford, U.K., June 30-July 3, 1986.
M. Minagawa, N. Okino, and Y. Kakazu, “Development of full automatic dimensioning system based on 3D solid geometry”, Proc. Prolamat ’85, Paris, France, pp. 263–272, June 11–13, 1985.
M. E. Mortenson, Geometric Modelling. New York: John Wiley and Sons, 1985.
N. Okino, Y. Kakazu, and M. Morimoto, “Extended depth-buffer algorithms for hidden-surface visualization”, IEEE Computer Graphics and Applications, Vol. 4, No. 5, pp. 79–88, May 1984.
A. Parkinson “The use of solid models in BUILD as a database for NC machining”, Proc. Prolamat ’85, Paris, France, June 11–13, 1985, pp. 293–299.
J. Pegna, “Variable sweep geometric modeling”, Ph.D. Dissertation, Mechanical Engr. Dept., Stanford Univ., October 1987.
D. P. Peterson, “Boundary to constructive solid geometry mapping: A focus on 2-D issues”, Computer-Aided Design, Vol. 18, No. 1, pp. 3–14, January/February 1986.
H.-U. Pfeifer, “Methods used for intersecting entities in the GPM module for volume geometry”, Computer-Aided Design, Vol. 17, No. 7, pp. 311–318, September 1985.
J. Ponce and D. Chelberg, “Localized intersections computation for solid modelling with straight homogeneous generalized cylinders”, Proc. IEEE 1987 Intl. Conf. on Robotics and Automation, Raleigh, NC, March 31-April 3, 1987, pp. 1481–1486.
R. Popplestone, personal communication, 1988.
F. H. Post and F. Klok, “Deformations of sweep objects in solid modelling”, in A. A. G. Requicha, Ed., Eurographics ’86. Amsterdam: North-Holland, 1986.
M. J. Pratt and A. D. Geisow, “Surface/surface intersection problems”, in J. A. Gregory, Ed., The mathematics of surfaces. Oxford: Clarendon Press, 1986, pp. 117–142.
F. P. Preparata and M. I. Shamos, Computational Geometry. New York: Springer-Verlag, 1985.
A. A. G. Requicha, “Mathematical models of rigid solid objects”, Tech. Memo. No. 28, Production Automation Project, Univ. of Rochester, November 1977.
A. A. G. Requicha, “Representations for rigid solids:Theory, methods, and systems”, ACM Computing Surveys, Vol. 12, No. 4, pp. 437–464, December 1980.
A. A. G. Requicha, “Representation of tolerances in solid modeling: Issues and alternative approaches”, in M. S. Pickett and J. W. Boyse, Eds., Solid Modeling by Computers. New York: Plenum Press, 1984, pp. 3–22.
A. A. G. Requicha, “Growing and shrinking solids for blending, tolerancing and other applications”, Proc. CAD Kolloquium, Technical University of Berlin, Berlin, West Germany, November 24–25, 1986.
A. A. G. Requicha and S. C Chan, “Representation of geometric features, tolerances and attributes in solid modellers based on constructive geometry”, IEEE Journal of Robotics and Automation, Vol. RA- 2, No. 3, pp. 156–186, September 1986. (Also published as Tech. Memo. No. 48, Production Automation Project, Univ. of Rochester, October 1985.)
A. A. G. Requicha and J. H. Vandenbrande, “Automatic process planning and part programming”, in A. Kusiak, Ed., Artificial Intelligence: Implications f or CIM. New York: Springer Verlag, 1987, pp. 299–326. (Published also as Rept. No. 217, Institute for Robotics and Intelligent Systems, University of Southern California, April 1987.)
A. A. G. Requicha and H. B. Voelcker, “Solid modeling: a historical summary and contemporary assessment”, IEEE Computer Graphics and Applications, Vol. 2, No. 2, pp. 9–24, March 1982. (An Italian translation appeared in PIXEL, Vol. 5, No. 1, pp. 21–26, and No. 2, pp. 27–36, 1984.)
A. A. G. Requicha and H. B. Voelcker, “Solid modeling: current status and research directions”, IEEE Computer Graphics and Applications, Vol. 3, No. 7, pp. 25–37, October 1983.
A. A. G. Requicha and H. B. Voelcker, “Boolean operations in solid modelling: boundary evaluation and merging algorithms”, Proc. IEEE, Vol. 73, No. 1, pp. 30–44, January 1985.
A. P. Rockwood, “Introducing sculptured surfaces into a geometric modeler”, in M. S. Pickett and J. W. Boyse, Eds., Solid Modeling by Computers. New York: Plenum Press, 1984, pp. 237–258.
J. R. Rossignac, “Constraints in constructive solid geometry”, Proc. 1986 ACM Workshop on Interactive 3D Graphics, Chapel Hill, NC, October 23–24, 1986, pp. 93–110.
J. R. Rossignac and A. A. G. Requicha, “Constant-radius blending in solid modeling”, ASME Computers in Mechanical Engineering (CIME), Vol. 3, No. 1, pp. 65–73, July 1984.
J. R. Rossignac and A. A. G. Requicha, “Offsetting operations in solid modelling”, Computer-Aided Geometric Design, Vol. 3, No. 2, pp. 129–148, August 1986.(Also published as Tech. Memo. No. 53, Production Automation Project, Univ. of Rochester, June 1985.)
J. R. Rossignac and A. A. G. Requicha, “Depth buffering display techniques for Constructive Solid Geometry”, IEEE Computer Graphics and Applications, Vol. 6, No. 9, pp. 29–39, September 1986. (Also published as Tech. Memo. No. 31, Production Automation Project, Univ. of Rochester, September 1985.)
J. R. Rossignac and H. B. Voelcker, “Active zones in CSG for accelerating boundary evaluation, redundancy elimination, interference detection, and shading algorithms”, to appear in ACM Trans. on Graphics, 1988. (An earlier version is available as IBM Research Rept. No. RC 11991, June 1986.)
H. Samet and M. Tamminen, “Bintrees, CSG trees, and time”, ACM Computer Graphics, Vol. 19, No. 3, pp. 121–130, July 1985. (Proc. SIGGRAPH ’85.)
T. Sata, F. Kimura, H. Suzuki and T. Fujita, “Designing machine assembly structure using geometric constraints in product modelling”, Annals of the CIRP, Vol. 34, No. 1, pp. 169–172, 1985.
J. Schwartz and M. Sharir, “On the ‘piano movers’ problem, II. General techniques for computing topological properties of real algebraic manifolds”, Rept. No. 41, Computer Science Dept., New York University, 1982.
T. W. Sederberg, “Implicit and parametric curves and surfaces for computer aided geometric design”, Ph.D. Dissertation, Purdue Univ., August 1983.
T. W. Sederberg and R. N. Goldman, “Algebraic geometry for computer-aided geometric design”, IEEE Computer Graphics and Applications, Vol. 6, No. 6, pp. 52–59, June 1986.
T. W. Sederberg and S. R. Parry, “Free-form deformation of solid geometric models”, ACM Computer Graphics, Vol. 20, No. 4, pp. 151–160, August 1986. (Proc. SIGGRAPH ’86.)
M. Segal and C H. Séquin, “Consistent calculations for solids modeling”, Proc. ACM Symp. on Computational Geometry, Yorktown Heights, NY, 1986.
R, Smith, M. Self and P. Cheeseman, “Estimating uncertain spatial relationships in robotics”, Proc. IEEE 1987 Intl. Conf. on Robotics and Automation, Raleigh, NC, March 31-April 3, 1987.
H. Soto, M. Ishii, K. Sato, and M. Ikesaka, “Fast image generation of constructive solid geometry using a cellular array processor”, ACM Computer Graphics, Vol. 19, No. 3, pp. 95–102, July 1985. (Proc. SIGGRAPH ’85.)
T. W. Stacey and A. E. Middleditch, “The geometry of machining for computer-aided manufacture”, Robotica, Vol. 4, No. 2, pp. 83–91, April/June 1986.
K. Sugihara, Machine Interpretation of Line Drawings. Cambridge, MA: MIT Press, 1986.
K. Sugihara, “On finite-precision representation of geometric objects”, Memo. RMI 87–06, Dept. Mathematical Engineering and Information Systems, Univ. Tokyo, Japan, October 1987.
U. A. Sungurtekin and H. B. Voelcker, “Graphical simulation and automatic verification of NC machining programs”, Proc. 1986 IEEE Intl. Conf. on Robotics and Automation, San Francisco, CA, pp. 156–165, April 7–10, 1986.
S. T. Tan, M. F. Yuen and K. C. Hui, “Modelling solids with sweep primitives”, ASME Computers in Mechanical Engineering (CIME), Vol. 6, No. 2, pp. 60–73, September/October 1987.
D. Terzopoulos, J. Platt, A. Barr and K. Fleischer, “Elastically deformable models”, ACM Computer Graphics, Vol. 21, No. 4, pp. 205–214, July 1987(Proc. SIGGRAPH ’87)
“Set operations on polyhedra using binary space partitioning trees”, ACM Computer Graphics, Vol. 21, No. 4, pp. 153–162, July 1987. (Proc. SIGGRAPH ’87.)
R. B. Tilove, “A null-object detection algorithm for constructive solid geometry”, Commun. ACM, Vol. 27, No. 7, pp. 684–694, July 1984.
R. B. Tilove, A. A. G. Requicha, and M. R. Hopkins, “Efficient editing of solid models by exploiting structural and spatial locality”, Computer-Aided Geometric Design, Vol. 1, pp. 227–239, 1984.
J. U. Turner, “Tolerances in computer-aided geometric design”, Ph.D. Dissertation, Rensselaer Polytechnic Institute, May 1987.
D. L. Vossler, “Sweep-to-CSG conversion using pattern recognition techniques”, IEEE Computer Graphics and Applications, Vol. 5, No. 8, pp. 61–68, August 1985.
W. P. Wang, “Integration of solid geometric modelling for computerized process planning”, in C. R. Liu, T. C Chang, and R. Komanduri, Eds., Computer-Aided/Intelligent Process Planning, ASME Winter Annual Meeting, Miami Beach, FL, PED-voi. 19, pp. 177–187, November 17–22, 1985.
W. P. Wang and K. K. Wang, “Real-time verification of multiaxis NC programs with raster graphics”, Proc. 1986 IEEE Intl. Conf. on Robotics and Automation, San Francisco, CA, pp. 166–171, April 7–10, 1986.
W. P. Wang and K. K. Wang, “Geometric modeling of swept volume of solids and its applications”, IEEE Computer Graphics and Applications, Vol. 6, No. 12, pp. 8–17, December 1986.
K. J. Weiler, “Topological structures for geometric modeling”, Ph.D. Dissertation, Rensselaer Polytechnic Institute, August 1986.
J. J. van Wijk, “Ray tracing objects defined by sweeping a sphere”, Computers and Graphics, Vol. 9, No. 3, pp. 283–290, 1985.
P. R. Wilson, “Conic representations for shape description”, IEEE Computer Graphics and Applications, Vol. 7, No. 4, pp. 23–30, April 1987.
B. Wördenweber, “Finite element mesh generation”, Computer-Aided Design, Vol. 16, No. 5, pp. 285–291, September 1984.
J. D. Wolter, R. A. Volz, and A. C. Woo, “Automatic generation of gripping positions”, IEEE Transactions on Systems, Man, and Cybernetics, Vol. SMC-15, No. 2, pp. 204–213, March/April 1985.
T. C Woo and T. Thomasma, “An algorithm for generating solid elements in objects with holes”, Computers and Structures, Vol. 8, No. 2, pp. 333–342, 1984.
K. Yamaguchi et al., “Octree-related data structures and algorithms”, IEEE Computer Graphics and Applications, Vol. 4, No. 1, pp. 53–59, January 1984.
F. Yamaguchi and T. Tokieda, “A solid modeler with a 4 x 4 determinant processor”, IEEE Computer Graphics and Applications, Vol. 5, No. 4, pp. 51–59, April 1985.
C. K. Yap, “Algorithmic motion planning”, in J. T. Schwartz and C. K. Yap, Eds., Advances in Robotics. New York: Lawrence Erlbaum Assoc, 1986.
M. A. Yerry and M. S. Shepard, “Automatic mesh generation for three-dimensional solids”, Computers and Structures, Vol. 20, pp. 31–39, 1985.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1988 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Requicha, A.A.G. (1988). Solid Modelling — A 1988 Update. In: Ravani, B. (eds) CAD Based Programming for Sensory Robots. NATO ASI Series, vol 50. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83625-1_1
Download citation
DOI: https://doi.org/10.1007/978-3-642-83625-1_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-83627-5
Online ISBN: 978-3-642-83625-1
eBook Packages: Springer Book Archive