Solid modelling—A 1988 update

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, Mantyla 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.

[1]  Bernard Faverjon.  Object level programming of industrial robots , 1986, Proceedings. 1986 IEEE International Conference on Robotics and Automation.

[2]  John E. Hopcroft,et al.  Towards implementing robust geometric computations , 1988, SCG '88.

[3]  Thomas W. Sederberg,et al.  Free-form deformation of solid geometric models , 1986, SIGGRAPH.

[4]  Requicha,et al.  Solid Modeling: A Historical Summary and Contemporary Assessment , 1982, IEEE Computer Graphics and Applications.

[5]  Rida T. Farouki,et al.  Exact offset procedures for simple solids , 1985, Comput. Aided Geom. Des..

[6]  Aristides A. G. Requicha,et al.  Representation of Tolerances in Solid Modeling: Issues and Alternative Approaches , 1984 .

[7]  Martti Mäntylä,et al.  Introduction to Solid Modeling , 1988 .

[8]  K. Sugihara.  Machine interpretation of line drawings , 1986, MIT Press series in artificial intelligence.

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

[10]  Donald L. Vossler.  Sweep-to-CSG Conversion Using Pattern Recognition Techniques , 1985, IEEE Computer Graphics and Applications.

[11]  J. T. Shwartz,et al.  On the Piano Movers' Problem : III , 1983 .

[12]  Tosiyasu L. Kunii,et al.  Octree-Related Data Structures and Algorithms , 1984, IEEE Computer Graphics and Applications.

[13]  Vincent Hayward,et al.  Fast collision detection scheme by recursive decomposition of a manipulator workspace , 1986, Proceedings. 1986 IEEE International Conference on Robotics and Automation.

[14]  Beat D. Brüderlin,et al.  Constructing three-dimensional geometric objects defined by constraints , 1987, I3D '86.

[15]  Jarke J. van Wijk,et al.  Ray tracing objects defined by sweeping a sphere , 1984, Comput. Graph..

[16]  Alan E. Middleditch,et al.  The geometry of machining for computer-aided manufacture , 1986, Robotica.

[17]  John F. Canny,et al.  Collision Detection for Moving Polyhedra , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[18]  Jarek Rossignac,et al.  Active zones in CSG for accelerating boundary evaluation, redundancy elimination, interference detection, and shading algorithms , 1988, TOGS.

[19]  Bruce F. Naylor,et al.  Set operations on polyhedra using binary space partitioning trees , 1987, SIGGRAPH.

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

[21]  Alyn P. Rockwood,et al.  Introducing Sculptured Surfaces into a Geometric Modeler , 1984 .

[22]  Hanan Samet,et al.  Bintrees, CSG trees, and time , 1985, SIGGRAPH.

[23]  R. Farouki.  Trimmed-surface algorithms for the evaluation and interrogation of solid boundary representations , 1987 .

[24]  Mark S. Shephard,et al.  AUTOMATIC MESH GENERATION FOR THREE-DIMENSIONAL SOLIDS , 1985 .

[25]  Henry Fuchs,et al.  Fast constructive-solid geometry display in the pixel-powers graphics system , 1986, SIGGRAPH.

[26]  Kunwoo Lee,et al.  Inference of the positions of components in an assembly: part 2 , 1985 .

[27]  Alan Fleming.  Analysis of Uncertainties in a Structure of Parts , 1985, IJCAI.

[28]  Aristides A. G. Requicha,et al.  Offsetting operations in solid modelling , 1986, Comput. Aided Geom. Des..

[29]  John E. Hopcroft,et al.  Simulation of physical systems from geometric models , 1987, IEEE J. Robotics Autom..

[30]  Martti Mäntylä,et al.  Boolean operations of 2-manifolds through vertex neighborhood classification , 1986, TOGS.

[31]  J. A. Gregory.  The Mathematics of Surfaces. , 1987 .

[32]  D. P. Peterson.  Boundary to constructive solid geometry mappings: a focus on 2D issues , 1986 .

[33]  Vijay Srinivasan,et al.  Geometric Tolerancing: I. Virtual Boundary Requirements , 1989, IBM J. Res. Dev..

[34]  Stephen Alan Cameron,et al.  Modelling solids in motion , 1984 .

[35]  Gary A. Crocker,et al.  Boundary evaluation of non-convex primitives to produce parametric trimmed surfaces , 1987, SIGGRAPH '87.

[36]  Hugh F. Durrant-Whyte.  Uncertain geometry in robotics , 1988, IEEE J. Robotics Autom..

[37]  Sudhir P. Mudur,et al.  Theoretical Framework for Shape Representation and Analysis , 1985 .

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

[39]  J. Schwartz,et al.  On the “piano movers” problem. II. General techniques for computing topological properties of real algebraic manifolds , 1983 .

[40]  Chandrajit L. Bajaj,et al.  Generation of configuration space obstacles: the case of a moving sphere , 1988, IEEE J. Robotics Autom..

[41]  K. K. Wang,et al.  Real-time verification of multiaxis NC programs with raster graphics , 1986, Proceedings. 1986 IEEE International Conference on Robotics and Automation.

[42]  T. Sederberg.  Implicit and parametric curves and surfaces for computer aided geometric design , 1983 .

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

[44]  Richard A. Volz,et al.  Automatic generation of gripping positions , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[45]  S. A. Cameron,et al.  Determining the minimum translational distance between two convex polyhedra , 1986, Proceedings. 1986 IEEE International Conference on Robotics and Automation.

[46]  S. Sathiya Keerthi,et al.  A fast procedure for computing the distance between complex objects in three-dimensional space , 1988, IEEE J. Robotics Autom..

[47]  Robert P. Markot,et al.  Surface algorithms using bounds on derivatives , 1986, Comput. Aided Geom. Des..

[48]  Jarek Rossignac,et al.  Constraints in constructive solid geometry , 1987, I3D '86.

[49]  Chee Yap,et al.  Algorithmic motion planning , 1987 .

[50]  Bahram Ravani,et al.  Computer-Aided Off-Line Planning and Programming of Robot Motion , 1986 .

[51]  J. Hopcroft,et al.  Quadratic blending surfaces , 1985 .

[52]  Rida T. Farouki,et al.  The characterization of parametric surface sections , 1986, Comput. Vis. Graph. Image Process..

[53]  Mark Henderson.  EXTRACTION AND ORGANIZATION OF FORM FEATURES. , 1986 .

[54]  H. Voelcker,et al.  Solid modeling: current status and research directions , 1983, IEEE Computer Graphics and Applications.

[55]  Yukinori Kakazu,et al.  Extended Depth-Buffer Algorithms for Hidden-Surface Visualization , 1984, IEEE Computer Graphics and Applications.

[56]  Rida T. Farouki,et al.  Computational issues in solid boundary evaluation , 1988, Inf. Sci..

[57]  David H. Laidlaw,et al.  Constructive solid geometry for polyhedral objects , 1986, SIGGRAPH.

[58]  Chaman L. Sabharwal,et al.  Implementation of a divide-and-conquer method for intersection of parametric surfaces , 1985, Comput. Aided Geom. Des..

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

[60]  William H. Frey,et al.  An apporach to automatic three‐dimensional finite element mesh generation , 1985 .

[61]  John C. Platt,et al.  Elastically deformable models , 1987, SIGGRAPH.

[62]  John R. Dixon,et al.  Creating and using a features data base , 1986 .

[63]  K. K. Wang,et al.  Geometric Modeling for Swept Volume of Moving Solids , 1986, IEEE Computer Graphics and Applications.

[64]  Aristides A. G. Requicha,et al.  Representation of geometric features, tolerances, and attributes in solid modelers based on constructive geometry , 1986, IEEE J. Robotics Autom..

[65]  Oliver Günther,et al.  Efficient Structures for Geometric Data Management , 1988, Lecture Notes in Computer Science.

[66]  Bernard Faverjon,et al.  Obstacle avoidance using an octree in the configuration space of a manipulator , 1984, ICRA.

[67]  Robert B. Tilove.  A null-object detection algorithm for constructive solid geometry , 1984, CACM.

[68]  Chandrajit L. Bajaj,et al.  Tracing surface intersections , 1988, Comput. Aided Geom. Des..

[69]  Alfred V. Aho,et al.  Data Structures and Algorithms , 1983 .

[70]  I. Faux,et al.  Computational Geometry for Design and Manufacture , 1979 .

[71]  Alan H. Barr,et al.  Global and local deformations of solid primitives , 1984, SIGGRAPH.

[72]  Roger Clinton Evans,et al.  Shaping geometric objects by cumulative translational sweeps , 1987 .

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

[74]  B Wördenweber.  Finite element mesh generation , 1984 .

[75]  Kevin Weiler.  Topological Structures for Geometric Modeling , 1986 .

[76]  John E. Hopcroft,et al.  Robust set operations on polyhedral solids , 1987, IEEE Computer Graphics and Applications.

[77]  Wei-Chung Lin,et al.  A Syntactic Approach to 3-D Object Representation , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[78]  John W. Boyse,et al.  Solid Modeling by Computers , 1984, Springer US.

[79]  Fujio Yamaguchi,et al.  A Solid Modeler with a 4 x 4 Determinant Processor , 1985, IEEE Computer Graphics and Applications.

[80]  Alan E. Middleditch,et al.  Blend surfaces for set theoretic volume modelling systems , 1985, SIGGRAPH '85.

[81]  Leonidas J. Guibas,et al.  Computing convolutions by reciprocal search , 1986, SCG '86.

[82]  Victor J. Milenkovic,et al.  Verifiable Implementations of Geometric Algorithms Using Finite Precision Arithmetic , 1989, Artif. Intell..

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

[84]  Mark Richard Henderson.  EXTRACTION OF FEATURE INFORMATION FROM THREE-DIMENSIONAL CAD DATA , 1984 .

[85]  Randall Smith,et al.  Estimating Uncertain Spatial Relationships in Robotics , 1987, Autonomous Robot Vehicles.

[86]  Carlo H. Séquin,et al.  Consistent calculations for solids modeling , 1985, SCG '85.

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

[88]  Kunwoo Lee,et al.  A hierarchical data structure for representing assemblies: part I , 1985 .

[89]  Moshe M. Barash.  Advances in CAD/CAM , 1984 .

[90]  Etienne Dombre,et al.  Trends in CAD/CAM systems for robotics , 1986, Proceedings. 1986 IEEE International Conference on Robotics and Automation.

[91]  Matthew Ming Fai Yuen,et al.  Modelling Solids with Sweep Primitives , 1987 .

[92]  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.

[93]  E. A. Warman.  Computer Applications in Production and Engineering , 1985 .

[94]  Pere Brunet,et al.  Object representation by means of nonminimal division quadtrees and octrees , 1985, TOGS.

[95]  Karl G. Kempf,et al.  A collision detection algorithm based on velocity and distance bounds , 1986, Proceedings. 1986 IEEE International Conference on Robotics and Automation.

[96]  Ingrid Carlbom,et al.  A Hierarchical Data Structure for Representing the Spatial Decomposition of 3-D Objects , 1985, IEEE Computer Graphics and Applications.

[97]  Aristides A. G. Requicha,et al.  Efficient editing of solid models by exploiting structural and spatial locality , 1984, Comput. Aided Geom. Des..

[98]  Fumihiko Kimura,et al.  Designing Machine Assembly Structure Using Geometric Constraints in Product Modelling , 1985 .

[99]  Michael I. Jordan,et al.  Surface/surface intersection , 1987, Comput. Aided Geom. Des..

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

[101]  Heedong Ko,et al.  Automatic assembling procedure generation from mating conditions , 1987 .

[102]  Hans-Ulrich Pfeifer.  Methods used for intersecting geometrical entities in the GPM module for volume geometry , 1985 .

[103]  Ron Goldman,et al.  Algebraic Geometry for Computer-Aided Geometric Design , 1986, IEEE Computer Graphics and Applications.

[104]  Herbert Edelsbrunner,et al.  Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms , 1988, SCG '88.

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

[106]  James T. Kajiya,et al.  A symbolic method for calculating the integral properties of arbitrary nonconvex polyhedra , 1984, IEEE Computer Graphics and Applications.

[107]  Jean Ponce,et al.  Localized intersections computation for solid modelling with straight homogenous generalized cylinders , 1987, Proceedings. 1987 IEEE International Conference on Robotics and Automation.

[108]  Frits H. Post,et al.  Deformations of Sweep Objects in Solid Modelling , 1986, Eurographics.

[109]  Rida T. Farouki,et al.  On the numerical condition of algebraic curves and surfaces 1. Implicit equations , 1988, Comput. Aided Geom. Des..