Modelling with constraints: a bibliographical survey

Nowadays, constraint solvers play a fundamental role in many graphical applications, including geometrical and mechanical CAD systems, layouts, user interfaces and animation. These applications use constraints to conveniently describe the relations between objects. Constraints are automatically maintained and satisfied by a constraint solver. So, numerical and tedious tasks are left to the solver and the designer can concentrate on the design process. In this paper, we present the concepts of constraints and constraint solvers. We classify the principal resolution methods, giving their drawbacks and shortcomings. We also examine different application domains using constraint solvers.

[1]  R. Light,et al.  Modification of geometric models through variational geometry , 1982 .

[2]  WitkinAndrew,et al.  Variational surface modeling , 1992 .

[3]  George Celniker,et al.  Deformable curve and surface finite-elements for free-form shape design , 1991, SIGGRAPH.

[4]  Michael Sannella.  Skyblue: a multi-way local propagation constraint solver for user interface construction , 1994, UIST '94.

[5]  Patrick Prosser,et al.  HYBRID ALGORITHMS FOR THE CONSTRAINT SATISFACTION PROBLEM , 1993, Comput. Intell..

[6]  Andreas Buja,et al.  Painting multiple views of complex objects , 1990, OOPSLA/ECOOP '90.

[7]  Steven John Sistare.  A graphical editor for three-dimensional constraint-based geometric modeling , 1991 .

[8]  Bjørn N. Freeman-Benson.  Converting an existing user interface to use constraints , 1993, UIST '93.

[9]  J. C. Owen,et al.  Algebraic solution for geometry from dimensional constraints , 1991, SMA '91.

[10]  Andrew P. Witkin,et al.  Variational surface modeling , 1992, SIGGRAPH.

[11]  Nicolas Beldiceanu,et al.  Extending CHIP in order to solve complex scheduling and placement problems , 1993, JFPL.

[12]  Michael Gleicher,et al.  Manipulating surfaces differentially , 1991 .

[13]  Alan Borning,et al.  Constraint hierarchies , 1992 .

[14]  Alan K. Mackworth.  Constraint Satisfaction , 1985 .

[15]  Maureen C. Stone,et al.  Snap-dragging , 1986, SIGGRAPH.

[16]  Z. Huang,et al.  A constraint-based manipulator toolset for editing 3D objects , 1997, SMA '97.

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

[18]  Steven L. Rohall,et al.  The Rendezvous architecture and language for constructing multiuser applications , 1994, TCHI.

[19]  Winfried Graf,et al.  The Constraint-Based Layout Framework LayLab and Its Applications , 1996 .

[20]  A. Witkin,et al.  Differential Manipulation * , 1991 .

[21]  Ralph D. Hill.  A 2-D Graphics System for Multi-User Interactive Graphics Based on Objects and Constraints , 1991 .

[22]  René Caubet,et al.  Interactive constraint system for solid modeling objects , 1997, SMA '97.

[23]  K. Ghassan,et al.  Controlling object natural behaviors in a 3D declarative modeler , 1998 .

[24]  R. Dechter.  to Constraint Satisfaction , 1991 .

[25]  Michael Gleicher,et al.  A graphics toolkit based on differential constraints , 1993, UIST '93.

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

[27]  George Celniker,et al.  Linear constraints for deformable non-uniform B-spline surfaces , 1992, I3D '92.

[28]  Ernest Davis,et al.  Constraint Propagation with Interval Labels , 1987, Artif. Intell..

[29]  Daniele Chauvat.  Le projet voluformes : un exemple de modelisation declarative avec controle spatial , 1994 .

[30]  Ivan E. Sutherland,et al.  Sketchpad: a man-machine graphical communication system , 1899, AFIPS '63 (Spring).

[31]  Bradley T. Vander Zanden.  An Incremental Planning Algorithm for Ordering Equations in a Multilinear System of Constraints , 1988 .

[32]  William Leler,et al.  Constraint programming languages: their specification and generation , 1988 .

[33]  Ricky Yeung,et al.  TBAG: a high level framework for interactive, animated 3D graphics applications , 1994, SIGGRAPH.

[34]  Robert Duisberg.  Animation Using Temporal Constraints: An Overview of the Animus System , 1987, Hum. Comput. Interact..

[35]  Greg Nelson,et al.  Juno, a constraint-based graphics system , 1985, SIGGRAPH.

[36]  Michael R. Wilk.  Equate: an object-oriented constraint solver , 1991, OOPSLA 1991.

[37]  Paul S. Barth.  An object-oriented approach to graphical interfaces , 1986, TOGS.

[38]  Christopher J. Van Wyk,et al.  A High-Level Language for Specifying Pictures , 1982, TOGS.

[39]  René Caubet,et al.  Dynamic and Hierarchical Constraints Solver with Continuous Variables , 1997 .

[40]  François Poulet,et al.  Modelling Megalithic Sites , 1996, Comput. Graph. Forum.

[41]  Gerard Hegron,et al.  An incremental declarative modelling applied to urban layout and design , 1997 .

[42]  Satoshi Matsuoka,et al.  Declarative programming of graphical interfaces by visual examples , 1992, UIST '92.

[43]  David L. Waltz,et al.  Understanding Line drawings of Scenes with Shadows , 1975 .

[44]  Terrence Fernando,et al.  Direct 3D Manipulation Techniques for Interactive Constraint‐based Solid Modelling , 1993, Comput. Graph. Forum.

[45]  Allan Heydon,et al.  The Juno-2 Constraint-Based Drawing Editor , 1994 .

[46]  Beat D. Brüderlin,et al.  Using geometric rewrite rules for solving geometric problems symbolically , 1993, Theor. Comput. Sci..

[47]  G. Sunde,et al.  A CAD System with Declarative Specification of Shape , 1987 .

[48]  Jean-Yves Martin,et al.  Working modes with a declarative modeler , 1997, Comput. Networks.

[49]  Pascal Van Hentenryck,et al.  CLP(Intervals) Revisited , 1994, ILPS.

[50]  Barry Fowler,et al.  Geometric manipulation of tensor product surfaces , 1992, I3D '92.

[51]  Koichi Kondo,et al.  PIGMOD: parametric and interactive geometric modeller for mechanical design , 1991, Comput. Aided Des..

[52]  Olivier Lhomme,et al.  Consistency Techniques for Numeric CSPs , 1993, IJCAI.

[53]  Eero Hyvönen,et al.  Constraint Reasoning Based on Interval Arithmetic: The Tolerance Propagation Approach , 1992, Artif. Intell..

[54]  N. Bose.  Gröbner Bases: An Algorithmic Method in Polynomial Ideal Theory , 1995 .

[55]  Bruce Horn.  Properties of user interface systems and the Siri programming language , 1992 .

[56]  CelnikerGeorge,et al.  Deformable curve and surface finite-elements for free-form shape design , 1991 .

[57]  John H. Maloney.  Using constraints for user interface construction , 1992 .

[58]  James Arthur Gosling,et al.  Algebraic constraints , 1983 .

[59]  Roger B. Dannenberg,et al.  Garnet: comprehensive support for graphical, highly interactive user interfaces , 1990, Computer.

[60]  Bjørn N. Freeman-Benson,et al.  An incremental constraint solver , 1990, CACM.

[61]  Bradley T. Vander Zanden,et al.  An incremental algorithm for satisfying hierarchies of multiway dataflow constraints , 1996, TOPL.

[62]  Frédéric Benhamou,et al.  Applying Interval Arithmetic to Real, Integer, and Boolean Constraints , 1997, J. Log. Program..

[63]  Mark S. Fox,et al.  WRIGHT: a constraint based spatial layout system , 1992 .

[64]  Boi Faltings,et al.  Global Consistency for Continuous Constraints , 1994, ECAI.

[65]  Wu Wen-tsun.  Basic principles of mechanical theorem proving in elementary geometries , 1986 .

[66]  Gerald Jay Sussman,et al.  CONSTRAINTS - A Language for Expressing Almost-Hierarchical Descriptions , 1980, Artif. Intell..

[67]  Enrico Gobbetti,et al.  Supporting Interactive Animation Using Multi-way Constraints , 1995, Eurographics Workshop on Programming Paradigms in Graphics.

[68]  Daniel Thalmann,et al.  VB2: an architecture for interaction in synthetic worlds , 1993, UIST '93.

[69]  Dimitri Plemenos,et al.  Increasing the efficiency of declarative modelling . Constraint evaluation for the hierarchical decomposition approach , 1997 .

[70]  Tomás Lozano-Pérez,et al.  Spatial Planning: A Configuration Space Approach , 1983, IEEE Transactions on Computers.

[71]  Dan R. Olsen,et al.  Creating interactive techniques by symbolically solving geometric constraints , 1990, UIST '90.

[72]  Roger B. Dannenberg,et al.  Garnet: comprehensive support for graphical, highly interactive user interfaces , 1995 .

[73]  Stéphane Donikian,et al.  A Declarative Design Method for 3D Scene Sketch Modeling , 1993, Comput. Graph. Forum.

[74]  G. Kwaiter,et al.  Oranos : un solveur dynamique de contraintes hiérarchiques et géométriques , 1997 .

[75]  Alan Borning,et al.  The Programming Language Aspects of ThingLab, a Constraint-Oriented Simulation Laboratory , 1981, TOPL.

[76]  Christian Colin.  Modélisation déclarative de scènes à base de polyèdres élémentaires : le projet Pastoformes , 1990 .

[77]  Scott E. Hudson,et al.  Incremental attribute evaluation: a flexible algorithm for lazy update , 1991, TOPL.

[78]  K. Kondo,et al.  Algebraic method for manipulation of dimensional relationships in geometric models , 1992, Comput. Aided Des..