Bruderlin B. Constructing three-dimensional geometric object defined by constraints. In ACM SIGGRAPH. Chapel Hill, 1986.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....recent years, there has been a considerable amount of interest in the development of constraintbased solid modelling systems. Several approaches have been used to implement these systems, such as the numerical approach[8, 11] the algebraic approach[7, 14, 12, 4] the geometric reasoning approach[3, 1, 9] and the transformation operational approach[13, 2, 6] The important issues which need to be considered when developing a constraint based solid modelling system are constraint representation, constraint satisfaction and user interaction. Recently, degrees of freedom (DOF) analysis has been used ....

B. Bruderlin. Constructing three-dimensional geometric objects defined by constraints. In F. Crow and S. M. Pizer, editors,

....the set of expressible geometric constraints, and to prevent the merging of geometric constraints and of engineering ones, but it seemed more suited to rule based approaches than the equational formulation. Up to now, all rule based or qualitative approaches (as opposed to numerical methods) Bru86, VSR92] rely on the predicates formulation. In contrast, this paper will show that the equational formulation also permits a qualitative study as well. 1 1.1 Solving Systems of Constraints Constraints based modellers have to solve in some way the set of constraints by one of the following ....

....numerical one, the second one stems from graph theory and does not consider the numeric details of equations, or geometric constraints. So it can be applied to geometric constraints represented by predicates (in opposition to equations) say Prolog predicates like in Bruderlin s works [Bru86] Section 2 presents the probabilistic and numerical method. It is first applied to systems of equations and then extended to systems of geometric constraints. Section 3 presents the graph based approach, similarly it is first applied to systems of equations and then extended to systems of ....

B. Bruderlin. Constructing three-dimensional geometric objects defined by constraints. In Interactive 3D Graphics, pages 111--129, October 1986.

....[ Du, 1995 ] maintains invariant relationships in geometrical modelling via CAD oriented constraint processing in an object oriented system. Paltrinieri, 1995 ] features object oriented abstraction to visualize the constraint network. 5. 3 CSP Modification and Inconsistency Handling The work [ Bruderlin, 1986 ] deals with 2 and 3 dimensional objects; in case of an inconsistency of the underlying CSP the user has to replace a constraint or even to delete one. Serrano and Gossard, 1987 ] mentions the constraint oriented philosophy of design and also allows constraints to get modified. Vander ....

Beat Bruderlin. Constructing Three-Dimensional Geometric Objects Defined by Constraints. In F. Crow and S. M. Pizer, editors, Workshop on Interactive 3D Graphics, pages 111--129, Chapel Hill, North Carolina, October 23/24, 1986. ACM SIGGRAPH, New York, NY, U.S.A. Conference proceedings.

....in some order that may or may not be fixed. This is more natural for the user and makes the approach suitable for interactively debugging a sketch. 2.2.1 Rule Constructive Solvers Rule constructive solers use rewrite rules to discover and execute the construction steps. Bruderlin and Sohrt [3, 28] solve constraints in this way and incorporate the Knuth Bendix critical pairs algorithm [16] They show that their method is correct and solves all problems that can be constructed using ruler and compass. Other rule constructive solvers include Aldefeld [1] and Sunde [30] In [35] and in [33] ....

B. Bruderlin. Constructing Three-Dimensional Geometric Objects Defined by Constraints. In Workshop on Interactive 3D Graphics, pages 111--129. ACM, October 23-24 1986.

....years, there has been a considerable amount of interest in the development of constraintbased solid modelling systems. Several approaches have been used to implement these systems, such as the numerical approach[10, 13] the algebraic approach[9, 16, 14, 6, 5] the geometric reasoning approach[4, 17, 1, 12, 3] and the transformation operational approach[15, 2, 8] The important issues which need to be considered when developing a constraint based solid modelling system are constraint representation, constraint satisfaction and user interaction. Recently, degrees of freedom (DOF) analysis has been used ....

B. Bruderlin. Constructing three-dimensional geometric objects defined by constraints. In F. Crow and S. M. Pizer, editors, 1986 Workshop on Interactive 3D Graphics, pages 111--130, Chapel Hill, N.C., October 1986. ACM Press.

....the set of expressible geometric constraints, and to prevent the merging of geometric constraints and of engineering ones, but it seemed more suited to rule based approaches than the equational formulation. Up to now, all rule based or qualitative approaches (as opposed to numerical methods) Bru86, VSR92] rely on the predicates formulation. In contrast, this chapter will show that the equational formulation also permits a qualitative study as well. Solving Systems of Constraints Constraints based modelers have to solve in some way the set of constraints by one of the following ....

....numerical one, the second one stems from graph theory and does not consider the numeric details of equations, or geometric constraints. So it can be applied to geometric constraints represented by predicates (in opposition to equations) say Prolog predicates like in Bruderlin s works [Bru86] Of course it also applies to equations, or geometric constraints represented by equations, but only unknown equation incidences are taken into account. The probabilistic and numerical method is presented first. It is first applied to systems of equations and then extended to systems of ....

B. Bruderlin. Constructing three-dimensional geometric objects defined by constraints. In Interactive 3D Graphics, pages 111--129, October 1986.

....for prototyping and experimentation, the extensive search and match algorithms that it uses (borrowed from Logic Programming) make it inherently slow. A method that guarantees termination, ruler and compass completeness and uniqueness using the Knuth Bendix critical pair algorithm is presented in [Bru86, Soh91]. This method can be proved to confirm theorems that are provable under the system of axioms given, the rules for determining automatically the desired unique solution are not discussed in these papers. A system based on this method was implemented in Prolog. Aldefeld in [Ald88] uses a forward ....

Beat Bruderlin. Constructing Three-Dimensional Geometric Objects Defined by Constraints. In Workshop on Interactive 3D Graphics, pages 111--129. ACM, October 23-24 1986.

....symbolic or numerical computations. The decomposition is performed either by the inference engine of some expert system like in Buthion [But79] or Verroust et al. [VSR92] to cite a few, either by the matching mecanism provided by some programming language such as Prolog, as for example Bruderlin [Bru86] or by searches in graphs, like Owen [Owe91] Bouma et al. [BFH 93] Ait et al. [AAJM93] and many others. Symbolic computation is used for instance by Ericson and Yap [EY88] and by Kondo [Kon92] This method typically uses Grobner bases, some kind of resultants, or other elimination ....

B. Bruderlin. Constructing three-dimensional geometric objects defined by constraints. In Interactive 3D Graphics, pages 111--129, October 1986.

....execute the construction steps. We call this approach rule constructive solving. Although a Logic Programming style of programming is a good approach for prototyping and experimentation, the extensive computations searching and matching rewrite rules constitute a liability. Bruderlin and Sohrt [6, 46] solve constraints in this way and incorporate the Knuth Bendix critical pairs algorithm [29] They show that their method is correct and solves all problems that can be constructed using ruler and compass. The method can also be proved to confirm geometric theorems that are provable in their ....

B. Bruderlin. Constructing Three-Dimensional Geometric Objects Defined by Constraints. In Workshop on Interactive 3D Graphics, pages 111--129. ACM, October 23-24 1986.

No context found.

Bruderlin B. Constructing three-dimensional geometric object defined by constraints. In ACM SIGGRAPH. Chapel Hill, 1986.

No context found.

Beat Bruderlin. Constructing Three-Dimensional Geometric Objects Defined by Constraints. In F. Crow and S. M. Pizer, editors, Workshop on Interactive 3D Graphics, pages 111--129, Chapel Hill, North Carolina, October 23/24, 1986. ACM SIGGRAPH, New York, NY, U.S.A. Conference proceedings.

No context found.

Bruderlin, B. 1986 Constructing three dimensional geometric objects defined by constraints, In Workshop on Interactive 3D Graphics, Vol. 23-24, October, pp 111-129.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC