Geometric Constraints

Geometric constraints, specifying the relations between elements of a geometric model symbolically, are a powerful tool to express and reason about the design intent of geometric models. State of the art methods are limited to 2D constraints and simple 3D cases. This project aims to develop a clean theory for general geometric constraint systems to expand existing algorithm to more general cases. In particular it focuses on detecting hidden dependencies between constraints and handling inequality constraints, which cannot be processed by current methods. The new methods should be able to provide high-level information about the solvability of a constraint system. Especially the reasons for inconsistencies and cases where there are too many or not enough constraints to find a unique solution should be identified. The results may be used for high-level user interfaces for CAD applications and automated geometric reasoning


      Publications

      • F. C Langbein, C. H. Gao, B. I. Mills, A. D. Marshall, R. R. Martin. Topological and Geometric Beautification of Reverse Engineered Geometric Models. In: G. Elber, P. Brunet (eds), Proc. ACM Symp. Solid Modelling and Applications, pp. 255-260, 2004. [Details]

      Presentations

      • F. C. Langbein, C. H. Gao, B. I. Mills, A. D. Marshall, R. R. Martin. Topological and Geometric Beautification of Reverse Engineered Geometric Models. Poster, ACM Symp. Solid Modelling and Applications, Genova, Italy, 9-11 June, 2004. [Details]
      • F. C. Langbein. Topological Structures for Geometric Constraints. Vision Lunch Seminar, School of Computer Science, Cardiff University, 10th February, 2004. [Details]
      • F. C. Langbein. Algebraic Topology and Geometric Constraints. Geometric Modelling Society Meeting, Bath University, 7th January, 2004. [Details]
      • F. C. Langbein. Notes on Geometric Constraint Systems. Vision Lunch Seminar, Dept. Computer Science, Cardiff University, June 2003. [Details]
      • F. C. Langbein. Constraint Satisfaction Problems. Vision Lunch Seminar, Dept. Computer Science, Cardiff University, February 2001. [Details]

            Partners

            Funding