Constraint programming languages: their specification and generation
Constraint programming languages: their specification and generation
Variation of geometrics based on a geometric-reasoning method
Computer-Aided Design
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Communications of the ACM
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Constructive Geometric Constraint Solving: A New Application of Genetic Algorithms
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SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
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Elements for a modular dynamic geometry system
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A constraint-based dynamic geometry system
Proceedings of the 2008 ACM symposium on Solid and physical modeling
A constraint-based system for product design and manufacturing
Robotics and Computer-Integrated Manufacturing
A C-tree decomposition algorithm for 2D and 3D geometric constraint solving
Computer-Aided Design
A constraint solver to define correctly dimensioned and overdimensioned parts
Computer-Aided Design
A non-rigid cluster rewriting approach to solve systems of 3D geometric constraints
Computer-Aided Design
A constraint-based dynamic geometry system
Computer-Aided Design
Using the witness method to detect rigid subsystems of geometric constraints in CAD
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
Decomposition of geometrical constraint systems with reparameterization
Proceedings of the 27th Annual ACM Symposium on Applied Computing
The Reachability Problem in Constructive Geometric Constraint Solving Based Dynamic Geometry
Journal of Automated Reasoning
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We present a rule-based geometric constraint solver. The solver handles 2-D, variational, constraint-defined geometric objects. The solver computes a solution in two phases. First, the solver builds a sequence of construction steps. Then the construction steps are carried out to generate an instance of the geometric object for the current dimension values. We prove that the solver is correct. First, we formalize the solver as a rewrite system whose rewriting rules are geometric construction steps. Then we prove that, for well-constrained geometric objects, the sequence in which the solver applies the construction steps defines a terminating confluent reduction system.