Mechanical geometry theorem proving
Mechanical geometry theorem proving
Algebraic solution for geometry from dimensional constraints
SMA '91 Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications
Using geometric rewrite rules for solving geometric problems symbolically
Theoretical Computer Science
A graph-constructive approach to solving systems of geometric constraints
ACM Transactions on Graphics (TOG)
Geometric construction by assembling solved subfigures
Artificial Intelligence
A systematic framework for solving geometric constraints analytically
Journal of Symbolic Computation
Decomposition plans for geometric constraint systems, part I: performance measures for CAD
Journal of Symbolic Computation
Solving Geometric Constraints By Homotopy
IEEE Transactions on Visualization and Computer Graphics
Transforming an under-constrained geometric constraint problem into a well-constrained one
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Geometric constraint solving via C-tree decomposition
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Variational geometry in computer-aided design
SIGGRAPH '81 Proceedings of the 8th annual conference on Computer graphics and interactive techniques
Classification and Solving of Merge Patterns in Geometric Constraint Solving
SMI '03 Proceedings of the Shape Modeling International 2003
A correct rule-based geometric constraint solver
Computers and Graphics
Generalized Stewart-Gough platforms and their direct kinematics
IEEE Transactions on Robotics
Artificial Intelligence for Engineering Design, Analysis and Manufacturing
Detecting approximate incomplete symmetries in discrete point sets
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Detecting approximate symmetries of discrete point subsets
Computer-Aided Design
Treedecomposition of geometric constraint graphs based on computing graph circuits
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
A non-rigid cluster rewriting approach to solve systems of 3D geometric constraints
Computer-Aided Design
Detecting design intent in approximate CAD models using symmetry
Computer-Aided Design
Tracking topological changes in parametric models
Computer Aided Geometric Design
Solving systems of 3D geometric constraints with non-rigid clusters
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
Using the witness method to detect rigid subsystems of geometric constraints in CAD
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
Body-and-cad geometric constraint systems
Computational Geometry: Theory and Applications
Classification of direct kinematics to planar generalized Stewart platforms
Computational Geometry: Theory and Applications
Decomposition of geometrical constraint systems with reparameterization
Proceedings of the 27th Annual ACM Symposium on Applied Computing
Combinatorics and the rigidity of CAD systems
Computer-Aided Design
Coordinate-free geometry and decomposition in geometrical constraint solving
Computer-Aided Design
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In this paper, we propose a method which can be used to decompose a 2D or 3D constraint problem into a C-tree. With this decomposition, a geometric constraint problem can be reduced into basic merge patterns, which are the smallest problems we need to solve in order to solve the original problem in certain sense. Based on the C-tree decomposition algorithm, we implemented a software package MMP/Geometer. Experimental results show that MMP/Geometer finds the smallest decomposition for all the testing examples efficiently.