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
Mechanical theorem proving in geometries
Mechanical theorem proving in geometries
Graph-based approach for solving geometric constraint problems
Graph-based approach for solving geometric constraint problems
Combining constructive and equational geometric constraint-solving techniques
ACM Transactions on Graphics (TOG)
A systematic framework for solving geometric constraints analytically
Journal of Symbolic Computation
A constraint solving-based approach to analyze 2D geometric problems with interval parometers
Proceedings of the sixth ACM symposium on Solid modeling and applications
Solving Geometric Constraints By Homotopy
IEEE Transactions on Visualization and Computer Graphics
A Hybrid Constraint Solver Using Exact and Iterative Geometric Constructions
CAD Systems Development: Tools and Methods [Dagstuhl Seminar, 1995]
Variational geometry in computer-aided design
SIGGRAPH '81 Proceedings of the 8th annual conference on Computer graphics and interactive techniques
A correct rule-based geometric constraint solver
Computers and Graphics
Geometric constraint solving via C-tree decomposition
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
A framework for geometric constraint satisfaction problem
Proceedings of the 2006 ACM symposium on Applied computing
Using Cayley-Menger determinants for geometric constraint solving
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Proceedings of the 2007 ACM symposium on Applied computing
Combining symbolic and numerical solvers to simplify indecomposable systems solving
Proceedings of the 2008 ACM symposium on Applied computing
Multivariate root finding with search space decomposition and randomisation
Proceedings of the 2009 ACM symposium on Applied Computing
Geometric constraint solving: The witness configuration method
Computer-Aided Design
Using invariance under the similarity group to solve geometric constraint systems
Computer-Aided Design
Solving geometric constraints invariant modulo the similarity group
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartIII
Sensor network localization using sensor perturbation
ACM Transactions on Sensor Networks (TOSN)
Interrogating witnesses for geometric constraint solving
Information and Computation
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
Leading a continuation method by geometry for solving geometric constraints
Computer-Aided Design
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A basic idea of geometric constraint solving is to decompose the constraint problem into smaller ones according to some basic configurations. In this paper, we find all spatial basic configurations involving points, lines, and planes containing up to six geometric primitives in an automated way. Many of these basic configurations still resist effective analytical solutions. We propose the locus intersection method for geometric constraint solving, which is used to solve all these basic configurations.