Some examples of the use of distances as coordinates for Euclidean geometry
Journal of Symbolic Computation
Algorithms in invariant theory
Algorithms in invariant theory
Solving geometric constraints by homotopy
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
A constraint solving-based approach to analyze 2D geometric problems with interval parometers
Proceedings of the sixth ACM symposium on Solid modeling and applications
Geometric Constraint Solving and Applications
Geometric Constraint Solving and Applications
Solving spatial basic geometric constraint configurations with locus intersection
Proceedings of the seventh ACM symposium on Solid modeling and applications
SMI '99 Proceedings of the International Conference on Shape Modeling and Applications
Symbolic and numerical techniques for constraint solving
Symbolic and numerical techniques for constraint solving
Numerical decomposition of geometric constraints
Proceedings of the 2005 ACM symposium on Solid and physical modeling
Geometric constraints solving: some tracks
Proceedings of the 2006 ACM symposium on Solid and physical modeling
Nonlinear systems solver in floating-point arithmetic using LP reduction
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Geometric constraint solving: The witness configuration method
Computer-Aided Design
Constructing a tetrahedron with prescribed heights and widths
ADG'06 Proceedings of the 6th international conference on Automated deduction in geometry
A 2D geometric constraint solver using a graph reduction method
Advances in Engineering Software
Interrogating witnesses for geometric constraint solving
Information and Computation
Coordinate-free geometry and decomposition in geometrical constraint solving
Computer-Aided Design
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We use Cayley-Menger Determinants (CMDs) to obtain an intrinsic formulation of geometric constraints. First, we show that classical CMDs are very convenient to solve the Stewart platform problem. Second, issues like distances between points, distances between spheres, cocyclicity and cosphericity of points are also addressed. Third, we extend CMDs to deal with asymmetric problems. In 2D, the following configurations are considered: 3 points and a line; 2 points and 2 lines; 3 lines. In 3D, we consider: 4 points and a plane; 2 points and 3 planes; 4 planes.