Variation of geometrics based on a geometric-reasoning method
Computer-Aided Design
Algebraic solution for geometry from dimensional constraints
SMA '91 Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications
What is a parametric family of solids?
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
A graph-constructive approach to solving systems of geometric constraints
ACM Transactions on Graphics (TOG)
Necessary conditions for boundary representation variance
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Boundary representation deformation in parametric solid modeling
ACM Transactions on Graphics (TOG)
Consistent updates in dual representation systems
Proceedings of the fifth ACM symposium on Solid modeling and applications
Sketch-based pruning of a solution space within a formal geometric constraint solver
Artificial Intelligence
Decomposition plans for geometric constraint systems, part I: performance measures for CAD
Journal of Symbolic Computation
Decomposition plans for geometric constraint problems, part II: new algorithms
Journal of Symbolic Computation
Solving spatial basic geometric constraint configurations with locus intersection
Proceedings of the seventh ACM symposium on Solid modeling and applications
On Spatial Constraint Solving Approaches
ADG '00 Revised Papers from the Third International Workshop on Automated Deduction in Geometry
On the Domain of Constructive Geometric Constraint Solving Techniques
SCCG '01 Proceedings of the 17th Spring conference on Computer graphics
Characterizing 1-dof Henneberg-I graphs with efficient configuration spaces
Proceedings of the 2009 ACM symposium on Applied Computing
A correct rule-based geometric constraint solver
Computers and Graphics
A constraint-based dynamic geometry system
Computer-Aided Design
The Reachability Problem in Constructive Geometric Constraint Solving Based Dynamic Geometry
Journal of Automated Reasoning
| Hi-index | 0.00 |
In parametric design, changing values of parameters to get different solution instances to the problem at hand is a paramount operation. One of the main issues when generating the solution instance for the actual set of parameters is that the user does not know in general which is the set of parameter values for which the parametric solution is feasible. Similarly, in constraint-based dynamic geometry, knowing the set of critical points where construction feasibility changes would allow to avoid unexpected and unwanted behaviors. We consider parametric models in the Euclidean space with one internal degree of freedom. In this scenario, in general, the set of values of the variant parameter for which the parametric model is realizable and defines a valid shape is a set of intervals on the real line. In this work we report on our experiments implementing the van der Meiden Approach to compute the set of parameter values that bound intervals for which the parametric object is realizable. The implementation is developed on top of a constructive, ruler-and-compass geometric constraint solver. We formalize the underlying concepts and prove that our implementation is correct, that is, the approach exactly computes all the feasible interval bounds.