Conditions for unique graph realizations
SIAM Journal on Computing
A graph-constructive approach to solving systems of geometric constraints
ACM Transactions on Graphics (TOG)
Handbook of discrete and computational geometry
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
FRONTIER: fully enabling geometric constraints for feature-based modeling and assembly
Proceedings of the sixth ACM symposium on Solid modeling and applications
Constraint solving for computer-aided design
Constraint solving for computer-aided design
Graph and combinatorial algorithms for geometric constraint solving
Graph and combinatorial algorithms for geometric constraint solving
Geometric constraints within feature hierarchies
Computer-Aided Design
Geometric constraints within feature hierarchies
Computer-Aided Design
Feature-based 3D morphing based on geometrically constrained spherical parameterization
Computer Aided Geometric Design
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We study the well documented problem of systematically navigating the potentially exponentially many roots or realizations of well-constrained, variational geometric constraint systems. We give a scalable method called the Equation and Solution Manager (ESM) that can be used both for automatic searches and visual, user-driven searches for desired realizations. The method incrementally assembles the desired solution of the entire system and avoids combinatorial explosion by offering the user a visual walk-through of the solutions to recursively constructed subsystems and by permitting the user to make gradual, adaptive solution choices.We isolate requirements on companion methods that are essential and desirable for efficient, meaningful solution space navigation. Specifically, they permit (a) incorporation of many existing approaches to solution space steering or navigation into the ESM; and (b) integration of the ESM into a standard geometric constraint solver architecture. We address the latter challenge and explain how the integration is achieved. Additionally, we sketch the ESM implementation as part of an opensource, 2D and 3D geometric constraint solver, FRONTIER.