Variation of geometrics based on a geometric-reasoning method
Computer-Aided Design
A k-tree generalization that characterized consistency of dimensioned engineering drawings
SIAM Journal on Discrete Mathematics
Algebraic solution for geometry from dimensional constraints
SMA '91 Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications
PIGMOD: parametric and interactive geometric modeller for mechanical design
Computer-Aided Design
An approach to computer-aided parametric
Computer-Aided Design
Parametric design and its impact on solid modeling applications
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
Solving geometric constraints by homotopy
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)
Symbolic constraints in constructive geometric constraint solving
Journal of Symbolic Computation - Special issue: parametric algebraic curves and applications
Constructing three-dimensional geometric objects defined by constraints
I3D '86 Proceedings of the 1986 workshop on Interactive 3D graphics
Representing Dimensions, Tolerances, and Features in MCAE Systems
IEEE Computer Graphics and Applications
A Hybrid Constraint Solver Using Exact and Iterative Geometric Constructions
CAD Systems Development: Tools and Methods [Dagstuhl Seminar, 1995]
A Hybrid Method for Solving Geometric Constraint Problems
ADG '00 Revised Papers from the Third International Workshop on Automated Deduction in Geometry
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This paper proposes a DOF-based graph reduction approach to geometric constraint solving. The proposed approach incrementally solves a geometric constraint problem that is not ruler-and-compass constructible by incrementally identifying a set of constrained geometric entities with 3 DOF (degree of freedom) as a rigid body and determining the geometric entities in the rigid body using one of the two solving procedures: algebraic method and numerical method, instead of solving it simultaneously using a numerical method. However, the use of the numerical method is restricted to solve only those parts that must be solved numerically. By combining the advantages of algebraic solving with the universality of numerical solving, the proposed method can maximize the efficiency, robustness, and extensibility of a geometric constraint solver.