lec4 - Geometric Constraint Lecture Instructor Meera...

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Geometric Constraint Lecture Instructor: Meera Sitharam, Recorded by Heping Gao Jan 31, 2006 1 Demo 1 from Solidwork software: Hexagon with three diagonals in 2D Figure 1 is a Hexgagon with three diagonals in 2D and the whole graph is rigid(wellconstrainted, dense). The minimal rigid subgraph (wellconstrained subgraph, dense subgraph) is the whole graph. (Note: trival rigid subgraph, such as two vertices and one distance between them in 2D, is not considered!) So, the only DR-plan for this example is shown in the Figure 2. 1 2 3 4 5 6 Figure 1: Hexagon with three diagonals in 2D Figrue 3 has a DR-plan shown in Figure 4. The fan-in (the maximum number of the children of a cluster in the DR-plan) is 3 in Figure 4 while the fan-in in Figure 2 is 6, so intuitively hexagon is more difficult to solve. Please recall the difference bewteen Computational Geometry and Geomet- ric Constraint Solving that we have introduced before: in Computational Geometry, the size of the minimum equation/inequality system we need to solve is bound by some constant, while in Geometric Constraint Solving, the 1
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