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Combining constructive and numerical approach for geometric constraint solving

出版	Faculty of Electrical Engineering and Computer Science, Laboratory for geometric modelling and multimedia algorithms, 2004
URL	http://books.google.com.hk/books?id=2HpGOQAACAAJ&hl=&source=gbs_api

註釋In the report, we present some ideas how to extend the drawing scope and to improve the interactivity and f1exibility of constraint-based geometric modellers and drawing systems. These ideas were employed in the experimental 2D drawing system GemmaCAD 2D. Its main feature is the early exit for constraint problems solvable by an insertion of redundant constraints. This task is based on simple rules for solving triangles and calculation of sums of adjacent angles, and some more powerful rules for solving quadrangies. If a problem cannot be solved by local propagation after insertion of redundant distances and angles, it is partitioned into independent subproblems, and these are then solved by the well-known numerical optimisation method BFGS. We propose some ideas addressing partition and preparation of equations. All constraints are presented by the point coordinates. only. This transformation usually improves convergence, enables simple calculation of derivatives required by BFGS in symbolic form, and allows us to extend the constraint set by new constraint types.