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  • Handling the geometrical redundancy in 2D geometric constraint solving
    Podgorelec, David ; Špelič, Denis
    In this report, we present an original constTUctive geometric constraint solver for 2D geometric design. The algorithm is based on the welI-known concepts of sets of vectors with constrained mutual ... angles (CA sets) and sets of points with constrained distance s (CD sets). It is a representative of the shape recognition based (SR-based) geometric constraint solvers but, unlike the other algorithms ITom this group, it is aimed towards the generality. The existent general geometric constraint solvers are pre-processed by a degree-of-freedom analysis, which usually enables efficient graph decomposition and recombination. However, they are all based on the assumption that structural solvability automatically assures geometri cal solvability. With other words, these systems assume that the geometric constraint problems without the stmctural redmldancy are also free of the geometrical redundancy. We show in the report that this assumption fails in numerous, even the most basic, configurations. We introduce a simple but efficient algorithm for handling the geometrical redundancy in such cases. Another novelty deals with the conditional constraints between three or more geometric elements, with mles for their simplification, and with a redundancy check. A T1umerical solver is eventually employed only as the last resort if the sequence of graph simplifications does not result in a single CD set. It is worth to note that the obtained system of equations is in a special fonn where all the variables are the points' coordinates.
    Type of material - treatise, study
    Publication and manufacture - Maribor : Faculty of Electrical Engineering and Computer Science, Laboratory for geometric modelling and multimedia algorithms, 2006
    Language - english
    COBISS.SI-ID - 13074710

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