Using Gröbner bases for computation of general offsets and their self-intersections
BASTL, B. Using Gröbner bases for computation of general offsets and their self-intersections. Institut of Applied Geometry, JKU Linz, 2007.
|Anglický název:||Using Gröbner bases for computation of general offsets and their self-intersections|
|Místo konání:||Institut of Applied Geometry, JKU Linz|
|Abstrakt EN:||The undercut in 3-axis and 5-axis milling causes serious problems because of unexpected damages of the machined surface. The motion of the cutter is planned along an general offset surface and a self-intersection of the general offset surface indicates the undercut during the milling. The talk introduces a special class of surfaces, called GRC surfaces, which are given by rational parametrization and for which also the convolution surface (i.e. also arbitrary general offset surface) with arbitrary rational surface is rational. Groebner bases theory is usefull in identification of such surfaces. For these surfaces, the self-intersection of the general offset surface can be computed using the symbolic-numeric algorithm based on variables elimination methods (Grobner bases, resultants) followed by finding points of implicitly defined curve in the parametric domain of the general offset surface.|