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Potential field based geometric modelling using the method of fundamental solutions
Authors:Roman Tankelevich  Graeme Fairweather  Andreas Karageorghis  Yiorgos‐Sokratis Smyrlis
Abstract:We propose a new geometric modelling method based on the so‐called potential field (PF) modelling technique. The harmonic problem associated with this technique is solved numerically using the method of fundamental solutions (MFS). We investigate the applicability of the proposed approach to parametrically defined curves of varying complexity. Based on the MFS, we also provide definitions of the Boolean operations associated with the geometric modelling. Finally, we give practical applications of the method to computer‐aided design and manufacturing problems. Copyright © 2006 John Wiley & Sons, Ltd.
Keywords:implicit geometric modelling  potential field method  method of fundamental solutions  computer‐aided design (CAD)  computer‐aided geometric modelling  level sets  equipotential curves
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