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Method of boundary based smooth shape design

By Hassan Ugail

Abstract

The discussion in this paper focuses on how boundary\ud based smooth shape design can be carried out. For this we\ud treat surface generation as a mathematical boundary-value\ud problem. In particular, we utilize elliptic Partial Differential\ud Equations (PDEs) of arbitrary order. Using the methodology\ud outlined here a designer can therefore generate the\ud geometry of shapes satisfying an arbitrary set of boundary\ud conditions. The boundary conditions for the chosen PDE\ud can be specified as curves in 3-space defining the profile\ud geometry of the shape.\ud We show how a compact analytic solution for the chosen\ud arbitrary order PDE can be formulated enabling complex\ud shapes to be designed and manipulated in real time.\ud This solution scheme, although analytic, satisfies exactly,\ud even in the case of general boundary conditions, where the\ud resulting surface has a closed form representation allowing\ud real time shape manipulation. In order to enable users\ud to appreciate the powerful shape design and manipulation\ud capability of the method, we present a set of practical example

Topics: Smooth shape design, ; Boundary-value problems, ; PDEs
Year: 2005
OAI identifier: oai:bradscholars.brad.ac.uk:10454/2431
Provided by: Bradford Scholars

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