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Method of boundary based smooth shape design
Ugail, Hassan
Ugail, Hassan
Publication Date
2005
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© 2005 IASTED and ACTA Press. Reproduced in accordance with the publisher's self-archiving policy.
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Open Access status
Accepted for publication
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Abstract
The discussion in this paper focuses on how boundary
based smooth shape design can be carried out. For this we
treat surface generation as a mathematical boundary-value
problem. In particular, we utilize elliptic Partial Differential
Equations (PDEs) of arbitrary order. Using the methodology
outlined here a designer can therefore generate the
geometry of shapes satisfying an arbitrary set of boundary
conditions. The boundary conditions for the chosen PDE
can be specified as curves in 3-space defining the profile
geometry of the shape.
We show how a compact analytic solution for the chosen
arbitrary order PDE can be formulated enabling complex
shapes to be designed and manipulated in real time.
This solution scheme, although analytic, satisfies exactly,
even in the case of general boundary conditions, where the
resulting surface has a closed form representation allowing
real time shape manipulation. In order to enable users
to appreciate the powerful shape design and manipulation
capability of the method, we present a set of practical examples
Version
Accepted Manuscript
Citation
Ugail, H. (2005). Method of Boundary Based Smooth Shape Design. In: Hamza, M .H. (ed.) Proceedings of the IASTED International Conference on Computer Graphics and Imaging (CGIM 2005) August 15-17, 2005, Honolulu, Hawaii. Calgary: ACTA Press: 54-59.
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Type
Conference paper