Discrete Coons patches

We investigate surfaces which interpolate given boundary curves. We show that the discrete bilinearly blended Coons patch can be defined as the solution of a linear system. With the goal of producing better shape than the Coons patch, this idea is generalized, resulting in a new method based on a bl...

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Bibliographic Details
Published in:Computer aided geometric design 1999, Vol.16 (7), p.691-700
Main Authors: Farin, Gerald, Hansford, Dianne
Format: Article
Language:English
Subjects:
Applied sciences
Computer aided design
Computer science
control theory
systems
Coons patches
Discrete surfaces
Exact sciences and technology
Interpolation
curve fitting
Mathematical methods in physics
Numerical approximation and analysis
Physics
Software
Variational principles
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Summary:We investigate surfaces which interpolate given boundary curves. We show that the discrete bilinearly blended Coons patch can be defined as the solution of a linear system. With the goal of producing better shape than the Coons patch, this idea is generalized, resulting in a new method based on a blend of variational principles. We show that no single blend of variational principles can produce “good” shape for all boundary curve geometries. We also discuss triangular Coons patches and point out the connections to the rectangular case.
ISSN:0167-8396
1879-2332
DOI:10.1016/S0167-8396(99)00031-X