Generating blending surfaces with a pseudo-lévy series solution to fourth order partial differential equations

In our previous work, a more general fourth order partial differential equation (PDE) with three vector-valued parameters was introduced. This equation is able to generate a superset of the blending surfaces of those produced by other existing fourth order PDEs found in the literature. Since it is u...

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Bibliographic Details
Published in:	Computing 2003-11, Vol.71 (4), p.353-373
Main Authors:	YOU, L. H, ZHANG, Jian J, COMNINOS, P
Format:	Article
Language:	eng
Subjects:	Accuracy Applied sciences Artificial intelligence Boundary conditions CAD Computer aided design Computer science control theory systems Exact sciences and technology Mathematical analysis Mathematics Metal forming Methods Numerical analysis Numerical analysis. Scientific computation Numerical methods in mathematical programming, optimization and calculus of variations Partial differential equations Partial differential equations, initial value problems and time-dependant initial-boundary value problems Pattern recognition. Digital image processing. Computational geometry Sciences and techniques of general use
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Summary:	In our previous work, a more general fourth order partial differential equation (PDE) with three vector-valued parameters was introduced. This equation is able to generate a superset of the blending surfaces of those produced by other existing fourth order PDEs found in the literature. Since it is usually more difficult to solve PDEs analytically than numerically, many references are only concerned with numerical solutions, which unfortunately are often inefficient. In this paper, we have developed a fast and accurate resolution method, the pseudo-Lévy series method. Due to its analytical nature, the comparison with other existing methods indicates that the developed method can generate blending surfaces almost as quickly and accurately as the closed form resolution method, and has higher computational accuracy and efficiency than existing Fourier series and pseudo-spectral methods as well as other numerical methods. In addition, it can be used to solve complex surface blending problems which cannot be tackled by the closed form resolution method. To demonstrate the potential of this new method we have applied it to various surface blending problems, including the generation of the blending surface between parametric primary surfaces, general second and higher degree surfaces, and surfaces defined by explicit equations.
ISSN:	0010-485X 1436-5057