Abstract
This paper presents an optimal method for constructing bicubically Coons surface based upon twist vectors at rectangular grid points. These twists are determined by using a new optimal criterion. By variational principle, the minimization problem is based on the Euler-Lagrange PDE. By applying it at corner points on each patch, we introduce a new minimization problem, whoes solution is approximately optimal for Euler-Lagrange PDE on every patch. A linear equations system with symmetrical block tridiagonal coefficient matrix is established to solve the minimization problem. Its coefficient matrix, which can be written as the Kronecker product of two identical interesting special matrices, is proved to be non-singular. Numerical solution is stable and examples validate its effectiveness.
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