Patent ID: 7425959

Claim:
A computer implemented method for generating a parameterized representation of an implicit function, the method comprising: receiving a definition of one or more parameterization regions related to one or more parameterizing variables of the implicit function wherein the parameterization regions for at least one of the one or more parameterizing variables are based on a non-singularity property associated with a dependent derivative matrix related to a corresponding one of the one or more parameterizing variables; selecting a first range of values of the one or more parameterizing variables of the one or more parameterizing regions for applying an intervalized super convergence test, wherein applying the intervalized super convergence test comprises determining whether the selected range satisfies a Kantorovich condition; continuing to select subsequent ranges of values of the parameterizing variables for applying the intervalized super convergence test by sub-dividing the one or more parameterizing regions for a selected number of iterations or until the intervalized super convergence test is satisfied; and generating the parameterized representation of the implicit function based on one or more ranges of values of the one or more parameterizing variables that satisfy the intervalized super convergence test.