Patent ID: 7369972

Claim:
A method for surface re-parameterization of a surface wound extraordinary vertices of a computer three-dimensional Catmull-Clark model with a plurality of vertices, at least one extraordinary vertex, and iso-parameter lines with a natural spacing, the method comprising the step of: re-parameterizing one or more subdivision surfaces of the Catmull-Clark model around one or more of the extraordinary vertices into a re-parameterized surface with a new spacing that is different than the natural spacing as the iso-parameter lines approach the extraordinary vertex; and at least one of storing the iso-parameter lines with the new spacing and displaying the iso-parameter lines with the new spacing, where the re-parameterizing comprises the following steps: computing four subdominant eigenvalues corresponding to each of the vertices of a face, being face vertices, of a quadrilateral mesh containing one or more points being evaluated; re-parameterizing the surface around each of the face vertices using a re-parameterization of vanishing derivatives, such that x ⁢ → F k ⁢  x  α k - 1 ⁢ x , where k identifies the face vertex and x is the point being evaluated in a parameter domain, and the re-parameterization is subject to the constraint α k > - log ⁢ ⁢ 2 log ⁢ ⁢ λ k where λ k is the subdominant eigenvalue corresponding to face vertex k and α k is an exponent parameter of the re-parameterization for the respective face vertex; and blending the re-parameterizations of each face vertex that is re-parameterized.