1. A computer implemented method for constructing an optimal parameterization for a discrete surface patch, comprising: selecting a three-dimensional image having a surface displayed by a computer device; constructing an initial parameterization of the surface onto a two-dimensional plane displayed by the computer device; measuring a distortion induced by the initial parameterization; specifying a length parameter α l , an area parameter α a , and an angle parameter α c ; and using the computer device for optimizing the initial parameterization through a discrete deformation of a parameter domain that minimizes the distortion of the parameterized surface displayed by the computer device on the two-dimensional plane based on the length, area, and angle parameters.