A method, apparatus, and article of manufacture provide the ability to construct an optimal parameterization for a discrete surface patch. A three-dimensional image having a surface is selected. An initial parameterization of the surface onto a two-dimensional plane is constructed. A distortion of the initial parameterization is measured. A length parameter, an area parameter, and an angle parameter are specified. The initial parameterization is then optimized through a discrete deformation of a parameter domain that minimizes the distortion based on the length, area, and angle parameter.