Equiareal Parameterization of Triangular Bézier Surfaces

Parameterization is the key property of a parametric surface and significantly affects many kinds applications. To improve quality parameterization, equiareal parameterization minimizes energy, which presented as measure to describe uniformity iso-parametric curves. With help binary Möbius transformation, extended triangular Bézier on domain for first time. The solution corresponding nonlinear minimization problem can be equivalently converted into solving system bivariate polynomial equations with an order three. All exact solutions obtained, one them chosen global optimal problem. Particularly, coefficients in explicitly formulated from control points. Equiareal keeps degree, points, shape unchanged. It improves distribution curves only. new expression are more uniform than original one, displayed by numerical examples.