Surface parameterizations have been widely applied in computer-aided design for the geometric processing tasks of surface registration, remeshing, texture mapping, and so on. In this paper, we present an efficient balanced energy minimization algorithm for the computation of simply connected open surface parameterizations with balanced angle and area distortions. The existence of a nontrivial accumulation function of the proposed algorithm is guaranteed under some mild conditions, and the limiting function is shown to be one-to-one. Comparisons of the proposed algorithm with angle- and area-preserving parameterizations show that the angular distortion is close to that of an angle-preserving parameterization while the area distortion is significantly improved. An application of the proposed algorithm involving surface remeshing, registration, and morphing to the Chinese virtual broadcasting technique is demonstrated.
- Balanced energy minimization
- Simply connected open surface
- Surface parameterization
- Virtual broadcasting