A Novel Stretch Energy Minimization Algorithm for Equiareal Parameterizations

Chin-Tien Wu

Abstract:

Surface parameterizations have been widely applied to computer graphics and digital geometry
processing. In this paper, we propose a novel stretch energy minimization (SEM)algorithm
for the computation of equiareal parameterizations of simply connected open surfaces with
very small area distortions and highly improved computational efficiencies. In addition, the
existence of nontrivial limit points of the SEM algorithm is guaranteed under some mild
assumptions of the mesh quality. Numerical experiments indicate that the accuracy, effectiveness,
and robustness of the proposed SEM algorithm outperform the other state-of-the-art
algorithms. Applications of the SEM on surface remeshing, registration and morphing for
simply connected open surfaces are demonstrated thereafter. Thanks to the SEM algorithm,
the computation for these applications can be carried out efficiently and reliably.