Title: A Novel Stretch Energy Minimization Algorithm for Equiareal Parameterizations,
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 a very small area distortion and a
highly improved computational efficiency. 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
efficiency, accuracy, and robustness of the proposed SEM algorithm outperform
other state-of-the-art algorithms. Applications of the SEM on surface remeshing
and surface registration for simply connected open surfaces are demonstrated
thereafter. Thanks to the SEM algorithm, the computations for these
applications can be carried out efficiently and robustly.