  In this paper, we present a surface remeshing method with high approximation
quality based on Principal Component Analysis. Given a triangular mesh and a
user assigned polygon/vertex budget, traditional methods usually require the
extra curvature metric field for the desired anisotropy to best approximate the
surface, even though the estimated curvature metric is known to be imperfect
and already self-contained in the surface. In our approach, this anisotropic
control is achieved through the optimal geometry partition without this
explicit metric field. The minimization of our proposed partition energy has
the following properties: Firstly, on a C2 surface, it is theoretically
guaranteed to have the optimal aspect ratio and cluster size as specified in
approximation theory for L1 piecewise linear approximation. Secondly, it
captures sharp features on practical models without any pre-tagging. We develop
an effective merging-swapping framework to seek the optimal partition and
construct polygonal/triangular mesh afterwards. The effectiveness and
efficiency of our method are demonstrated through the comparison with other
state-of-the-art remeshing methods.
