  In mesh simplification, common requirements like accuracy, triangle quality,
and feature alignment are often considered as a trade-off. Existing algorithms
concentrate on just one or a few specific aspects of these requirements. For
example, the well-known Quadric Error Metrics (QEM) approach prioritizes
accuracy and can preserve strong feature lines/points as well but falls short
in ensuring high triangle quality and may degrade weak features that are not as
distinctive as strong ones. In this paper, we propose a smooth functional that
simultaneously considers all of these requirements. The functional comprises a
normal anisotropy term and a Centroidal Voronoi Tessellation (CVT) energy term,
with the variables being a set of movable points lying on the surface. The
former inherits the spirit of QEM but operates in a continuous setting, while
the latter encourages even point distribution, allowing various surface
metrics. We further introduce a decaying weight to automatically balance the
two terms. We selected 100 CAD models from the ABC dataset, along with 21
organic models, to compare the existing mesh simplification algorithms with
ours. Experimental results reveal an important observation: the introduction of
a decaying weight effectively reduces the conflict between the two terms and
enables the alignment of weak features. This distinctive feature sets our
approach apart from most existing mesh simplification methods and demonstrates
significant potential in shape understanding.
