We propose a novel curvature-aware simplification technique for point-sampled geometry based on the locally optimal projection (LOP) operator. Our algorithm includes two new developments. First

a weight term related to surface variation at each point is introduced to the classic LOP operator. It produces output points with a spatially adaptive distribution. Second

for speeding up the convergence of our method

an initialization process is proposed based on geometry-aware stochastic sampling. Owing to the initialization

the relaxation process achieves a faster convergence rate than those initialized by uniform sampling. Our simplification method possesses a number of distinguishing features. In particular

it provides resilience to noise and outliers

and an intuitively controllable distribution of simplification. Finally

we show the results of our approach with publicly available point cloud data

and compare the results with those obtained using previous methods. Our method outperforms these methods on raw scanned data.