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Abstract

In this paper, we propose a new method for approximating an unorganized set of
points scattered over a piecewise smooth surface by a triangle mesh. The method
is based on the Garland-Heckbert local quadric error minimization strategy.
First an adaptive spherical cover and auxiliary points corresponding to the
cover elements are generated. Then the intersections between the spheres of the
cover are analyzed and the auxiliary points are connected. Finally the
resulting mesh is cleaned from nonmanifold parts. The method allows us to
control the approximation accuracy, process noisy data, and reconstruct sharp
edges and corners. Further, the vast majority of the triangles of the generated
mesh have their aspect ratios close to optimal. Thus our approach integrates
the mesh reconstruction, smoothing, decimation, feature restoration, and
remeshing stages together.