Weighted Quasi Interpolant Spline Approximation of 3D point clouds via local refinement
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We present a new surface approximation, the Weighted Quasi Interpolant Spline Approximation (w-QISA), to approximate very large and noisy point clouds. We adopt local implicit representations based on three key ingredients: 1) a local mesh for the piecewise implicit representation z=f(x,y) that defines where the approximation will be more detailed, 2) a weight function for the approximation of the control points that captures the local behavior of the point cloud, and 3) a criterion for global (or local) refinement. The present contribution addresses the theoretical properties of the method, focusing on global and local bounds, shape preservation, local shape control and robustness. The accuracy of this representation is tested against real data from different types of surfaces.
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