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Computer Aided Geometric Design
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We present a new surface reconstruction framework, which uses the implicit PHT-spline for shape representation and allows us to efficiently reconstruct surface models from very large sets of points. A PHT-spline is a piecewise tri-cubic polynomial over a 3D hierarchical T-mesh, the basis functions of which have good properties such as nonnegativity, compact support and partition of unity. Given a point cloud, an implicit PHT-spline surface is constructed by interpolating the Hermitian information at the basis vertices of the T-mesh, and the Hermitian information is obtained by estimating the geometric quantities on the underlying surface of the point cloud. We take full advantage of the natural hierarchical structure of PHT-splines to reconstruct surfaces adaptively, with simple error-guided local refinements that adapt to the regional geometric details of the target object. Examples show that our approach can produce high quality reconstruction surfaces very efficiently. We also present the multi-threaded algorithm of our approach and show its parallel scalability.