Adaptive surface reconstruction based on implicit PHT-splines

We present a new shape representation, the implicit PHT-spline, which allows us to efficiently reconstruct surface models from very large sets of points. A PHT-spline is a piece-wise tricubic polynomial over a 3D hierarchical T-mesh, the basis functions of which have good properties such as non-negativity, 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 use 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. Unlike some previous methods that heavily depend on the normal information of the point cloud, our approach only uses it for orientation and is insensitive to the noise of normals. Examples show that our approach can produce high quality reconstruction surfaces very efficiently.