基于分级T-网格隐式样条的自适应曲面重构

We present a new shape representation, the implicit PHT-spline surface, which allows us to efficiently reconstruct surface models from very large sets of points. A PHT-spline is a piecewise tricubic polynomial over a 3D hierarchical T-mesh, the basis functions of which have important properties such as nonnegativity, compact support and partition of unity. Given a set of point cloud, the implicit PHT-spline surface is constructed by interpolating the Hermitian information at 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 the 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 determination. Examples suggest that our approach can produce high quality reconstruction surface very efficiently.