Meshing Non-uniformly Sampled and Incomplete Data Based on Displaced T-spline Level Sets

We propose a new method for constructing a piecewise smooth mesh from a set of unorganized data points, which may be non-uniformly sampled, noisy, and even containing holes. The method is based on the construction of an implicit representation of the surface, by using smooth (C² in our case) T-spline scalar functions. We first generate the T- spline control grid, and use an evolution process such that the resulting T-spline level sets capture the topology and outline of the object to be reconstructed. The initial mesh with high quality is obtained from the implicit T-spline function through the marching triangulation method. Then we project each data point to the initial mesh, and get a scalar displacement field. Detailed features will be captured by the displaced mesh. We also propose an additional evolution process, which combines data-driven velocities and feature- preserving bilateral filters, in order to reproduce sharp features.