Shape synthesis with optimization of parametric values grid and THB-Spline parameterization model

This paper presents method for fitting unorganized point cloud with Truncated Hierarchical B-Spline (THB-Spline) based on optimal parametric values. THB-Spline defines sequence of nested tensor-product basis functions where desired areas of parametric domain are refined. This type of parameterization enables better manipulation of certain areas with more degrees of freedom. Initially, input point cloud is parameterized into rectangular unit domain with uniform parametric values. From there, least squares fitting procedure is applied from which initial solution of B-Spline surface is obtained. Afterwards, parametric values grid is optimized in order to create B-Spline surface with better fit. Finally, THB-Spline parameterization is applied in areas with higher geometric error and new B-Spline parameters are optimized to create best possible fitted B-Spline surface.