Weighted quadrature for hierarchical B-splines

Deformation With Hierarchical B-Splines

Deformation has received wide attention in the eld of Computer Graphics, Computer Vision and Image Processing. This paper describes a new method which is based on the concept of hierarchical BSplines. Compared with existing methods, our approach is adaptive in that it puts more e ort in complex regions which need more attention. It also provides an elegent tool for curve or surface matching tog...

Multiresolution Surface Reconstruction for Hierarchical B-splines

This paper presents a method for automatically generating a hierarchical B-spline surface from an initial set of control points. Given an existing mesh of control points , a mesh with half the resolution , is constructed by simultaneously approximating the finer mesh while minimizing a smoothness constraint using weighted least squares. Curvature measures of are used to identify features that n...

Conversion between T-Splines and Hierarchical B-Splines

T-splines is a recently developed surface modelling technique which is a generalization of B-splines and allows true local refinement. Another well established method supporting local refinement is hierarchical B-splines. This paper presents algorithms for transformation between T-splines and hierarchical (rational) B-splines. With the transformation, a surface expressed in terms of T-splines c...

Quasi-hierarchical Powell-Sabin B-splines

Hierarchical Powell-Sabin splines are C-continuous piecewise quadratic polynomials defined on a hierarchical triangulation. The mesh is obtained by partitioning an initial conforming triangulation locally with a triadic split, so that it is no longer conforming. We propose a normalized quasi-hierarchical basis for this spline space. The B-spline basis functions have a local support, they form a...

Finite Element Approximation with Hierarchical B-Splines