A normalized basis for quintic Powell–Sabin splines

A normalized basis for quintic Powell-Sabin splines

We construct a suitable normalized B-spline representation for C-continuous quintic Powell-Sabin splines. The basis functions have a local support, they are nonnegative, and they form a partition of unity. The construction is based on the determination of a set of triangles that must contain a specific set of points. We are able to define control points and cubic control polynomials which are t...

A normalized basis for reduced Clough-Tocher splines

We present the construction of a suitable normalized B-spline representation for reduced Clough-Tocher splines. The basis functions have a local support, they are nonnegative, and they form a partition of unity. Geometrically, the problem can be interpreted as the determination of a set of triangles that must contain a specific set of points. This leads to a natural definition of tangent contro...

Data Interpolation by C 2 Quintic Splines

Refinable bivariate quartic and quintic C2-splines for quadrilateral subdivisions

Refinable compactly supported bivariate C quartic and quintic spline function vectors on the four-directional mesh are introduced in this paper to generate matrix-valued templates for approximation and Hermite interpolatory surface subdivision schemes, respectively, for both the √ 2 and 1-to-4 split quadrilateral topological rules. These splines have their full local polynomial preservation ord...

A new basis for PHT-splines

PHT-splines (polynomials splines over hierarchical T-meshes) are a generalization of B-splines over hierarchical T-mesheswhich possess a very efficient local refinement property. This property makes PHT-splines preferable in geometric processing, adaptive finite elements and isogeometric analysis. In this paper, we first make analysis of the previously constructed basis functions of PHT-splines...