The NURBS book
A note on Farin points for rational triangular Be´zier patches
Computer Aided Geometric Design
Smoothing rational B-spline curves using the weights in an optimization procedure
Computer Aided Geometric Design
On calculating normalized Powell-Sabin B-splines
Computer Aided Geometric Design
Subdivision of uniform Powell—Sabin splines
Computer Aided Geometric Design
Using Farin points for rational Bézier surfaces
Computer Aided Geometric Design
Piecewise Quadratic Approximations on Triangles
ACM Transactions on Mathematical Software (TOMS)
NURPS for special effects and quadrics
Mathematical Methods for Curves and Surfaces
A Simple Technique for NURBS Shape Modification
IEEE Computer Graphics and Applications
Local subdivision of Powell-Sabin splines
Computer Aided Geometric Design
Quasi-hierarchical Powell--Sabin B-splines
Computer Aided Geometric Design
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NURPS surfaces are the rational extension of Powell-Sabin splines in their normalized B-spline representation. In this paper we study the influence of modifying the weights of a NURPS surface. We describe the relation between the weights associated with a control triangle and the points on the NURPS surface by means of a double volume ratio. We also extend the concept of Farin points for rational Bezier curves to NURPS surfaces, resulting in weight points and weight triangles. They admit a local weight control in a geometrically intuitive way.