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.
Speleers, H., Dierckx, P., Vandewalle, S. (2007). Weight control for modelling with NURPS surfaces. COMPUTER AIDED GEOMETRIC DESIGN, 24(3), 179-186 [10.1016/j.cagd.2007.01.005].
Weight control for modelling with NURPS surfaces
Speleers H.;
2007-04-01
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
