From NURBS to NURPS geometries

From NURBS to NURPS geometries

Quadratic Powell-Sabin splines and their rational extension, the socalled NURPS surfaces, are an interesting alternative for classical tensor-product NURBS in the context of isogeometric analysis, because they allow the use of local refinements while retaining a Bspline like representation and exact description of conic sections. In this paper we present a simple and effective strategy to conve...

From PS{splines to NURPS

In Ehresmann’s Footsteps: from Group Geometries to Groupoid Geometries

The geometric understanding of Cartan connections led Charles Ehresmann from the Erlangen program of (abstract) transformation groups to the enlarged program of Lie groupoid actions, via the basic concept of structural groupoid acting through the fibres of a (smooth) principal fibre bundle or of its associated bundles, and the basic examples stemming from the manifold of jets (fibred by its sou...

Weight control for modelling with NURPS surfaces

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 ration...

Mixed-element volume completion from NURBS surfaces

In this paper we present a methodology to create a volumetric representation from a 2-manifold without boundaries represented with untrimmed NURBS surfaces. A trivariate NURBS representation is difficult to construct from such a representation, especially when the input surface patches were created with only a boundary representation as the goal. These kinds of inputs arise in numerous existing...