We begin the mathematical study of Isogeometric Analysis based on NURBS (non-uniform rational B-splines.) Isogeometric Analysis is a generalization of classical Finite Element Analysis (FEA) which possesses improved properties. For example, NURBS are capable of more precise geometric representation of complex objects and, in particular, can exactly represent many commonly engineered shapes, suc...

We introduce a novel method to convert trimmed NURBS surfaces to untrimmed subdivision surfaces with Bézier edge conditions. We take a NURBS surface and its trimming curves as input, from this we automatically compute a base mesh, the limit surface of which fits the trimmed NURBS surface to a specified tolerance. We first construct the topology of the base mesh by performing a cross-field based...

In this paper, a new representational model is introduced for the rational family of ruled surfaces in Computer Graphics. The surface parameterization is constructed using the NURBS basis functions and line geometry. The ruled surface is defined by interpolating directly dual unit vectors representing lines, which is a single parametric surface and its shape depends on the control lines. All th...

The Free From Deformations are the most spread methods to modify the shape of geometrical objects, described with vertices and faces. Many applications have been developed to extend this approach, allowing different constraint specifications or actions. It has also been adapted to deform subdivision or implicit surfaces. This paper introduces an improvement for NURBS surfaces, allowing a point ...

In this project we numerically simulate electrophysiological models for cardiac applications by means of Isogeometric Analysis. Specifically, we aim at understanding the advantages of using high order continuous NURBS (Non-Uniform Rational B-Splines) basis functions in the approximation of the traveling waves of the action potential. As application, we consider the numerical simulations on the ...

Real-time high quality rendering of complex models remains a big challenge. Simply splitting the models into several parts which can be simplified and rendered independently introduces disturbing gaps along the common borders. Recent approaches for viewdependent rendering of huge models either neglect the artifacts introduced by the gaps or try to maintain the connectivity of the models. Unfort...

This paper presents MUG, a multi-user environment for collaborative conceptual shape design. The majority of current research prototypes and commercial systems for collaborative modeling emphasize data sharing and markup. Collaborative 3D environments and virtual worlds usually restrict themselves to models with display representations (e.g., VRML) and asynchronous sharing of distinct objects. ...

Isogeometric analysis (IGA) is a novel computational approach recently developed by Hughes et al. [1]with the aim of integrating computer aided design (CAD) into structural analysis. It uses non uniform rational B-splines (NURBS) for both description of the geometry and approximation of thesolution field. NURBS are the most common basis functions in the CAD systems. Using CAD basis functions di...