In this paper, we present Hierarchical D-NURBS as a new shape modeling representation that generalizes powerful, physics-based D-NURBS for interactive geometric design. Our Hierarchical D-NURBS can be viewed as a collection of standard D-NURBS finite elements, organized hierarchically in a tree structure and subject to continuity constraints across the shared boundaries of adjacent D-NURBS elem...

A Texture Atlas is a two dimensional representation of a 3D model usable for paint systems or as a sewing pattern. The field of texture atlas generation from polygonal models has been well exploited in the recent years. The developed algorithms work on piecewise linear surface representations, but not on parametric surfaces like NURBS, that are still the main surface representation in CAD syste...

We explore T-splines, a generalization of NURBS enabling local refinement, as a basis for isogeometric analysis. We review T-splines as a surface design methodology and then develop it for engineering analysis applications. We test T-splines on some elementary twodimensional and three-dimensional fluid and structural analysis problems and attain good results in all cases. We summarize current l...

We present different innovative formulations for shear deformable beams and plates exploiting the high inter-element continuity provided by NURBS basis functions. We develop isogeometric collocation methods in standard and mixed formulations as well as Galerkin methods using an alternative set of discrete variables. All methods are free of shear locking, which is confirmed by numerical tests.

This paper presents a new unified and optimized method for evaluating and displaying trimmed NURBS surfaces using the Graphics Processing Unit (GPU). Trimmed NURBS surfaces, the de facto standard in commercial mechanical CAD modeling packages, are currently being tessellated into triangles before being sent to the graphics card for display since there is no native hardware support for NURBS. Ot...

We develop a dynamic, free-form surface model which is useful for representing a broad class of objects with symmetries and topological variability. The new model is based upon swung NURBS surfaces, and it inherits their desirable cross-sectional design properties. It melds these geometric features with the demonstrated conveniences of surface design within a physics-based framework. We demonst...

A new method for structural topology optimization is introduced which employs the Isogeometric Analysis (IA) method. In this approach, an implicit function is constructed over the whole domain by Non-Uniform Rational B-Spline (NURBS) basis functions which are also used for creating the geometry and the surface of solution of the elasticity problem. Inspiration of the level set method zero level...

In this paper, we consider the numerical approximation of high order Partial Differential Equations (PDEs) by means of NURBS–based Isogeometric Analysis (IGA) in the framework of the Galerkin method, for which global smooth basis functions with degree of continuity higher than C can be used. We derive a priori error estimates for high order elliptic PDEs under h–refinement, by extending existin...

In this paper a scheme of utilizing shape independent basis functions for the hierarchical multiresolution image compression is shown. For a given image texture region segmentation method is used. Following polygonal approximation of created segments causes a degradation of their boundaries. Using NURBS and Bézier interpolation and approximation segments’ boundaries are created, thus achieving ...