The design of free form surfaces is usually based on NURBS and it works well to quickly get shapes that a designer intends to create. Such surfaces then have desired properties like given border lines and C1 or C2 continuity along lines where several surfaces touch. Our approach is to create surfaces with certain physical properties that designers often need. Given a closed or not closed border...

This paper develops the manifold T-splines, which naturally extend the concept and the currently available algorithms/techniques of the popular planar tensor-product NURBS and T-splines to arbitrary manifold domain of any topological type. The key idea is the global conformal parameterization that intuitively induces a tensor-product structure with a finite number of zero points, and hence offe...

The purpose of this research is to investigate a computer-aided approach to tolerance analysis for assemblies and mechanisms. A CAD system which can generate NURBS surfaces is used to produce imperfect-form, variant models. A method is developed for simulating the mating of these imperfect-form components by formulating surface mating relationships as a nonlinear programming problem. Using this...

Simulations of the Transverse Susceptibility (TS) signal for single-domain and for systems of ferromagnetic particles are presented. When calculating the TS for single domains, details are provided concerning the uniaxial and cubic anisotropies. For the uniaxial single-domain particles a 2D critical approach can be used. The TS for cubic anisotropy is essentially a 3D problem that was solved wi...

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...

This paper proposes a segmentation scheme jointly exploiting color and depth data within a recursive region splitting framework. A set of multi-dimensional vectors is built from color and depth data and the scene is segmented in two parts using normalized cuts spectral clustering. Then a NURBS model is fitted on each of the two parts and various metrics based on the surface fitting results are ...

This paper presents a new finite element (FE) formulation for liquid shells that is based on an explicit, 3D surface discretization using C1-continuous finite elements constructed from NURBS interpolation. Both displacement-based and mixed FE formulations are proposed. The latter is needed for area-incompressible material behavior, where penalty-type regularizations can lead to misleading resul...

A p-adic version of Gromov-Witten invariants for counting plane curves of genus g and degree d through a given number of points is discussed. The multiloop version of p-adic string theory considered by Chekhov and others motivates us to ask how many of these curves are Mumford curves, i.e. uniformisable by a domain at the boundary of the Bruhat-Tits tree for PGL2(Qp). Generally, the number of M...

In geometric design, it is often useful to be able to give an arc length reparametrization for NURBS curves, that keeps the curve a NURBS too. Since parametric rational curves, except for straight lines, cannot be parametrized by arc length, we developed a numerical method of approximating the arc length parametrization function. In this way it was possible to obtain a good parametrization of a...

We present algorithms for interactive rendering of largescale NURBS models. The algorithms convert the NURBS surfaces to Bézier surfaces, tessellate each Bézier surface into triangles and render them using the triangle-rendering capabilities common to current graphics systems. This paper presents algorithms for computing tight bounds on surface properties in order to generate high quality tesse...