Virtual interactive examination of the quality of car body surfaces is an important issue in the development process of a car. The method is based on simulating reflection lines using striped environment maps and strong specular highlights. For this purpose high quality meshes are created from the NURBS surfaces. However, the meshes have a fixed resolution, hence a closer examination requires a...

We construct a Teichmüller curve uniformized by the Fuchsian triangle group ∆(m, n, ∞) for every m < n ≤ ∞. Our construction includes the Teichmüller curves constructed by Veech and Ward as special cases. The construction essentially relies on properties of hypergeometric differential operators. We interprete some of the so-called Lyapunov exponents of the Kontsevich–Zorich cocycle as normalize...

We consider the numerical solution of second order Partial Differential Equations (PDEs) on lower dimensional manifolds, specifically on surfaces in three dimensional spaces. For the spatial approximation, we consider Isogeometric Analysis which facilitates the encapsulation of the exact geometrical description of the manifold in the analysis when this is represented by B–splines or NURBS. Our ...

Developable surfaces possess qualities that are desirable in the manufacturing processes of CAD/CAM models. Specifically, models formed out of developable surfaces can be manufactured from planar sheets of material without distortion. This quality proves most useful when dealing with materials such as paper, leather or sheet metal, which cannot be easily stretched or deformed during production....

We propose a new method for an auto-meshing algorithm for an acoustic analysis of the vocal tract using the Finite Element Method (FEM). In our algorithm, the domain of the 3 dimensional figure of the vocal tract is decomposed into two domains; one is a surface domain and the other is an inner domain in order to employ the overlapping domain decomposition method. The meshing of surface blocks c...

An integer version of the well-known de Casteljau algorithm of NURBS curves is presented here. The algorithm is used to render NURBS curves of any degree on a raster device by turning on pixels that are closest to the curve. The approximation is independent of the parametrization, that is, it is independent of the weights used. The algorithm works entirely in the screen coordinate system and pr...

This paper proposes a method of constructing a dynamic model of a ventricle based on isogeometric simulation so as to diagnose cardiac disease more accurately. Isogeometric simulation is an accurate simulation technology based on NURBS, which has evolved into an essential tool for a semi-analytical representation of geometric entities. Especially, a new method of moving control points is used t...

In this paper, a new method for constructing NURBS surfaces from scattered and unorganized points is presented. The method is easy to implement and allows fitting a NURBS surface to a scattered point cloud without constructing either NURBS patches networks or polygon meshes. Based on the projection of the points onto the regression plane of the cloud, the method detects both regions where the c...

We derive new trace inequalities for NURBS-mapped domains. In addition to Sobolev-type inequalities, we derive discrete trace inequalities for use in NURBS-based isogeometric analysis. All dependencies on shape, size, polynomial order, and the NURBS weighting function are precisely specified in our analysis, and explicit values are provided for all bounding constants appearing in our estimates....

Curves as a subject of differential geometry have been intriguing for researchers throughout mathematical history and so they have been one of the interesting research fields. Regular curves play a central role in the theory of curves in differential geometry. In the theory of curves, there are some special curves such as Bertrand curves, Mannheim curves, involute and evolute curves, and pedal ...