Given A spline curves and A patch surfaces that are implicitly de ned on triangles and tetrahedra we determine their NURBS representations We provide a trimmed NURBS form for A spline curves and a parametric tensor product NURBS form for A patch surfaces We concentrate on cubic A patches providing a C continuous surface that interpolates a given triangulation together with surface normals at th...

In this paper, we present the geodesic-like algorithm for the computation of the shortest path between two objects on NURBS surfaces and periodic surfaces. This method can improve the distance problem not only on surfaces but in R. Moreover, the geodesic-like algorithm also provides an efficient approach to simulate the minimal geodesic between two holes on a NURBS surfaces.

In this paper we present a NURBS version of the rational interpolating spline with tension introduced in [2], and we extend our proposal to the rectangular topology case. In particular we present some rational interpolating techniques that enable us to reconstruct shape-preserving bivariate NURBS and allow us to interactively modify the resulting surface by a set of tension parameters.

Surface reconstruction is a very challenging step in Reverse Engineering. It generates a surface from point cloud acquired from a part surface. NURBS surfaces are commonly used for freeform surface reconstruction. There are several algorithms of NURBS surface reconstruction including: Least Squares Methods, simulated annealing, and particle swarm optimization. The major problem of these methods...

This paper shows a new approach for non-linear least squares fitting with NURBS as curves and surfaces to measured data by the Gauss-Newton method. A Trust Region algorithm is used to reach global convergence as well as variable substitution and simple bounds. Key–Words: Non-linear least squares, NURBS, curve and surface fitting, reverse engineering, optimisation, GaussNewton

The isogeometric analysis is a rather new variant of the finite element method (FEM). The key concept of this method is to directly employ a geometric model described by parametric functions as a mesh for the FEM. The models for the isogeometric analysis have been usually based on non-uniform rational B-Splines (NURBS). The applications so far include both twoand three-dimensional models. This ...

Image processing techniques are used to detect the edges of a hand-drawn sketch. Generally, various types of gradation are expressed in the background of a hand-drawn sketch. Therefore, the original image is transformed into a logarithmic image. The entire image has to be binarized for edge detection. To smooth the edge of the binary image, feature based erosion and dilation is applied. A Lapla...

Today scene graphs are ubiquitous in computer graphics: since they provide both a well suited data structure and an abstraction layer, almost all modern graphics applications employ some sort of scene graph. Unfortunately most scene graphs do not support higher order primitives (such as trimmed NURBS) adequately, even though in Computer Aided Design (CAD) systems the de facto standard surface r...

Computational fluid dynamics (CFD) simulations of flow over complex objects have been performed traditionally using fluid-domain meshes that conform to the shape of the object. However, creating shape conforming meshes for complicated geometries like automobiles require extensive geometry preprocessing. This process is usually tedious and requires modifying the geometry, including specialized o...