We present a method for painting texture maps directly onto trimmed NURBS models using a haptic interface. The haptic interface enables an artist to use a natural painting style while creating a texture. It avoids the traditional difficulty of mapping between the 2D texture space and the 3D model space by using parametric information available from our haptic tracing algorithm. The system maps ...

The design of curves and surfaces in C.A.D. systems has many applications in car, plane or ship industry. Because they offer more flexibility, rational functions are often prefered to polynomial functions to modelize curves and surfaces. In this work, several methods to generate rational Bezier curves and surfaces which minimize some functionals are proposed. The functionals measure a technical...

Resumen—Este artículo presenta un método para ajustar objetos 3D con par ches NURBS (B­Splines Racionales No Unifor mes), los cuales son optimizados mediante una Estr ategia Evolutiva Abstract—This article presents a method to fit 3D objects with patches NURBS (Non Un iform Rational B­Splines), which ar e optimized by means of Evolutionary Strategies (ES), which they determine the weights of th...

SUMMARY A NURBS Enhanced eXtended Finite Element Approach is proposed for the unfitted simulation of structures defined by means of CAD parametric surfaces. In contrast to classical X-FEM that uses levelsets to define the geometry of the computational domain, exact CAD description is considered here. Following the ideas developed in the context of the NURBS-Enhanced Finite Element Method, NURBS...

By its dual representation, a developable surface can be viewed as a curve of dual projective 3-space. After introducing an appropriate metric in the dual space and restricting ourselves to special parametrizations of the surfaces involved, we derive linear approximation algorithms for developable NURBS surfaces, including multiscale approximations. Special attention is paid to controlling the ...

We find a surface of degree 7 in È 3 (Ê) with 99 real nodes within a family of surfaces with dihedral symmetry: First, we consider this family over some small prime fields, which allows us to test all possible parameter sets using computer algebra. In this way we find some examples of 99-nodal surfaces over some of these finite fields. Then, the examination of the geometry of these surfaces all...

Isogenies of elliptic curves over finite fields have been well-studied, in part because there are several cryptographic applications. Using Vélu’s formula, isogenies can be constructed explicitly given their kernel. Vélu’s formula applies to elliptic curves given by a Weierstrass equation. In this paper we show how to similarly construct isogenies on Edwards curves and Huff curves. Edwards and ...

Human figures have been animated using a wide variety of geometric models including stick figures, polygonal models, and NURBS-based models with muscles, flexible skin, or clothing. This paper reports on experiments designed to ascertain whether a viewer’s perception of motion characteristics is affected by the geometric model used for rendering. Subjects were shown a series of paired motion se...

In this paper, we study the moment map image of algebraic curves in toric surfaces. We are particularly interested in the situations that we are able to perturb the moment map so that the moment map image of the algebraic curve is a graph. To put our problem into proper context, let’s start with CP. Consider the natural real n-torus (T ) action on CP given by e(x) = (ex1, e x2, · · · , exn). Pa...

In this paper, we propose a method to obtain a constrained approximation of a rational Bézier curve by a polynomial Bézier curve. This problem is reformulated as an approximation problem between two polynomial Bézier curves based on weighted least-squares method, where weight functions ρ(t) = ω(t) and ρ(t) = ω(t) are studied respectively. The efficiency of the proposed method is tested using so...