The process of implicitization generates an implicit representation of a curve or surface from a given parametric one. This process is potentially interesting for applications in Computer Aided Design, where the robustness and efficiency of intersection algorithm can be improved by simultaneously considering implicit and parametric representations. This paper gives an brief survey of the existi...

This chapter details the different 3D representation models, commonly used in computer graphics and 3D modeling. We distinguish three main representation schemes: polygonal meshes; surface-based models, such as parametric, implicit and subdivision surfaces; and volumetric models including primitivebased models (superquadric, hyperquadric), voxel representation and constructive solid geometry. F...

We introduce a novel approximation method for multiobjective optimization problems called PAINT–SiCon. The method can construct consistent parametric representations of Pareto sets, especially for nonconvex problems, by interpolating between nondominated solutions of a given sampling both in the decision and objective space. The proposed method is especially advantageous in computationally expe...

Parametric-stereo coding is a technique to efficiently code a stereo audio signal as a monaural signal plus a small amount of parametric overhead to describe the stereo image. The stereo properties are analyzed, encoded, and reinstated in a decoder according to spatial psychoacoustical principles. The monaural signal can be encoded using any (conventional) audio coder. Experiments show that the...

We address the following problem: given a curve in parametric form, compute the implicit representation of another one that approximates the parametric curve on a certain domain of interest. We study this problem from the numerical point of view: what happens with the output curve if the input curve is slightly changed? It is shown that for any approximate parameterization of the given curve, t...

For g = sl(n) we construct a two parametric U h (g)-invariant family of algebras, (Sg) t,h , that is a quantization of the function algebra Sg on the coadjoint representation. Along the parameter t the family gives a quantiza-tion of the Lie bracket. This family induces a two parametric U h (g)-invariant quantization on the maximal orbits, which includes a quantization of the Kirillov-Kostant-S...

The triangulation of boundary representation geomet-ries (BRep geometries) is neccessary for display generation , stereo-lithography applications and also nite element mesh (FE mesh) generation. The accuracy of the tesselation is of great signiic-ance not only for stereo-lithography and rendering algorithms but also for FE mesh generation, since even minor simpliications of the geometry of the ...

We describe a new method to simplify combinational circuits while preserving the set of all possible values (that is, the range) on the outputs. This method is performed iteratively and on the fly while building BDDs of the circuits. The method is composed of three steps; 1) identifying a cut in the circuit, 2) identifying a group of nets within the cut, 3) replacing the logic driving the group...

Dependence on the parameter is continuous when perturbations of the parameter preserves strict preference for one alternative over another. We characterise this property via a utility function over alternatives that depends continuously on the parameter. The class of parameter spaces where such a representation is guaranteed to exist is also identified. When the parameter is the type or belief ...

The theory of multidimensional systems gained enormous importance in the last years. Similar to the one-dimensional case, stability of such systems plays a crucial role. In this context so called scattering Hurwitz polynomials (in the continuous case) and scattering Schur polynomials (in the discrete) case are in the focus of interest. In the present paper a parametric representation for real t...