On real functions and parametric curves (Part I)

Parametric Optimal Design Part I

Real Analysis: Part I

Finite Representations of Real Parametric Curves and Surfaces

Global parameterizations of parametric algebraic curves or surfaces are defined over infinite parameter domains. In this paper we show how to replace these global real parameterizations with a finite number of alternate bounded parameterizations, each defined over a fixed, bounded part of the real parameter domain space. The new bounded parameterizations together generate all real points of the...

Real root classification of parametric spline functions

The real root classification of a given parametric spline function is a collection of possible cases of its real root distribution on every interval, together with the conditions of its coefficients must be satisfied for each case. This paper presents an algorithm to deal with the real root classification of a given parametric spline function. Two examples are provided to illustrate the propose...

Aggregation Functions. Part I: Means

The two-parts state-of-art overview of aggregation theory summarizes the essential information concerning aggregation issues. Overview of aggregation properties is given, including the basic classification of aggregation functions. In this first part, the stress is put on means, i.e., averaging aggregation functions, both with fixed arity (n-ary means) and with open arity (extended means).