Interval sets in applied geometry

Abstract

Geometric modeling of interval sets of multidimensional space is considered. The interval set is determined as a set of k-planes of uncertain interval parameters. Interval parameters may be given by means of interval basis which are k-simplexes having vertex coordinates which are not fully presented (only up to range of values). Geometric images of the sets have combinatorial structure formed by some part of the space and bordered by a set of peace linear hyper-surfaces. Analytic model is a system of interval equations which may be transformed to equations with uncertain parameters. The set of interval parameters generate an interval function and geometric image of it is some domain in parametric space. Analyses of mutual position of all domains allows us to determine the behavior of interval sets. Some properties of interval line sets are considered in detail as examples of the proposed approach.

Keywords

• geometric model
• interval set
• parametric determination
• k-plane
• piecewise linear structure
• interval parameter
• hyper-plane