A note on the approximation of linear and affine functions: The case of bounded slope
type: Item
instance of: scholarly article
title: A note on the approximation of linear and affine functions: The case of bounded slope
zbMATH Open document ID: 0671.52004
DOI: 10.1007/BF01188690
author: Christian Ronse
published in: Archiv der Mathematik
publication date: 1990-01-01T00:00:00Z
review text: One considers a set S of pairs (x,C), with x a point in n-dimensional space and C a convex subset of k-dimensional space. Criteria are given for the existence of a linear or affine function f such that for each (x,C) in S, f(x) is in C, with the further constraint that f must belong to a given convex set K of functions (for example, those having their slope within certain bounds). This generalizes the author's paper in Archiv Math. 46, 371-384 (1986; Zbl 0566.52003), where no such constraint was imposed on f. The main results are applied to the problem of digitizing hyperplanes.
reviewed by: Christian Ronse
Mathematics Subject Classification ID: 52A20
zbMATH DE Number: 4098182
zbMATH Keywords: convexity
zbMATH Keywords: transversals
zbMATH Keywords: digital geometry
zbMATH Keywords: linear function
zbMATH Keywords: approximation
zbMATH Keywords: affine function
MaRDI profile type: Publication
cites work: Three-Dimensional Digital Planes
cites work: A simple proof of Rosenfeld's characterization of digital straight line segments
cites work: Criteria for approximation of linear and affine functions
cites work: Digital Straight Line Segments
description: scientific article; zbMATH DE number 4098182