Algorithms for Minkowski products and implicitly-defined complex sets
type: Item
instance of: scholarly article
title: Algorithms for Minkowski products and implicitly-defined complex sets
zbMATH Open document ID: 0948.65016
DOI: 10.1023/A:1018910412112
author: Rida T. Farouki
author: Hwan Pyo Moon
author: Bahram Ravani
published in: Advances in Computational Mathematics
publication date: 2000-07-09T00:00:00Z
review text: In another paper (to appear in Geom. Dedicata), the authors study a geometric algebra of point sets in the complex plane, based on the Minkowski sum and product operations. This has applications and connections to shape generation/analysis, description of wavefront reflection and refraction in geometric optics, stability analysis for dynamical systems and extension of interval arithmetic to the complex plane. The main focus of the paper under review is on formulation and analysis for Minkowski products with general set operands and the evaluation of the `implicitly-defined' complex sets. The authors also propose \(inter alia\), the following directions for future investigations. Implicitly-defined sets dependent on more than two given complex sets, sets defined by algebraic operations on complex sets, etc.
Mathematics Subject Classification ID: 65D18
Mathematics Subject Classification ID: 65E05
Mathematics Subject Classification ID: 51B20
zbMATH DE Number: 1470919
zbMATH Keywords: Minkowski geometric algebra
zbMATH Keywords: Minkowski sums and products
zbMATH Keywords: implicitly-defined complex sets
zbMATH Keywords: boundary evaluation algorithms
zbMATH Keywords: shape generation
zbMATH Keywords: wavefront reflection
zbMATH Keywords: refraction in geometric optics
zbMATH Keywords: dynamical systems
zbMATH Keywords: interval arithmetic
reviewed by: H. P. Dikshit
MaRDI profile type: Publication
full work available at URL: a:1018910412112
OpenAlex ID: W244957858
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description: scientific article; zbMATH DE number 1470919