Algorithms for Minkowski products and implicitly-defined complex sets
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.
scientific article; zbMATH DE number 1470919