Artistic Aspects of the Wigner Caustic and the Centre Symmetry Set

2024/08/14 by Iza Danielewska, Dawid Poławski, Danielewska, Iza +5
Materials Science · Mathematics · #52A38 #52A40 #58K70 #Algebraic and Geometric Analysis #FOS: Mathematics #General Mathematics (math.GM) #Mathematics and Applications #Quasicrystal Structures and Properties

paper · pdf · doi:10.48550/arxiv.2409.04443

openalex publication_date 2024/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Wigner caustic and the Centre Symmetry Set of a closed smooth planar curve are known singular sets which generically admit only cusp singularities. Applications of these objects in semi-classical quantum physics, in chaos theory, in singularity theory, in convex geometry, have been studied since the 1970s until today. These sets can be viewed as envelopes of special families of lines and thanks to that they have many geometric artistic values.

Related

• The Geometry of the Wigner Caustic and a Decomposition of a Curve Into Parallel Arcs
• Generic symmetry defect set of an algebraic curve
• The Geometry of the Centre Symmetry Set of a Planar Curve
• Models from the 19th Century used for Visualizing Optical Phenomena and Line Geometry
• The Geometry of the Secant Caustic of a Planar Curve