Shape Metrics: A Unified Approach to Shape Inversions and Custom Distance Functions
Risto A. Paju

Proceedings of Bridges 2020: Mathematics, Art, Music, Architecture, Education, Culture
Pages 407–410
Short Papers

Abstract

I present a new approach to shape inversions that provides both computational simplicity and an alternative, unified understanding of the inversion operation. Instead of modifying the circle inversion formula for different shapes, my method changes the metric from Euclidean to a shape-dependent one. As a by-product, I outline a technique to construct new metrics and pseudo-metrics from given shapes, and suggest various non-inversion applications.

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