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

Year: 2020 Authors: Risto A. Paju

Core claim

Shape inversion can be expressed as ordinary inversion in a metric defined by the shape itself, enabling simpler formulas and new non-inversion uses.

Topics

shape inversion, shape metrics, fractal art, Voronoi diagrams, 3D graphics

Domains

metric geometry, Euclidean and non-Euclidean distance, pseudo-metrics, high-dimensional geometry, mathematical art, fractal imagery, generative graphics, visual pattern design

Methods

distance-function reformulation, shape inversion, Voronoi coloring, ray marching

Media

lattice figures, cube and octahedron models, Voronoi diagrams, computer-generated images

Source status

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