Stiefel Manifolds and Polygons

Year: 2019 Authors: Clayton Shonkwiler

Core claim

A polygon can be encoded as an orthonormal 2-frame in ℝ^n, and this Stiefel-manifold model supports efficient sampling and interpolation.

Topics

random polygons, shape interpolation, parameter spaces, polygon spaces

Domains

Stiefel manifolds, differential geometry, probability theory, linear algebra, generative art, deterministic art, shape morphing, visualization

Methods

Gram-Schmidt sampling, QR decomposition, orthonormal 2-frames, parametrized paths

Media

Mathematica notebook, polygon edge vectors, Gaussian random matrices, polygon morphs

Source status

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