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Square-densities, and volume forms
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Heron's formula from antiquity, for the area of a triangle, is used to relate volume form and infinitesimal square-volume of certain infinitesimal simplices in a Riemannian manifold
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Measuring Distortion in the Empty Regions of Dimensionality Reduction Scatterplots with the Gap Index
The Gap Index quantifies visual distortion in empty regions of DR scatterplots via Delaunay triangle area deformation and is more sensitive to salient gap artifacts than stress or trustworthiness.
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