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Elastic Analysis of Augmented Curves and Constrained Surfaces

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arxiv 2402.04944 v3 pith:L3HYRK6Z submitted 2024-02-07 math.DG cs.NAmath.NA

Elastic Analysis of Augmented Curves and Constrained Surfaces

classification math.DG cs.NAmath.NA
keywords curvessurfacesanalysisapproachaugmentedgeometrictransformationapplications
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The square root velocity transformation provides a convenient and numerically efficient approach to functional and shape data analysis of curves. We study fundamental geometric properties of curves under this transformation. Moreover, utilizing natural geometric constructions, we employ the approach for intrinsic comparison within several classes of surfaces and augmented curves, which arise in the real world applications such as tubes, ruled surfaces, spherical strips, protein molecules and hurricane tracks.

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