2020
DOI: 10.1137/19m1260803
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Computation of Circular Area and Spherical Volume Invariants via Boundary Integrals

Abstract: We show how to compute the circular area invariant of planar curves, and the spherical volume invariant of surfaces, in terms of line and surface integrals, respectively. We use the Divergence Theorem to express the area and volume integrals as line and surface integrals, respectively, against particular kernels; our results also extend to higher dimensional hypersurfaces. The resulting surface integrals are computable analytically on a triangulated mesh. This gives a simple computational algorithm for computi… Show more

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Cited by 3 publications
(1 citation statement)
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References 33 publications
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“…Braun, Pante, & Archer, 2016;Gümrükçu & Pante, 2018;Pante et al, 2017;Schmidt, Moore, & Leifheit, 2012), and other digital data extraction methods (e.g. Bello, Verveniotou, Cornish, & Parfitt, 2011;O'Neill et al, 2020;Yezzi-Woodley et al, 2021). Many of these new methods rely on digital imaging, in particular 3D scanning, which has become another prominent avenue of research (e.g.…”
Section: Introductionmentioning
confidence: 99%
“…Braun, Pante, & Archer, 2016;Gümrükçu & Pante, 2018;Pante et al, 2017;Schmidt, Moore, & Leifheit, 2012), and other digital data extraction methods (e.g. Bello, Verveniotou, Cornish, & Parfitt, 2011;O'Neill et al, 2020;Yezzi-Woodley et al, 2021). Many of these new methods rely on digital imaging, in particular 3D scanning, which has become another prominent avenue of research (e.g.…”
Section: Introductionmentioning
confidence: 99%