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Alpha Shapes Herbert Edelsbrunner Duke University, Computer Science (Raindrop) Geomagic LEIDEN 2006

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I.1 Van der Waals diagram I.2 Solvent accessible diagram I.3 Alpha shape I. Molecular Models

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II.1 Homotopy equivalence II.2 Betti numbers II.3 Incremental algorithm II. Connectivity

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III.1 Voids III.2 Pockets III. Empty Space

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IV.1 PIE formula IV.2 Void formula IV.3 Area derivative IV.4 Volume derivative IV. Size

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V.1 Definition V.2 Deformation V. Molecular Surface

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VI.1 Skin surfaces VI.2 Coaxal system VI.3 Mixed complex VI.4 Complementarity VI. Shape

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Collaborators 2d: David Kirkpatrick, Raimund Seidel 1983 3d: Ernst Muecke 1994 Betti numbers: Cecil Delfinado 1995 Pockets and size: Michael Facello, Ping Fu, Jie Liang 1995 Derivatives: Patrice Koehl 2003

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