Alpha Shapes

Herbert Edelsbrunner

Duke University, Computer Science(Raindrop) Geomagic

LEIDEN 2006

I.1 Van der Waals diagram

I.2 Solvent accessible diagram

I.3 Alpha shape

I. Molecular Models

II.1 Homotopy equivalence

II.2 Betti numbers

II.3 Incremental algorithm

II. Connectivity

III.1 Voids

III.2 Pockets

III. Empty Space

IV.1 PIE formula

IV.2 Void formula

IV.3 Area derivative

IV.4 Volume derivative

IV. Size

V.1 Definition

V.2 Deformation

V. Molecular Surface

VI.1 Skin surfaces

VI.2 Coaxal system

VI.3 Mixed complex

VI.4 Complementarity

VI. Shape

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