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Seminario di geometria algebrica applicata alla rappresentazione dei gruppi spaziali

Segnaliamo questa iniziativa del socio D.M. Proserpio.

SEMINARI CHIMICI (University of Milan): 3D Space Group Visualization with Interactive Crystal Symmetry Software

Dates:
Wednesday 3 March 2010, 14.15-16.15
Thursday 4 March 2010, 14.15-16.15

Venue:
Università degli studi di Milano, Dipartimento di Chimica Strutturale e Stereochimica Inorganica, Aula H, Via Venezian, 21 – MILANO, Italy,
URL: dcssi.istm.cnr.it

Speaker:
Dr. Eckhard Hitzer, Department of Applied Physics, University of Fukui – Japan, Email: hitzer_at_mech.fukui-u.ac.jp

Title:
3D Space Group Visualization with Interactive Crystal Symmetry Software

Coordinator:
Prof. Davide M. Proserpio, Dipartimento di Chimica Strutturale e Stereochimica Inorganica, Università degli studi di Milano, Email: davide.proserpio_at_unimi.it

Abstract:
A new interactive software tool (www.spacegroup.info) is described, that visualizes 3D space group symmetries, as tabulated in the Int. Tables of Crystallography (T. Hahn, Springer, 2005). The software computes with Clifford (geometric) algebra. The Space Group Visualizer (SGV) originated as a script for the geometric visualization platform CLUCalc, which fully supports geometric algebra computation. Selected generators (Hestenes and Holt, JMP, 2007) form a multivector generator basis of each space group. The approach corresponds to an algebraic implementation of groups generated by reflections (Coxeter and Moser, 4th ed., 1980). The basic operation is the reflection. Two reflections at non-parallel planes yield a rotation, two reflections at
parallel planes a translation, etc. Combination of reflections corresponds to the geometric product of vectors describing the individual reflection planes.

We begin by demonstrating how to use the SGV for 3D space group visualization, beginning with space group selection. The interactive computer graphics shows a perspective view of one cell (domain expandable) with all its symmetry elements and general positions. Mouse interaction allows to animate symmetry operations, move general positions, navigate through the cell, etc. Dropdown menus provide scene rotation (like a movie), orthographic projection, changes of background, lighting conditions, 3D stereo views (anaglyphs). There is also a multi functional toolbar. Next we demonstrate 3D point groups interactively rendered in 3D with a free CLUCalc script, and in the SGV. We then show how to use the SGV for visualizing the 17 plane groups (two dimensional space groups) and for many subperiodic groups. Finally, we will give some insights into the Clifford geometric algebra description of space groups.

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