| Pawel Winter | Henrik Sterner | Peter Sterner |
| Dept. of Computer Science, Univ. of Copenhagen, Universitetsparken 1, 2100 Copenhagen O, Denmark, e-mail: pawel@diku.dk |
E-mail: henrik.sterner@gmail.com | E-mail: psterner@gmail.com |
Abstract |
| We provide a unified description of (weighted)
α-shapes, $\beta$-shapes and the corresponding simplicial complexes. We
discuss their applicability to various protein-related problems. We
also discuss filtrations of α-shapes and
touch upon related persistence issues. We claim that the full potential
of α-shapes and related geometrical constructs in protein-related problems
yet remains to be
realized and verified. We suggest parallel algorithms for (weighted)
α-shapes, and we argue that future use of filtrations and kinetic variants for larger proteins will need such implementations. |
Article is available in ps, dvi, pdf. |
Software |
Limited space does not permit us to list various types of open source libraries,
software and applets in one way or another way related to α-shapes.
However, this list can be found at AppletsVoronoi diagrams and Delaunay triangulations applets in 2d can be found at http://www.cs.cornell.edu/Info/People/chew/Delaunay.html
http://cgm.cs.mcgill.ca/~godfried/teaching/projects97/belair/alpha.html Computational Geometry LibrariesCGAL is an open source library of reliable and efficient computational geometry algorithms written in \textit{C++}. It supports construction and visualization of Delaunay triangulations,regular triangulations, Voronoi diagrams, power diagrams, unweighted and weighted α-shapes, and filtrations of the latter in 2d and 3d. A kinetic data structure framework is integrated supporting Delaunay triangulations in 2d and 3d and regular triangulations in 3d. It can be found at LEDA QHULL supports computation of Delaunay triangulations and Voronoi diagrams in 2d and 3d. Available at Hull is an ANSI C program that computes the convex hull of a point set in general
(but small!) dimension. The program can also compute Delaunay triangulations and α-shapes, http://www.netlib.org/voronoi/hull.html α-Shape SoftwareCAVE and Alvis - Cave Automatic Virtual Environment (CAVE); one of its applications is modeling 3D protein structures, generating both outside-in and inside-out views of geometric models. The successors of CAVE, called ALpha Shapes VISualizer (ALVIS) and Virtual ALVIS (VALVIS) available at ftp://ftp.ncsa.uiuc.edu/Visualization/Alpha-shape/ BioGeometry 3d α-shape software is available at http://biogeometry.duke.edu/software/alphashapes/software.html 3d α-Shapes software is available at http://www.loria.fr/~pougetma/software/alpha_shape/alpha_shape.html Biomolecular SoftwareCASTp server uses the weighted Delaunay triangulation and the
α-complex for shape
measurements. It provides identification and measurements of surface accessible
Progeom is a program for computing protein surface, volume, and their derivatives. Available at
APROPOS is a program for the detection of pockets in proteins. APROPOS was written in C and was available for Sun and SGI machines on request. See http://www.csb.yale.edu/userguides/datamanip/apropos/apropos_descrip.html Pocket is a program for detecting protein pockets available at http://koehllab.genomecenter.ucdavis.edu/people/koehl/research/proshape MolAxis is available on line and as a standalone program. Available at http://bioinfo3d.cs.tau.ac.il/MolAxis/ CIEL a software package for generating protein-protein interface surfaces from protein structural data. Available at |