Almost-Delaunay simplices: Robust neighbor relations for imprecise 3D points using CGAL

This paper describes a new computational geometry technique, almost-Delaunay simplices, that was implemented for 3D points using CGAL. Almost-Delaunay simplices capture possible sets of Delaunay neighbors in the presence of a bounded perturbation, and give a framework for nearest neighbor analysis in imprecise point sets such as protein structures. The use of CGAL helps us tune our implementation so that it is reasonably fast and also performs robust computation for all inputs, and also lets us distribute our technique to potential users in a portable, reusable and extensible form. The implementation, available on http://www.cs.unc.edu/~debug/software is faster and more memory efficient than our prototype MATLAB implementation, and enables us to scale our neighbor analysis to large sets of protein structures, each with 100-3000 residues.

[1]  Sylvain Pion,et al.  Interval arithmetic yields efficient dynamic filters for computational geometry , 1998, SCG '98.

[2]  Wei Wang,et al.  Mining protein family specific residue packing patterns from protein structure graphs , 2004, RECOMB.

[3]  H Edelsbrunner,et al.  Analytical shape computation of macromolecules: II. Inaccessible cavities in proteins , 1998, Proteins.

[4]  H. Edelsbrunner,et al.  Anatomy of protein pockets and cavities: Measurement of binding site geometry and implications for ligand design , 1998, Protein science : a publication of the Protein Society.

[5]  Wei Wang,et al.  Comparing Graph Representations of Protein Structure for Mining Family-Specific Residue-Based Packing Motifs , 2005, J. Comput. Biol..

[6]  Jinze Liu,et al.  Structure‐based function inference using protein family‐specific fingerprints , 2006, Protein science : a publication of the Protein Society.

[7]  Olivier Devillers,et al.  Efficient Exact Geometric Predicates for Delauny Triangulations , 2003, ALENEX.

[8]  Mariette Yvinec,et al.  Triangulations in CGAL , 2002, Comput. Geom..

[9]  Kevin Q. Brown.  Geometric transforms for fast geometric algorithms , 1979 .

[10]  Jack Snoeyink,et al.  Almost-Delaunay simplices: nearest neighbor relations for imprecise points , 2004, SODA '04.

[11]  Geert-Jan Giezeman,et al.  The CGAL Kernel: A Basis for Geometric Computation , 1996, WACG.

[12]  Michael Hoffmann,et al.  An adaptable and extensible geometry kernel , 2001, Comput. Geom..

[13]  Jack Snoeyink,et al.  A geometric framework for robust nearest neighbor analysis of protein structure and function , 2006 .

[14]  Alexander Tropsha,et al.  Development of a four-body statistical pseudo-potential to discriminate native from non-native protein conformations , 2003, Bioinform..

[15]  Iosif I. Vaisman,et al.  Delaunay Tessellation of Proteins: Four Body Nearest-Neighbor Propensities of Amino Acid Residues , 1996, J. Comput. Biol..

[16]  Andrei Alexandrescu,et al.  Modern C++ design: generic programming and design patterns applied , 2001 .

[17]  Remco C. Veltkamp,et al.  Applications of the Generic Programming Paradigm in the Design of CGAL , 1998, Generic Programming.

[18]  C. Branden,et al.  Introduction to protein structure , 1991 .

[19]  Scott Meyers,et al.  Effective STL: 50 Specific Ways to Improve Your Use of the Standard Template Library , 2001 .

[20]  Douglas Gregor,et al.  C++ Templates: The Complete Guide , 2002 .

[21]  David P. Dobkin,et al.  The quickhull algorithm for convex hulls , 1996, TOMS.

[22]  Jonathan Richard Shewchuk,et al.  Robust adaptive floating-point geometric predicates , 1996, SCG '96.

[23]  Matthew H. Austern.  Generic programming and the STL - using and extending the C++ standard template library , 1999, Addison-Wesley professional computing series.

[24]  Kevin Barraclough,et al.  I and i , 2001, BMJ : British Medical Journal.

[25]  Dirk Bakowies,et al.  Water in protein cavities: A procedure to identify internal water and exchange pathways and application to fatty acid‐binding protein , 2002, Proteins.

[26]  A. Tropsha,et al.  Four-body potentials reveal protein-specific correlations to stability changes caused by hydrophobic core mutations. , 2001, Journal of molecular biology.

[27]  H. Wako,et al.  Novel method to detect a motif of local structures in different protein conformations. , 1998, Protein engineering.