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RADI: Computation of the Radius and Diameter of a spatial set

Reference:

M. Petitjean, Applications of the Radius-Diameter Diagram to
the Classification of Topological and Geometrical Shapes of
Chemical Compounds, J.Chem.Inf.Comput.Sci. 1992,32[4],331-337

Author email: petitjean@itodys.jussieu.fr

RADI reads the cartesian coordinates of the molecule. It extracts
the convex hull of the atomic positions, then computes the diameter
and the radius of the hull. Three shape coefficients are computed,
all related to the convex hull of the set.


Input data and parameters:
-------------------------

INPUT  FORMAT:
  CAS : Reserved for internal purposes
  HIN : Hyperchem-type files
  MDL : Cambridge Crystallographic Model files
  ML2 : SYBYL Mol2 files
  PDB : Protein Data Bank or Nucleic Acid Data Bank files
        (only HEADER, ATOM, ENDMDL and END records are recognized)
  BIO : Biosym (MSI) files
  ISU : Reserved for internal purposes

INPUT  MOLEC FILE NAME: name of the input file containing the molecule


Output results:
--------------

3D CONVEX HULL: the K atoms of the hull, i.e. the K vertices of the
                smallest convex polyhedron containing the set of the
                N atomic positions

3D MOL. MEAN POINT: arithmetic mean of the N atomic positions

3D HULL MEAN POINT: arithmetic mean of the K atoms of the hull

The SURFACE and VOLUME of the full 3D convex hull (no cavity is considered)

DIAMETER: the distance D of the longest atom-pair of the molecule

RADIUS: the radius R of the smallest sphere containing the N atoms

MIN SPHERE CENTER: the center of this minimal sphere

GEOMETRICAL CONVEX-SHAPE COEFFICIENT : the ratio (D-R)/R

SURFACIC CONVEX-SHAPE COEFFICIENT :
 The ratio: surface of the hull, divided by the surface of the minimal sphere,
 followed by the square root of this ratio

VOLUMIC CONVEX-SHAPE COEFFICIENT :
 The ratio: volume of the hull, divided by the volume of the minimal sphere,
 followed by the cubic root of this ratio


Remarks:
-------

The number of atoms is currently limited to 15000 for each molecule.
The source has to be recompiled to read larger molecules.

Perfectly planar molecules are not handled. When there are at least
four atoms in the molecule, it is suggested to slightly modify one
atomic coordinate to get a spatial set.

The computing time is worst-case bounded by O(K**5), K being the number
of vertices of the hull, and K is at worst equal to N.
The worst situation is not expected in chemistry, even for proteins.

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