Author: Lawrence R. Dodd This program will find the total and individual volume and
exposed surface area of an arbitrary collection of spheres of
arbitrary radii cut by an arbitrary collection of planes
analytically by analyzing the plane/sphere intersections.
Algorithm by: Doros N. Theodorou and Lawrence R. Dodd
Coded by: L.R. Dodd
Created on: March 21, 1990
Phase 1 Completed on: March 23, 1990
Phase 2 Completed on: April 16, 1990
Phase 3 Completed on: May 17, 1990
Phase 4 Completed on: June 5, 1990
Phase 5 Completed on: July 26, 1990
Reference:
"Analytical treatment of the volume and surface area of
molecules formed by an arbitrary collection of unequal
spheres intersected by planes"
L.R. Dodd and D.N. Theodorou
MOLECULAR PHYSICS, Volume 72, Number 6, 1313-1345, April 1991
Acknowlegement:
LRD wishes to thank his mentor DNT for a stimulating and
enjoyable post-doctoral experience.
General Notes On Program:
This program has been written with an eye towards both
efficiency and clarity. On a philosophical note, many believe
that these ideals are mutually exclusive but in general they
are not. There are, however, a few instances where one ideal
has been given more prominence over the other. The comments in
the program, together with the associated journal article,
should help to explain any apparent logical leaps in the
algorithm.
The program was intended to be used as a subroutine called
repeatly by some main program. In this case the subroutine
"VOLUME" is called by some main routine which has placed the
necessary information in common block /Raw Data/. The answers
are returned in common block /Volume Output/. I must apologize
for the poor input/output for the program. For example, the
area/volume of each sphere is not placed in /Volume Output/.
This program was developed on a Sun SPARCstation 330 using Sun
FORTRAN 1.3.1 (all trademarks of Sun Microsystems, Inc.). We
have used some of extensions to the ANSI standard including:
o long variable names (i.e., more than six characters)
The advantage of using non-standard FORTRAN is that it makes it C
considerably easier to follow the flow of a program. There are
no extraneous statement labels in this program that may have
obscured the logic (not a single GOTO was used). The previews
of the new F90 standard appear to adopt many of the features
already implemented in VMS, Sun, Cray, and IBM FORTRAN.
Note that this algorithm is completely parallelizable.
Note:
Plane_Ordering of common block /Debug/ is, as the name
implies, for debugging purposes only as is routine ORDERING.
The information contain therein is not necessary for solving
the sphere plane problem but proved incredibly useful during
program development.
Maintainer: Lawrence R. Dodd
Created: March 21, 1990
Version: 2.0
Date: 1994/07/22 15:45:51
Keywords: volume and area determination
Time-stamp: <94/07/22 11:02:23 dodd>
Copyright (c) 1990, 1991, 1992, 1993, 1994
by Lawrence R. Dodd and Doros N. Theodorou.
Plane Sphere Intersections
dodd@mycenae.cchem.berkeley.edu
Department of Chemical Engineering
ollege of Chemistry
University of California at Berkeley
Berkeley, California 94720-9989
(415) 643-7691 (LRD)
(415) 643-8523 (DNT)
(415) 642-5927 (Lab)
dodd@mycenae.cchem.berkeley.edu
doros@mycenae.cchem.berkeley.edu
The National Helleni rosen@cyclades.nrcps.ariadne-t.gr
Research Foundation,
Organic and Pharaceutical Institute, phone: ++30-1-7238958 (direct)
Vas. Konstantinou 48, phone: ++30-1-7247913(secrtry.Mary)
Athens 116-35, fax: ++30-1-7247913
Greece
or
NCRS "Democritos", phone: ++30-1-6513112-5 X219
c/o Dr. G.Kordas, e-mail john@john.nrcps.ariadne-t.gr
Material Science Institute,
Aghia Paraskevi,
Attikis,
Athens 153-10,
Greece