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From: Ivan Degtyarenko (imd_at_fyslab.hut.fi)
Date: Sun Sep 24 2006 - 04:17:52 CDT
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Dear All, to anyone interested. Since that utilities measuring angles and
dihedrals are still missing from VMD, here is a small dirty Tcl code which
takes coordinates of three points as input and returns angle between them
in degrees. It is not a state of art, but works and might be useful at
some point. Corrections/improvements are welcome.
YT, Ivan Degtyarenko
# compute angle between three arbitrary points in space
# (initially has been written for hydrogen bond angles,
# notation has been kept: D-H...A)
# usage: angle {x1 y1 z1} {x2 y2 z2} {x3 y3 z3}
proc angle {D H A} {
# cosine of the angle between three points
# cos = ( v1 * v2 ) / |v1| * |v2|, where v1 and v2 are vectors
# get Pi 3.14159265358979323846
global M_PI
# initialize arrays
set d() 0; set h() 0; set a() 0; set hd() 0; set ha() 0;
# split coordinates
set d(x) [lindex $D 0]; set d(y) [lindex $D 1]; set d(z) [lindex $D 2];
set h(x) [lindex $H 0]; set h(y) [lindex $H 1]; set h(z) [lindex $H 2];
set a(x) [lindex $A 0]; set a(y) [lindex $A 1]; set a(z) [lindex $A 2];
# setup vectors hd and ha
set hd(x) [expr $d(x) - $h(x)];
set hd(y) [expr $d(y) - $h(y)];
set hd(z) [expr $d(z) - $h(z)];
set ha(x) [expr $a(x) - $h(x)];
set ha(y) [expr $a(y) - $h(y)];
set ha(z) [expr $a(z) - $h(z)];
# compute cosine
set cosine [expr \
($hd(x)*$ha(x) + $hd(y)*$ha(y) + $hd(z)*$ha(z)) / \
(sqrt(pow($hd(x),2) + pow($hd(y),2) + pow($hd(z),2)) * \
sqrt(pow($ha(x),2) + pow($ha(y),2) + pow($ha(z),2)))];
# convert cosine to angle in degrees
set angle [expr acos($cosine)*(180.0/$M_PI)]
return $angle;
}
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