.TH GEODESICS 1 "20 July 1989" "Project Riemann"
.SH NAME
symgeod, numgeod - compute the geodesics on 3D surfaces
.SH SYNOPSIS
\fBsymgeod\fR [\fB-t \fItitle\fR] [\fB-v \fIx y z\fR] [\fB-s \fIstep\fR] 
[\fB-i \fIiterations\fR] [\fB-g \fIgeodesics\fR] [\fIfile\fR]   
\fB-e \fIexpression \fR| \fB-p \fIpolynomial\fR

\fBnumgeod\fR [\fB-t \fItitle\fR] [\fB-v \fIx y z\fR] [\fB-s \fIstep\fR] 
[\fB-i \fIiterations\fR] [\fB-g \fIgeodesics\fR] [\fIfile\fR] 
\fB-e \fIexpression \fR| \fB-p \fIpolynomial\fR
.SH DESCRIPTION
.PP
\fISymgeod\fR and \fInumgeod\fR both compute the geodesics on three-dimensional
algebraic surfaces.  Both programs appear identical to the user but 
\fIsymgeod\fR does its work symbolically while \fInumgeod\fR does its work 
numerically.  \fISymgeod\fR is typically about twice as fast as \fInumgeod\fR; 
the speed advantage is greater for expressions than polynomials.  Both 
programs take as input an implicit description of the surface, either
a polynomial or a general algebraic expression (see SPECIFYING SURFACES below),
and some other parameters.  Both programs then compute the geodesics on the 
surface emanating radially from the specified initial 
point.  The programs' output can either go to a file or to standard output.  The
output is in a form that can be displayed by the project Riemann X-Windows 
program \fIxdisp\fR or edited with a text editor.  Note that \fIxdisp\fR can
accept input from standard input and thus the user can pipe the output of
\fIsymgeod\fR and \fInumgeod\fR to \fIxdisp\fR.
.so userinterface
either a polynomial or an expression must be specified.
.SH OPTIONS
.TP .5i
\fB-t \fItitle\fR
Specifies the title to be placed in the output file and displayed by 
\fIxdisp\fR.
.TP .5i
\fB-v \fIx y z\fR
Specifies the initial point (\fBv\fR stands for vector).  This point must be on
the surface and is the point from which all the geodesics emanate.
.TP .5i
\fB-s \fIstep\fR
Specifies the step size.  A point is computed and output every \fIstep\fR units
along each geodesic.
.TP .5i
\fB-i \fIiterations\fR
Specifies the number of iterations the program should go through for each 
geodesic.  In other words, each geodesic is \fIiterations\fR steps long.
.TP .5i
\fB-g \fIgeodesics\fR
Specifies the number of geodesics to compute.
.TP .5i
\fIfile\fR
Specifies the file to hold the output.  If no file is specified the output goes
to standard output.
.TP .5i
\fB-e \fIexpression\fR | \fB-p \fIpolynomial\fR
Specifies the surface.  One of these options must be present.  See SPECIFYING
SURFACES below.  \fIExpression\fR and \fIpolynomial\fR usually need to be 
enclosed in quotes to prevent evaluation by the shell.  The speed advantage of 
polynomials over expressions is greater for \fInumgeod\fR than \fIsymgeod\fR.
.so surfaces
.so surfaces_test
.so author

