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#!/usr/bin/perl
#
# Direct extraction of the VectorReal POD synopsis
#
# location of my libraries (I normally set this via PERL5LIB)
# # #use lib '/home/anthony/lib/perl5'; # location of my libraries
use FindBin;
use lib "$FindBin::Bin/blib/lib";
use Math::VectorReal qw(:all); # Include O X Y Z axis constant vectors
$a = vector( 1, 2, .5 );
print "Vector as string (default ouput format)\n\$a => ", $a;
print "\n";
print "Specified output format\n";
print $a->stringify("\$a => { %g, %g, %g }\n");
print "\n";
# I hate newline in the default output format (defined as MatrixReal)
$Math::VectorReal::FORMAT = "[ %.5f %.5f %.5f ]";
print "Modified default output format\n\$a => $a\n";
print "\n";
print "General Vector Mathematics\n";
print "length\n", $a->length, "\n";
print "normalised\n", $a->norm, "\n";
print 'string concat $a."**" = ', $a."**", "\n";
print 'vector constant X = ', X, "\n";
print 'subtraction $a - Z = ', $a - Z, "\n";
print 'scalar divide $a / 3 = ', $a / 3, "\n";
print 'dot product $a . Y = ', $a . Y, "\n";
print 'cross product $a x Y = ', $a x Y, "\n";
print "\n";
print "Plane containing points X, \$a, Z (in anti-clockwise order)\n";
($n,$d) = plane( X, $a, Z ); # return normal and disance from O
print ' normal = $n = ', $n, "\n";
print ' disance from O = $d = ', $d, "\n";
print ' Y axis intersect = $d/($n.Y) = ', $d/($n.Y), "\n";
print "\n";
use Math::MatrixReal; # Not required for pure vector math as above
print "Conversions to MatrixReal objects\n";
$r = $a->vector2matrix_row; # convert to MatrixReal Row Vector
$c = $a->vector2matrix_col; # convert to MatrixReal Column Vector
print 'Vector as a MatrixReal Row $r (vector -> matrix) => ', "\n", $r;
print 'Vector as a MatrixReal Col $c (vector -> matrix) => ', "\n", $c;
print "\n";
print "Rotation Matrix from 3 Vectors\n";
$nx = $a->norm; $ny = $nx x Z; $nz = $nx x $ny; # orthogonal vectors
$R = vector_matrix( $nx, $ny, $nz ); # make the rotation matrix
print '$R => ',"\n", $R, "\n";
print "Extract the Y row from the matrix as a VectorReal\n";
print '$R->matrix_row2vector(1) => ', $R->matrix_row2vector(1), "\n\n";
print "Rotate a vector with above rotation matrix\n";
print '$a * $R (vector -> vector)',"\n", $a * $R, "\n\n";
print "Rotate a MatrixReal column (post multiply)\n";
print "(NB: matrix must be transposed (~) to match column format)\n";
print '~$R * $c (col_matrix -> col_matrix) =>',"\n", ~$R * $c, "\n";
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