
NAMEMath::VectorReal  Module to handle 3D Vector MathematicsSYNOPSIS#!/usr/bin/perl use Math::VectorReal; $a = vector( 1, 2, .5 ); print "Vector as string (MatrixReal default format)\n\$a => ", $a; print $a>stringify("Formated Output \$a => { %g, %g, %g }\n"); # I hate newline in the default output format (defined as MatrixReal) $Math::VectorReal::FORMAT = "[ %.5f %.5f %.5f ]"; print "Modified default output format \$a => $a\n"; print 'length => ', $a>length, "\n"; print 'normalised => ', $a>norm, "\n"; use Math::VectorReal qw(:all); # Include O X Y Z axis constant vectors 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 = ', $a x Y, "\n"; print "Plane containing points X, \$a, Z (in anticlockwise order)\n"; ($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 "VectorReal and MatrixReal interaction\n\n"; use Math::MatrixReal; # Not required for pure vector math as above $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; $nx = $a>norm; $ny = $nx x Z; $nz = $nx x $ny; # orthogonal vectors $R = vector_matrix( $nx, $ny, $nz ); # make the rotation matrix print 'Rotation Matrix from 3 Vectors $R => ',"\n", $R, "\n"; print "Extract the Y row from the matrix as a VectorReal..\n"; print '$R>matrix_row2vector(1) => ', $R>matrix_row2vector(1), "\n"; print "Rotate a vector with above rotation matrix\n"; print '$a * $R (vector > vector)',"\n", $a * $R, "\n"; print "Rotate a MatrixReal column (post multiply)...\n"; print "(NB: matrix must be transposed (~) to match column format)\n"; print '~$R * $c (col_matrix > col_matrix) =>',"\n", ~$R * $c, "\n"; DESCRIPTIONThe "Math::VectorReal" package defines a 3D mathematical "vector", in a way that is compatible with the previous CPAN module "Math::MatrixReal". However it provides a more vector oriented set of mathematical functions and overload operators, to the "MatrixReal" package. For example the normal perl string functions "x" and "." have been overloaded to allow vector cross and dot product operations. Vector math formula thus looks like vector math formula in perl programs using this package. While this package is compatible with Math::MatrixReal, you DO NOT need to have that package to perform purely vector orientated calculations. You will need it however if you wish to do matrix operations with these vectors. The interface has been designed with this package flexibility in mind. The vectors are defined in the same way as a "row" "Math::MatrixReal" matrix, instead of that packages choice of "column" definition for vector operations. Such vectors are multiplied to matices with the vector on the left and the matrix on the right. EG: v * M > 'v Not only is this the way I prefer to handle vectors, but it is the way most graphics books use vectors. As a bonus it results in no overload conflicts between this package and that of Math::MatrixReal, (the left objects overload operator is called to do the mathematics). It also is a lot simpler than "MatrixReal" column vector methods, which were designed for equation solving rather than 3D geometry operations. The vector_matrix() function provided, simplifies the creation a "MatrixReal" object from 3 (usually orthogonal) vectors. This with its vector orientated math operators makes it very easy to define orthogonal rotation matrices from "Math::VectorReal" objects. See a rough example in the synopsis above, or in the file "matrix_test" in the packages source. NOTE: the 6th element the "Math::MatrixReal" array object is used to hold the length of the vector so that it can be reused without needing to be recalculated all the time. This means the expensive sqrt() function, need not be called unless nessary. This usage should not effect the direct use of these objects in the "Math::MatrixReal" functions.CONSTANTSFour constant vectors are available for export (using an ":all" tag). these are0 = [ 0 0 0 ] the zero vector or origin X = [ 1 0 0 ]  Y = [ 0 1 0 ] > Unit axis vectors Z = [ 0 0 1 ]  CONSTRUCTORS
METHODS
VECTOR/MATRIX CONVERSIONThe following functions provide links between the "Math::VectorReal" and "Math::MatrixReal" packages. NOTE: While this package is closely related to "Math::MatrixReal", it does NOT require that that package to be installed unless you actually want to perform matrix operations. Also the overload operations will automatically handle vector/matrix mathematics (See below).Vector to Matrix Conversion
Matrix to Vector Conversion
OPERATOR OVERLOADINGOverload operations are provided to perform the usual string conversion, addition, subtraction, unary minus, scalar multiplation & division. On top of this however the multiply have been expanded to look for and execute "MatrixReal" multiplation. The Main purpose of this package however was to provide the special vector product operations: dot product "." and cross product "x". In perl these operations are normally used for string operations, but if either argument is a "VectorReal" object, the operation will attempt the approprate vector math operation instead. Note however that if one side of the dot "." operator is already a string, then the vector will be converted to a sting and a string concatantion will be performed. The cross operator "x" will just croak() as it is nonsensical to either repeat the string conversion of a vector, OR to repeat a string, vector, times! Overloaded operator summery...neg unary minus  multiply vector by 1 "" automatic string conversion using stringify() function + vector addition  vector subtraction / scalar division (left argument must be the vector) * scalar multiplication OR MatrixReal multiplication x vector/cross product of two vectors . dot product of two vectors OR vector/string concatanation Posible future addition '~' to transpose a "VectorReal" into a "MatrixReal" column vector (as per that operator on "MatrixReal" objects). It was not added as it just did not seem to be needed. SEE ALSOThe "Math::MatrixReal" CPAN Module by Steffen Beyer and the "Math::MatrixRealExt1" CPAN extension by Mike SouthAUTHORAnthony Thyssen < anthony@cit.gu.edu.au>COPYRIGHTCopyright (c) 2001 Anthony Thyssen. All rights reserved. This program is free software; you can redistribute it and/or modify it under the same terms as Perl itself. I would appreciate any suggestions however.POD ERRORSHey! The above document had some coding errors, which are explained below:
Visit the GSP FreeBSD Man Page Interface. 