NAME
Math::Geometry::Construction - intersecting lines and circles
VERSION
Version 0.004
SYNOPSIS
use Math::Geometry::Construction;
use Math::Geometry::Construction::Derivate::IntersectionLineLine;
my $construction = Math::Geometry::Construction->new
(width => 500, height => 300);
my $p1 = $construction->add_point('x' => 100, 'y' => 150, hidden => 1);
my $p2 = $construction->add_point('x' => 120, 'y' => 150, hidden => 1);
my $p3 = $construction->add_point('x' => 200, 'y' => 50);
my $p4 = $construction->add_point('x' => 200, 'y' => 250);
my $l1 = $construction->add_line(extend => 10,
label => 'g',
label_offset_y => 13);
$l1->add_support($p1);
$l1->add_support($p2);
my $l2 = $construction->add_line;
$l2->add_support($p3);
$l2->add_support($p4);
my $i1 = $construction->add_object
('Math::Geometry::Construction::Derivate::IntersectionLineLine',
input => [$l1, $l2]);
my $p5 = $i1->create_derived_point
(point_selector => ['indexed_point', [0]],
label => 'S',
label_offset_x => 5,
label_offset_y => -5);
print $construction->as_svg(width => 800, height => 300)->xmlify;DESCRIPTION
This is alpha software. The API is likely to change, input checks and documentation are sparse, the test suite barely exists. But release early, release often, so here we go.
Aims
This distribution serves two purposes:
Carrying out geometric constructions like with compass and straight edge. You can define points, lines through two points, and (in the future) circles around a given center and through a given point. You can let these objects intersect to gain new points to work with.
Creating illustrations for geometry. This task is similar to the one above, but not the same. For illustrations, the priorities are usually different and more powerful tools like choosing a point on a given object, drawing circles with fixed radius etc. are handy.
Motivation
Problems of these kinds can be solved using several pieces of geometry software. However, I have not found any with sufficiently powerful automization features. This problem has two aspects:
For some project, I want to create many illustrations. I have certain rules for the size of output images, usage of colors etc.. With the programs I have used so far, I have found it difficult to set these things in a consistent way for all of my illustrations without the need to set them each time I start the program or to change consistently later on.
For actual constructions, most macro languages are not powerful enough. For example, the intersection between two circles sometimes yields two points. There are situations where I want to choose the one which is further away from some given point or the one which is not the one I already had before or things like that. The macro languages of most geometry programs do not allow that. It is somehow determined internally which one is first intersection point and which the second, so from the user point of view the choice is arbitrary. Or, for example, I have come across the situation where I needed to double an angle iteratively until it becomes larger than a given angle. Impossible in most macro languates. With this module, you have Perl as your "macro language".
Intersection Concept
Intersecting two objects consists of two steps. First, you create a Math::Geometry::Construction::Derivate object that holds the intersecting partners and "knows" how to calculate the intersection points. Second, you create a Math::Geometry::Construction::DerivedPoint from the Derivate. The DerivedPoint object holds information about which of the intersection points to use. This can be based distance to a given point, being the extreme point with respect to a given direction etc..
The DerivedPoint object only holds information about how to select the right point. Only when you actually ask for the position of the point it is actually calculated.
The classes are called Derivate and DerivedPoint because this concept is applicable beyond the case of intersections. It could, for example, be used to calculate the center of a circle given by three points. Whenever some operation based on given objects results in a finite number of points, it fits into this concept.
Output
Each line or similar object holds a number of "points of interest". This are - in case of the line - the two points that define the line and all intersection points the line is involved in. At drawing time, the object determines the most extreme points and they define the end points of the drawn line segment. The extend attribute allows to extend the line for a given length beyond these points because this often looks better. A similar concept will be implemented for circles and other objects.
Current Status
At the moment, you can define points and lines, and you can intersect lines. Points and lines can have labels. Essentially, the whole current functionality is summarized in the SYNOPSIS.
Next Steps
Circles
Extend documentation
Improve performance
Improve automatic positioning of labels
Improve test suite along the way
INTERFACE
Constructors
new
$construction = Math::Geometry::Construction->new(%args)Creates a new Math::Geometry::Construction object and initializes attributes. This is the default Moose|Moose constructor.
Public Attributes
Methods
add_point
add_line
add_object
as_svg
DIAGNOSTICS
Exceptions
Warnings
BUGS AND LIMITATIONS
Please report any bugs or feature requests to bug-math-geometry-construction at rt.cpan.org, or through the web interface at http://rt.cpan.org/NoAuth/ReportBug.html?Queue=Math-Geometry-Construction. I will be notified, and then you will automatically be notified of progress on your bug as I make changes.
AUTHOR
Lutz Gehlen, <perl at lutzgehlen.de>
LICENSE AND COPYRIGHT
Copyright 2011 Lutz Gehlen.
This program is free software; you can redistribute it and/or modify it under the terms of either: the GNU General Public License as published by the Free Software Foundation; or the Artistic License.
See http://dev.perl.org/licenses/ for more information.