Kore Nordmann - PHP / Projects / Politics
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:Author: 		Kore Nordmann
:Date:			Fri, 27 Jul 2007 20:26:41 +0200
:Revision: 		5
:Copyright:		CC by-sa


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Image_Turtle & Image_Curve
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:Description: While learning for a lecture in computer science which covers
  several algorithms on graphic manipulation I implemented some of the
  algorithms for personal education and these are the results...

The last days I was busy learning for a lecture for computer science which
covers a lot of algorithms in graphics manipulation. For personal education I
tried to implement some of them in the language I know best ... `PHP`__ .

__ http://www.php.net

Image_Turtle
============

.. image:: tree.png
   :alt: Lindemayer system rendered with PHP

This implements the `Lindenmayer system`__ in PHP. This is a system to draw
images based on simple grammars. Most used for fractals or to simulate natural
growth of plants. You perhaps wonder because of the name of this class, but
the cursor which draws the objects is often called "turtle". It is really fun
to play around with these grammars and the options which defines the route the
turtle takes.

__ http://en.wikipedia.org/wiki/L-system

For the tree on the right side you just need this simple grammar with an angle
of 25 degrees and recursion depth of 3:

::

	w -> FFF[+F+F+F][-F+F+F+F+F]
	F -> FFF[+F+F+F][-F+F+F+F+F]

"w" is the starting symbol in this case.

I wrote some simple examples and you download them together with the classes
`here`__ .

__ http://kore-nordmann.de/home/php_code_snippets/image_turtle

Image_Curve
===========

.. image:: bezier_3d.png
   :alt:   Threedimension bezier curve

Another thing I needed to understand - and imho the easiest way is just to
implement it - are bezier curves and BSplines. Hunting the errors in the
implementation solved all misunderstandings in the profs script ;-).

This class offers a simple way to draw lines, bezier curves or BSplines from
an array with points. You can download the class `here`__ .

You want to see an example? Ever implemented bezier curves on the base of the
`Bernsteinpolynom`__ you know that it is really trivial to implement a 3D
version - of course I implemented it for `Image_3D`__ . I hope to release a
new version of Image_3D next weekend, so that you can render it by yourself.

__ http://kore-nordmann.de/home/php_code_snippets/image_curve
__ http://en.wikipedia.org/wiki/Bernstein_polynomial
__ http://pear.php.net/package/Image_3D


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