threedp - project s(t,u) = (x(t,u), y(t,u), z(t,u)) onto an arbitrary plane in R^3

This program is not finished. It is the product of some simple vector geometry that I refreshed for a Mathematics course at university.

Furthermore, the program is currently completely undocumented albeit somewhat commented. It has no user interface of any kind either, so you will need to edit the source to modify its output. (Not too hard if you ever touched Perl sources.)

Let me explain in a little more detail what this program does: Given three component functions of one or two parameters t, u x(t,u), y(t,u), and z(t,u), it constructs the three dimensional vector function s(t,u). Not too hard, but how can you display three dimensional functions on a computer screen?
threedp solves this problem by projecting a number of calculated vectors p=s(t,u) onto an arbitrary plane. Like your screen.
Mathematically, the program calculates the intersection of the plane given by D + a*E + b*F and the line s(t,u) + c*N where N is orthogonal to E and F. The intersection can be found by solving a linear equation system (3 equations x 3 unknown values).

It is trivial to implement s(N) with N being a matrix of higher order than 2. Unfortunately, drawing complexity rises exponentially with more dimensions, so that it is not a smart move to sacrifice performance in all cases when this feature is only useful in very rare occasions. Modify the code as needed.

I am lazy; code reuse is good and, to be honest, the most efficient and robust algorithms for solving linear equation systems are beyond me. Hence I am using the handily powerful module Math::MatrixReal by Steffen Beyer et al (See search.cpan.org).
You will need to install GD and Math::MatrixReal on your system as well as Perl 5.6.0 or higher. (Tested with 5.6.1)

Downloads (currently only the newest version availlable):

Source code (rename to threedp.pl under systems that do not interpret the shebang (Win))
Resource file with some functions the program relies on. Name it 'functions.res'.
Examples:
- Example 1 ( x(t) = t, y(t) = t*t, z(t) = 3*sin(t) )
- Example 2 similar to Example 1, but z(t) = 3*sin(t/large number)
- Example 3 ( x(t) = t, y(t) = sin(t), z(t) = cos(t) )
- Example 4 ( x(t) = n*sin(t/largish number), y(t) = sin(t), z(t) = cos(t) )
- Example 5 sphere: ( x(t,u) = sin(t)*cos(u), y(t,u) = sin(t)*sin(u), z(t,u) = cos(t) )
- Example 6 deformed sphere, like Example 5, but x *= t
- Example 7 sphere, like Example 5, with semi-randomized surface
- Example 8 randomized screw with increasing y-randomness
- Example 9 screw with 2-norm (distance) of s(t) from the projection plane expressed by its shade of grey.