I finally got most of the precision issues under control now, whereas there
are still cases where everything would break apart depending on the stiffness
of a given equation with respect to some hard precision limits. But what the
demo shows is now very smooth within this regard, which was/is all hard work.
Well, I can now generate surfaces from basic parameterized elements combined
with some matrix operation. I've skipped the sphere, cylinder, and the torus
from the demonstration for now, since each of those can be generated easily
from their known parametrization and wouldn't show the flexibility my approach
has, since my approach lets me change the shape, the path, and the orientation
at every single point. The entire object in the demo is generated anew each
frame. To show that the object is quite dynamic I changed many of its
parameters during runtime.
The next step is to enhance the description of the generation process, i.e.
translating almost everything into matrix notation, and to decouple/abstract
the elements used to generate parts of the surface, such that for example any
polygon you see may transform into a spinning cube etc. without the surface
generation process even knowing. Another important part I have to consider is
to match different descriptions together such that one description may
continuously transforms into another one.
But before doing this, I'm going to build my first gaming content. Nothing
huge, mind you, but for me the start of the game as such. Finally! Damn!