Re: [pygame] shadow demo

["Alistair Buxton" <a.j.buxton@xxxxxxxxx>]

On 22/03/2008, Ian Mallett <geometrian@xxxxxxxxx> wrote:
> Hasn't anyone figured this out?  One would think that it can't be too
> difficult.  One quad over another--how hard could it be?

It's pretty easy really, when you consider that opengl is a system
designed around the idea of projecting 3d coordinates into 2d
coordinates in a plane, based on a transformation matrix.

When you draw your world, you project the 3d geometry into the screen
plane based on the eye point.

When you draw the shadows, you project the 3d geometry into the
shadowed surface plane, based on the light source point.

So, you see, it's exactly the same thing.

This has the following implications:

* A shadow can no more have a soft edge than a polygon can have a soft
edge. You can fake it by doing multiple samples, but then you have to
draw everything multiple times. Doing this for your shadow rendering
gives you the penumbra(1) effect, doing it for your world view gives
you a depth of field(2) effect.

* If every triangle can shadow every other triangle, then rendering
the shadows requires drawing n*n*l triangles where n = number of
triangles and l = number of light sources. You have to do this for
every single sample you do, if you are trying to do soft shadows.

Of course, you can optimize using depth tests, bounding boxes etc. But
then you are getting into the kind of complex algorithms(3) that take
people years to perfect...

(1) http://en.wikipedia.org/wiki/Umbra
(2) http://en.wikipedia.org/wiki/Depth_of_field
(3) http://graphics.cs.lth.se/research/shadows/

-- 
Alistair Buxton
a.j.buxton@xxxxxxxxx