Not looking for details, but just a nudge in the general direction:

I've got a complex shaped object which is in reality a
512x512 texel RGBA texture. There is a pattern "painted"
on the complex geometric shaped and the alpha (transparency)
is set to everything that is not the complex geometric object.


Using texture coordinates of [0,1] and object coordinates of [0,10],
I then resize the object. Make it bigger.

The overall dimensions of the object are now correct (for my game), but
obviously the "painted" pattern is now blown up and looks unnatural at
this new scale.

Is there some technique I can use to rectify this cosmetic problem?

I don't suppose there is a method of repeating a texture of a pattern
onto a complex geometric object?

Thanks.

When you set up your texture's, you can do something like this:

Then try using different numbers for your texture coordinates, for example, if you blew up the polygon by 2x, try using 2, or .5, I can't really remember. You'll learn better just by playing with it anyway.

If the texture is set to repeat and you give it a u or v greater than 1, it should tile the texture.

Wow, is it that simple. I thought that repeating pattern would simply
give me a solid rectangle of the pattern. Covering everything of
the complex geometric shape. So the alpha is preserved.

If you set the texture mode to modulate, the alpha will be preserved. Example:
glTexEnvi(GL_TEXTURE_ENV, GL_TEXTURE_ENV_MODE, GL_MODULATE);

There should be no border between textures. It is that simple.

I tried to do a simple replacement of my GL_REPLACE with GL_MODULATE but nothing changes
so I don't think I still get it. I've been reading the "Texture Functions" section in the Red Book
over and over, but I'm now more confused than ever.

First, is this an application of multi-texturing? If so, I'll go off and study that more.

Let's make the example even simpler. Let's say I've got an RGBA image (texture) of
an oval: the oval is 1024x256 pixels and it is solid white. The alpha defines the part
that is not the oval (the anti-oval). I want to lay over the oval a "wood plank" texture of
an 128x128 texture. (The texture is tileable so it will look pretty if the texture repeats)

So I display a blue screen, and display a white oval. So far so fine, But what to do next.
should I change the glTexEnv() to GL_MODULATE and repeat the display operation
with the oval's object coordinates, but now using the wooden plank's texture?