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Texture Splatting Alpha Blending

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Hi, I just stumbled across this article at www.cbloom.com/3d/techdocs/splatting.txt about texture splatting. In the article, Charles talks about using 32x32 element (or tile or quad) chunks and then using a 64x64 pixel texture for alpha map for each chunk. This basically equates to 2x2 pixels per element. In other words, each quad in the chunk is represented by 4 pixels on the alpha map (is that correct?). What I don't understand is how anyone can achieve smooth blending with just 4 pixels that map to an entire quad. In order to have a nice gradient (on the alpha map) fade away from the any given element, you would probably need a good 16+ pixels. That would mean that your texture would fade away across the four surrounding quads when rendered. What if you just want a quad's texture to blend in with the immediately adjacent quads? I must be missing something here, or I don't understand the article, I thought I did until I read this particular bit (which is discussed about 20% of the way down the article, just above the little gird picture). Maybe someone higher up the food chain can explain this to me like I'm a five year old.

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So let me get this straight.

Despite the fact that only 4 pixels on the alpha texture map to each quad, it will still produce a smooth gradient due to the filtering? I just thought that the first alpha pixel would map to the top-right quarter of the quad, the second pixel would map to the top-left quarter and so on. This would result in a very "blocky" looking blending.

But your saying that the filtering will smooth it out. It makes sense I guess. I've just never tried it so I didn't understand it.

One more question: The method requires some quads to be rendered multiple times. Wouldn't this cause z fighting? How would you prevent this?

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