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Map Question

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I'm wondering... Let's say that I have a base line that extends horizontaly across the screen. Now, imagine there are dots above that line that are positioned so that they fluxuate up and down, making a wave pattern. Suppose I am to connect the dots together, to make fluent wave. Now suppose I am to texture the underside of the wave, and make this whole project into a 2d- Side Scroller Map. All well and dandy. One question. If I am to texture the underside, I wouldn't want to make a polygon that uses each dot as a vertex, in case I want to use different textures for different parts of the map. People usually use triangle strips, but I don't see how that would work. Please help me. And thank you for those who will!

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