You store control points in the texture, and linear texture sampling calculates curve points. Extends to higher orders/piecewise.
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It would be neat to see how it extends to surfaces too... includes in browser working webgl demo and also C++/GL source code.
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Could something like this be used to accelerate bezier tessellation on the GPU rather than the CPU?
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Maybe! Reading a texture to generate verts could be done. Not sure about efficiency. Interesting idea, worth looking into :P
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Can you extend this via Lie Algebras to polytopes?
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I don't know about those things so not sure. Are you able to explain in a first principles kind of way?

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UMM, this is way cool! Doesn't this essentially mean that I can store vector graphics in tiny bitmaps..?
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Thanks! "yes" but i couldn't find very good ways to make that happen. I'll bet with some creativity, or a proper usage case (where the limitations aren't a problem) it could work ok for vector graphics.
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i feel it necessary to mention that bandwidth is way more limited than compute atm, and that lookup textures are should only be
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used when (spatially related) lookups hardly ever miss cache
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