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Gradients Are the New Intervals
England Symposium on Graphics, James Tompkin compared graphics researchers to magpies: they're easily distracted by shiny objects and pretty renderings. While this is true, the analogy also holds from a different angle: when I'm reading graphics papers, I'm constantly looking for ideas to steal bring back to my nest.
This blog post assumes a vague understanding of implicit surface rasterization, and how interval arithmetic is used to both skip regions of space and simplify complex expressions. We introduce an efficient hierarchical tree pruning method based on the Lipschitz property of SDFs, which is compatible with hard and smooth CSG operators. Because the pseudo-interval considers the green circle (rather than the red square of the interval evaluator), it can't prove this entire region outside of the shape, and therefore has to subdivide it.
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