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solid texture bump mapping

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I''m wondering about this thing... Ken Perlin has that bump-mapped sphere on his website. If anyone has been there, it''s the black and gold one, with the color coinciding with the normal perturbation. Black is 0 height, gold is 1 height, above the surface of the sphere. Anyway, he said he used a height field-type function to make it. I was wondering how you would do that for an implicit surface. I know how to do bump mapping, from a height map, on a plane, that''s easy. What I want to do is have H(x,y,z) and use that for a sphere. The problem comes in when you try to find the normal gradient, which is normally very easy. I thought about using three different functions X(x,y,z), Y(x,y,z), Z(x,y,z) for normal displacement, but I can''t because I need to have only one function. Does anyone know how to do this?

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