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sphere tracing metablobs

Richard Baker
in Computer Science

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(PDF) Sphere Tracing: A Geometric Method for the Antialiased Ray Tracing of Implicit Surfaces (researchgate.net)   On page 5-113 of this article, it says that the distance to the implicit blend is greater than 2/3 times f(x) times the sum of radiuses but it also says the Lipschitz constant of a single contributing sphere equals 3/(2r).  It also says that the Lipschitz constant of a sum is bounded by the sum of the Lipschitz constants. Is this an error? The inverse of the sum of the  Lipschitz constants does not equal the sum of the inverse of the Lipschitz constants.  My question is what is the Lipschitz constant of the level set of a metablob?  

Thank you.

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