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intersection between line and implicit function

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How to find the intersection between a line and an implicit function like x ^3 + sqrt(y) + cos(2/z) = 85 ? It''s for a raytracer experiment Thanks.

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This is essentially a root finding problem. If G(x) is your implicit surface, and R(t) is your ray, then you are trying to find the smallest solution to G(R(t)) = 0 for t > 0. There are ways of solving this, but Newton''s Method or Interval Newtons Method come to mind.

"Math is hard" -Barbie

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