New blog post attempting to demystify floating point a bit. Aimed at people like myself who usually regard floating point as a black box that is to be used but not trusted :Phttps://blog.demofox.org/2017/11/21/floating-point-precision/ …
RE: When precision falls apart. Lots of math relies on temporarily large numbers. Pythagorean Theorem, for example. The sqrt in 'sqrt(dot(a,b))' brings a large number down. Which basically means anything that takes a dot is suspect.
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Length of a vector alone cuts out 90% of the 2D and 3D algorithms game programming heavily relies on. And once you lose precision, you don't get it back.
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There was a convo some months back about how uint64 can measure between earth and pluto with change to spare. In a straight line, yes. In terms of 3D math -- not a chance.
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I don't think temporarily large numbers are so much an issue, since float precision is relative to the magnitude of the value. The real killer is catastrophic cancelation—subtracting two numbers that have a small difference.
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This is what causes errors with transforms, animation, etc far from the world origin: camera position and object/bone/vertex position are both "big" numbers with a small difference.
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