# Fast Distance Approximation

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I've implemented ropes in my simulation, but it gets really slow with many ropes and many particles. Does anyone know a way to quickly approximate the distance between two points, or maybe a fast square root approximation? Thanks in advance, Mr. Big

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Read this for a fast (and pretty exact) square root appriximation:
http://www.math.purdue.edu/~clomont/Math/Papers/2003/InvSqrt.pdf

If you want code look at the end.

Thanks!

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You might want to look into SSE. It has special operations for fast square root and fast inverse square root. Since you're simulating many ropes and particles you're probably applying the same algorithms to them. If this is the case using SSE could result in up to a 4x improvement in speed (assuming a good implementation) since it performs 4 floating point operations in parallel.

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Quote:
 Original post by mrbigDoes anyone know a way to quickly approximate the distance between two points, or maybe a fast square root approximation?

d = (A.a - B.a)*(A.a - B.a) + (A.b - B.b) * ...
or
d = (A - B) dot (A - B)

Re SSE

If it will not be killed in throughput and latency.

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Quote:
 Original post by Raghard = (A.a - B.a)*(A.a - B.a) + (A.b - B.b) * ...or d = (A - B) dot (A - B)

This will compute |A-B|², the square of the distance.

If you can tolerate a maximum error of 6.5%, you should use an octagonal approximation: Approximate the unit circle with an octagon, giving a case-analysis on eight linear functions. The hexadecagon approximation is better yet, but (although still considerably faster than a sqrt) is a fair bit slower than the octagonal function, and is a pain to code.

More accurate approximations yet can be produced using Richardson Extrapolation (daniel_i_l's article seems like a good implementation) and if you are prepared to do the work yourself, you can tailor the speed/error tradeoff to suit your needs.

Regards

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