CODEWITHSUNDEEP
algorithmvectorlanguage-agnosticlinear-algebraprojection
user173342
user173342

Reputation: 1840

Subtract a constant from a vector's magnitude (shorten the vector) without using square root?

I have a 2 dimensional vector V represented with integers, and I subtract a constant C from V's magnitude and get a vector W that has the same direction as V but obviously the magnitude of |V| minus C.

The magnitude requires a square root, and integer square roots are an annoyance. I really don't want to convert to floats for this, and in the past I've managed to manipulate equations to remove square roots (like projecting one vector to another)... But this is a tricky one. So anyway, the basic equation is W = (|V| - C) * (V / |V|), I think. I've tried manipulating it but can't remove a magnitude at some point in it.

Is it even possible to subtract from a vector's magnitude without using a square root?

Upvotes: 0

Views: 641

Answers (2)

Blender
Blender

Reputation: 298432

Rewrite your last equation:

W = (|V| - C) * (V / |V|)
  = V * (|V| - C) / |V|
  = V * (1 - C / |V|)

Your scale factor depends on the magnitude of V, which isn't always rational.

Upvotes: 1

David Eisenstat
David Eisenstat

Reputation: 65498

No – if you shorten (1, 1) by 1, then you get (1 - 1/√2, 1 - 1/√2), and there's no way to write 1 - 1/√2 using only +, -, *, /, and integers.

Upvotes: 6

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