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i'm working on a small c# program that uses xinput to read the xbox 360 thumb stick.

i have no problem with reading the coordinates and normalizing the values so i get a float between -1 and +1 for X and Y directions. the problem i have is that the stick itself is physically limited to a circle and in my case i would like to "stretch out" the coordinates so it becomes more of a square than a circle.

the reason is that each direction is controlling a motor and if i move the stick for example top right i would like both X and Y to become 1. since the stick is circular this is not possible and this also makes it impossible to make both motors run at full speed.

any advice?

T J
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1 Answers1

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So you want a point on a circle of radius r to be mapped to a point on a square of radius r on the same ray through the origin. Toward that goal you have to compute the radius using the usual formula

r = sqrt(x*x+y*y)

and then from that the scale factor 

f = r / max ( abs(x), abs(y) )

and in the end replace x by f*x and y by f*y.

One can vary this computation by noting that the factor is

f = sqrt ( 1 + (x*x)/(y*y) )

if abs(y) > abs(x) and

f = sqrt ( 1 + (y*y)/(x*x) )

in the opposite case. Or by noting that the largest coordinate gets replaced by r and the smaller scaled accordingly, which also does not reduce the logistics by much.

Lutz Lehmann
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  • thanks, that helped. now i just need to find out why my normalization sometimes makes x and y larger than 1. i bet i have some other errors, time for a bit of debugging. – T J Aug 25 '14 at 21:34