Is there an approximate way to calculate distance between two points?
Normally I would use
D = sqrt( dx^2 + dy^2 ).
But I didn't want to use sqrt().
Note: I have assumed that dx and dy are always positive by using absolute values.
Consider a case where dx >= dy:
After normalizing by dividing dx and dy by dx,
D' = D / dx = sqrt( 1 + (dy/dx)^2 )
Plotting this from 0 to 1 shows a flat-ish curve. It could be approximated by a straight line or, as I have done, by a quadratic.
D' = Ax^2 + B
Plugging in two extreme points (0,1) and (1,sqrt(2))
When x=0, D'=1 therefore B=1
And when x=1, D'=sqrt(2) therefore A=sqrt(2) - 1 (about 0.4142)
So, for dx>=dy (and dx!=0)
D = 0.4142 * dy^2 / dx + dx
And for dx<dy (and dy!=0),
D = 0.4142 * dx^2 / dy + dy (dx and dy are swapped)
Average error seems to be less than 1% - good enough for what I want and simple.
By using different 'tuning' points, better accuracy can be achieved
Another approach (using a linear approximation I suspect) can be found here.
