Posted on February 10, 2010.
Is it possible to draw a spiral (preferably logarithmic) is not around the pole? I need to make a drawing using polar equations and I intend to add a spiral, but the place I want to, it is around the pole and all the equations I find around him .
Sure, but why would you? If the spiral will not be around the pole, then using polar coordinates is a mistake.
Suppose you want the center to have <X, y>, then Cartesian coordinates of the spiral would be:
http://en.wikipedia.org/wiki/Logarithmic ...
x (t) = X + ae ^ (bt) cos t
y (t) = Y + ae ^ (bt) t sin
You can then use the standard Cartesian polar transformation:
r (t) = sqrt (x (t) ^ 2 + y (t) ^ 2)
@ (T) = arctangent (x (t), Y (t))
but the result is a disorder that does not simplify.