exponential interpolation ? like in ultrafractal

[cKleinhuis]

hi all, i can not get my head around the "exponential interpolation" feature of ultrafractal, as described here:
http://www.ultrafractal.com/help/index.html?/help/tutorials/basicskills/bs-zoom.html

i want to implement such an interpolation method of my own, but i can not figure it out, and the internet seems
to be not providing any information as well, is it so easy no one writes about it ?!

question: i have a linear interpolation between point x and y. i now want to interpolate the values exponentially as described in the uf link...

[hobold]

If I am not mistaken, you can can get exponential interpolation by working in logarithmic space. Conceptually that is a three step process:

if you want to interpolate a variable from value A to value B according to a time parameter t (with 0.0 <= t <= 1.0), then:

1. take the logarithm of A and B (any base of logarithm will do, as long as you are consistent later)

    logA = log(A);
    logB = log(B);

2. now interpolate the transformed values as you normally would, either linearly, or with a spline, or however you wish:

    logInterpolatedValue = interpolate(t, logA, logB);

3. finally, the interpolated value from log space needs to be mapped back (use the same base as with the log of step 1)

    interpolatedValue = exp(logInterpolatedValue);

That should do the trick. There are some limitations, because A and B may not be zero and must have the same sign. But that is a fundamental limitation of logarithmic space, not of this specific algorithm.

[cKleinhuis]

very cool, thank you, it seems to work

[hobold]

Math works! 

[cKleinhuis]

right, and i never get how easy working with logarithms actually is
and for the zoom factors it is a MUST to get it continuously smooth
thank you for the pointing !!!