Zbigniew Karno napisa (a):
different napisa (a):
> I have a program which reads a file containing integer values between 0
> and 10. I already use a linear mapping which takes this values and maps
> them in a different range.
> Now I want to map the values using a logarithmic scale.
> For example I want to map from [0;10] to [0.2;5] and values have to
> grow following the logarithmic scale.
> I can I do that?
Instead of the function log(x), rather you have
to use the following one: log(x - 1), for x >= 0.
Then the interpolation formula for x in [x_1,x_2]
with ratio f = a/(a+b), looks as follows:
(log(x_2 -1) - log(x - 1)) / (log(x - 1) - log(x_1 - 1)) = (1/f) - 1
After a simple calculation one can get
x = (x_1 - 1)^{f - 1} * (x_2 - 1)^{f} + 1 ,
what you expect.
Best Regards,
Z. Karno
Incorrect.
The sign - should be replaced by +.
So, the following function has to be used:
log(x + 1), for x >= 0.
In this case, the interpolation formula looks as
follows:
(log(x_2 +1) - log(x + 1)) / (log(x + 1) - log(x_1 + 1)) = (1/f) -
1.
Thus
x = (x_1 + 1)^{f -1} * (x_2 + 1)^{f} - 1 .
Regards,
Z. Karno
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