logarithmic interpolation

[different]

Hi, I have a program which reads a file containing integers in [0,10].
The program reads the value of a variable every 2 seconds, then maps it
to another interval, say [20,22000], obtaining a new value.
I already have a function which updates the variable, gradually
changing from the old one to the new one during the 2 seconds, which
uses a linear function.
Know I need to make the value of the variable change between old and
new in a "logarithmic way", that is the values between old and new must
follow a logarithmic scale.
How can I do that?

[Victor Bazarov]

Post by different
Hi, I have a program which reads a file containing integers in [0,10].
The program reads the value of a variable every 2 seconds, then maps
it to another interval, say [20,22000], obtaining a new value.
I already have a function which updates the variable, gradually
changing from the old one to the new one during the 2 seconds, which
uses a linear function.
Know I need to make the value of the variable change between old and
new in a "logarithmic way", that is the values between old and new
must follow a logarithmic scale.
How can I do that?

Is there a C++ language question hiding here?

[Richard Herring]

Post by Victor Bazarov

Post by different
Hi, I have a program which reads a file containing integers in [0,10].
The program reads the value of a variable every 2 seconds, then maps
it to another interval, say [20,22000], obtaining a new value.
I already have a function which updates the variable, gradually
changing from the old one to the new one during the 2 seconds, which
uses a linear function.
Know I need to make the value of the variable change between old and
new in a "logarithmic way", that is the values between old and new
must follow a logarithmic scale.
How can I do that?

Is there a C++ language question hiding here?

If there is, the answer probably involves <cmath>, std::pow() and
std::log[10]().

[Mark P]

Post by different
Hi, I have a program which reads a file containing integers in [0,10].
The program reads the value of a variable every 2 seconds, then maps it
to another interval, say [20,22000], obtaining a new value.
I already have a function which updates the variable, gradually
changing from the old one to the new one during the 2 seconds, which
uses a linear function.
Know I need to make the value of the variable change between old and
new in a "logarithmic way", that is the values between old and new must
follow a logarithmic scale.
How can I do that?

First you question is off-topic. Try comp.programming in the future
(followup-to reset).

Besides being off-topic, your question is not well defined. What is "a
logarithmic way"? I'll take a wild guess and suppose you mean log(new)
= m * old + b, for constants m and b. Let 0 map to 20 and 10 map to
22000, then solve for m and b. Then new = exp( m * old + b). Or is
"logarithmic way" supposed to mean something else?

[Zbigniew Karno]

Post by different
Hi, I have a program which reads a file containing integers in [0,10].
The program reads the value of a variable every 2 seconds, then maps it
to another interval, say [20,22000], obtaining a new value.
I already have a function which updates the variable, gradually
changing from the old one to the new one during the 2 seconds, which
uses a linear function.
Know I need to make the value of the variable change between old and
new in a "logarithmic way", that is the values between old and new must
follow a logarithmic scale.
How 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

[Zbigniew Karno]

Post by Zbigniew Karno

Post by different
Hi, I have a program which reads a file containing integers in [0,10].
The program reads the value of a variable every 2 seconds, then maps it
to another interval, say [20,22000], obtaining a new value.
I already have a function which updates the variable, gradually
changing from the old one to the new one during the 2 seconds, which
uses a linear function.
Know I need to make the value of the variable change between old and
new in a "logarithmic way", that is the values between old and new must
follow a logarithmic scale.
How 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]
(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