"marc" <tra### [at] freefr> wrote:
> hi
> newbie here
> in interpolation confusion
>
> >>> reading 1st :
>
> - doc : 3.2.2.8.4  "Returning a Value Like a Function"
>         Interpolate(T,T1,T2,P1,P2) (P1+(T1+T/(T2-T1))*(P2-P1))    5 args
>         scenes/language/macros/macro3.pov
>         author: Chris Young

The macro you refer to here looks wrong.

  #macro Interpolate(T,T1,T2,P1,P2)
     (P1+(T1+T/(T2-T1))*(P2-P1))
  #end


It should probably have been made like this:


  #macro LinearInterpolate(T, T1, T2, P1, P2)

     (P1 + (T - T1)/(T2 - T1)*(P2 - P1))

  #end // macro LinearInterpolate


Here is how I arrived at that formula:

  (P - P1)/(T - T1) = (P2 - P1)/(T2 - T1)
  P - P1 = (T - T1)*(P2 - P1)/(T2 - T1)
  P = P1 + (T - T1)*(P2 - P1)/(T2 - T1)
  P = P1 + (T - T1)/(T2 - T1)*(P2 - P1)

--
Tor Olav
http://subcube.com

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