[daip] Re: AIPS task OGEOM interpolation question

[Eric Greisen]

Clayton Hogen writes:
 > Hello,
 > 
 > I need to know how OGEOM calculates the new pixel values when the image is 
 > translated by a non-integer pixel value.  Thank you for your prompt
 > response.
 > 
 > Cheers,
 > Clayton Hogen-Chin
 > chogen at astro.umn.edu

I did not design this software and so am not entirely familiar with
it.  In $APLOOP/INTERPLATE.FOR there are a variety of subroutines.
The actual function is recomputed at every pixel by subroutine IMINFN.
The term Lagrangian is mentioned in the comments.

      INT(1) = POS
C                                       Fractional pixel
      IPOS = POS + 0.5
C                                       Set first pixel
      CEN = IPOS - IHALF
      CEN = MAX (1, MIN (CEN, (N-IWID+1)))
C                                       Make 0 rel
      CEN = CEN - 1
C                                       Set "x" at first pixel to 1.0
      XX = POS - CEN
C                                       Compute interpolating kernal
      DO 50 J = 1,IWID
         PROD = DENOM(J)
         DO 30 I = 1,IWID
            IF (I.NE.J) PROD = PROD * (XX - I)
 30         CONTINUE
         INT(J+1) = PROD
 50      CONTINUE

is the actual code and

C                                       Calculate Lagrangian
C                                       denominators
      DO 210 J = 1,IWID
         PROD = 1.0
         DO 200 I = 1,IWID
            IF (I.NE.J) PROD = PROD * (J - I)
 200        CONTINUE
         DENOM(J) = 1.0 / PROD
 210     CONTINUE

is done at the start.

Eric Greisen