Filling in Degrees in a Circle (Astronomy)

[Lie]

On Aug 23, 6:12 am, "W. eWatson" <notval... at sbcglobal.net> wrote:
> The other night I surveyed a site for astronomical use by measuring the
> altitude (0-90 degrees above the horizon) and az (azimuth, 0 degrees north
> clockwise around the site to 360 degrees, almost north again) of obstacles,
> trees. My purpose was to feed this profile of obstacles (trees) to an
> astronomy program that would then account for not sighting objects below the
> trees.
>
> When I got around to entering them into the program by a file, I found it
> required the alt at 360 azimuth points in order from 0 to 360 (same as 0).
> Instead I have about 25 points, and expected the program to be able to do
> simple linear interpolation between those.
>
> Is there some simple operational device in Python that would allow me to
> create an array (vector) of 360 points from my data by interpolating between
> azimuth points when necessary? All my data I rounded to the nearest integer.
> Maybe there's an interpolation operator?
>
> As an example, supposed I had made 3 observations: (0,0) (180,45) and
> (360,0). I would want some thing like (note the slope of the line from 0 to
> 179 is 45/180 or 0.25):
> alt: 0, 0.25, 0.50, 0.75, ... 44.75, 45.0
> az : 0, 1,    2,    3,              180
>
> Of course, I don't need the az.
>
> --
>             Wayne Watson (Watson Adventures, Prop., Nevada City, CA)
>
>               (121.015 Deg. W, 39.262 Deg. N) GMT-8 hr std. time)
>                Obz Site:  39° 15' 7" N, 121° 2' 32" W, 2700 feet
>
>                      Web Page: <www.speckledwithstars.net/>

Linear interpolation is simple, any mathematician would know. It's
just like this:

hA = height at point A
hB = height at point B
hN = height at point N (what we're finding)
l = horizontal distance between A and B
n = horizontal position measured from A

hN = hA + ((n / l) * (hB - hA))

so:

def interpolate(n, A, B):
    # A, B is two-tuple of (angle, height) of
    # the nearest known points surrounding n
    oA, hA = A
    oB, hB = B
    l = oB - oA
    return hA + ((n / l) * (hB - hA))