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MathGroup Archive 2000

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HELP!! 3D --> 2D math problems..

  • To: mathgroup at smc.vnet.net
  • Subject: [mg24399] HELP!! 3D --> 2D math problems..
  • From: * <keen at ulster.net>
  • Date: Wed, 12 Jul 2000 23:13:42 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

hello!! i'm having a little problem with what i guess would be spherical
trig..

i divided the Earth into 12 identical pentagons - 3 at each pole and 6
around the equator.. using Lightwave i rendered an image of each of the
pentagons face on.. i know the coordinates, in latitude and longitude,
of each point of each pentagon.. so given the coordinates of a location
somewhere on the globe - NYC (40N42, 74W00) for example - i can tell
which pentagon it's in.. my problem is plotting an accurate
representation of the location on the rendered image.. i was given very
helpful math on how to convert 3D coordinates to 2D which i translated
(roughly) into this code:

-- -- -- -- -- -- -- -- -- --
  loc = location coord
  centre = pentagon centre coord

  sloc = loc - centre -- subtract centre from loc coord to make it
relative to the centre of the pentagon

  theta = (PI * sloc.horz) / 180 -- convert coord to radians..
  phi = (PI * sloc.vert) / 180

  r = 3.5530 -- radius of the sphere in Lightwave

  x = r * sin(theta) * cos(phi)
  y = r * sin(phi)
  z = r * cos(theta) * cos(phi)

  f = .4696 -- focal length in Lightwave
  d = 6.3682 -- the distance between the centre of the sphere and the
viewer in Lightwave

  sx = (f * x) / (d - z) -- 2D coords of the loc..
  sy = (f * y) / (d - z)
-- -- -- -- -- -- -- -- -- --

the problem i am encountering now is that this doesn't account for the
way latitude curves around the globe - this is especially noticable
around the poles where it would be most severe.. it is treating all
locations as if the pentagon is centred on the equator and prime
meridian.. does this make sense?? any help to get this routine to work
would be greatly appreciated.. thanks!!

y'r pal -kK



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