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From: shirley@m.cs.uiuc.edu
Newsgroups: comp.graphics
Subject: Re: World to Eye coordinate transforms
Message-ID: <4400055@m.cs.uiuc.edu>
Date: 19 Dec 89 01:29:58 GMT
References: <13513@<1989Dec15>
Lines: 39
Nf-ID: #R:<1989Dec15:13513:m.cs.uiuc.edu:4400055:000:718
Nf-From: m.cs.uiuc.edu!shirley    Dec 18 09:04:00 1989




There's a trick Don Hearn taught me that has cleaned up my
viewing code a lot.  Given the orthonormal unit vector set
      
      x_hat = (1, 0, 0)
      y_hat = (0, 1, 0)
      z_hat = (0, 0, 1)

which is just the xyz axes, and a different orthonormal set

      u_hat = (ux, uy, uz)
      v_hat = (vx, vy, vz)
      w_hat = (wx, wy, wz)

We can write down a matrix M s.t. 

      x_hat = u_hat * M
      y_hat = v_hat * M
      z_hat = w_hat * M

      | ux uy uz |
  M = | vx vy vz |
      | wx wy wz |

Then we can write down a matrix N s.t. 

      u_hat = x_hat * N
      v_hat = w_hat * N
      w_hat = z_hat * N

      | ux vx wx |
  N = | uy vy wy |
      | uz vz wz |


pete shirley
shirley@m.cs.uiuc.edu