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From: farestam@ORION.CERFACS.FR (Stefan Farestam)
Newsgroups: comp.sys.sgi
Subject: Re: question: lookat() command and twist
Message-ID: <9101170614.AA25522@ultima.cerfacs.fr>
Date: 17 Jan 91 06:14:08 GMT
Sender: daemon@ucbvax.BERKELEY.EDU
Organization: The Internet
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In article <1991Jan16.181821.20724@athena.mit.edu>, Matthew A Machlis 
<bloom-beacon.mit.edu!bloom-picayune.mit.edu!news> writes

  > I am developing a 3-D realtime simulation on a Personal IRIS which has
  > head-tracking capability to display what the user is actually looking at.
  > I am using the lookat() command to actually do the transformation involved
  > in head-tracking.  I have run into an unfortunate aspect of the lookat
  > command: everything is fine when I am looking straight ahead (along the
  > positive z-axis) with zero twist.  But as the "look vector" is rotated
  > downward (towards the negative y axis), still with zero twist, the 
  > direction which is "up" in terms of what is displayed on the screen
  > rotates 180 degrees as the head rotates through straight down.
  > How can I compensate for this twisting of the up direction with lookat?

I'm not sure I understand your problem, but the following might prove useful
for you:

Suppose that :

* view_point is the point you are looking from

* ref_point is the point you are looking towards

* up_vec is a vector that represents the direction up (i.e. if you would
  plot up_vec after lookat was applied it would be a vertical vector
  pointing upwards on the screen)

* v = view_point - ref_point

* w = (up_vec) x (v)   where 'x' signifies the vector product

* v and w are normalized

then the twist angle used in lookat can be calculated by:

   swy = (int) copysign(1.0, wy) ;

   twist = swy * acos((wx*vz - wz*vx) / sqrt(vx*vx         + vz*vz)
                                      / sqrt(wx*wx + wy*wy + wz*wz)) ;

and the call to lookat would look like:

   lookat(view_point->x, view_point->y, view_point->z,
           ref_point->x,  ref_point->y,  ref_point->z, twist * 180/PI * 10) ;

/Stefan Farestam


--

   .................................................................   
 .             Stefan Farestam <farestam@cerfacs.fr>                 .
.   __ __  __ _  _ _                                                  .
.  /  |_ )|_ /_\/ (          European Centre for Research and         .
 . \_ |__\| /   \__)    Advanced Training in Scientific Computation  .
   .................................................................