_C_ License Applicability. Except to the extent portions of this file are
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_C_ Software License B, Version 1.1 (the "License"), the contents of this
_C_ file are subject only to the provisions of the License. You may not use
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_C_ 
_C_ Original Code. The Original Code is: OpenGL Sample Implementation,
_C_ Version 1.2.1, released January 26, 2000, developed by Silicon Graphics,
_C_ Inc. The Original Code is Copyright (c) 1991-2000 Silicon Graphics, Inc.
_C_ Copyright in any portions created by third parties is as indicated
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_C_ Additional Notice Provisions: The application programming interfaces
_C_ established by SGI in conjunction with the Original Code are The
_C_ OpenGL(R) Graphics System: A Specification (Version 1.2.1), released
_C_ April 1, 1999; The OpenGL(R) Graphics System Utility Library (Version
_C_ 1.3), released November 4, 1998; and OpenGL(R) Graphics with the X
_C_ Window System(R) (Version 1.3), released October 19, 1998. This software
_C_ was created using the OpenGL(R) version 1.2.1 Sample Implementation
_C_ published by SGI, but has not been independently verified as being
_C_ compliant with the OpenGL(R) version 1.2.1 Specification.
_C_
_C_ $Date: 2004/03/14 08:29:09 $ $Revision: 1.1.1.4 $
_C_ The first character in this file must be an '_'!
_C_ Anything on a line after _C_ is ignored
_define(_filters,eqn)_C_
_C_      eqn is automatically replaced with neqn for nroff
_header(LookAt, define a viewing transformation)
_names(LookAt)
.EQ
delim $$
.EN
.SH PARAMETERS
_phead(_param1 _param2 _param3)
Specifies the position of the eye point.
_phead(_param4 _param5 _param6)
Specifies the position of the reference point.
_phead(_param7 _param8 _param9)
Specifies the direction of the \f2up\fP vector.
.SH DESCRIPTION
_cmnd creates a viewing matrix derived from an eye point, a reference
point indicating the center of the scene, and an \f2UP\fP vector.  
.P
The matrix
maps the reference point to the negative \f2z\fP axis and the
eye point to the origin.
When a typical projection matrix is used,
the center of the scene therefore maps to the center of the viewport.
Similarly, the direction described by the \f2UP\fP
vector projected onto the viewing plane is mapped to the positive \f2y\fP 
axis so that it points upward in the viewport.
The \f2UP\fP vector must not be parallel to the line of sight from the
eye point to the reference point.
.P
Let 
.sp
.EQ
F ~=~ left (  down 20 { ~ matrix {
   ccol {_eqnparam4 above _eqnparam5 above _eqnparam6}
   ccol { ~-~ above ~-~ above ~-~}
   ccol {_eqnparam1 above _eqnparam2 above _eqnparam3}
} } ~~ right )

.EN

.sp
Let \f2UP\fP be the vector $(_eqnparam7, _eqnparam8, _eqnparam9)$. 
.P
Then normalize as follows: 
.EQ
f ~=~ F over {|| F ||}
.EN
.P
.EQ
UP sup prime ~=~ UP over {|| UP ||}
.EN
.sp
.P
Finally, let $s ~=~ f ~times~ UP sup prime$, and $u ~=~ s ~times~ f$.
.P
.sp
M is then constructed as follows:
.EQ
M ~=~ left (  matrix {
   ccol { ~s[0] above ~u[0] above -f[0] above 0 }
   ccol { ~s[1] above ~u[1] above -f[1] above 0 }
   ccol { ~s[2] above ~u[2] above -f[2] above 0 }
   ccol { 0 above 0 above 0  above 1 }
} ~~right )
.EN
.P
and _cmnd is equivalent to 
.Ex
glMultMatrixf(M);
glTranslated (-eyex, -eyey, -eyez);
.Ee
.SH SEE ALSO
_glcmnd(Frustum), _cmnd(Perspective)