_C_ License Applicability. Except to the extent portions of this file are
_C_ made subject to an alternative license as permitted in the SGI Free
_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
_C_ this file except in compliance with the License. You may obtain a copy
_C_ of the License at Silicon Graphics, Inc., attn: Legal Services, 1600
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_C_ 
_C_ http://oss.sgi.com/projects/FreeB
_C_ 
_C_ Note that, as provided in the License, the Software is distributed on an
_C_ "AS IS" basis, with ALL EXPRESS AND IMPLIED WARRANTIES AND CONDITIONS
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_C_ PARTICULAR PURPOSE, AND NON-INFRINGEMENT.
_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
_C_ elsewhere herein. All Rights Reserved.
_C_ 
_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: 2004/12/14 16:20:38 $ $Revision: 1.1.1.1 $
_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(UnProject4, map window and clip coordinates to object coordinates)
_names(UnProject4)
.EQ
delim $$
.EN
.SH PARAMETERS
_phead(_param1 _param2 _param3)
Specify the window coordinates to be mapped.
_phead(_param4)
Specify the clip w coordinate to be mapped.
_phead(_param5)
Specifies the modelview matrix (as from a _glcmnd(GetDoublev) call).
_phead(_param6)
Specifies the projection matrix (as from a _glcmnd(GetDoublev) call).
_phead(_param7)
Specifies the viewport (as from a _glcmnd(GetIntegerv) call).
_phead(_param8 _param9)
Specifies the near and far planes (as from a _glcmnd(GetDoublev) call).
_phead(_param10 _param11 _param12 _param13)
Returns the computed object coordinates.
.SH DESCRIPTION
_cmnd maps the specified window coordinates _param1, _param2 and _param3
and its clip w coordinate _param4
into object 
coordinates (_param10, _param11, _param12, _param13)
using _param5, _param6 and _param7. _param4 can be other than
1 as for vertices in _glcmnd(FeedbackBuffer) when data type 
_const(4D_COLOR_TEXTURE) is returned.
This also handles the case
where the _param8 and _param9 planes are different from the default,
0 and 1, respectively.
A return 
value of _const(TRUE) indicates success; a return value of _const(FALSE)
indicates failure.
.P
To compute the coordinates (_param10, _param11, _param12 and _param13),
_cmnd multiplies the normalized device coordinates by the inverse of
_param5*_param6 as follows:

.P
.ce
.EQ
left ( down 70 {cpile { ~_eqnparam10 above ~_eqnparam11 above ~_eqnparam12
above ~_eqnparam13}} ~~ right ) ~=~ INV(P M) 
left ( down 140 {cpile { 
{ {2(_eqnparam1 ~-~ _eqnparam7[0])} over {_eqnparam7[2]} ~-~ 1 }
above 
{ {2(_eqnparam2 ~-~ _eqnparam7[1])} over {_eqnparam7[3]} ~-~ 1 }
above 
{ {2(_eqnparam3 ~-~ _eqnparam8)} over {(_eqnparam9 ~-~ _eqnparam8)} ~-~ 1 }
above 
_eqnparam4}} ~~ right )
.EN
.sp
$INV()$ denotes matrix inversion. 
.P
_cmnd is equivalent to _cmnd(UnProject) when _param4 is 1, _param8 is 0 and
_param9 is 1.
.SH NOTES
_cmnd is available only if the GLU version is 1.3 or greater.
.SH SEE ALSO
_glcmnd(Get),
_glcmnd(FeedbackBuffer),
_cmnd(Project),
_cmnd(UnProject)
