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+_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
+_C_ Amphitheatre Parkway, Mountain View, CA 94043-1351, or at:
+_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
+_C_ DISCLAIMED, INCLUDING, WITHOUT LIMITATION, ANY IMPLIED WARRANTIES AND
+_C_ CONDITIONS OF MERCHANTABILITY, SATISFACTORY QUALITY, FITNESS FOR A
+_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: 2004/03/14 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(Perspective, set up a perspective projection matrix)
+_names(Perspective)
+.EQ
+delim $$
+.EN
+.SH PARAMETERS
+_phead(_param1)
+Specifies the field of view angle, in degrees, in the \f2y\fP direction.
+_phead(_param2)
+Specifies the aspect ratio that determines
+the field of view in the \f2x\fP direction.
+The aspect ratio is the ratio of \f2x\fP (width) to \f2y\fP (height).
+_phead(_param3)
+Specifies the distance from the viewer to the near clipping plane
+(always positive).
+_phead(_param4)
+Specifies the distance from the viewer to the far clipping plane
+(always positive).
+.SH DESCRIPTION
+_cmnd specifies a viewing frustum into the world coordinate system.
+In general, the aspect ratio in _cmnd should match the aspect ratio
+of the associated viewport. For example, $ _eqnparam2 ~=~ 2.0 $ means
+the viewer's
+angle of view is twice as wide in \f2x\fP as it is in \f2y\fP.
+If the viewport is
+twice as wide as it is tall, it displays the image without distortion.
+.P
+The matrix generated by _cmnd is multipled by the current matrix,
+just as if _glcmnd(MultMatrix) were called with the generated matrix.
+To load the perspective matrix onto the current matrix stack instead,
+precede the call to _cmnd with a call to _glcmnd(LoadIdentity).
+.P
+Given \f2f\fP defined as follows:
+.sp
+.ce
+.EQ
+f ~=~ cotangent"("{_eqnparam1 over 2}")"
+.EN
+.bp
+The generated matrix is
+.sp
+.ce
+.EQ
+left ( ~~ down 130 { matrix {
+ ccol { {f over _eqnparam2} above 0 above 0 above 0 }
+ ccol { 0 above f above 0 above 0 }
+ ccol { 0 above 0 above {{_eqnparam4 + _eqnparam3} over {_eqnparam3 - _eqnparam4}} above -1 }
+ ccol { 0 above 0 above {{2 * _eqnparam4 * _eqnparam3} over {_eqnparam3 - _eqnparam4}} above 0}
+}} ~~~ right )
+.EN
+
+.SH NOTES
+Depth buffer precision is affected by the values specified for
+_param3 and _param4.
+The greater the ratio of _param4 to _param3 is,
+the less effective the depth buffer will be at distinguishing between
+surfaces that are near each other.
+If
+.sp
+.ce
+$r ~=~ _eqnparam4 over _eqnparam3$
+.sp
+.P
+roughly $log sub 2 r$ bits of depth buffer precision are lost.
+Because $r$ approaches infinity as _param3 approaches 0,
+_param3 must never be set to 0.
+.SH SEE ALSO
+_glcmnd(Frustum), _glcmnd(LoadIdentity),
+_glcmnd(MultMatrix), _cmnd(Ortho2D)