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_C_ License Applicability. Except to the extent portions of this file are
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_C_ made subject to an alternative license as permitted in the SGI Free
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_C_ Software License B, Version 1.1 (the "License"), the contents of this
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_C_ file are subject only to the provisions of the License. You may not use
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_C_ this file except in compliance with the License. You may obtain a copy
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_C_ of the License at Silicon Graphics, Inc., attn: Legal Services, 1600
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_C_ Amphitheatre Parkway, Mountain View, CA 94043-1351, or at:
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_C_ http://oss.sgi.com/projects/FreeB
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_C_ Note that, as provided in the License, the Software is distributed on an
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_C_ "AS IS" basis, with ALL EXPRESS AND IMPLIED WARRANTIES AND CONDITIONS
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_C_ DISCLAIMED, INCLUDING, WITHOUT LIMITATION, ANY IMPLIED WARRANTIES AND
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_C_ CONDITIONS OF MERCHANTABILITY, SATISFACTORY QUALITY, FITNESS FOR A
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_C_ PARTICULAR PURPOSE, AND NON-INFRINGEMENT.
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_C_ Original Code. The Original Code is: OpenGL Sample Implementation,
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_C_ Version 1.2.1, released January 26, 2000, developed by Silicon Graphics,
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_C_ Inc. The Original Code is Copyright (c) 1991-2000 Silicon Graphics, Inc.
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_C_ Copyright in any portions created by third parties is as indicated
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_C_ elsewhere herein. All Rights Reserved.
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_C_ Additional Notice Provisions: The application programming interfaces
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_C_ established by SGI in conjunction with the Original Code are The
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_C_ OpenGL(R) Graphics System: A Specification (Version 1.2.1), released
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_C_ April 1, 1999; The OpenGL(R) Graphics System Utility Library (Version
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_C_ 1.3), released November 4, 1998; and OpenGL(R) Graphics with the X
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_C_ Window System(R) (Version 1.3), released October 19, 1998. This software
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_C_ was created using the OpenGL(R) version 1.2.1 Sample Implementation
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_C_ published by SGI, but has not been independently verified as being
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_C_ compliant with the OpenGL(R) version 1.2.1 Specification.
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_C_ The first character in this file must be an '_'!
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_C_ Anything on a line after _C_ is ignored
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_define(_filters,eqn)_C_
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_C_ eqn is automatically replaced with neqn for nroff
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_header(Perspective, set up a perspective projection matrix)
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Specifies the field of view angle, in degrees, in the \f2y\fP direction.
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Specifies the aspect ratio that determines
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the field of view in the \f2x\fP direction.
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The aspect ratio is the ratio of \f2x\fP (width) to \f2y\fP (height).
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Specifies the distance from the viewer to the near clipping plane
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Specifies the distance from the viewer to the far clipping plane
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_cmnd specifies a viewing frustum into the world coordinate system.
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In general, the aspect ratio in _cmnd should match the aspect ratio
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of the associated viewport. For example, $ _eqnparam2 ~=~ 2.0 $ means
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angle of view is twice as wide in \f2x\fP as it is in \f2y\fP.
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twice as wide as it is tall, it displays the image without distortion.
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The matrix generated by _cmnd is multipled by the current matrix,
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just as if _glcmnd(MultMatrix) were called with the generated matrix.
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To load the perspective matrix onto the current matrix stack instead,
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precede the call to _cmnd with a call to _glcmnd(LoadIdentity).
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Given \f2f\fP defined as follows:
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f ~=~ cotangent"("{_eqnparam1 over 2}")"
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The generated matrix is
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left ( ~~ down 130 { matrix {
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ccol { {f over _eqnparam2} above 0 above 0 above 0 }
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ccol { 0 above f above 0 above 0 }
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ccol { 0 above 0 above {{_eqnparam4 + _eqnparam3} over {_eqnparam3 - _eqnparam4}} above -1 }
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ccol { 0 above 0 above {{2 * _eqnparam4 * _eqnparam3} over {_eqnparam3 - _eqnparam4}} above 0}
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Depth buffer precision is affected by the values specified for
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The greater the ratio of _param4 to _param3 is,
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the less effective the depth buffer will be at distinguishing between
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surfaces that are near each other.
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$r ~=~ _eqnparam4 over _eqnparam3$
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roughly $log sub 2 r$ bits of depth buffer precision are lost.
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Because $r$ approaches infinity as _param3 approaches 0,
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_param3 must never be set to 0.
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_glcmnd(Frustum), _glcmnd(LoadIdentity),
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_glcmnd(MultMatrix), _cmnd(Ortho2D)