1
_C_ License Applicability. Except to the extent portions of this file are
2
_C_ made subject to an alternative license as permitted in the SGI Free
3
_C_ Software License B, Version 1.1 (the "License"), the contents of this
4
_C_ file are subject only to the provisions of the License. You may not use
5
_C_ this file except in compliance with the License. You may obtain a copy
6
_C_ of the License at Silicon Graphics, Inc., attn: Legal Services, 1600
7
_C_ Amphitheatre Parkway, Mountain View, CA 94043-1351, or at:
9
_C_ http://oss.sgi.com/projects/FreeB
11
_C_ Note that, as provided in the License, the Software is distributed on an
12
_C_ "AS IS" basis, with ALL EXPRESS AND IMPLIED WARRANTIES AND CONDITIONS
13
_C_ DISCLAIMED, INCLUDING, WITHOUT LIMITATION, ANY IMPLIED WARRANTIES AND
14
_C_ CONDITIONS OF MERCHANTABILITY, SATISFACTORY QUALITY, FITNESS FOR A
15
_C_ PARTICULAR PURPOSE, AND NON-INFRINGEMENT.
17
_C_ Original Code. The Original Code is: OpenGL Sample Implementation,
18
_C_ Version 1.2.1, released January 26, 2000, developed by Silicon Graphics,
19
_C_ Inc. The Original Code is Copyright (c) 1991-2000 Silicon Graphics, Inc.
20
_C_ Copyright in any portions created by third parties is as indicated
21
_C_ elsewhere herein. All Rights Reserved.
23
_C_ Additional Notice Provisions: The application programming interfaces
24
_C_ established by SGI in conjunction with the Original Code are The
25
_C_ OpenGL(R) Graphics System: A Specification (Version 1.2.1), released
26
_C_ April 1, 1999; The OpenGL(R) Graphics System Utility Library (Version
27
_C_ 1.3), released November 4, 1998; and OpenGL(R) Graphics with the X
28
_C_ Window System(R) (Version 1.3), released October 19, 1998. This software
29
_C_ was created using the OpenGL(R) version 1.2.1 Sample Implementation
30
_C_ published by SGI, but has not been independently verified as being
31
_C_ compliant with the OpenGL(R) version 1.2.1 Specification.
33
_C_ The first character in this file must be an '_'!
34
_C_ Anything on a line after _C_ is ignored
35
_define(_filters,eqn)_C_
36
_C_ eqn is automatically replaced with neqn for nroff
37
_header(Frustum,multiply the current matrix by a perspective matrix)
43
_phead(_param1 _param2)
44
Specify the coordinates for the left and right vertical clipping planes.
45
_phead(_param3 _param4)
46
Specify the coordinates for the bottom and top horizontal clipping planes.
47
_phead(_param5 _param6)
48
Specify the distances to the near and far depth clipping planes.
49
Both distances must be positive.
51
_cmnd describes a perspective matrix that produces a perspective projection.
52
The current matrix (see _cmnd(MatrixMode)) is multiplied by this matrix
53
and the result replaces the current matrix, as if
54
_cmnd(MultMatrix) were called with the following matrix
63
ccol { {{2 ~ _eqnparam5} over {_eqnparam2 ~-~ _eqnparam1}} above 0 above 0 above 0 }
64
ccol { 0 above {{2 ~ _eqnparam5} over {_eqnparam4 ~-~ _eqnparam3}} ~ above 0 above 0 }
65
ccol { A ~~~~ above B ~~~~ above C ~~~~ above -1 ~~~~}
66
ccol { 0 above 0 above D above 0}
74
{A ~=~ {_eqnparam2 ~+~ _eqnparam1} over {_eqnparam2 ~-~ _eqnparam1}}
80
{B ~=~ {_eqnparam4 ~+~ _eqnparam3} over {_eqnparam4 ~-~ _eqnparam3}}
86
{C ~=~ -{{_eqnparam6 ~+~ _eqnparam5} over {_eqnparam6 ~-~ _eqnparam5}}}
92
{D ~=~ -^{{2 ~ _eqnparam6 ~ _eqnparam5} over {_eqnparam6 ~-~ _eqnparam5}}}
96
Typically, the matrix mode is _const(PROJECTION), and
97
(_param1, _param3, \-_param5) and (_param2, _param4, \-_param5)
98
specify the points on the near clipping plane that are mapped
99
to the lower left and upper right corners of the window,
100
assuming that the eye is located at (0, 0, 0).
101
\-_param6 specifies the location of the far clipping plane.
102
Both _param5 and _param6 must be positive.
104
Use _cmnd(PushMatrix) and _cmnd(PopMatrix) to save and restore
105
the current matrix stack.
107
Depth buffer precision is affected by the values specified for
109
The greater the ratio of _param6 to _param5 is,
110
the less effective the depth buffer will be at distinguishing between
111
surfaces that are near each other.
115
$r ~=~ _eqnparam6 over _eqnparam5$
117
roughly $log sub 2 (r)$ bits of depth buffer precision are lost.
118
Because $r$ approaches infinity as _param5 approaches 0,
119
_param5 must never be set to 0.
121
_const(INVALID_VALUE) is generated if _param5 or _param6 is not
122
positive, or if _param1 = _param2, or _param3 = _param4.
124
_const(INVALID_OPERATION) is generated if _cmnd
125
is executed between the execution of _cmnd(Begin)
126
and the corresponding execution of _cmnd(End).
128
_cmnd(Get) with argument _const(MATRIX_MODE)
130
_cmnd(Get) with argument _const(MODELVIEW_MATRIX)
132
_cmnd(Get) with argument _const(PROJECTION_MATRIX)
134
_cmnd(Get) with argument _const(TEXTURE_MATRIX)
136
_cmnd(Get) with argument _const(COLOR_MATRIX)