cv/mgflib/translat.txt

                TRANSLATING TO MGF FROM OTHER FORMATS
                SCCSid "$SunId$ LBL"

The description of the parser and the MGF specification should provide
enough information to get you started using MGF scene files, but we
thought it would be helpful to also provide some hints and
suggestions for translating to MGF from other formats.
Specifically, we will discuss several issues that come up repeatedly
when converting from more usual computer graphics scene formats to
MGF, most of them having to do with materials.  First, let's look at
some geometry-related issues.

Vertex Naming
=============
Many scene formats do not name vertices; many do not even share
vertices.  Does it matter what names are given to vertices in MGF?
Not a lot, but it can affect memory and file size.  In a way, vertex
sharing is nothing more than a form of file compression, and the
better you are at sharing vertex information, the smaller your file
will be.  (Vertex sharing is also important for some rendering
algorithms, which depend on it for computing surface adjacency.)

If you are translating from a format that shares unnamed vertices,
such as Wavefront's .OBJ format, you will want to name your MGF
vertices according to some simple pattern.  In most cases, a name
such as "v%d" will do, where %d is replaced by an incremented
integer.

If, on the other hand, you are translating from a format that does
not share vertices, you should do one of two things.  You should
either select your MGF vertex names from a small, recycled pool of
names, or figure out some way to share vertices that were not shared
before.  In the first case, you will just allocate as many vertex
names as you need for any given object, then reuse these names and
therefore the parsers memory for other objects.  In the second case,
you will cache vertex names and values in some LRU table of
predetermined size, and use this table to merge vertices in the
file.  (See rad2mgf.c as an example of how this can be done.)

For some objects, there may be little point in merging vertices, and
you may want to treat these surfaces separately.  For example,
putting out an MGF ring means putting out a central vertex, which
must have both a position point and a normal direction.  It is somewhat
unlikely that any other MGF entity will share this point, and quite
unlikely that it will share the normal direction, so there is little
sense in trying to merge or otherwise reuse it.

Points and Lines
================
Although points and lines are really 3-d surfaces, many CAD
systems include them in their models.  The question then is,
what do we do with these in MGF?  If the idea is to produce a point
or line on the final display that is one or two pixels wide, there
is little one can do to guarantee such a thing will happen because
the pixel size is dependent on view and display parameters as well
as scene location.

There are two ways of dealing with points and lines in MGF.  The
first is to say, "Hey, these are 0 and 1 dimensional entities, so
they won't appear in 3 dimensions," and get rid of them.  The second
approach is to assign some user-specified dimension for the "width"
of points and lines, and turn them into spheres and cylinders.  It
might be best to instead create minimal polyhedron analogs, such as
tetrahedra for points and triangular prisms for lines.  That way, an
itty-bitty point won't be converted into 200 polygons because the
translator reading in the MGF file can't handle curved surfaces.

Polygons with Holes
===================
There is no explicit representation of holes in MGF.  A hole must be
represented implicitly by connecting vertices to form "seams."  For
example, a wall with a window in it might look like this:

      v1.-----------------------------------------------.v4
        |                                               |
        |             v8.---------------.v5             |
        |               |               |               |
        |               |               |               |
        |             v7.---------------.v6             |
        |                                               |
        |                                               |
      v2.-----------------------------------------------.v3

In many systems, the wall itself would be represented with the first
list of vertices, (v1,v2,v3,v4) and the hole associated with that
wall as a second set of vertices (v5,v6,v7,v8).  In MGF, we must
give the whole thing as a single polygon, connecting the vertices so
as to create a "seam," thus:

      v1.----------------------<------------------------.v4
        |                                  _____--><---'|
        |             v8.------->-------.v5             |
        |               |               v               |
        v               ^               |               ^
        |             v7.-------<-------.v6             |
        |                                               |
        |                                               |
      v2.---------------------->------------------------.v3

which could be written in MGF as "f v1 v2 v3 v4 v5 v6 v7 v8 v5 v4".

It is very important that the order of the hole be opposite to the
order of the outer perimeter, otherwise the polygon will be
"twisted" on top of itself.  Note also that the seam was traversed
in both directions, once going from v4 to v5, and again returning
from v5 to v4.  This is a necessary condition for a proper seam.
(The final edge from v4 back to v1 is implied in MGF.)

The choice of vertices to make into a seam is somewhat arbitrary, but
some rendering systems may not give sane results if you cross over a
hole with part of your seam.  If we had chosen to create the seam
between v2 and v5 in the above example instead of v4 and v5, the seam
would cross our hole and may not render correctly.  (For systems that
are sensitive to this, it is probably necessary that their MGF
loader/translator re-expresses seams in terms of holes again, which can
be done easily so long as vertices are shared in the above fashion.)

Non-planar Polygons
===================
Polygons in MGF should be planar.  There is nothing about the format
that enforces this, but the rendering or modeling software on the other
end may have real problems if this requirement is violated.  The parser
itself does not test for non-planar polygons, so when in doubt about a
model it is safest to test for planarity and break a polygon into triangles
if it is even slightly non-planar.

NURBS, CSG, Blobbies, Etc.
==========================
Sorry, folks, this is just plain hard.  If and until MGF supports these
higher-order entities, it will be necessary for you to convert them to
smoothed triangle meshes.  Fortunately, a lot of modeling software
already knows how to do this, so if you wrote the modeler, you probably
have access to the necessary code.  (By the way, if you ever want to see
these primitives in MGF, you might just think about sharing the wealth,
because the MGF parser needs to mesh every primitive it supports.)

Materials
=========
The MGF material model was designed to accommodate most common
physical surfaces.  Included are reasonable models for plastic
and metal, thin glass and translucent surfaces.  Not included at
this time are surfaces with anisotropic reflection, refraction and/or
surface textures.  These were deemed either unnecessary or too
difficult to standardize for the initial format.  Also, light
sources are known only by the emissive nature of their surface(s),
and MGF itself only provides for diffuse emission.  (As MGF is
destined to be part of the IES luminaire data standard, it was
assumed that this combined format would be used for such purposes as
describing light source output and geometry.)

The "sides" entity is used to control the number of sides a surface
should have.  In the real world, a surface can have only one side,
defining the interface between one volume and another.  Many
object-space rendering packages (e.g. z-buffer algorithms) take
advantage of this fact by culling back-facing polygons and thus saving
roughly 50% of the calculation time.  However, many models rely on an
approximation whereby a single surface is used to represent a very thin
volume, such as a pane of glass, and this also can provide significant
calculational savings in an image-space algorithm (such as
ray-tracing).  Since both types of surfaces are useful and both types
of rendering algorithms may ultimately be applied, MGF provides a way
to specify sidedness rather than picking one model or the other.

So-called specular reflection and transmission are modeled using a
Gaussian distribution of surface normals.  The "alpha_r" and
"alpha_t" parameters to the respective "rs" and "ts" entities specify
the root-mean-squared (RMS) surface facet slope, which varies from 0
for a perfectly smooth surface to around .2 for a fairly rough one.
The effect this will have on the reflected component distribution is
well-defined, but predicting the behavior of the transmitted
component requires further assumptions.  We assume that the surface
scatters light passing through it just as much as it scatters
reflected light.  This assumption is approximately correct for a
two-sided transparent material with an index of refraction of 1.5
(about that of glass) and both sides having the given RMS facet
slope.

Oftentimes, one is translating from a Phong exponent on the cosine
of the half-vector-to-normal angle to the more physical but less
familiar Gaussian model of MGF.  The hardest part is translating
the specular power to a roughness value.  For this, we recommend
the following approximation:

        roughness = 0.6/sqrt(specular_power)

It's not a perfect correlation, but it's about as good as you can get.

Colors
======
Unlike most graphics languages, MGF does not use an RGB color model,
simply because there is no recognized definition for this model.
It is based on computer monitor phosphors, which vary from one
CRT to the next.  (There is an RGB standard defined in the TV
industry, but this has a rather poor correlation to most graphics.)

MGF uses two alternative, well-defined standards.  The first is the CIE
standard for chromaticity coordinates.  With this standard, any viewable
color may be exactly reproduced.  Unfortunately, the interaction between
colors (i.e. colored light sources and interreflections) cannot be
specified exactly with any finite coordinate set, including CIE
chromaticities.  So, MGF offers the ability to give reflectance,
transmittance or emittance as a function of wavelength over the visible
spectrum.  This function is still discretized, but at a user-selectable
resolution.  Furthermore, spectral colors may be mixed, providing (nearly)
arbitrary basis functions, which can produce more accurate results in
some cases and are a convenience in others.

Conversion back and forth between CIE chromaticity coordinates and spectral
samples is provided within the MGF parser.  Unfortunately, conversion
to and from RGB values depends on a particular RGB definition, and as we
have said, there is no recognized standard.  We therefore recommend that
you decide yourself what chromaticity values to use for each RGB primary,
and adopt the following code to convert between CIE and RGB coordinates.

#ifdef  NTSC
#define  CIE_x_r                0.670           /* standard NTSC primaries */
#define  CIE_y_r                0.330
#define  CIE_x_g                0.210
#define  CIE_y_g                0.710
#define  CIE_x_b                0.140
#define  CIE_y_b                0.080
#define  CIE_x_w                0.3333          /* monitor white point */
#define  CIE_y_w                0.3333
#else
#define  CIE_x_r                0.640           /* nominal CRT primaries */
#define  CIE_y_r                0.330
#define  CIE_x_g                0.290
#define  CIE_y_g                0.600
#define  CIE_x_b                0.150
#define  CIE_y_b                0.060
#define  CIE_x_w                0.3333          /* monitor white point */
#define  CIE_y_w                0.3333
#endif

#define CIE_D           (       CIE_x_r*(CIE_y_g - CIE_y_b) + \
                                CIE_x_g*(CIE_y_b - CIE_y_r) + \
                                CIE_x_b*(CIE_y_r - CIE_y_g)     )
#define CIE_C_rD        ( (1./CIE_y_w) * \
                                ( CIE_x_w*(CIE_y_g - CIE_y_b) - \
                                  CIE_y_w*(CIE_x_g - CIE_x_b) + \
                                  CIE_x_g*CIE_y_b - CIE_x_b*CIE_y_g     ) )
#define CIE_C_gD        ( (1./CIE_y_w) * \
                                ( CIE_x_w*(CIE_y_b - CIE_y_r) - \
                                  CIE_y_w*(CIE_x_b - CIE_x_r) - \
                                  CIE_x_r*CIE_y_b + CIE_x_b*CIE_y_r     ) )
#define CIE_C_bD        ( (1./CIE_y_w) * \
                                ( CIE_x_w*(CIE_y_r - CIE_y_g) - \
                                  CIE_y_w*(CIE_x_r - CIE_x_g) + \
                                  CIE_x_r*CIE_y_g - CIE_x_g*CIE_y_r     ) )

#define CIE_rf          (CIE_y_r*CIE_C_rD/CIE_D)
#define CIE_gf          (CIE_y_g*CIE_C_gD/CIE_D)
#define CIE_bf          (CIE_y_b*CIE_C_bD/CIE_D)

float  xyz2rgbmat[3][3] = {     /* XYZ to RGB */
        {(CIE_y_g - CIE_y_b - CIE_x_b*CIE_y_g + CIE_y_b*CIE_x_g)/CIE_C_rD,
         (CIE_x_b - CIE_x_g - CIE_x_b*CIE_y_g + CIE_x_g*CIE_y_b)/CIE_C_rD,
         (CIE_x_g*CIE_y_b - CIE_x_b*CIE_y_g)/CIE_C_rD},
        {(CIE_y_b - CIE_y_r - CIE_y_b*CIE_x_r + CIE_y_r*CIE_x_b)/CIE_C_gD,
         (CIE_x_r - CIE_x_b - CIE_x_r*CIE_y_b + CIE_x_b*CIE_y_r)/CIE_C_gD,
         (CIE_x_b*CIE_y_r - CIE_x_r*CIE_y_b)/CIE_C_gD},
        {(CIE_y_r - CIE_y_g - CIE_y_r*CIE_x_g + CIE_y_g*CIE_x_r)/CIE_C_bD,
         (CIE_x_g - CIE_x_r - CIE_x_g*CIE_y_r + CIE_x_r*CIE_y_g)/CIE_C_bD,
         (CIE_x_r*CIE_y_g - CIE_x_g*CIE_y_r)/CIE_C_bD}
};

float  rgb2xyzmat[3][3] = {     /* RGB to XYZ */
        {CIE_x_r*CIE_C_rD/CIE_D,CIE_x_g*CIE_C_gD/CIE_D,CIE_x_b*CIE_C_bD/CIE_D},
        {CIE_y_r*CIE_C_rD/CIE_D,CIE_y_g*CIE_C_gD/CIE_D,CIE_y_b*CIE_C_bD/CIE_D},
        {(1.-CIE_x_r-CIE_y_r)*CIE_C_rD/CIE_D,
         (1.-CIE_x_g-CIE_y_g)*CIE_C_gD/CIE_D,
         (1.-CIE_x_b-CIE_y_b)*CIE_C_bD/CIE_D}
};


cie_rgb(rgbcolor, ciecolor)             /* convert CIE to RGB */
register float  *rgbcolor, *ciecolor;
{
        register int  i;

        for (i = 0; i < 3; i++) {
                rgbcolor[i] =   xyz2rgbmat[i][0]*ciecolor[0] +
                                xyz2rgbmat[i][1]*ciecolor[1] +
                                xyz2rgbmat[i][2]*ciecolor[2] ;
                if (rgbcolor[i] < 0.0)
                        rgbcolor[i] = 0.0;
        }
}


rgb_cie(ciecolor, rgbcolor)             /* convert RGB to CIE */
register float  *ciecolor, *rgbcolor;
{
        register int  i;

        for (i = 0; i < 3; i++)
                ciecolor[i] =   rgb2xyzmat[i][0]*rgbcolor[0] +
                                rgb2xyzmat[i][1]*rgbcolor[1] +
                                rgb2xyzmat[i][2]*rgbcolor[2] ;
}

Another alternative is to use the MGF "cmix" entity to convert from RGB
directly by naming the three primaries in terms of their chromaticities, e.g:

        c r =
                cxy 0.640 0.330
        c g =
                cxy 0.290 0.600
        c b =
                cxy 0.150 0.060

Then, converting from RGB to MGF colors is as simple as multiplying each
component by its relative luminance in a cmix statement, for instance:

        c white =
                cmix 0.265 r 0.670 g 0.065 b

For the chosen RGB standard, the above specification would result a pure
white.  The reason the coefficients are not all 1 as you might expect is
that cmix uses relative luminance as the standard for its weights.  Since
blue is less luminous for the same energy than red, which is in turn
less luminous than green, the weights cannot be the same to achieve an
even spectral balance.  Unfortunately, computing these relative weights
is not straightforward, so it is given in the above macros as CIE_rf,
CIE_gf and CIE_bf.
Revision:	1.1
Committed:	Wed Sep 7 16:32:20 1994 UTC (29 years, 7 months ago) by greg
Content type:	text/plain
Branch:	MAIN
Log Message:	Initial revision
#	User	Rev	Content
1	greg	1.1	TRANSLATING TO MGF FROM OTHER FORMATS
2			SCCSid "$SunId$ LBL"
3
4			The description of the parser and the MGF specification should provide
5			enough information to get you started using MGF scene files, but we
6			thought it would be helpful to also provide some hints and
7			suggestions for translating to MGF from other formats.
8			Specifically, we will discuss several issues that come up repeatedly
9			when converting from more usual computer graphics scene formats to
10			MGF, most of them having to do with materials. First, let's look at
11			some geometry-related issues.
12
13			Vertex Naming
14			=============
15			Many scene formats do not name vertices; many do not even share
16			vertices. Does it matter what names are given to vertices in MGF?
17			Not a lot, but it can affect memory and file size. In a way, vertex
18			sharing is nothing more than a form of file compression, and the
19			better you are at sharing vertex information, the smaller your file
20			will be. (Vertex sharing is also important for some rendering
21			algorithms, which depend on it for computing surface adjacency.)
22
23			If you are translating from a format that shares unnamed vertices,
24			such as Wavefront's .OBJ format, you will want to name your MGF
25			vertices according to some simple pattern. In most cases, a name
26			such as "v%d" will do, where %d is replaced by an incremented
27			integer.
28
29			If, on the other hand, you are translating from a format that does
30			not share vertices, you should do one of two things. You should
31			either select your MGF vertex names from a small, recycled pool of
32			names, or figure out some way to share vertices that were not shared
33			before. In the first case, you will just allocate as many vertex
34			names as you need for any given object, then reuse these names and
35			therefore the parsers memory for other objects. In the second case,
36			you will cache vertex names and values in some LRU table of
37			predetermined size, and use this table to merge vertices in the
38			file. (See rad2mgf.c as an example of how this can be done.)
39
40			For some objects, there may be little point in merging vertices, and
41			you may want to treat these surfaces separately. For example,
42			putting out an MGF ring means putting out a central vertex, which
43			must have both a position point and a normal direction. It is somewhat
44			unlikely that any other MGF entity will share this point, and quite
45			unlikely that it will share the normal direction, so there is little
46			sense in trying to merge or otherwise reuse it.
47
48			Points and Lines
49			================
50			Although points and lines are really 3-d surfaces, many CAD
51			systems include them in their models. The question then is,
52			what do we do with these in MGF? If the idea is to produce a point
53			or line on the final display that is one or two pixels wide, there
54			is little one can do to guarantee such a thing will happen because
55			the pixel size is dependent on view and display parameters as well
56			as scene location.
57
58			There are two ways of dealing with points and lines in MGF. The
59			first is to say, "Hey, these are 0 and 1 dimensional entities, so
60			they won't appear in 3 dimensions," and get rid of them. The second
61			approach is to assign some user-specified dimension for the "width"
62			of points and lines, and turn them into spheres and cylinders. It
63			might be best to instead create minimal polyhedron analogs, such as
64			tetrahedra for points and triangular prisms for lines. That way, an
65			itty-bitty point won't be converted into 200 polygons because the
66			translator reading in the MGF file can't handle curved surfaces.
67
68			Polygons with Holes
69			===================
70			There is no explicit representation of holes in MGF. A hole must be
71			represented implicitly by connecting vertices to form "seams." For
72			example, a wall with a window in it might look like this:
73
74			v1.-----------------------------------------------.v4
75			\| \|
76			\| v8.---------------.v5 \|
77			\| \| \| \|
78			\| \| \| \|
79			\| v7.---------------.v6 \|
80			\| \|
81			\| \|
82			v2.-----------------------------------------------.v3
83
84			In many systems, the wall itself would be represented with the first
85			list of vertices, (v1,v2,v3,v4) and the hole associated with that
86			wall as a second set of vertices (v5,v6,v7,v8). In MGF, we must
87			give the whole thing as a single polygon, connecting the vertices so
88			as to create a "seam," thus:
89
90			v1.----------------------<------------------------.v4
91			\| _____--><---'\|
92			\| v8.------->-------.v5 \|
93			\| \| v \|
94			v ^ \| ^
95			\| v7.-------<-------.v6 \|
96			\| \|
97			\| \|
98			v2.---------------------->------------------------.v3
99
100			which could be written in MGF as "f v1 v2 v3 v4 v5 v6 v7 v8 v5 v4".
101
102			It is very important that the order of the hole be opposite to the
103			order of the outer perimeter, otherwise the polygon will be
104			"twisted" on top of itself. Note also that the seam was traversed
105			in both directions, once going from v4 to v5, and again returning
106			from v5 to v4. This is a necessary condition for a proper seam.
107			(The final edge from v4 back to v1 is implied in MGF.)
108
109			The choice of vertices to make into a seam is somewhat arbitrary, but
110			some rendering systems may not give sane results if you cross over a
111			hole with part of your seam. If we had chosen to create the seam
112			between v2 and v5 in the above example instead of v4 and v5, the seam
113			would cross our hole and may not render correctly. (For systems that
114			are sensitive to this, it is probably necessary that their MGF
115			loader/translator re-expresses seams in terms of holes again, which can
116			be done easily so long as vertices are shared in the above fashion.)
117
118			Non-planar Polygons
119			===================
120			Polygons in MGF should be planar. There is nothing about the format
121			that enforces this, but the rendering or modeling software on the other
122			end may have real problems if this requirement is violated. The parser
123			itself does not test for non-planar polygons, so when in doubt about a
124			model it is safest to test for planarity and break a polygon into triangles
125			if it is even slightly non-planar.
126
127			NURBS, CSG, Blobbies, Etc.
128			==========================
129			Sorry, folks, this is just plain hard. If and until MGF supports these
130			higher-order entities, it will be necessary for you to convert them to
131			smoothed triangle meshes. Fortunately, a lot of modeling software
132			already knows how to do this, so if you wrote the modeler, you probably
133			have access to the necessary code. (By the way, if you ever want to see
134			these primitives in MGF, you might just think about sharing the wealth,
135			because the MGF parser needs to mesh every primitive it supports.)
136
137			Materials
138			=========
139			The MGF material model was designed to accommodate most common
140			physical surfaces. Included are reasonable models for plastic
141			and metal, thin glass and translucent surfaces. Not included at
142			this time are surfaces with anisotropic reflection, refraction and/or
143			surface textures. These were deemed either unnecessary or too
144			difficult to standardize for the initial format. Also, light
145			sources are known only by the emissive nature of their surface(s),
146			and MGF itself only provides for diffuse emission. (As MGF is
147			destined to be part of the IES luminaire data standard, it was
148			assumed that this combined format would be used for such purposes as
149			describing light source output and geometry.)
150
151			The "sides" entity is used to control the number of sides a surface
152			should have. In the real world, a surface can have only one side,
153			defining the interface between one volume and another. Many
154			object-space rendering packages (e.g. z-buffer algorithms) take
155			advantage of this fact by culling back-facing polygons and thus saving
156			roughly 50% of the calculation time. However, many models rely on an
157			approximation whereby a single surface is used to represent a very thin
158			volume, such as a pane of glass, and this also can provide significant
159			calculational savings in an image-space algorithm (such as
160			ray-tracing). Since both types of surfaces are useful and both types
161			of rendering algorithms may ultimately be applied, MGF provides a way
162			to specify sidedness rather than picking one model or the other.
163
164			So-called specular reflection and transmission are modeled using a
165			Gaussian distribution of surface normals. The "alpha_r" and
166			"alpha_t" parameters to the respective "rs" and "ts" entities specify
167			the root-mean-squared (RMS) surface facet slope, which varies from 0
168			for a perfectly smooth surface to around .2 for a fairly rough one.
169			The effect this will have on the reflected component distribution is
170			well-defined, but predicting the behavior of the transmitted
171			component requires further assumptions. We assume that the surface
172			scatters light passing through it just as much as it scatters
173			reflected light. This assumption is approximately correct for a
174			two-sided transparent material with an index of refraction of 1.5
175			(about that of glass) and both sides having the given RMS facet
176			slope.
177
178			Oftentimes, one is translating from a Phong exponent on the cosine
179			of the half-vector-to-normal angle to the more physical but less
180			familiar Gaussian model of MGF. The hardest part is translating
181			the specular power to a roughness value. For this, we recommend
182			the following approximation:
183
184			roughness = 0.6/sqrt(specular_power)
185
186			It's not a perfect correlation, but it's about as good as you can get.
187
188			Colors
189			======
190			Unlike most graphics languages, MGF does not use an RGB color model,
191			simply because there is no recognized definition for this model.
192			It is based on computer monitor phosphors, which vary from one
193			CRT to the next. (There is an RGB standard defined in the TV
194			industry, but this has a rather poor correlation to most graphics.)
195
196			MGF uses two alternative, well-defined standards. The first is the CIE
197			standard for chromaticity coordinates. With this standard, any viewable
198			color may be exactly reproduced. Unfortunately, the interaction between
199			colors (i.e. colored light sources and interreflections) cannot be
200			specified exactly with any finite coordinate set, including CIE
201			chromaticities. So, MGF offers the ability to give reflectance,
202			transmittance or emittance as a function of wavelength over the visible
203			spectrum. This function is still discretized, but at a user-selectable
204			resolution. Furthermore, spectral colors may be mixed, providing (nearly)
205			arbitrary basis functions, which can produce more accurate results in
206			some cases and are a convenience in others.
207
208			Conversion back and forth between CIE chromaticity coordinates and spectral
209			samples is provided within the MGF parser. Unfortunately, conversion
210			to and from RGB values depends on a particular RGB definition, and as we
211			have said, there is no recognized standard. We therefore recommend that
212			you decide yourself what chromaticity values to use for each RGB primary,
213			and adopt the following code to convert between CIE and RGB coordinates.
214
215			#ifdef NTSC
216			#define CIE_x_r 0.670 /* standard NTSC primaries */
217			#define CIE_y_r 0.330
218			#define CIE_x_g 0.210
219			#define CIE_y_g 0.710
220			#define CIE_x_b 0.140
221			#define CIE_y_b 0.080
222			#define CIE_x_w 0.3333 /* monitor white point */
223			#define CIE_y_w 0.3333
224			#else
225			#define CIE_x_r 0.640 /* nominal CRT primaries */
226			#define CIE_y_r 0.330
227			#define CIE_x_g 0.290
228			#define CIE_y_g 0.600
229			#define CIE_x_b 0.150
230			#define CIE_y_b 0.060
231			#define CIE_x_w 0.3333 /* monitor white point */
232			#define CIE_y_w 0.3333
233			#endif
234
235			#define CIE_D ( CIE_x_r*(CIE_y_g - CIE_y_b) + \
236			CIE_x_g*(CIE_y_b - CIE_y_r) + \
237			CIE_x_b*(CIE_y_r - CIE_y_g) )
238			#define CIE_C_rD ( (1./CIE_y_w) * \
239			( CIE_x_w*(CIE_y_g - CIE_y_b) - \
240			CIE_y_w*(CIE_x_g - CIE_x_b) + \
241			CIE_x_gCIE_y_b - CIE_x_bCIE_y_g ) )
242			#define CIE_C_gD ( (1./CIE_y_w) * \
243			( CIE_x_w*(CIE_y_b - CIE_y_r) - \
244			CIE_y_w*(CIE_x_b - CIE_x_r) - \
245			CIE_x_rCIE_y_b + CIE_x_bCIE_y_r ) )
246			#define CIE_C_bD ( (1./CIE_y_w) * \
247			( CIE_x_w*(CIE_y_r - CIE_y_g) - \
248			CIE_y_w*(CIE_x_r - CIE_x_g) + \
249			CIE_x_rCIE_y_g - CIE_x_gCIE_y_r ) )
250
251			#define CIE_rf (CIE_y_r*CIE_C_rD/CIE_D)
252			#define CIE_gf (CIE_y_g*CIE_C_gD/CIE_D)
253			#define CIE_bf (CIE_y_b*CIE_C_bD/CIE_D)
254
255			float xyz2rgbmat[3][3] = { /* XYZ to RGB */
256			{(CIE_y_g - CIE_y_b - CIE_x_bCIE_y_g + CIE_y_bCIE_x_g)/CIE_C_rD,
257			(CIE_x_b - CIE_x_g - CIE_x_bCIE_y_g + CIE_x_gCIE_y_b)/CIE_C_rD,
258			(CIE_x_gCIE_y_b - CIE_x_bCIE_y_g)/CIE_C_rD},
259			{(CIE_y_b - CIE_y_r - CIE_y_bCIE_x_r + CIE_y_rCIE_x_b)/CIE_C_gD,
260			(CIE_x_r - CIE_x_b - CIE_x_rCIE_y_b + CIE_x_bCIE_y_r)/CIE_C_gD,
261			(CIE_x_bCIE_y_r - CIE_x_rCIE_y_b)/CIE_C_gD},
262			{(CIE_y_r - CIE_y_g - CIE_y_rCIE_x_g + CIE_y_gCIE_x_r)/CIE_C_bD,
263			(CIE_x_g - CIE_x_r - CIE_x_gCIE_y_r + CIE_x_rCIE_y_g)/CIE_C_bD,
264			(CIE_x_rCIE_y_g - CIE_x_gCIE_y_r)/CIE_C_bD}
265			};
266
267			float rgb2xyzmat[3][3] = { /* RGB to XYZ */
268			{CIE_x_rCIE_C_rD/CIE_D,CIE_x_gCIE_C_gD/CIE_D,CIE_x_b*CIE_C_bD/CIE_D},
269			{CIE_y_rCIE_C_rD/CIE_D,CIE_y_gCIE_C_gD/CIE_D,CIE_y_b*CIE_C_bD/CIE_D},
270			{(1.-CIE_x_r-CIE_y_r)*CIE_C_rD/CIE_D,
271			(1.-CIE_x_g-CIE_y_g)*CIE_C_gD/CIE_D,
272			(1.-CIE_x_b-CIE_y_b)*CIE_C_bD/CIE_D}
273			};
274
275
276			cie_rgb(rgbcolor, ciecolor) /* convert CIE to RGB */
277			register float rgbcolor, ciecolor;
278			{
279			register int i;
280
281			for (i = 0; i < 3; i++) {
282			rgbcolor[i] = xyz2rgbmat[i][0]*ciecolor[0] +
283			xyz2rgbmat[i][1]*ciecolor[1] +
284			xyz2rgbmat[i][2]*ciecolor[2] ;
285			if (rgbcolor[i] < 0.0)
286			rgbcolor[i] = 0.0;
287			}
288			}
289
290
291			rgb_cie(ciecolor, rgbcolor) /* convert RGB to CIE */
292			register float ciecolor, rgbcolor;
293			{
294			register int i;
295
296			for (i = 0; i < 3; i++)
297			ciecolor[i] = rgb2xyzmat[i][0]*rgbcolor[0] +
298			rgb2xyzmat[i][1]*rgbcolor[1] +
299			rgb2xyzmat[i][2]*rgbcolor[2] ;
300			}
301
302			Another alternative is to use the MGF "cmix" entity to convert from RGB
303			directly by naming the three primaries in terms of their chromaticities, e.g:
304
305			c r =
306			cxy 0.640 0.330
307			c g =
308			cxy 0.290 0.600
309			c b =
310			cxy 0.150 0.060
311
312			Then, converting from RGB to MGF colors is as simple as multiplying each
313			component by its relative luminance in a cmix statement, for instance:
314
315			c white =
316			cmix 0.265 r 0.670 g 0.065 b
317
318			For the chosen RGB standard, the above specification would result a pure
319			white. The reason the coefficients are not all 1 as you might expect is
320			that cmix uses relative luminance as the standard for its weights. Since
321			blue is less luminous for the same energy than red, which is in turn
322			less luminous than green, the weights cannot be the same to achieve an
323			even spectral balance. Unfortunately, computing these relative weights
324			is not straightforward, so it is given in the above macros as CIE_rf,
325			CIE_gf and CIE_bf.