ray/doc/ray.1

.\" RCSid "$Id: ray.1,v 1.48 2025/05/29 16:42:28 greg Exp $"
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.DA 12/09/2024
.LP
.tl """Copyright \(co 2024 Regents, University of California
.sp 2
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The
.so ../src/rt/VERSION
.br
Synthetic Imaging System
.AU
Building Technologies Department
.br
Lawrence Berkeley Laboratory
.br
1 Cyclotron Rd., MS 90-3111
.br
Berkeley, CA  94720
.NH 1
Introduction
.PP
RADIANCE was developed as a research tool
for predicting the distribution of visible radiation in
illuminated spaces.
It takes as input a three-dimensional geometric model of
the physical environment, and produces a map of
spectral radiance values in a color image.
The technique of ray-tracing follows light backwards
from the image plane to the source(s).
Because it can produce realistic images from a simple description,
RADIANCE has a wide range of applications in graphic arts,
lighting design, computer-aided engineering and architecture.
.KF
.sp 25
.ce
.B "Figure 1."
.sp
.KE
.PP
The diagram in Figure 1 shows the flow between programs (boxes) and
data (ovals).
The central program is
.I rpict,
which produces a picture from a scene description.
.I Rview
is a variation of
.I rpict
that computes and displays images interactively.
Other programs (not shown) connect many of these elements together, 
such as the executive programs
.I rad
and
.I ranimate,
the interactive rendering program
.I rholo,
and the animation program
.I ranimove.
The program
.I obj2mesh
acts as both a converter and scene compiler, converting a Wavefront .OBJ
file into a compiled mesh octree for efficient rendering.
.PP
A scene description file lists the surfaces and materials
that  make up a specific environment.  
The current surface types are  spheres,  polygons,  cones,  and  cylinders.
There is also a composite surface type, called mesh, and a pseudosurface
type, called instance, which facilitates very complex geometries.
Surfaces can be made from materials such as plastic, metal, and glass.  
Light sources can be distant disks as well as  local spheres, disks
and polygons.
.PP
From a three-dimensional scene description and a specified view,
.I rpict
produces a two-dimensional image.
A picture file is a compressed binary representation of the
pixels in the image.
This picture can be scaled in size and
brightness, anti-aliased, and sent to a graphics output device.
.PP
A header in each picture file lists the program(s) and
parameters that produced it.
This is useful for identifying a picture 
without having to display it.
The information can be read by the program
.I getinfo.
.NH 1
Scene Description
.PP
A scene description file represents a
three-dimensional physical environment
in Cartesian (rectilinear) world coordinates.
It is stored as ASCII text, with the following basic format:
.DS
# comment

modifier type identifier
n S1 S2 "S 3" .. Sn
0
m R1 R2 R3 .. Rm

modifier alias identifier reference

! command

 ...
.DE
.PP
A comment line begins with a pound sign, `#'.
.PP
The scene description
.I primitives
all have the same general format, and can
be either surfaces or modifiers.
A primitive has a modifier, a type, and an identifier.
A modifier is either the identifier of a
.I "previously defined"
primitive, or "void"\(dg.
.FS
\(dgThe most recent definition of a modifier is the one used,
and later definitions do not cause relinking of loaded
primitives.
Thus, the same identifier may be used repeatedly, and each new
definition will apply to the primitives following it.
.FE
An identifier can be any string (i.e., any sequence of non-white characters).
The
.I arguments
associated with a primitive can be strings or real numbers.
The first integer following the identifier is the number
of string arguments, and it is followed by the arguments themselves
(separated by white space or enclosed in quotes).
The next integer is the number of integer arguments, and is followed
by the integer arguments.
(There are currently no primitives that use them, however.)
The next integer is the real argument count, and it is followed
by the real arguments.
.PP
An alias gets its type and arguments from a previously defined primitive.
This is useful when the same material is used with a different
modifier, or as a convenient naming mechanism.
The reserved modifier name "inherit" may be used to specificy that
an alias will inherit its modifier from the original.
Surfaces cannot be aliased.
.PP
A line beginning with an exclamation point, `!',
is interpreted as a command.
It is executed by the shell, and its output is read as input to
the program.
The command must not try to read from its standard input, or
confusion will result.
A command may be continued over multiple lines using a backslash, `\\',
to escape the newline.
.PP
White space is generally ignored, except as a separator.
The exception is the newline character after a command or comment.
Commands, comments and primitives may appear in any combination, so long
as they are not intermingled.
.NH 2
Primitive Types
.PP
Primitives can be surfaces, materials, textures or patterns.
Modifiers can be materials, mixtures, textures or patterns.
Simple surfaces must have one material in their modifier list.
.NH 3
Surfaces
.PP
A scene description will consist mostly of surfaces.
The basic types are given below.
.LP
.UL Source
.PP
A source is not really a surface, but a solid angle.
It is used for specifying light sources that are very distant.
The direction to the center of the source and the number of degrees
subtended by its disk are given as follows:
.DS
mod source id
0
0
4 xdir ydir zdir angle
.DE
.LP
.UL Sphere
.PP
A sphere is given by its center and radius:
.DS
mod sphere id
0
0
4 xcent ycent zcent radius
.DE
.LP
.UL Bubble
.PP
A bubble is simply a sphere whose surface normal points inward.
.LP
.UL Polygon
.PP
A polygon is given by a list of three-dimensional vertices,
which are ordered counter-clockwise as viewed from
the front side (into the surface normal).
The last vertex is automatically connected to the first.
Holes are represented in polygons as interior vertices connected to
the outer perimeter by coincident edges (seams).
.DS
mod polygon id
0
0
3n
        x1      y1      z1
        x2      y2      z2
        ...
        xn      yn      zn
.DE
.LP
.UL Cone
.PP
A cone is a megaphone-shaped object.
It is truncated by two planes perpendicular to its axis,
and one of its ends may come to a point.
It is given as two axis endpoints, and the starting
and ending radii:
.DS
mod cone id
0
0
8
        x0      y0      z0
        x1      y1      z1
        r0      r1
.DE
.LP
.UL Cup
.PP
A cup is an inverted cone (i.e., has an inward surface normal).
.LP
.UL Cylinder
.PP
A cylinder is like a cone, but its starting and ending radii are
equal.
.DS
mod cylinder id
0
0
7
        x0      y0      z0
        x1      y1      z1
        rad
.DE
.LP
.UL Tube
.PP
A tube is an inverted cylinder.
.LP
.UL Ring
.PP
A ring is a circular disk given by its center, surface
normal, and inner and outer radii:
.DS
mod ring id
0
0
8
        xcent   ycent   zcent
        xdir    ydir    zdir
        r0      r1
.DE
.LP
.UL Mesh
.PP
A mesh is a compound surface, made up of many triangles and
an octree data structure to accelerate ray intersection.
It is typically converted from a Wavefront .OBJ file using the
.I obj2mesh
program.
.DS
mod mesh id
1+ meshfile transform
0
0
.DE
If the modifier is "void", then surfaces will use the modifiers given
in the original mesh description.
Otherwise, the modifier specified is used in their place.
The transform moves the mesh to the desired location in the scene.
Multiple instances using the same meshfile take little extra memory,
and the compiled mesh itself takes much less space than individual
polygons would.
In the case of an unsmoothed mesh, using the mesh primitive reduces
memory requirements by a factor of 30 relative to individual triangles.
If a mesh has smoothed surfaces, we save a factor of 50 or more,
permitting very detailed geometries that would otherwise exhaust the
available memory.
In addition, the mesh primitive can have associated (u,v) coordinates
for pattern and texture mapping.
These are made available to function files via the Lu and Lv variables.
.LP
.UL Instance
.PP
An instance is a compound surface, given by the contents of an
octree file (created by oconv).
.DS
mod instance id
1+ octree transform
0
0
.DE
If the modifier is "void", then surfaces will use the modifiers given
in the original description.
Otherwise, the modifier specified is used in their place.
The transform moves the octree to the desired location in the scene.
Multiple instances using the same octree take little extra memory,
hence very complex descriptions can be rendered using this primitive.
.PP
There are a number of important limitations to be aware of when using
instances.
First, the scene description used to generate the octree must stand on
its own, without referring to modifiers in the parent description.
This is necessary for oconv to create the octree.
Second, light sources in the octree will not be incorporated correctly
in the calculation, and they are not recommended.
Finally, there is no advantage (other than convenience) to
using a single instance of an octree, or an octree containing only a
few surfaces.
An xform command on the subordinate description is prefered in such cases.
.NH 3
Materials
.PP
A material defines the way light interacts with a surface.
The basic types are given below.
.LP
.UL Light
.PP
Light is the basic material for self-luminous surfaces (i.e., light
sources).
In addition to the source surface type, spheres, discs (rings with zero
inner radius), cylinders (provided they are long enough), and
polygons can act as light sources.
Polygons work best when they are rectangular.
Cones cannot be used at this time.
A pattern may be used to specify a light output distribution.
Light is defined simply as a RGB radiance value (watts/steradian/m2):
.DS
mod light id
0
0
3 red green blue
.DE
.LP
.UL Illum
.PP
Illum is used for secondary light sources with broad distributions.
A secondary light source is treated like any other
light source, except when viewed directly.
It then acts like it is made of a different material (indicated by
the string argument), or becomes invisible (if no string argument is given,
or the argument is "void").
Secondary sources are useful when modeling windows or
brightly illuminated surfaces.
.DS
mod illum id
1 material
0
3 red green blue
.DE
.LP
.UL Glow
.PP
Glow is used for surfaces that are self-luminous, but limited
in their effect.
In addition to the radiance value, a maximum radius for
shadow testing is given:
.DS
mod glow id
0
0
4 red green blue maxrad
.DE
If maxrad is zero, then the surface will never be tested
for shadow, although it may participate in an interreflection calculation.
If maxrad is negative, then the surface will never contribute to scene
illumination.
Glow sources will never illuminate objects on the other side of an
illum surface.
This provides a convenient way to illuminate local light fixture
geometry without overlighting nearby objects.
.LP
.UL Spotlight
.PP
Spotlight is used for self-luminous surfaces having directed output.
As well as radiance, the full cone angle (in degrees)
and orientation (output direction) vector are given.
The length of the orientation vector is the distance
of the effective focus behind the source center (i.e., the focal length).
.DS
mod spotlight id
0
0
7 red green blue angle xdir ydir zdir
.DE
.LP
.UL Mirror
.PP
Mirror is used for planar surfaces that produce virtual
source reflections.
This material should be used sparingly, as it may cause the light
source calculation to blow up if it is applied to many small surfaces.
This material is only supported for flat surfaces such as polygons
and rings.
The arguments are simply the RGB reflectance values, which should be
between 0 and 1.
An optional string argument may be used like the illum type to specify a
different material to be used for shading non-source rays.
If this alternate material is given as "void", then the mirror surface
will be invisible.
This is only appropriate if the surface hides other (more detailed)
geometry with the same overall reflectance.
.DS
mod mirror id
1 material
0
3 red green blue
.DE
While alternate materials that are reflective will appear as normal,
indirect rays will use the mirror's reflectance rather than the
alternate type.
Transmitting materials are an exception, where both transmission and
reflection will use the alternate type for all rays not specifically
targeting virtual light sources.
In this case, it is important that any reflections be purely specular
(mirror-like) and equal to the mirror's reflectivity
to maintain a valid result.
A pure diffuse reflection may be added if desired.
.PP
The mirror material type reflects light sources only from the front side
of a surface, regardless of any alternate material.
If virtual source generation is desired on both sides, two coincident
surfaces with opposite normal orientations may be employed to achieve
this effect.
The reflectance and alternate material type may be 
different for the overlapped surfaces,
and the two sides will behave accordingly.
.LP
.UL Prism1
.PP
The prism1 material is for general light redirection from prismatic
glazings, generating virtual light sources.
It can only be used to modify a planar surface (i.e., a polygon or disk)
and should not result in either light concentration or scattering.
The new direction of the ray can be on either side of the material,
and the definitions must have the correct bidirectional properties
to work properly with virtual light sources.
The arguments give the coefficient for the redirected light
and its direction.
.DS
mod prism1 id
5+ coef dx dy dz funcfile transform
0
n A1 A2 .. An
.DE
The new direction variables
.I "dx, dy"
and
.I dz
need not produce a normalized vector.
For convenience, the variables
.I "DxA, DyA"
and
.I DzA
are defined as the normalized direction to the target light source.
See section 2.2.1 on function files for further information.
.LP
.UL Prism2
.PP
The material prism2 is identical to prism1 except that
it provides for two ray redirections rather than one.
.DS
mod prism2 id
9+ coef1 dx1 dy1 dz1 coef2 dx2 dy2 dz2 funcfile transform
0
n A1 A2 .. An
.DE
.LP
.UL Mist
.PP
Mist is a virtual material used to delineate a volume
of participating atmosphere.
A list of important light sources may be given, along with an
extinction coefficient, scattering albedo and scattering eccentricity
parameter.
The light sources named by the string argument list
will be tested for scattering within the volume.
Sources are identified by name, and virtual light sources may be indicated
by giving the relaying object followed by '>' followed by the source, i.e:
.DS
3  source1  mirror1>source10  mirror2>mirror1>source3
.DE
Normally, only one source is given per mist material, and there is an
upper limit of 32 to the total number of active scattering sources.
The extinction coefficient, if given, is added to the global
coefficient set on the command line.
Extinction is in units of 1/distance (distance based on the world coordinates),
and indicates the proportional loss of radiance over one unit distance.
The scattering albedo, if present, will override the global setting within
the volume.
An albedo of 0\00\00 means a perfectly absorbing medium, and an albedo of
1\01\01\0 means
a perfectly scattering medium (no absorption).
The scattering eccentricity parameter will likewise override the global
setting if it is present.
Scattering eccentricity indicates how much scattered light favors the
forward direction, as fit by the Henyey-Greenstein function:
.DS
P(theta) = (1 - g*g) / (1 + g*g - 2*g*cos(theta))^1.5
.DE
A perfectly isotropic scattering medium has a g parameter of 0, and
a highly directional material has a g parameter close to 1.
Fits to the g parameter may be found along with typical extinction
coefficients and scattering albedos for various atmospheres and
cloud types in USGS meteorological tables.
(A pattern will be applied to the extinction values.)\0
.DS
mod mist id
N src1 src2 .. srcN
0
0|3|6|7 [ rext gext bext [ ralb galb balb [ g ] ] ]
.DE
There are two usual uses of the mist type.
One is to surround a beam from a spotlight or laser so that it is
visible during rendering.
For this application, it is important to use a cone (or cylinder) that
is long enough and wide enough to contain the important visible portion.
Light source photometry and intervening objects will have the desired
effect, and crossing beams will result in additive scattering.
For this application, it is best to leave off the real arguments, and
use the global rendering parameters to control the atmosphere.
The second application is to model clouds or other localized media.
Complex boundary geometry may be used to give shape to a uniform medium,
so long as the boundary encloses a proper volume.
Alternatively, a pattern may be used to set the line integral value
through the cloud for a ray entering or exiting a point in a given
direction.
For this application, it is best if cloud volumes do not overlap each other,
and opaque objects contained within them may not be illuminated correctly
unless the line integrals consider enclosed geometry.
.LP
.UL Plastic
.PP
Plastic is a material with uncolored highlights.
It is given by its RGB reflectance, its fraction of specularity,
and its roughness value.
Roughness is specified as the rms slope of surface facets.
A value of 0 corresponds to a perfectly smooth surface, and
a value of 1 would be a very rough surface.
Specularity fractions greater than 0.1 and
roughness values greater than 0.2 are not very
realistic.
(A pattern modifying plastic will affect the material color.)
.DS
mod plastic id
0
0
5 red green blue spec rough
.DE
.LP
.UL Metal
.PP
Metal is similar to plastic, but specular highlights
are modified by the material color.
Specularity of metals is usually .9 or greater.
As for plastic, roughness values above .2 are uncommon.
.LP
.UL Trans
.PP
Trans is a translucent material, similar to plastic.
The transmissivity is the fraction of penetrating light that
travels all the way through the material.
The transmitted specular component is the fraction of transmitted
light that is not diffusely scattered.
Transmitted and diffusely reflected light is modified by the material color.
Translucent objects are infinitely thin.
.DS
mod trans id
0
0
7 red green blue spec rough trans tspec
.DE
.LP
.UL Plastic2
.PP
Plastic2 is similar to plastic, but with anisotropic
roughness.
This means that highlights in the surface will appear elliptical rather
than round.
The orientation of the anisotropy is determined by the unnormalized
direction vector
.I "ux uy uz".
These three expressions (separated by white space) are evaluated in
the context of the function file
.I funcfile.
If no function file is required (i.e., no special variables or
functions are required), a period (`.') may be given in its
place.
(See the discussion of Function Files in the Auxiliary Files section).
The
.I urough
value defines the roughness along the
.B u
vector given projected onto the surface.
The
.I vrough
value defines the roughness perpendicular to this vector.
Note that the highlight will be narrower in the direction of the
smaller roughness value.
Roughness values of zero are not allowed for efficiency reasons
since the behavior would be the same as regular plastic in that
case.
.DS
mod plastic2 id
4+ ux uy uz funcfile transform
0
6 red green blue spec urough vrough
.DE
.LP
.UL Metal2
.PP
Metal2 is the same as plastic2, except that the highlights are
modified by the material color.
.LP
.UL Trans2
.PP
Trans2 is the anisotropic version of trans.
The string arguments are the same as for plastic2, and the real
arguments are the same as for trans but with an additional roughness
value.
.DS
mod trans2 id
4+ ux uy uz funcfile transform
0
8 red green blue spec urough vrough trans tspec
.DE
.LP
.UL Ashik2
.PP
Ashik2 is the anisotropic reflectance model by Ashikhmin & Shirley.
The string arguments are the same as for plastic2, but the real
arguments have additional flexibility to specify the specular color.
Also, rather than roughness, specular power is used, which has no
physical meaning other than larger numbers are equivalent to a smoother
surface.
Unlike other material types, total reflectance is the sum of
diffuse and specular colors, and should be adjusted accordingly.
.DS
mod ashik2 id
4+ ux uy uz funcfile transform
0
8 dred dgrn dblu sred sgrn sblu u-power v-power
.DE
.LP
.UL WGMDfunc
.PP
WGMDfunc is a more programmable version of trans2,
with separate modifier paths and variables to control each component.
(WGMD stands for Ward-Geisler-Moroder-Duer, which is the basis for
this empirical model, similar to the previous ones beside Ashik2.)\0
The specification of this material is given below.
.DS
mod WGMDfunc id
13+ rs_mod  rs  rs_urough rs_vrough
    ts_mod  ts  ts_urough ts_vrough
    td_mod
    ux uy uz  funcfile  transform
0
9+  rfdif gfdif bfdif
    rbdif gbdif bbdif
    rtdif gtdif btdif
    A10 ..
.DE
The sum of specular reflectance (
.I rs
), specular transmittance (
.I ts
), diffuse reflectance (
.I "rfdif gfdif bfdif"
for front and
.I "rbdif gbdif bbdif"
for back)
and diffuse transmittance (
.I "rtdif gtdif btdif"
) should be less than 1 for each
channel.
.PP
Unique to this material, separate modifier channels are
provided for each component.
The main modifier is used on the diffuse reflectance, both
front and back.
The
.I rs_mod
modifier is used for specular reflectance.
If "void" is given for
.I rs_mod,
then the specular reflection color will be white.
The special "inherit" keyword may also be given, in which case
specular reflectance will share the main modifier.
This behavior is replicated for the specular transmittance modifier
.I ts_mod,
which has its own independent roughness expressions.
Finally, the diffuse transmittance modifier is given as
.I td_mod,
which may also be "void" or "inherit".
Note that any spectra or color for specular components must be
carried by the named modifier(s).
.PP
The main advantage to this material over BRTDfunc and
other programmable types described below is that the specular sampling is
well-defined, so that all components are fully computed.
.LP
.UL Dielectric
.PP
A dielectric material is transparent, and it refracts light
as well as reflecting it.
Its behavior is determined by the index of refraction and
transmission coefficient in each wavelength band per unit length.
Common glass has a index of refraction (n) around 1.5,
and a transmission coefficient of roughly 0.92 over an inch.
An additional number, the Hartmann constant, describes how
the index of refraction changes as a function of wavelength.
It is usually zero.
(A pattern modifies only the refracted value.)
.DS
mod dielectric id
0
0
5 rtn gtn btn n hc
.DE
.LP
.UL Interface
.PP
An interface is a boundary between two dielectrics.
The first transmission coefficient and refractive index are for the inside;
the second ones are for the outside.
Ordinary dielectrics are surrounded by a vacuum (1 1 1 1).
.DS
mod interface id
0
0
8 rtn1 gtn1 btn1 n1 rtn2 gtn2 btn2 n2
.DE
.LP
.UL Glass
.PP
Glass is similar to dielectric, but it is optimized for thin glass
surfaces (n = 1.52).
One transmitted ray and one reflected ray is produced.
By using a single surface is in place of two, internal reflections
are avoided.
The surface orientation is irrelevant, as it is for plastic,
metal, and trans.
The only specification required is the transmissivity at normal
incidence.
(Transmissivity is the amount of light not absorbed in one traversal
of the material.
Transmittance -- the value usually measured -- is the total light
transmitted through the pane including multiple reflections.)\0
To compute transmissivity (tn) from transmittance (Tn) use:
.DS
tn = (sqrt(.8402528435+.0072522239*Tn*Tn)-.9166530661)/.0036261119/Tn
.DE
Standard 88% transmittance glass has a transmissivity of 0.96.
(A pattern modifying glass will affect the transmissivity.)
If a fourth real argument is given, it is interpreted as the index of
refraction to use instead of 1.52.
.DS
mod glass id
0
0
3 rtn gtn btn
.DE
.LP
.UL Plasfunc
.PP
Plasfunc in used for the procedural definition of plastic-like
materials with arbitrary bidirectional reflectance distribution
functions (BRDF's).
The arguments to this material include the color and specularity,
as well as the function defining the specular distribution and the
auxiliary file where it may be found.
.DS
mod plasfunc id
2+ refl funcfile transform
0
4+ red green blue spec A5 ..
.DE
The function
.I refl
takes four arguments, the x, y and z
direction towards the incident light, and the solid angle
subtended by the source.
The solid angle is provided to facilitate averaging, and is usually
ignored.
The
.I refl
function should integrate to 1 over
the projected hemisphere to maintain energy balance.
At least four real arguments must be given, and these are made
available along with any additional values to the reflectance
function.
Currently, only the contribution from direct light sources is
considered in the specular calculation.
As in most material types, the surface normal is always
altered to face the incoming ray.
.LP
.UL Metfunc
.PP
Metfunc is identical to plasfunc and takes the same arguments, but
the specular component is multiplied also by the material color.
.LP
.UL Transfunc
.PP
Transfunc is similar to plasfunc but with an arbitrary bidirectional
transmittance distribution as well as a reflectance distribution.
Both reflectance and transmittance are specified with the same function.
.DS
mod transfunc id
2+ brtd funcfile transform
0
6+ red green blue rspec trans tspec A7 ..
.DE
Where
.I trans
is the total light transmitted and
.I tspec
is the non-Lambertian fraction of transmitted light.
The function
.I brtd
should integrate to 1 over each projected hemisphere.
.LP
.UL BRTDfunc
.PP
The material BRTDfunc gives the maximum flexibility over surface
reflectance and transmittance, providing for spectrally-dependent
specular rays and reflectance and transmittance distribution functions.
.DS
mod BRTDfunc id
10+  rrefl  grefl  brefl
     rtrns  gtrns  btrns
     rbrtd  gbrtd  bbrtd
     funcfile  transform
0
9+   rfdif gfdif bfdif
     rbdif gbdif bbdif
     rtdif gtdif btdif
     A10 ..
.DE
The variables
.I "rrefl, grefl"
and
.I brefl
specify the color coefficients for
the ideal specular (mirror) reflection of the surface.
The variables
.I "rtrns, gtrns"
and
.I btrns
specify the color coefficients for the ideal specular transmission.
The functions
.I "rbrtd, gbrtd"
and
.I bbrtd
take the direction to the incident light (and its solid angle)
and compute the color coefficients for the directional diffuse part of
reflection and transmission.
As a special case, three identical values of '0' may be given in place of
these function names to indicate no directional diffuse component.
.PP
Unlike most other material types, the surface normal is not altered to
face the incoming ray.
Thus, functions and variables must pay attention to the orientation of
the surface and make adjustments appropriately.
However, the special variables for the perturbed dot product and surface
normal,
.I "RdotP, NxP, NyP"
and
.I NzP
are reoriented as if the ray hit the front surface for convenience.
.PP
A diffuse reflection component may be given for the front side with
.I "rfdif, gfdif"
and
.I bfdif
for the front side of the surface or
.I "rbdif, gbdif"
and
.I bbdif
for the back side.
The diffuse transmittance (must be the same for both sides by physical law)
is given by
.I "rtdif, gtdif"
and
.I btdif.
A pattern will modify these diffuse scattering values,
and will be available through the special variables
.I "CrP, CgP"
and
.I CbP.
.PP
Care must be taken when using this material type to produce a physically
valid reflection model.
The reflectance functions should be bidirectional, and under no circumstances
should the sum of reflected diffuse, transmitted diffuse, reflected specular,
transmitted specular and the integrated directional diffuse component be
greater than one.
.LP
.UL Plasdata
.PP
Plasdata is used for arbitrary BRDF's that are most conveniently
given as interpolated data.
The arguments to this material are the data file and coordinate index
functions, as well as a function to optionally modify the data
values.
.DS
mod plasdata id
3+n+
        func datafile
        funcfile x1 x2 .. xn transform
0
4+ red green blue spec A5 ..
.DE
The coordinate indices
.I "(x1, x2,"
etc.) are themselves functions of
the x, y and z direction to the incident light, plus the solid angle
subtended by the light source (usually ignored).
The data function
.I (func)
takes five variables, the
interpolated value from the n-dimensional data file, followed by the
x, y and z direction to the incident light and the solid angle of the source.
The light source direction and size may of course be ignored by the function.
.LP
.UL Metdata
.PP
As metfunc is to plasfunc, metdata is to plasdata.
Metdata takes the same arguments as plasdata, but the specular
component is modified by the given material color.
.LP
.UL Transdata
.PP
Transdata is like plasdata but the specification includes transmittance
as well as reflectance.
The parameters are as follows.
.DS
mod transdata id
3+n+
        func datafile
        funcfile x1 x2 .. xn transform
0
6+ red green blue rspec trans tspec A7 ..
.DE
.LP
.UL BSDF
.PP
The BSDF material type loads an XML (eXtensible Markup Language)
file describing a bidirectional scattering distribution function.
Real arguments to this material may define additional
diffuse components that augment the BSDF data.
String arguments are used to define thickness for proxied
surfaces and the "up" orientation for the material.
.DS
mod BSDF id
6+ thick BSDFfile ux uy uz funcfile transform
0
0|3|6|9
     rfdif gfdif bfdif
     rbdif gbdif bbdif
     rtdif gtdif btdif
.DE
The first string argument is a "thickness" parameter that may be used
to hide detail geometry being proxied by an aggregate BSDF material.
If a view or shadow ray hits a BSDF proxy with non-zero thickness,
it will pass directly through as if the surface were not there.
Similar to the illum type, this permits direct viewing and
shadow testing of complex geometry.
The BSDF is used when a scattered (indirect) ray hits the surface,
and any transmitted sample rays will be offset by the thickness amount
to avoid the hidden geometry and gather samples from the other side.
In this manner, BSDF surfaces can improve the results for indirect
scattering from complex systems without sacrificing appearance or
shadow accuracy.
If the BSDF has transmission and back-side reflection data,
a parallel BSDF surface may be
placed slightly less than the given thickness away from the front surface
to enclose the complex geometry on both sides.
The sign of the thickness is important, as it indicates whether the
proxied geometry is behind the BSDF surface (when thickness is positive)
or in front (when thickness is negative).
.LP
The second string argument is the name of the BSDF file, which is
found in the usual auxiliary locations.
The following three string parameters name variables for an "up" vector,
which together with the surface normal, define the
local coordinate system that orients the BSDF.
These variables, along with the thickness, are defined in a function
file given as the next string argument.
An optional transform is used to scale the thickness and reorient the up vector.
.LP
If no real arguments are given, the BSDF is used by itself to determine
reflection and transmission.
If there are at least 3 real arguments, the first triplet is an
additional diffuse reflectance for the front side.
At least 6 real arguments adds diffuse reflectance to the rear side of the surface.
If there are 9 real arguments, the final triplet will be taken as an additional
diffuse transmittance.
All diffuse components as well as the non-diffuse transmission are
modified by patterns applied to this material.
The non-diffuse reflection from either side are unaffected.
Textures perturb the effective surface normal in the usual way.
.LP
The surface normal of this type is not altered to face the incoming ray,
so the front and back BSDF reflections may differ.
(Transmission is identical front-to-back by physical law.)\0
If back visibility is turned off during rendering and there is no
transmission or back-side reflection, only then the surface will be
invisible from behind.
Unlike other data-driven material types, the BSDF type is fully
supported and all parts of the distribution are properly sampled.
.LP
.UL aBSDF
.PP
The aBSDF material is identical to the BSDF type with two important
differences.
First, proxy geometry is not supported, so there is no thickness parameter.
Second, an aBSDF is assumed to have some specular through component
(the 'a' stands for "aperture"), which
is treated specially during the direct calculation and when viewing the
material.
Based on the BSDF data, the coefficient of specular transmission is
determined and used for modifying unscattered shadow and view rays.
.DS
mod aBSDF id
5+ BSDFfile ux uy uz funcfile transform
0
0|3|6|9
     rfdif gfdif bfdif
     rbdif gbdif bbdif
     rtdif gtdif btdif
.DE
.LP
If a material has no specular transmitted component, it is much better
to use the BSDF type with a zero thickness than to use aBSDF.
.LP
.UL Antimatter
.PP
Antimatter is a material that can "subtract" volumes from other volumes.
A ray passing into an antimatter object becomes blind to all the specified
modifiers:
.DS
mod antimatter id
N mod1 mod2 .. modN
0
0
.DE
The first modifier will also be used to shade the area leaving the
antimatter volume and entering the regular volume.
If mod1 is void, the antimatter volume is completely invisible.
If shading is desired at antimatter surfaces, it is important
that the related volumes are closed with outward-facing normals.
Antimatter surfaces should not intersect with other antimatter boundaries,
and it is unwise to use the same modifier in nested antimatter volumes.
The viewpoint must be outside all volumes concerned for a correct
rendering.
.NH 3
Textures
.PP
A texture is a perturbation of the surface normal, and
is given by either a function or data.
.LP
.UL Texfunc
.PP
A texfunc uses an auxiliary function file
to specify a procedural texture:
.DS
mod texfunc id
4+ xpert ypert zpert funcfile transform
0
n A1 A2 .. An
.DE
.LP
.UL Texdata
.PP
A texdata texture uses three data files to get the surface
normal perturbations.
The variables 
.I xfunc, 
.I yfunc
and 
.I zfunc
take three arguments
each from the interpolated values in
.I xdfname,
.I ydfname
and
.I zdfname.
.DS
mod texdata id
8+ xfunc yfunc zfunc xdfname ydfname zdfname vfname x0 x1 .. xf
0
n A1 A2 .. An
.DE
.NH 3
Patterns
.PP
Patterns are used to modify the reflectance of materials.
The basic types are given below.
.LP
.UL Colorfunc
.PP
A colorfunc is a procedurally defined color pattern.
It is specified as follows:
.DS
mod colorfunc id
4+ red green blue funcfile transform
0
n A1 A2 .. An
.DE
.LP
.UL Brightfunc
.PP
A brightfunc is the same as a colorfunc, except it is monochromatic.
.DS
mod brightfunc id
2+ refl funcfile transform
0
n A1 A2 .. An
.DE
.LP
.UL Colordata
.PP
Colordata uses an interpolated data map to modify a material's color.
The map is n-dimensional, and is stored in three
auxiliary files, one for each color.
The coordinates used to look up and interpolate the data are
defined in another auxiliary file.
The interpolated data values are modified by functions of
one or three variables.
If the functions are of one variable, then they are passed the
corresponding color component (red or green or blue).
If the functions are of three variables, then they are passed the
original red, green, and blue values as parameters.
.DS
mod colordata id
7+n+
        rfunc gfunc bfunc rdatafile gdatafile bdatafile
        funcfile x1 x2 .. xn transform
0
m A1 A2 .. Am
.DE
.LP
.UL Brightdata
.PP
Brightdata is like colordata, except monochromatic.
.DS
mod brightdata id
3+n+
        func datafile
        funcfile x1 x2 .. xn transform
0
m A1 A2 .. Am
.DE
.LP
.UL Colorpict
.PP
Colorpict is a special case of colordata, where the pattern is
a two-dimensional image stored in the RADIANCE picture format.
The dimensions of the image data are determined by the picture
such that the smaller dimension is always 1, and the other
is the ratio between the larger and the smaller.
For example, a 500x338 picture would have coordinates (u,v)
in the rectangle between (0,0) and (1.48,1).
.DS
mod colorpict id
7+
        rfunc gfunc bfunc pictfile
        funcfile u v transform
0
m A1 A2 .. Am
.DE
.LP
.UL Colortext
.PP
Colortext is dichromatic writing in a polygonal font.
The font is defined in an auxiliary file, such as
.I helvet.fnt.
The text itself is also specified in a separate file, or
can be part of the material arguments.
The character size, orientation, aspect ratio and slant is
determined by right and down motion vectors.
The upper left origin for the text block as well as
the foreground and background colors
must also be given.
.DS
mod colortext id
2 fontfile textfile
0
15+
        Ox Oy Oz
        Rx Ry Rz
        Dx Dy Dz
        rfore gfore bfore
        rback gback bback
        [spacing]
.DE
or:
.DS
mod colortext id
2+N fontfile . This is a line with N words ...
0
15+
        Ox Oy Oz
        Rx Ry Rz
        Dx Dy Dz
        rfore gfore bfore
        rback gback bback
        [spacing]
.DE
.LP
.UL Brighttext
.PP
Brighttext is like colortext, but the writing is monochromatic.
.DS
mod brighttext id
2 fontfile textfile
0
11+
        Ox Oy Oz
        Rx Ry Rz
        Dx Dy Dz
        foreground background
        [spacing]
.DE
or:
.DS
mod brighttext id
2+N fontfile . This is a line with N words ...
0
11+
        Ox Oy Oz
        Rx Ry Rz
        Dx Dy Dz
        foreground background
        [spacing]
.DE
.LP
By default, a uniform spacing algorithm is used that guarantees
every character will appear in a precisely determined position.
Unfortunately, such a scheme results in rather unattractive and difficult to
read text with most fonts.
The optional
.I spacing
value defines the distance between characters for proportional spacing.
A positive value selects a spacing algorithm that preserves right margins and
indentation, but does not provide the ultimate in proportionally spaced text.
A negative value insures that characters are properly spaced, but the
placement of words then varies unpredictably.
The choice depends on the relative importance of spacing versus formatting.
When presenting a section of formatted text, a positive spacing value is
usually preferred.
A single line of text will often be accompanied by a negative spacing value.
A section of text meant to depict a picture, perhaps using a special purpose
font such as hexbit4x1.fnt, calls for uniform spacing.
Reasonable magnitudes for proportional spacing are
between 0.1 (for tightly spaced characters) and 0.3 (for wide spacing).
.LP
.UL Spectrum
.PP
The spectrum primitive is the most basic type for introducing spectral
color to a material.
Since materials only provide RGB parameters, spectral patterns
are the only way to superimpose wavelength-dependent behavior.
.DS
mod spectrum id
0
0
5+ nmA nmB s1 s2 .. sN
.DE
The first two real arguments indicate the extrema of the
spectral range in nanometers.
Subsequent real values correspond to multipliers at each wavelength.
The nmA wavelength may be greater or less than nmB,
but they may not be equal, and their ordering matches
the order of the spectral values.
A minimum of 3 values must be given, which would act
more or less the same as a constant RGB multiplier.
As with RGB values, spectral quantities normally range between 0
and 1 at each wavelength, or average to 1.0 against a standard
sensitivity functions such as V(lambda).
The best results obtain when the spectral range and number
of samples match rendering options, though resampling will handle
any differences, zero-filling wavelenths outside the nmA to nmB
range.
A warning will be issued if the given wavelength range does not
adequately cover the visible spectrum.
.LP
.UL Specfile
.PP
The specfile primitive is equivalent to the spectrum type, but
the wavelength range and values are contained in a 1-dimensional
data file.
This may be a more convenient way to specify a spectral color,
especially one corresponding to a standard illuminant such as D65
or a library of measured spectra.
.DS
mod specfile id
1 datafile
0
0
.DE
As with the spectrum type, rendering wavelengths outside the defined
range will be zero-filled.
Unlike the spectrum type, the file may contain non-uniform samples.
.LP
.UL Specfunc
.PP
The specfunc primitive offers dynamic control over a spectral
pattern, similar to the colorfunc type.
.DS
mod specfunc id
2+ sfunc funcfile transform
0
2+ nmA nmB A3 ..
.DE
Like the spectrum primitive, the wavelength range is specified
in the first two real arguments, and additional real values are
set in the evaluation context.
This function is fed a wavelenth sample
between nmA and nmB as its only argument,
and it returns the corresponding spectral intensity.
.LP
.UL Specdata
.PP
Specdata is like brightdata and colordata, but with more
than 3 specular samples.
.DS
mod specdata id
3+n+
        func datafile
        funcfile x1 x2 .. xn transform
0
m A1 A2 .. Am
.DE
The data file must have one more dimension than the coordinate
variable count, as this final dimension corresponds to the covered
spectrum.
The starting and ending wavelengths are specified in "datafile"
as well as the number of spectral samples.
The function "func" will be called with two parameters, the
interpolated spectral value for the current coordinate and the
associated wavelength.
If the spectrum is broken into 12 components, then 12 calls
will be made to "func" for the relevant ray evaluation.
.LP
.UL Specpict
.PP
Specpict is a special case of specdata, where the pattern is
a hyperspectral image stored in the common-exponent file format.
The dimensions of the image data are determined by the picture
just as with the colorpict primitive.
.DS
mod specpict id
5+
        func specfile
        funcfile u v transform
0
m A1 A2 .. Am
.DE
The function "func" is called with the interpolated pixel value
and the wavelength sample in nanometers, the same as specdata,
with as many calls made as there are components in "specfile".
.NH 3
Mixtures
.PP
A mixture is a blend of one or more materials or textures and patterns.
Blended materials should not be light source types or virtual source types.
The basic types are given below.
.LP
.UL Mixfunc
.PP
A mixfunc mixes two modifiers procedurally.
It is specified as follows:
.DS
mod mixfunc id
4+ foreground background vname funcfile transform
0
n A1 A2 .. An
.DE
Foreground and background are modifier names that must be
defined earlier in the scene description.
If one of these is a material, then
the modifier of the mixfunc must be "void".
(Either the foreground or background modifier may be "void",
which serves as a form of opacity control when used with a material.)\0
Vname is the coefficient defined in funcfile that determines the influence
of foreground.
The background coefficient is always (1-vname).
.LP
.UL Mixdata
.PP
Mixdata combines two modifiers using an auxiliary data file:
.DS
mod mixdata id
5+n+
        foreground background func datafile
        funcfile x1 x2 .. xn transform
0
m A1 A2 .. Am
.DE
.LP
.UL Mixpict
.PP
Mixpict combines two modifiers based on a picture:
.DS
mod mixpict id
7+
        foreground background func pictfile
        funcfile u v transform
0
m A1 A2 .. Am
.DE
The mixing coefficient function "func" takes three
arguments, the red, green and blue values
corresponding to the pixel at (u,v).
.LP
.UL Mixtext
.PP
Mixtext uses one modifier for the text foreground, and one for the
background:
.DS
mod mixtext id
4 foreground background fontfile textfile
0
9+
        Ox Oy Oz
        Rx Ry Rz
        Dx Dy Dz
        [spacing]
.DE
or:
.DS
mod mixtext id
4+N
        foreground background fontfile .
        This is a line with N words ...
0
9+
        Ox Oy Oz
        Rx Ry Rz
        Dx Dy Dz
        [spacing]
.DE
.NH 2
Auxiliary Files
.PP
Auxiliary files used in textures and patterns
are accessed by the programs during image generation.
These files may be located in the working directory, or in
a library directory.
The environment variable
.I RAYPATH
can be assigned an alternate set of search directories.
Following is a brief description of some common file types.
.NH 3
Function Files
.PP
A function file contains the definitions of variables, functions
and constants used by a primitive.
The transformation that accompanies the file name contains the necessary
rotations, translations and scalings to bring the coordinates of
the function file into agreement with the world coordinates.
The transformation specification is the same as for the
.I xform
command.
An example function file is given below:
.DS
{
        This is a comment, enclosed in curly braces.
        {Comments can be nested.}
}
                        { standard expressions use +,-,*,/,^,(,) }
vname = Ny * func(A1) ;
                        { constants are defined with a colon }
const : sqrt(PI/2) ;
                        { user-defined functions add to library }
func(x) = 5 + A1*sin(x/3) ;
                        { functions may be passed and recursive }
rfunc(f,x) = if(x,f(x),f(-x)*rfunc(f,x+1)) ;
                        { constant functions may also be defined }
cfunc(x) : 10*x / sqrt(x) ;
.DE
Many variables and functions are already defined by the program,
and they are listed in the file
.I rayinit.cal.
The following variables are particularly important:
.DS
        Dx, Dy, Dz              - incident ray direction
        Nx, Ny, Nz              - surface normal at intersection point
        Px, Py, Pz              - intersection point
        T                       - distance from start
        Ts                      - single ray (shadow) distance
        Rdot                    - cosine between ray and normal
        arg(0)                  - number of real arguments
        arg(i)                  - i'th real argument
.DE
For mesh objects, the local surface coordinates are available:
.DS
        Lu, Lv                  - local (u,v) coordinates
.DE
For BRDF types, the following variables are defined as well:
.DS
        NxP, NyP, NzP           - perturbed surface normal
        RdotP                   - perturbed dot product
        CrP, CgP, CbP           - perturbed material color
.DE
A unique context is set up for each file so that the same variable
may appear in different function files without conflict.
The variables listed above and any others defined in
rayinit.cal are available globally.
If no file is needed by a given primitive because all the required
variables are global, a period (`.') can be given in
place of the file name.
It is also possible to give an expression instead of a straight
variable name in a scene file.
Functions (requiring parameters)
must be given as names and not as expressions.
.PP
Constant expressions are used as an optimization in function
files.
They are replaced wherever they occur in an expression by their
value.
Constant expressions are evaluated only once, so they must not
contain any variables or values that can change, such as the ray
variables Px and Ny or the primitive argument function arg().
All the math library functions such as sqrt() and cos() have the
constant attribute, so they will be replaced by immediate values
whenever they are given constant arguments.
Thus, the subexpression cos(PI*sqrt(2)) is immediately replaced
by its value, -.266255342, and does not cause any additional overhead
in the calculation.
.PP
It is generally a good idea to define constants and variables before
they are referred to in a function file.
Although evaluation does not take place until later, the interpreter
does variable scoping and constant subexpression evaluation based on
what it has compiled already.
For example, a variable that is defined globally in rayinit.cal then
referenced in the local context of a function file cannot
subsequently be redefined in the same file because the compiler
has already determined the scope of the referenced variable as global.
To avoid such conflicts, one can state the scope of a variable explicitly
by preceding the variable name with a context mark (a back-quote) for
a local variable, or following the name with a context mark for a global
variable.
.NH 3
Data Files
.PP
Data files contain n-dimensional arrays of real numbers used
for interpolation.
Typically, definitions in a function file determine how
to index and use interpolated data values.
The basic data file format is as follows:
.DS
N
beg1 end1 m1
0 0 m2 x2.1 x2.2 x2.3 x2.4 .. x2.m2
 ...
begN endN mN
DATA, later dimensions changing faster.
.DE
N is the number of dimensions.
For each dimension, the beginning and ending coordinate
values and the dimension size is given.
Alternatively, individual coordinate values can be given when
the points are not evenly spaced.
These values must either be increasing or decreasing monotonically.
The data is m1*m2*...*mN real numbers in ASCII form.
Comments may appear anywhere in the file, beginning with a pound
sign ('#') and continuing to the end of line.
.NH 3
Font Files
.PP
A font file lists the polygons which make up a character set.
Comments may appear anywhere in the file, beginning with a pound
sign ('#') and continuing to the end of line.
All numbers are decimal integers:
.DS
code n
        x0 y0
        x1 y1
         ...
        xn yn
 ...
.DE
The ASCII codes can appear in any order.
N is the number of vertices, and the last is automatically
connected to the first.
Separate polygonal sections are joined by coincident sides.
The character coordinate system is a square with lower left corner at
(0,0), lower right at (255,0) and upper right at (255,255).
.NH 2
Generators
.PP
A generator is any program that produces a scene description
as its output.
They usually appear as commands in a scene description file.
An example of a simple generator is
.I genbox.
.I Genbox
takes the arguments of width, height and depth to produce
a parallelepiped description.
.I Genprism
takes a list of 2-dimensional coordinates and extrudes them along a vector to
produce a 3-dimensional prism.
.I Genrev
is a more sophisticated generator
that produces an object of rotation from parametric functions
for radius and axis position.
.I Gensurf
tessellates a surface defined by the
parametric functions x(s,t), y(s,t), and z(s,t).
.I Genworm
links cylinders and spheres along a curve.
.I Gensky
produces a sun and sky distribution corresponding
to a given time and date.
.PP
.I Xform
is a program that transforms a scene description from one
coordinate space to another.
.I Xform
does rotation, translation, scaling, and mirroring.
.NH 1
Image Generation
.PP
Once the scene has been described in three-dimensions, it
is possible to generate a two-dimensional image from a
given perspective.
.PP
The image generating programs use an
.I octree
to efficiently trace rays through the scene.
An octree subdivides space into nested octants which
contain sets of surfaces.
In RADIANCE, an octree is created from a scene description by
.I oconv.
The details of this process are not important,
but the octree will serve as input to the ray-tracing
programs and directs the use of a scene description.
.PP
.I Rview
is ray-tracing program for viewing a scene interactively.
When the user specifies a new perspective,
.I rview
quickly displays a rough
image on the terminal, then progressively
increases the resolution as the user looks on.
He can select a particular section of the image to improve,
or move to a different view and start over.
This mode of interaction is useful for debugging scenes
as well as determining the best view for a final image.
.PP
.I Rpict
produces a high-resolution picture of a scene from
a particular perspective.
This program features adaptive sampling, crash
recovery and progress reporting, all of which are important
for time-consuming images.
.PP
A number of filters are available for manipulating picture files.
.I Pfilt
sets the exposure and performs anti-aliasing.
.I Pcompos
composites (cuts and pastes) pictures.
.I Pcond
conditions a picture for a specific display device.
.I Pcomb
performs arbitrary math on one or more pictures.
.I Protate
rotates a picture 90 degrees clockwise.
.I Pflip
flips a picture horizontally, vertically, or both (180 degree rotation).
.I Pvalue
converts a picture to and from simpler formats.
.PP
Pictures may be displayed directly under X11 using the program
.I ximage,
or converted a standard image format.
.I Ra_bmp
converts to and from Microsoft Bitmap images.
.I Ra_ppm
converts to and from Poskanzer Portable Pixmap formats.
.I Ra_ps
converts to PostScript color and greyscale formats.
.I Ra_rgbe
converts to and from Radiance uncompressed picture format.
.I Ra_t16
converts to and from Targa 16 and 24-bit image formats.
.I Ra_t8
converts to and from Targa 8-bit image format.
.I Ra_tiff
converts to and from TIFF.
.I Ra_xyze
converts to and from Radiance CIE picture format.
.NH 1
License
.PP
.DS
The Radiance Software License, Version 1.0

Copyright (c) 1990 - 2008 The Regents of the University of California,
through Lawrence Berkeley National Laboratory.   All rights reserved.

Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions
are met:

1. Redistributions of source code must retain the above copyright
        notice, this list of conditions and the following disclaimer.

2. Redistributions in binary form must reproduce the above copyright
      notice, this list of conditions and the following disclaimer in
      the documentation and/or other materials provided with the
      distribution.

3. The end-user documentation included with the redistribution,
          if any, must include the following acknowledgment:
            "This product includes Radiance software
                (http://radsite.lbl.gov/)
                developed by the Lawrence Berkeley National Laboratory
              (http://www.lbl.gov/)."
      Alternately, this acknowledgment may appear in the software itself,
      if and wherever such third-party acknowledgments normally appear.

4. The names "Radiance," "Lawrence Berkeley National Laboratory"
      and "The Regents of the University of California" must
      not be used to endorse or promote products derived from this
      software without prior written permission. For written
      permission, please contact [email protected].

5. Products derived from this software may not be called "Radiance",
      nor may "Radiance" appear in their name, without prior written
      permission of Lawrence Berkeley National Laboratory.

THIS SOFTWARE IS PROVIDED ``AS IS'' AND ANY EXPRESSED OR IMPLIED
WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED.   IN NO EVENT SHALL Lawrence Berkeley National Laboratory OR
ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF
USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
SUCH DAMAGE.
.DE
.NH 1
Acknowledgements
.PP
This work was supported by the Assistant Secretary of Conservation
and Renewable Energy, Office of Building Energy Research and
Development, Buildings Equipment Division of the U.S. Department of
Energy under Contract No. DE-AC03-76SF00098.
.PP
Additional work was sponsored by the Swiss federal government
under the Swiss LUMEN Project and was
carried out in the Laboratoire d'Energie Solaire (LESO Group) at
the Ecole Polytechnique Federale de Lausanne (EPFL University)
in Lausanne, Switzerland.
.NH 1
References
.LP
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.LP
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.LP
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vol. 160, 15 January 2018, pp 380-395.
.LP
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.LP
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98, 404-14, November 2013.
.LP
Ward, G., R. Mistrick, E.S. Lee, A. McNeil, J. Jonsson,
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.LP
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.LP
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.LP
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.LP
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.LP
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.LP
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.LP
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.LP
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.LP
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.LP
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Revision:	1.49
Committed:	Fri May 30 16:35:52 2025 UTC (2 days, 14 hours ago) by greg
Branch:	MAIN
CVS Tags:	HEAD
Changes since 1.48:	+5 -3 lines
Log Message:	docs: Improved wording on new mirror material behavior