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Revision: 1.1
Committed: Tue Mar 11 19:20:20 2003 UTC (21 years ago) by greg
Branch: MAIN
Log Message:
Added documentation to repository

File Contents

# Content
1 .\" RCSid "$Id"
2 .\" Print using the -ms macro package
3 .DA 1/20/99
4 .LP
5 .tl """Copyright \(co 1996 Regents, University of California
6 .sp 2
7 .TL
8 The
9 .so ../src/rt/VERSION
10 .br
11 Synthetic Imaging System
12 .AU
13 Greg Ward
14 .br
15 Lawrence Berkeley Laboratory
16 .br
17 1 Cyclotron Rd.
18 .br
19 Berkeley, CA 94720
20 .br
21 (510) 486-4757
22 .NH 1
23 Introduction
24 .PP
25 RADIANCE was developed as a research tool
26 for predicting the distribution of visible radiation in
27 illuminated spaces.
28 It takes as input a three-dimensional geometric model of
29 the physical environment, and produces a map of
30 spectral radiance values in a color image.
31 The technique of ray-tracing follows light backwards
32 from the image plane to the source(s).
33 Because it can produce realistic images from a simple description,
34 RADIANCE has a wide range of applications in graphic arts,
35 lighting design, computer-aided engineering and architecture.
36 .KF
37 .sp 25
38 .ce
39 .B "Figure 1."
40 .sp
41 .KE
42 .PP
43 The diagram in Figure 1 shows the flow between programs (boxes) and
44 data (ovals).
45 The central program is
46 .I rpict,
47 which produces a picture from a scene description.
48 .I Rview
49 is a variation of
50 .I rpict
51 that computes and displays images interactively.
52 .PP
53 A scene description file lists the surfaces and materials
54 that make up a specific environment.
55 The current surface types are spheres, polygons, cones,
56 and cylinders.
57 They can be made from materials such as plastic, metal,
58 and glass.
59 Light sources can be distant disks as well as local spheres, discs and
60 polygons.
61 .PP
62 From a three-dimensional scene description and a specified view,
63 .I rpict
64 produces a two-dimensional image.
65 A picture file is a compressed binary representation of the
66 pixels in the image.
67 This picture can be scaled in size and
68 brightness, anti-aliased, and sent to a graphics output device.
69 .PP
70 A header in each picture file lists the program(s) and
71 parameters that produced it.
72 This is useful for identifying a picture
73 without having to display it.
74 The information can be read by the program
75 .I getinfo.
76 .NH 1
77 Scene Description
78 .PP
79 A scene description file represents a
80 three-dimensional physical environment
81 in Cartesian (rectilinear) world coordinates.
82 It is stored as ASCII text, with the following basic format:
83 .DS
84 # comment
85
86 modifier type identifier
87 n S1 S2 S3 .. Sn
88 0
89 m R1 R2 R3 .. Rm
90
91 modifier alias identifier reference
92
93 ! command
94
95 ...
96 .DE
97 .PP
98 A comment line begins with a pound sign, `#'.
99 .PP
100 The scene description
101 .I primitives
102 all have the same general format, and can
103 be either surfaces or modifiers.
104 A primitive has a modifier, a type, and an identifier.
105 A modifier is either the identifier of a
106 .I "previously defined"
107 primitive, or "void"\(dg.
108 .FS
109 \(dgThe most recent definition of a modifier is the one used,
110 and later definitions do not cause relinking of loaded
111 primitives.
112 Thus, the same identifier may be used repeatedly, and each new
113 definition will apply to the primitives following it.
114 .FE
115 An identifier can be any string (i.e. sequence of non-blank
116 characters).
117 The
118 .I arguments
119 associated with a primitive can be strings or real numbers.
120 The first integer following the identifier is the number
121 of string arguments, and it is followed by the arguments themselves
122 (separated by white space).
123 The next integer is the number of integer arguments, and is followed
124 by the integer arguments.
125 (There are currently no primitives that use them, however.)
126 The next integer is the real argument count, and it is followed
127 by the real arguments.
128 .PP
129 An alias gets its type and arguments from a previously defined primitive.
130 This is useful when the same material is used with a different
131 modifier, or as a convenient naming mechanism.
132 Surfaces cannot be aliased.
133 .PP
134 A line beginning with an exclamation point, `!',
135 is interpreted as a command.
136 It is executed by the shell, and its output is read as input to
137 the program.
138 The command must not try to read from its standard input, or
139 confusion will result.
140 A command may be continued over multiple lines using a backslash, `\\',
141 to escape the newline.
142 .PP
143 Blank space is generally ignored, except as a separator.
144 The exception is the newline character after a command or comment.
145 Commands, comments and primitives may appear in any combination, so long
146 as they are not intermingled.
147 .NH 2
148 Primitive Types
149 .PP
150 Primitives can be surfaces, materials, textures or patterns.
151 Modifiers can be materials, textures or patterns.
152 Simple surfaces must have one material in their modifier list.
153 .NH 3
154 Surfaces
155 .PP
156 A scene description will consist mostly of surfaces.
157 The basic types are given below.
158 .LP
159 .UL Source
160 .PP
161 A source is not really a surface, but a solid angle.
162 It is used for specifying light sources that are very distant.
163 The direction to the center of the source and the number of degrees
164 subtended by its disk are given as follows:
165 .DS
166 mod source id
167 0
168 0
169 4 xdir ydir zdir angle
170 .DE
171 .LP
172 .UL Sphere
173 .PP
174 A sphere is given by its center and radius:
175 .DS
176 mod sphere id
177 0
178 0
179 4 xcent ycent zcent radius
180 .DE
181 .LP
182 .UL Bubble
183 .PP
184 A bubble is simply a sphere whose surface normal points inward.
185 .LP
186 .UL Polygon
187 .PP
188 A polygon is given by a list of three-dimensional vertices,
189 which are ordered counter-clockwise as viewed from
190 the front side (into the surface normal).
191 The last vertex is automatically connected to the first.
192 Holes are represented in polygons as interior vertices connected to
193 the outer perimeter by coincident edges (seams).
194 .DS
195 mod polygon id
196 0
197 0
198 3n
199 x1 y1 z1
200 x2 y2 z2
201 ...
202 xn yn zn
203 .DE
204 .LP
205 .UL Cone
206 .PP
207 A cone is a megaphone-shaped object.
208 It is truncated by two planes perpendicular to its axis,
209 and one of its ends may come to a point.
210 It is given as two axis endpoints, and the starting
211 and ending radii:
212 .DS
213 mod cone id
214 0
215 0
216 8
217 x0 y0 z0
218 x1 y1 z1
219 r0 r1
220 .DE
221 .LP
222 .UL Cup
223 .PP
224 A cup is an inverted cone (i.e. has an inward surface normal).
225 .LP
226 .UL Cylinder
227 .PP
228 A cylinder is like a cone, but its starting and ending radii are
229 equal.
230 .DS
231 mod cylinder id
232 0
233 0
234 7
235 x0 y0 z0
236 x1 y1 z1
237 rad
238 .DE
239 .LP
240 .UL Tube
241 .PP
242 A tube is an inverted cylinder.
243 .LP
244 .UL Ring
245 .PP
246 A ring is a circular disk given by its center, surface
247 normal, and inner and outer radii:
248 .DS
249 mod ring id
250 0
251 0
252 8
253 xcent ycent zcent
254 xdir ydir zdir
255 r0 r1
256 .DE
257 .LP
258 .UL Mesh
259 .PP
260 A mesh is a compound surface, made up of many triangles and
261 an octree data structure to accelerate ray intersection.
262 It is typically converted from a Wavefront .OBJ file using the
263 obj2mesh program.
264 .DS
265 mod mesh id
266 1+ meshfile transform
267 0
268 0
269 .DE
270 The transform moves the mesh to the desired location in the scene.
271 Multiple instances using the same meshfile take little extra memory,
272 and the compiled mesh itself takes much less space than individual
273 polygons would.
274 In the case of an unsmoothed mesh, using the mesh primitive reduces
275 memory requirements by a factor of 30 relative to individual triangles.
276 If a mesh has smoothed surfaces, we save a factor of 50 or more,
277 permitting very detailed geometries that would otherwise exhaust the
278 available memory.
279 In addition, the mesh primitive can have associated (u,v) coordinates
280 for pattern and texture mapping.
281 These are made available to function files via the Lu and Lu variables.
282 .LP
283 .UL Instance
284 .PP
285 An instance is a compound surface, given by the contents of an
286 octree file (created by oconv).
287 .DS
288 mod instance id
289 1+ octree transform
290 0
291 0
292 .DE
293 If the modifier is "void", then surfaces will use the modifiers given
294 in the original description.
295 Otherwise, the modifier specified is used in their place.
296 The transform moves the octree to the desired location in the scene.
297 Multiple instances using the same octree take little extra memory,
298 hence very complex descriptions can be rendered using this primitive.
299 .PP
300 There are a number of important limitations to be aware of when using
301 instances.
302 First, the scene description used to generate the octree must stand on
303 its own, without referring to modifiers in the parent description.
304 This is necessary for oconv to create the octree.
305 Second, light sources in the octree will not be incorporated correctly
306 in the calculation, and they are not recommended.
307 Finally, there is no advantage (other than convenience) to
308 using a single instance of an octree, or an octree containing only a
309 few surfaces.
310 An xform command on the subordinate description is prefered in such cases.
311 .NH 3
312 Materials
313 .PP
314 A material defines the way light interacts with a surface.
315 The basic types are given below.
316 .LP
317 .UL Light
318 .PP
319 Light is the basic material for self-luminous surfaces (i.e. light
320 sources).
321 In addition to the source surface type, spheres, discs (rings with zero
322 inner radius), cylinders (provided they are long enough), and
323 polygons can act as light sources.
324 Polygons work best when they are rectangular.
325 Cones cannot be used at this time.
326 A pattern may be used to specify a light output distribution.
327 Light is defined simply as a RGB radiance value (watts/steradian/m2):
328 .DS
329 mod light id
330 0
331 0
332 3 red green blue
333 .DE
334 .LP
335 .UL Illum
336 .PP
337 Illum is used for secondary light sources with broad distributions.
338 A secondary light source is treated like any other
339 light source, except when viewed directly.
340 It then acts like it is made of a different material (indicated by
341 the string argument), or becomes invisible (if no string argument is given,
342 or the argument is "void").
343 Secondary sources are useful when modeling windows or
344 brightly illuminated surfaces.
345 .DS
346 mod illum id
347 1 material
348 0
349 3 red green blue
350 .DE
351 .LP
352 .UL Glow
353 .PP
354 Glow is used for surfaces that are self-luminous, but limited
355 in their effect.
356 In addition to the radiance value, a maximum radius for
357 shadow testing is given:
358 .DS
359 mod glow id
360 0
361 0
362 4 red green blue maxrad
363 .DE
364 If maxrad is zero, then the surface will never be tested
365 for shadow, although it may participate in an interreflection calculation.
366 If maxrad is negative, then the surface will never contribute to scene
367 illumination.
368 Glow sources will never illuminate objects on the other side of an
369 illum surface.
370 This provides a convenient way to illuminate local light fixture
371 geometry without overlighting nearby objects.
372 .LP
373 .UL Spotlight
374 .PP
375 Spotlight is used for self-luminous surfaces having directed output.
376 As well as radiance, the full cone angle (in degrees)
377 and orientation (output direction) vector are given.
378 The length of the orientation vector is the distance
379 of the effective focus behind the source center (i.e. the focal length).
380 .DS
381 mod spotlight id
382 0
383 0
384 7 red green blue angle xdir ydir zdir
385 .DE
386 .LP
387 .UL Mirror
388 .PP
389 Mirror is used for planar surfaces that produce secondary
390 source reflections.
391 This material should be used sparingly, as it may cause the light
392 source calculation to blow up if it is applied to many small surfaces.
393 This material is only supported for flat surfaces such as polygons
394 and rings.
395 The arguments are simply the RGB reflectance values, which should be
396 between 0 and 1.
397 An optional string argument may be used like the illum type to specify a
398 different material to be used for shading non-source rays.
399 If this alternate material is given as "void", then the mirror surface
400 will be invisible.
401 This is only appropriate if the surface hides other (more detailed)
402 geometry with the same overall reflectance.
403 .DS
404 mod mirror id
405 1 material
406 0
407 3 red green blue
408 .DE
409 .LP
410 .UL Prism1
411 .PP
412 The prism1 material is for general light redirection from prismatic
413 glazings, generating secondary light sources.
414 It can only be used to modify a planar surface (i.e. a polygon or disk)
415 and should not result in either light concentration or scattering.
416 The new direction of the ray can be on either side of the material,
417 and the definitions must have the correct bidirectional properties
418 to work properly with secondary light sources.
419 The arguments give the coefficient for the redirected light
420 and its direction.
421 .DS
422 mod prism1 id
423 5+ coef dx dy dz funcfile transform
424 0
425 n A1 A2 .. An
426 .DE
427 The new direction variables
428 .I "dx, dy"
429 and
430 .I dz
431 need not produce a normalized vector.
432 For convenience, the variables
433 .I "DxA, DyA"
434 and
435 .I DzA
436 are defined as the normalized direction to the target light source.
437 See section 2.2.1 on function files for further information.
438 .LP
439 .UL Prism2
440 .PP
441 The material prism2 is identical to prism1 except that
442 it provides for two ray redirections rather than one.
443 .DS
444 mod prism2 id
445 9+ coef1 dx1 dy1 dz1 coef2 dx2 dy2 dz2 funcfile transform
446 0
447 n A1 A2 .. An
448 .DE
449 .LP
450 .UL Mist
451 .PP
452 Mist is a virtual material used to delineate a volume
453 of participating atmosphere.
454 A list of important light sources may be given, along with an
455 extinction coefficient, scattering albedo and scattering eccentricity
456 parameter.
457 The light sources named by the string argument list
458 will be tested for scattering within the volume.
459 Sources are identified by name, and virtual light sources may be indicated
460 by giving the relaying object followed by '>' followed by the source, i.e:
461 .DS
462 3 source1 mirror1>source10 mirror2>mirror1>source3
463 .DE
464 Normally, only one source is given per mist material, and there is an
465 upper limit of 32 to the total number of active scattering sources.
466 The extinction coefficient, if given, is added to the global
467 coefficient set on the command line.
468 Extinction is in units of 1/distance (distance based on the world coordinates),
469 and indicates the proportional loss of radiance over one unit distance.
470 The scattering albedo, if present, will override the global setting within
471 the volume.
472 An albedo of 0\00\00 means a perfectly absorbing medium, and an albedo of
473 1\01\01\0 means
474 a perfectly scattering medium (no absorption).
475 The scattering eccentricity parameter will likewise override the global
476 setting if it is present.
477 Scattering eccentricity indicates how much scattered light favors the
478 forward direction, as fit by the Heyney-Greenstein function:
479 .DS
480 P(theta) = (1 - g*g) / (1 + g*g - 2*g*cos(theta))^1.5
481 .DE
482 A perfectly isotropic scattering medium has a g parameter of 0, and
483 a highly directional material has a g parameter close to 1.
484 Fits to the g parameter may be found along with typical extinction
485 coefficients and scattering albedos for various atmospheres and
486 cloud types in USGS meteorological tables.
487 (A pattern will be applied to the extinction values.)\0
488 .DS
489 mod mist id
490 N src1 src2 .. srcN
491 0
492 0|3|6|7 [ rext gext bext [ ralb galb balb [ g ] ] ]
493 .DE
494 There are two usual uses of the mist type.
495 One is to surround a beam from a spotlight or laser so that it is
496 visible during rendering.
497 For this application, it is important to use a cone (or cylinder) that
498 is long enough and wide enough to contain the important visible portion.
499 Light source photometry and intervening objects will have the desired
500 effect, and crossing beams will result in additive scattering.
501 For this application, it is best to leave off the real arguments, and
502 use the global rendering parameters to control the atmosphere.
503 The second application is to model clouds or other localized media.
504 Complex boundary geometry may be used to give shape to a uniform medium,
505 so long as the boundary encloses a proper volume.
506 Alternatively, a pattern may be used to set the line integral value
507 through the cloud for a ray entering or exiting a point in a given
508 direction.
509 For this application, it is best if cloud volumes do not overlap each other,
510 and opaque objects contained within them may not be illuminated correctly
511 unless the line integrals consider enclosed geometry.
512 .LP
513 .UL Plastic
514 .PP
515 Plastic is a material with uncolored highlights.
516 It is given by its RGB reflectance, its fraction of specularity,
517 and its roughness value.
518 Roughness is specified as the rms slope of surface facets.
519 A value of 0 corresponds to a perfectly smooth surface, and
520 a value of 1 would be a very rough surface.
521 Specularity fractions greater than 0.1 and
522 roughness values greater than 0.2 are not very
523 realistic.
524 (A pattern modifying plastic will affect the material color.)
525 .DS
526 mod plastic id
527 0
528 0
529 5 red green blue spec rough
530 .DE
531 .LP
532 .UL Metal
533 .PP
534 Metal is similar to plastic, but specular highlights
535 are modified by the material color.
536 Specularity of metals is usually .9 or greater.
537 As for plastic, roughness values above .2 are uncommon.
538 .LP
539 .UL Trans
540 .PP
541 Trans is a translucent material, similar to plastic.
542 The transmissivity is the fraction of penetrating light that
543 travels all the way through the material.
544 The transmitted specular component is the fraction of transmitted
545 light that is not diffusely scattered.
546 Transmitted and diffusely reflected light is modified by the material color.
547 Translucent objects are infinitely thin.
548 .DS
549 mod trans id
550 0
551 0
552 7 red green blue spec rough trans tspec
553 .DE
554 .LP
555 .UL Plastic2
556 .PP
557 Plastic2 is similar to plastic, but with anisotropic
558 roughness.
559 This means that highlights in the surface will appear elliptical rather
560 than round.
561 The orientation of the anisotropy is determined by the unnormalized
562 direction vector
563 .I "ux uy uz".
564 These three expressions (separated by white space) are evaluated in
565 the context of the function file
566 .I funcfile.
567 If no function file is required (i.e. no special variables or
568 functions are required), a period (`.') may be given in its
569 place.
570 (See the discussion of Function Files in the Auxiliary Files section).
571 The
572 .I urough
573 value defines the roughness along the
574 .B u
575 vector given projected onto the surface.
576 The
577 .I vrough
578 value defines the roughness perpendicular to this vector.
579 Note that the highlight will be narrower in the direction of the
580 smaller roughness value.
581 Roughness values of zero are not allowed for efficiency reasons
582 since the behavior would be the same as regular plastic in that
583 case.
584 .DS
585 mod plastic2 id
586 4+ ux uy uz funcfile transform
587 0
588 6 red green blue spec urough vrough
589 .DE
590 .LP
591 .UL Metal2
592 .PP
593 Metal2 is the same as plastic2, except that the highlights are
594 modified by the material color.
595 .LP
596 .UL Trans2
597 .PP
598 Trans2 is the anisotropic version of trans.
599 The string arguments are the same as for plastic2, and the real
600 arguments are the same as for trans but with an additional roughness
601 value.
602 .DS
603 mod trans2 id
604 4+ ux uy uz funcfile transform
605 0
606 8 red green blue spec urough vrough trans tspec
607 .DE
608 .LP
609 .UL Dielectric
610 .PP
611 A dielectric material is transparent, and it refracts light
612 as well as reflecting it.
613 Its behavior is determined by the index of refraction and
614 transmission coefficient in each wavelength band per unit length.
615 Common glass has a index of refraction (n) around 1.5,
616 and a transmission coefficient of roughly 0.92 over an inch.
617 An additional number, the Hartmann constant, describes how
618 the index of refraction changes as a function of wavelength.
619 It is usually zero.
620 (A pattern modifies only the refracted value.)
621 .DS
622 mod dielectric id
623 0
624 0
625 5 rtn gtn btn n hc
626 .DE
627 .LP
628 .UL Interface
629 .PP
630 An interface is a boundary between two dielectrics.
631 The first transmission coefficient and refractive index are for the inside;
632 the second ones are for the outside.
633 Ordinary dielectrics are surrounded by a vacuum (1 1 1 1).
634 .DS
635 mod interface id
636 0
637 0
638 8 rtn1 gtn1 btn1 n1 rtn2 gtn2 btn2 n2
639 .DE
640 .LP
641 .UL Glass
642 .PP
643 Glass is similar to dielectric, but it is optimized for thin glass
644 surfaces (n = 1.52).
645 One transmitted ray and one reflected ray is produced.
646 By using a single surface is in place of two, internal reflections
647 are avoided.
648 The surface orientation is irrelevant, as it is for plastic,
649 metal, and trans.
650 The only specification required is the transmissivity at normal
651 incidence.
652 (Transmissivity is the amount of light not absorbed in one traversal
653 of the material.
654 Transmittance -- the value usually measured -- is the total light
655 transmitted through the pane including multiple reflections.)\0
656 To compute transmissivity (tn) from transmittance (Tn) use:
657 .DS
658 tn = (sqrt(.8402528435+.0072522239*Tn*Tn)-.9166530661)/.0036261119/Tn
659 .DE
660 Standard 88% transmittance glass has a transmissivity of 0.96.
661 (A pattern modifying glass will affect the transmissivity.)
662 If a fourth real argument is given, it is interpreted as the index of
663 refraction to use instead of 1.52.
664 .DS
665 mod glass id
666 0
667 0
668 3 rtn gtn btn
669 .DE
670 .LP
671 .UL Plasfunc
672 .PP
673 Plasfunc in used for the procedural definition of plastic-like
674 materials with arbitrary bidirectional reflectance distribution
675 functions (BRDF's).
676 The arguments to this material include the color and specularity,
677 as well as the function defining the specular distribution and the
678 auxiliary file where it may be found.
679 .DS
680 mod plasfunc id
681 2+ refl funcfile transform
682 0
683 4+ red green blue spec A5 ..
684 .DE
685 The function
686 .I refl
687 takes four arguments, the x, y and z
688 direction towards the incident light, and the solid angle
689 subtended by the source.
690 The solid angle is provided to facilitate averaging, and is usually
691 ignored.
692 The
693 .I refl
694 function should integrate to 1 over
695 the projected hemisphere to maintain energy balance.
696 At least four real arguments must be given, and these are made
697 available along with any additional values to the reflectance
698 function.
699 Currently, only the contribution from direct light sources is
700 considered in the specular calculation.
701 As in most material types, the surface normal is always
702 altered to face the incoming ray.
703 .LP
704 .UL Metfunc
705 .PP
706 Metfunc is identical to plasfunc and takes the same arguments, but
707 the specular component is multiplied also by the material color.
708 .LP
709 .UL Transfunc
710 .PP
711 Transfunc is similar to plasfunc but with an arbitrary bidirectional
712 transmittance distribution as well as a reflectance distribution.
713 Both reflectance and transmittance are specified with the same function.
714 .DS
715 mod transfunc id
716 2+ brtd funcfile transform
717 0
718 6+ red green blue rspec trans tspec A7 ..
719 .DE
720 Where
721 .I trans
722 is the total light transmitted and
723 .I tspec
724 is the non-Lambertian fraction of transmitted light.
725 The function
726 .I brtd
727 should integrate to 1 over each projected hemisphere.
728 .LP
729 .UL BRTDfunc
730 .PP
731 The material BRTDfunc gives the maximum flexibility over surface
732 reflectance and transmittance, providing for spectrally-dependent
733 specular rays and reflectance and transmittance distribution functions.
734 .DS
735 mod BRTDfunc id
736 10+ rrefl grefl brefl
737 rtrns gtrns btrns
738 rbrtd gbrtd bbrtd
739 funcfile transform
740 0
741 9+ rfdif gfdif bfdif
742 rbdif gbdif bbdif
743 rtdif gtdif btdif
744 A10 ..
745 .DE
746 The variables
747 .I "rrefl, grefl"
748 and
749 .I brefl
750 specify the color coefficients for
751 the ideal specular (mirror) reflection of the surface.
752 The variables
753 .I "rtrns, gtrns"
754 and
755 .I btrns
756 specify the color coefficients for the ideal specular transmission.
757 The functions
758 .I "rbrtd, gbrtd"
759 and
760 .I bbrtd
761 take the direction to the incident light (and its solid angle)
762 and compute the color coefficients for the directional diffuse part of
763 reflection and transmission.
764 As a special case, three identical values of '0' may be given in place of
765 these function names to indicate no directional diffuse component.
766 .PP
767 Unlike most other material types, the surface normal is not altered to
768 face the incoming ray.
769 Thus, functions and variables must pay attention to the orientation of
770 the surface and make adjustments appropriately.
771 However, the special variables for the perturbed dot product and surface
772 normal,
773 .I "RdotP, NxP, NyP"
774 and
775 .I NzP
776 are reoriented as if the ray hit the front surface for convenience.
777 .PP
778 A diffuse reflection component may be given for the front side with
779 .I "rfdif, gfdif"
780 and
781 .I bfdif
782 for the front side of the surface or
783 .I "rbdif, gbdif"
784 and
785 .I bbdif
786 for the back side.
787 The diffuse transmittance (must be the same for both sides by physical law)
788 is given by
789 .I "rtdif, gtdif"
790 and
791 .I btdif.
792 A pattern will modify these diffuse scattering values,
793 and will be available through the special variables
794 .I "CrP, CgP"
795 and
796 .I CbP.
797 .PP
798 Care must be taken when using this material type to produce a physically
799 valid reflection model.
800 The reflectance functions should be bidirectional, and under no circumstances
801 should the sum of reflected diffuse, transmitted diffuse, reflected specular,
802 transmitted specular and the integrated directional diffuse component be
803 greater than one.
804 .LP
805 .UL Plasdata
806 .PP
807 Plasdata is used for arbitrary BRDF's that are most conveniently
808 given as interpolated data.
809 The arguments to this material are the data file and coordinate index
810 functions, as well as a function to optionally modify the data
811 values.
812 .DS
813 mod plasdata id
814 3+n+
815 func datafile
816 funcfile x1 x2 .. xn transform
817 0
818 4+ red green blue spec A5 ..
819 .DE
820 The coordinate indices
821 .I "(x1, x2,"
822 etc.) are themselves functions of
823 the x, y and z direction to the incident light, plus the solid angle
824 subtended by the light source (usually ignored).
825 The data function
826 .I (func)
827 takes five variables, the
828 interpolated value from the n-dimensional data file, followed by the
829 x, y and z direction to the incident light and the solid angle of the source.
830 The light source direction and size may of course be ignored by the function.
831 .LP
832 .UL Metdata
833 .PP
834 As metfunc is to plasfunc, metdata is to plasdata.
835 Metdata takes the same arguments as plasdata, but the specular
836 component is modified by the given material color.
837 .LP
838 .UL Transdata
839 .PP
840 Transdata is like plasdata but the specification includes transmittance
841 as well as reflectance.
842 The parameters are as follows.
843 .DS
844 mod transdata id
845 3+n+
846 func datafile
847 funcfile x1 x2 .. xn transform
848 0
849 6+ red green blue rspec trans tspec A7 ..
850 .DE
851 .LP
852 .UL Antimatter
853 .PP
854 Antimatter is a material that can "subtract" volumes from other volumes.
855 A ray passing into an antimatter object becomes blind to all the specified
856 modifiers:
857 .DS
858 mod antimatter id
859 N mod1 mod2 .. modN
860 0
861 0
862 .DE
863 The first modifier will also be used to shade the area leaving the
864 antimatter volume and entering the regular volume.
865 If mod1 is void, the antimatter volume is completely invisible.
866 Antimatter does not work properly with the material type "trans",
867 and multiple antimatter surfaces should be disjoint.
868 The viewpoint must be outside all volumes concerned for a correct
869 rendering.
870 .NH 3
871 Textures
872 .PP
873 A texture is a perturbation of the surface normal, and
874 is given by either a function or data.
875 .LP
876 .UL Texfunc
877 .PP
878 A texfunc uses an auxiliary function file
879 to specify a procedural texture:
880 .DS
881 mod texfunc id
882 4+ xpert ypert zpert funcfile transform
883 0
884 n A1 A2 .. An
885 .DE
886 .LP
887 .UL Texdata
888 .PP
889 A texdata texture uses three data files to get the surface
890 normal perturbations.
891 The variables
892 .I xfunc,
893 .I yfunc
894 and
895 .I zfunc
896 take three arguments
897 each from the interpolated values in
898 .I xdfname,
899 .I ydfname
900 and
901 .I zdfname.
902 .DS
903 mod texdata id
904 8+ xfunc yfunc zfunc xdfname ydfname zdfname vfname x0 x1 .. xf
905 0
906 n A1 A2 .. An
907 .DE
908 .NH 3
909 Patterns
910 .PP
911 Patterns are used to modify the reflectance of materials.
912 The basic types are given below.
913 .LP
914 .UL Colorfunc
915 .PP
916 A colorfunc is a procedurally defined color pattern.
917 It is specified as follows:
918 .DS
919 mod colorfunc id
920 4+ red green blue funcfile transform
921 0
922 n A1 A2 .. An
923 .DE
924 .LP
925 .UL Brightfunc
926 .PP
927 A brightfunc is the same as a colorfunc, except it is monochromatic.
928 .DS
929 mod brightfunc id
930 2+ refl funcfile transform
931 0
932 n A1 A2 .. An
933 .DE
934 .LP
935 .UL Colordata
936 .PP
937 Colordata uses an interpolated data map to modify a material's color.
938 The map is n-dimensional, and is stored in three
939 auxiliary files, one for each color.
940 The coordinates used to look up and interpolate the data are
941 defined in another auxiliary file.
942 The interpolated data values are modified by functions of
943 one or three variables.
944 If the functions are of one variable, then they are passed the
945 corresponding color component (red or green or blue).
946 If the functions are of three variables, then they are passed the
947 original red, green, and blue values as parameters.
948 .DS
949 mod colordata id
950 7+n+
951 rfunc gfunc bfunc rdatafile gdatafile bdatafile
952 funcfile x1 x2 .. xn transform
953 0
954 m A1 A2 .. Am
955 .DE
956 .LP
957 .UL Brightdata
958 .PP
959 Brightdata is like colordata, except monochromatic.
960 .DS
961 mod brightdata id
962 3+n+
963 func datafile
964 funcfile x1 x2 .. xn transform
965 0
966 m A1 A2 .. Am
967 .DE
968 .LP
969 .UL Colorpict
970 .PP
971 Colorpict is a special case of colordata, where the pattern is
972 a two-dimensional image stored in the RADIANCE picture format.
973 The dimensions of the image data are determined by the picture
974 such that the smaller dimension is always 1, and the other
975 is the ratio between the larger and the smaller.
976 For example, a 500x338 picture would have coordinates (u,v)
977 in the rectangle between (0,0) and (1.48,1).
978 .DS
979 mod colorpict id
980 7+
981 rfunc gfunc bfunc pictfile
982 funcfile u v transform
983 0
984 m A1 A2 .. Am
985 .DE
986 .LP
987 .UL Colortext
988 .PP
989 Colortext is dichromatic writing in a polygonal font.
990 The font is defined in an auxiliary file, such as
991 .I helvet.fnt.
992 The text itself is also specified in a separate file, or
993 can be part of the material arguments.
994 The character size, orientation, aspect ratio and slant is
995 determined by right and down motion vectors.
996 The upper left origin for the text block as well as
997 the foreground and background colors
998 must also be given.
999 .DS
1000 mod colortext id
1001 2 fontfile textfile
1002 0
1003 15+
1004 Ox Oy Oz
1005 Rx Ry Rz
1006 Dx Dy Dz
1007 rfore gfore bfore
1008 rback gback bback
1009 [spacing]
1010 .DE
1011 or:
1012 .DS
1013 mod colortext id
1014 2+N fontfile . This is a line with N words ...
1015 0
1016 15+
1017 Ox Oy Oz
1018 Rx Ry Rz
1019 Dx Dy Dz
1020 rfore gfore bfore
1021 rback gback bback
1022 [spacing]
1023 .DE
1024 .LP
1025 .UL Brighttext
1026 .PP
1027 Brighttext is like colortext, but the writing is monochromatic.
1028 .DS
1029 mod brighttext id
1030 2 fontfile textfile
1031 0
1032 11+
1033 Ox Oy Oz
1034 Rx Ry Rz
1035 Dx Dy Dz
1036 foreground background
1037 [spacing]
1038 .DE
1039 or:
1040 .DS
1041 mod brighttext id
1042 2+N fontfile . This is a line with N words ...
1043 0
1044 11+
1045 Ox Oy Oz
1046 Rx Ry Rz
1047 Dx Dy Dz
1048 foreground background
1049 [spacing]
1050 .DE
1051 .LP
1052 By default, a uniform spacing algorithm is used that guarantees
1053 every character will appear in a precisely determined position.
1054 Unfortunately, such a scheme results in rather unattractive and difficult to
1055 read text with most fonts.
1056 The optional
1057 .I spacing
1058 value defines the distance between characters for proportional spacing.
1059 A positive value selects a spacing algorithm that preserves right margins and
1060 indentation, but does not provide the ultimate in proportionally spaced text.
1061 A negative value insures that characters are properly spaced, but the
1062 placement of words then varies unpredictably.
1063 The choice depends on the relative importance of spacing versus formatting.
1064 When presenting a section of formatted text, a positive spacing value is
1065 usually preferred.
1066 A single line of text will often be accompanied by a negative spacing value.
1067 A section of text meant to depict a picture, perhaps using a special purpose
1068 font such as hexbit4x1.fnt, calls for uniform spacing.
1069 Reasonable magnitudes for proportional spacing are
1070 between 0.1 (for tightly spaced characters) and 0.3 (for wide spacing).
1071 .NH 3
1072 Mixtures
1073 .PP
1074 A mixture is a blend of one or more materials or textures and patterns.
1075 The basic types are given below.
1076 .LP
1077 .UL Mixfunc
1078 .PP
1079 A mixfunc mixes two modifiers procedurally.
1080 It is specified as follows:
1081 .DS
1082 mod mixfunc id
1083 4+ foreground background vname funcfile transform
1084 0
1085 n A1 A2 .. An
1086 .DE
1087 Foreground and background are modifier names that must be
1088 defined earlier in the scene description.
1089 If one of these is a material, then
1090 the modifier of the mixfunc must be "void".
1091 (Either the foreground or background modifier may be "void",
1092 which serves as a form of opacity control when used with a material.)\0
1093 Vname is the coefficient defined in funcfile that determines the influence
1094 of foreground.
1095 The background coefficient is always (1-vname).
1096 Since the references are not resolved until runtime, the last
1097 definitions of the modifier id's will be used.
1098 This can result in modifier loops, which are detected by the
1099 renderer.
1100 .LP
1101 .UL Mixdata
1102 .PP
1103 Mixdata combines two modifiers using an auxiliary data file:
1104 .DS
1105 mod mixdata id
1106 5+n+
1107 foreground background func datafile
1108 funcfile x1 x2 .. xn transform
1109 0
1110 m A1 A2 .. Am
1111 .DE
1112 .LP
1113 .UL Mixpict
1114 .PP
1115 Mixpict combines two modifiers based on a picture:
1116 .DS
1117 mod mixpict id
1118 7+
1119 foreground background func pictfile
1120 funcfile u v transform
1121 0
1122 m A1 A2 .. Am
1123 .DE
1124 The mixing coefficient function "func" takes three
1125 arguments, the red, green and blue values
1126 corresponding to the pixel at (u,v).
1127 .LP
1128 .UL Mixtext
1129 .PP
1130 Mixtext uses one modifier for the text foreground, and one for the
1131 background:
1132 .DS
1133 mod mixtext id
1134 4 foreground background fontfile textfile
1135 0
1136 9+
1137 Ox Oy Oz
1138 Rx Ry Rz
1139 Dx Dy Dz
1140 [spacing]
1141 .DE
1142 or:
1143 .DS
1144 mod mixtext id
1145 4+N
1146 foreground background fontfile .
1147 This is a line with N words ...
1148 0
1149 9+
1150 Ox Oy Oz
1151 Rx Ry Rz
1152 Dx Dy Dz
1153 [spacing]
1154 .DE
1155 .NH 2
1156 Auxiliary Files
1157 .PP
1158 Auxiliary files used in textures and patterns
1159 are accessed by the programs during image generation.
1160 These files may be located in the working directory, or in
1161 a library directory.
1162 The environment variable
1163 .I RAYPATH
1164 can be assigned an alternate set of search directories.
1165 Following is a brief description of some common file types.
1166 .NH 3
1167 Function Files
1168 .PP
1169 A function file contains the definitions of variables, functions
1170 and constants used by a primitive.
1171 The transformation that accompanies the file name contains the necessary
1172 rotations, translations and scalings to bring the coordinates of
1173 the function file into agreement with the world coordinates.
1174 The transformation specification is the same as for the
1175 .I xform
1176 command.
1177 An example function file is given below:
1178 .DS
1179 {
1180 This is a comment, enclosed in curly braces.
1181 {Comments can be nested.}
1182 }
1183 { standard expressions use +,-,*,/,^,(,) }
1184 vname = Ny * func(A1) ;
1185 { constants are defined with a colon }
1186 const : sqrt(PI/2) ;
1187 { user-defined functions add to library }
1188 func(x) = 5 + A1*sin(x/3) ;
1189 { functions may be passed and recursive }
1190 rfunc(f,x) = if(x,f(x),f(-x)*rfunc(f,x+1)) ;
1191 { constant functions may also be defined }
1192 cfunc(x) : 10*x / sqrt(x) ;
1193 .DE
1194 Many variables and functions are already defined by the program,
1195 and they are listed in the file
1196 .I rayinit.cal.
1197 The following variables are particularly important:
1198 .DS
1199 Dx, Dy, Dz - incident ray direction
1200 Px, Py, Pz - intersection point
1201 Nx, Ny, Nz - surface normal at intersection point
1202 Rdot - cosine between ray and normal
1203 arg(0) - number of real arguments
1204 arg(i) - i'th real argument
1205 .DE
1206 For BRDF types, the following variables are defined as well:
1207 .DS
1208 NxP, NyP, NzP - perturbed surface normal
1209 RdotP - perturbed dot product
1210 CrP, CgP, CbP - perturbed material color
1211 .DE
1212 A unique context is set up for each file so that the same variable
1213 may appear in different function files without conflict.
1214 The variables listed above and any others defined in
1215 rayinit.cal are available globally.
1216 If no file is needed by a given primitive because all the required
1217 variables are global, a period (`.') can be given in
1218 place of the file name.
1219 It is also possible to give an expression instead of a straight
1220 variable name in a scene file, although such expressions should
1221 be kept simple as they cannot contain any white space.
1222 Also, functions (requiring parameters)
1223 must be given as names and not as expressions.
1224 .PP
1225 Constant expressions are used as an optimization in function
1226 files.
1227 They are replaced wherever they occur in an expression by their
1228 value.
1229 Constant expressions are evaluated only once, so they must not
1230 contain any variables or values that can change, such as the ray
1231 variables Px and Ny or the primitive argument function arg().
1232 All the math library functions such as sqrt() and cos() have the
1233 constant attribute, so they will be replaced by immediate values
1234 whenever they are given constant arguments.
1235 Thus, the subexpression cos(PI*sqrt(2)) is immediately replaced
1236 by its value, -.266255342, and does not cause any additional overhead
1237 in the calculation.
1238 .PP
1239 It is generally a good idea to define constants and variables before
1240 they are referred to in a function file.
1241 Although evaluation does not take place until later, the interpreter
1242 does variable scoping and constant subexpression evaluation based on
1243 what it has compiled already.
1244 For example, a variable that is defined globally in rayinit.cal then
1245 referenced in the local context of a function file cannot
1246 subsequently be redefined in the same file because the compiler
1247 has already determined the scope of the referenced variable as global.
1248 To avoid such conflicts, one can state the scope of a variable explicitly
1249 by preceding the variable name with a context mark (a back-quote) for
1250 a local variable, or following the name with a context mark for a global
1251 variable.
1252 .NH 3
1253 Data Files
1254 .PP
1255 Data files contain n-dimensional arrays of real numbers used
1256 for interpolation.
1257 Typically, definitions in a function file determine how
1258 to index and use interpolated data values.
1259 The basic data file format is as follows:
1260 .DS
1261 N
1262 beg1 end1 m1
1263 0 0 m2 x2.1 x2.2 x2.3 x2.4 .. x2.m2
1264 ...
1265 begN endN mN
1266 DATA, later dimensions changing faster.
1267 .DE
1268 N is the number of dimensions.
1269 For each dimension, the beginning and ending coordinate
1270 values and the dimension size is given.
1271 Alternatively, individual coordinate values can be given when
1272 the points are not evenly spaced.
1273 These values must either be increasing or decreasing monotonically.
1274 The data is m1*m2*...*mN real numbers in ASCII form.
1275 Comments may appear anywhere in the file, beginning with a pound
1276 sign ('#') and continuing to the end of line.
1277 .NH 3
1278 Font Files
1279 .PP
1280 A font file lists the polygons which make up a character set.
1281 Comments may appear anywhere in the file, beginning with a pound
1282 sign ('#') and continuing to the end of line.
1283 All numbers are decimal integers:
1284 .DS
1285 code n
1286 x0 y0
1287 x1 y1
1288 ...
1289 xn yn
1290 ...
1291 .DE
1292 The ASCII codes can appear in any order.
1293 N is the number of vertices, and the last is automatically
1294 connected to the first.
1295 Separate polygonal sections are joined by coincident sides.
1296 The character coordinate system is a square with lower left corner at
1297 (0,0), lower right at (255,0) and upper right at (255,255).
1298 .NH 2
1299 Generators
1300 .PP
1301 A generator is any program that produces a scene description
1302 as its output.
1303 They usually appear as commands in a scene description file.
1304 An example of a simple generator is
1305 .I genbox.
1306 .I Genbox
1307 takes the arguments of width, height and depth to produce
1308 a parallelepiped description.
1309 .I Genprism
1310 takes a list of 2-dimensional coordinates and extrudes them along a vector to
1311 produce a 3-dimensional prism.
1312 .I Genrev
1313 is a more sophisticated generator
1314 that produces an object of rotation from parametric functions
1315 for radius and axis position.
1316 .I Gensurf
1317 tessellates a surface defined by the
1318 parametric functions x(s,t), y(s,t), and z(s,t).
1319 .I Genworm
1320 links cylinders and spheres along a curve.
1321 .I Gensky
1322 produces a sun and sky distribution corresponding
1323 to a given time and date.
1324 .PP
1325 .I Xform
1326 is a program that transforms a scene description from one
1327 coordinate space to another.
1328 .I Xform
1329 does rotation, translation, scaling, and mirroring.
1330 .NH 1
1331 Image Generation
1332 .PP
1333 Once the scene has been described in three-dimensions, it
1334 is possible to generate a two-dimensional image from a
1335 given perspective.
1336 .PP
1337 The image generating programs use an
1338 .I octree
1339 to efficiently trace rays through the scene.
1340 An octree subdivides space into nested octants which
1341 contain sets of surfaces.
1342 In RADIANCE, an octree is created from a scene description by
1343 .I oconv.
1344 The details of this process are not important,
1345 but the octree will serve as input to the ray-tracing
1346 programs and directs the use of a scene description.
1347 .PP
1348 .I Rview
1349 is ray-tracing program for viewing a scene interactively.
1350 When the user specifies a new perspective,
1351 .I rview
1352 quickly displays a rough
1353 image on the terminal, then progressively
1354 increases the resolution as the user looks on.
1355 He can select a particular section of the image to improve,
1356 or move to a different view and start over.
1357 This mode of interaction is useful for debugging scenes
1358 as well as determining the best view for a final image.
1359 .PP
1360 .I Rpict
1361 produces a high-resolution picture of a scene from
1362 a particular perspective.
1363 This program features adaptive sampling, crash
1364 recovery and progress reporting, all of which are important
1365 for time-consuming images.
1366 .PP
1367 A number of filters are available for manipulating picture files.
1368 .I Pfilt
1369 sets the exposure and performs anti-aliasing.
1370 .I Pcompos
1371 composites (cuts and pastes) pictures.
1372 .I Pcond
1373 conditions a picture for a specific display device.
1374 .I Pcomb
1375 performs arbitrary math on one or more pictures.
1376 .I Protate
1377 rotates a picture 90 degrees clockwise.
1378 .I Pflip
1379 flips a picture horizontally, vertically, or both (180 degree rotation).
1380 .I Pvalue
1381 converts a picture to and from simpler formats.
1382 .PP
1383 Pictures may be displayed directly under X11 using the program
1384 .I ximage,
1385 or converted a standard image format.
1386 .I Ra_avs
1387 converts to and from AVS image format.
1388 .I Ra_pict
1389 converts to Macintosh 32-bit PICT2 format.
1390 .I Ra_ppm
1391 converts to and from Poskanzer Portable Pixmap formats.
1392 .I Ra_pr
1393 converts to and from Sun 8-bit rasterfile format.
1394 .I Ra_pr24
1395 converts to and from Sun 24-bit rasterfile format.
1396 .I Ra_ps
1397 converts to PostScript color and greyscale formats.
1398 .I Ra_rgbe
1399 converts to and from Radiance uncompressed picture format.
1400 .I Ra_t16
1401 converts to and from Targa 16 and 24-bit image formats.
1402 .I Ra_t8
1403 converts to and from Targa 8-bit image format.
1404 .I Ra_tiff
1405 converts to and from TIFF.
1406 .I Ra_xyze
1407 converts to and from Radiance CIE picture format.
1408 .NH 1
1409 License
1410 .PP
1411 Radiance is a registered copyright of The Regents of the University of
1412 California ("The Regents"). The Regents grant to you a nonexclusive,
1413 nontransferable license ("License") to use Radiance source code without fee.
1414 You may not sell or distribute Radiance to others without the prior express
1415 written permission of The Regents.
1416 You may compile and use this software on any machines to which you have
1417 personal access, and may share its use with others who have access to the
1418 same machines.
1419 .PP
1420 NEITHER THE UNITED STATES NOR THE UNITED STATES DEPARTMENT OF ENERGY, NOR ANY
1421 OF THEIR EMPLOYEES, MAKES ANY WARRANTY, EXPRESS OR IMPLIED, OR ASSUMES ANY
1422 LEGAL LIABILITY OR RESPONSIBILITY FOR THE ACCURACY, COMPLETENESS, OR
1423 USEFULNESS OF ANY INFORMATION, APPARATUS, PRODUCT, OR PROCESS DISCLOSED, OR
1424 REPRESENTS THAT ITS USE WOULD NOT INFRINGE PRIVATELY OWNED RIGHTS.
1425 By downloading, using or copying this software, you agree to abide by the
1426 intellectual property laws and all other applicable laws of the United
1427 States, and by the terms of this License Agreement. Ownership of the software
1428 shall remain solely in The Regents.
1429 The Regents shall have the right to terminate this License immediately by
1430 written notice upon your breach of, or noncompliance with, any of its terms.
1431 You shall be liable for any infringement or damages resulting from your
1432 failure to abide by the terms of this License Agreement.
1433 .PP
1434 NOTICE: The Government is granted for itself and others acting on its behalf
1435 a paid-up, nonexclusive irrevocable worldwide license in this data to
1436 reproduce, prepare derivative works, and perform publicly and display
1437 publicly. Beginning five (5) years after permission to assert copyright is
1438 granted, subject to two possible five year renewals, the Government is
1439 granted for itself and others acting on its behalf a paid-up, non-exclusive,
1440 irrevocable worldwide license in this data to reproduce, prepare derivative
1441 works, distribute copies to the public, perform publicly and display
1442 publicly, and to permit others to do so.
1443 .NH 1
1444 Acknowledgements
1445 .PP
1446 This work was supported by the Assistant Secretary of Conservation
1447 and Renewable Energy, Office of Building Energy Research and
1448 Development, Buildings Equipment Division of the U.S. Department of
1449 Energy under Contract No. DE-AC03-76SF00098.
1450 .PP
1451 Additional work was sponsored by the Swiss federal government
1452 under the Swiss LUMEN Project and was
1453 carried out in the Laboratoire d'Energie Solaire (LESO Group) at
1454 the Ecole Polytechnique Federale de Lausanne (EPFL University)
1455 in Lausanne, Switzerland.
1456 .NH 1
1457 References
1458 .LP
1459 Ward, G.,
1460 ``The Radiance Lighting Simulation and Rendering System,''
1461 .I "Computer Graphics",
1462 Orlando, July 1994.
1463 .LP
1464 Rushmeier, H., G. Ward,
1465 ``Energy-Preserving Non-Linear Filters,''
1466 .I "Computer Graphics",
1467 Orlando, July 1994.
1468 .LP
1469 Ward, G.,
1470 ``A Contrast-Based Scalefactor for Luminance Display,''
1471 .I "Graphics Gems IV",
1472 Edited by Paul Heckbert,
1473 Academic Press 1994.
1474 .LP
1475 Ward, G.,
1476 ``Measuring and Modeling Anisotropic Reflection,''
1477 .I "Computer Graphics",
1478 Chicago, July 1992.
1479 .LP
1480 Ward, G., P. Heckbert,
1481 ``Irradiance Gradients,''
1482 .I "Third Annual Eurographics Workshop on Rendering",
1483 to be published by Springer-Verlag, held in Bristol, UK, May 1992.
1484 .LP
1485 Ward, G.,
1486 ``Adaptive Shadow Testing for Ray Tracing,''
1487 .I "Second Annual Eurographics Workshop on Rendering",
1488 to be published by Springer-Verlag, held in Barcelona, SPAIN, May 1991.
1489 .LP
1490 Ward, G.,
1491 ``Visualization,''
1492 .I "Lighting Design and Application",
1493 Vol. 20, No. 6, June 1990.
1494 .LP
1495 Ward, G., F. Rubinstein, R. Clear,
1496 ``A Ray Tracing Solution for Diffuse Interreflection,''
1497 .I "Computer Graphics",
1498 Vol. 22, No. 4, August 1988.
1499 .LP
1500 Ward, G., F. Rubinstein,
1501 ``A New Technique for Computer Simulation of Illuminated Spaces,''
1502 .I "Journal of the Illuminating Engineering Society",
1503 Vol. 17, No. 1, Winter 1988.