AFIPS
CONFERENCE PROCEEDINGS
VOLUME 36
1970
SPRI NG JOI NT COMPUTER CONFERENCE
May 5 -7, 1970
Atlantic City, New Jersey
The ideas and opinions expressed herein are solely those of the authors and are not necessarily representative of or endorsed by the 1970 Spring Joint Computer Con- ference Committee or the American Federation of InformatioQ- Processing Societies.
Library of Congress Catalog Card Number 55-44701 AFIPS PRESS
210 Summit Avenue Montvale, New Jersey 07645 ~
©1970 by the American Federation of Information Processing Societies, Montvale, New .Jersey 07645. All rights reserved. This book, or parts thereof, may not be reproduced in any form without permission of the publisher.
Printed in the United States of America
CONTENTS
GRAPHICS-TELLING IT LIKE IT IS
An algorithm for producing half-tone computer graphics presentations with shadows and movable light sources ... . The case for a generalized graphic problem solver ... .
PATENTS AND COPYRIGHTS
(A Panel Session-No Papers in this Volume) 1\1ULTIPROCESSORS FOR l\1ILITARY SYSTEl\1S
(A Panel Session-No Papers in this Volume)
THE INFORMATION UTILITY AND SOCIAL CHOICE (A Panel Session-No Papers in this Volume)
ANALOG-HYBRID
A variance reduction technique for hybrid computer generated random walk solutions of partial differential equations ... . Design of automatic patching systems for analog computers ... . 18 Bit digital to analog conversion ... . A hybrid computer method for the analysis of time dependent river pollution problems. ~ ... . PROGRAl\1 TRANSFERABILITY
(Panel Session-No Papers in this Volume) COl\1PUTING IN STATE GOVERNl\1ENT
(Panel Session-No Papers in this Volume) TOPICS OF SPECIFIC INTEREST
Programmable indexing networks ... . The debugging system AIDS ... . Sequential feature extraction for waveform recognition ... . Pulse amplitude transmission system (PATSY) ... . ALGORITHl\1IC STRUCTURES
Termination of programs represented as interpreted graphs ... . A planarity algorithm based on the Kuratowski theorem ... . Combinational arithmetic systems for the approximation of functions
OPERATING SYSTEl\'lS
Operating systems architecture ... : ... . Computer resource accounting in a time sllaring environment ... .
1 11
19 31 39 43
51 59 65 77
83 91 95
109 119
J. Bouknight K. Kelley E. H. Sibley R. W. Taylor W. L. Ash
E. L. Johnson T. J. Gracon J. Raamot R. Vichnevetsky A. Tomalesky
K. Thurber R. Grishman S. Yau
W. J. Steingrandt N. Walters
Z. l\1anna N. Gibbs P. l\1ei C. Tung A. Avizienis
H. Katzan, Jr.
L. Selwyn
.:Vlultiple consoles-A basis for communication growth in large systems Hardware aspects of secure computing ... . TICKETRON-A successfully operating system without an operating system ... . ':Vlanipulation of data structures in a numerical analysis problem solving system-NAPSS ... . ::'VIICRO PROGRAl\LUING
A study of user-micro programmable computers ... . Firmware sort processor with LSI components ... . System/360 model 85 microdiagnostics ... ; ... . Use of read only memory in ILLIAC IV ... . LESSONS OF THE SIXTIES
(Panel Session-No Papers in this Volume) DIGITAL SIlVIULATION APPLICATIONS
A model and implementation of a universal time delay simulator for large digital nets ... .
UTS-I: A macro system for traffic network simulation ... . Real time space vehicle and ground support systems software simulator for launch programs checkout ... .
Remote real-time simulation ... . l\,fARSYAS-A software system for the digital simulation of physical
systems ... .
COlVIPUTERS IN EDUCATION: lVIECHANIZING HU~VrANS OR HUl\1ANIZING lVIACHINES
(A Panel Session-No Papers in this Volume) PROPRIETARY SOFTWARE-in the 1970's
(A Panel Session-No Papers in this Volume) HU1\1ANITIES
Picturelab-An interactive facility for experimentation in picture processing ... .
Power to the computers-A revolution in history? ... . l\1usic and the computer in the sixties ... . Natural language processing for stylistic analysis ... .
131 135 143
157
165 183 191 197
207
217 223
237
251
267
275 281 287
D. Andrews R. Radice L. l\IIolho H. Dubner J. Abate L. Symes
C. Ramamoorthy lVI. Tsuchiya H. Barsamian
N. Bartow R. l\1cGuire H. White E. K. C. Yu
A. Szygenda D. Rouse E. Thompson H. l\!Iorgan H. Trauboth
C. Rigby P. Brown R. Gerard O. Serlin H. Trauboth N. Prasad
W. Bartlett E. Arthurs D. Ladd R. Salmon J. Whipple S. Hackney R. Erickson H. Donow
INFOR1VIATION MANAGEl\1ENT SYSTEl\1S-FOUNDATION AND FUTURE
An approach to the development of an advanced information management system." ... . The dataBASIC language-A data processing language for
non-professional programmers ... . LISTAR-Lincoln Information Storage and Associative ... .
All-automatic processing for a large library .... ! - ' • • • • • • • • • • • • • • • • •
N aturallanguage inquiry to an open-ended data library ... . SYSTEM ARCHITECTURE
Computer instruction repertoire-Time for a change ... . The PlVIS and ISP descriptive systems for computer structures .... . Reliability analysis and architecture of a hybrid-redundant digital system: Generalized triple modular redundancy with self-repair ...
The architecture of a large associative processor ... '.' ... . NUl\1ERICAL ANALYSIS
Application of invariant imbedding to the solution of partial
differential equations by the continuous-space discrete-time method An initial value formulation for the CSDT method of solving partial
differential equations ... .' ... . An application of Hockney's method for solving Poisson's equation ..
Architecture of a real-time fast fourier radar signal ... . An improved generalized inverse algorithm for linear inequalities and
its applications ... .
SON OF SEPARATE PRICING
(Panel Session-No Papers in this Volume) SOCIAL Il\1PLICATIONS
The social impact of computers ... . COJ\1PUTER SYSTEl\1 l\10DELING AND ANALYSIS
A continum of time-sharing scheduling algorithms ... . The management of a multi-level non-paged memory system ... .
A study of interleaved memory systems ... .
297
3p7 313
323 333
343 351
375 385
397 403 409 417
437
449
453 459
467
J. l\1yers S. Chooljian P. Dressen A. Armenti S. Galley R. Goldberg J. Nolan A. Sholl N. Prywes B. Litofsky G. Potts
C. Church C. Bell A. Newell F. l\1athur A. Avizienis G. Lipovski
P. Nelson, Jr.
V. Vemuri R. Colony R. Reynolds S. Wong A. Zukin L. Geary C. Li
O. Dial
L. Kleinrock F. Baskett J. Browne W. Raike G.Burnett E. Coffman, Jr.
lV[EDICAL-DENTAL APPLICATIONS
A computer system for bedside medical research ... .
Linear programming in clinical dental education ... . Automatic computer recognition and analysis of dental x-ray film .. .
PROGRAl\llVIING LJiNGUAGES
A translation grammar for ALGOL 68 ... . BALl\1-An extendable list-processing language ... . Design and organization of a translator for a partial differential equation language ... . SCROLL-A pattern recording language ... . Al\-1TRAN-An interactive computing system ... .
RESOURCE SHARING C01\1PUTER NETWORKS
Computer network development to achieve resource sharing ... . The interface message processor for the ARPA computer network .. .
Analytic and simulation methods in computer network design ... . Topological considerations in the design of the ARPA computer network ... " ... .
HOST-HOST Communication protocol in the ARPA network ... .
REQUIRElVIENTS FOR DATA BASE l\1ANAGEl\1ENT (Panel Session---..:No Papers in this Volume)
l\/IAN-l\1ACHINE INTERFACE
A comparative stydy of management decision-lVlaking from
computer-terminals ... . An interactive keyboard for man-computer communication ... . Linear current division in resistive areas: Its application to computer graphics ... . Remote terminal character stream processing of multics ... . ARTIFICIAL INTELLIGENCE
A study of heuristic learning methods for optimization tasks requiring a sequence of decisions ... . l\1an-machine interaction for the discovery of h!gh-level patterns ... . Completeness results for E-resolution ... .
475
485 487
493 .507 513 525 537
543 551
569 581
589
599 607 613 621
629 649 653
S. Wixson E. Strand H. Perlis C. Crandell D. Levine H. Hopf lVI. Shakun V. Schneider 1\1. Harrison A. Cardenas W. Karplus l\1. Sargent III J. Reinfelds N. Eskelson H. Kopetz G. Kratky
L. Roberts F. Heart
R. Kahn S. Ornstein W. Crowther D. Walden L. Kleinrock H. Frank 1. Frisch W. Chou S. Carr S. Crocker V. Cerf
C. Jones J. Hughes L. Wear J. Turner G. Ritchie J. Ossanna J. Saltzer
L. Huesmann D. Foster R. Anderson
DATA COlVIlVION CARRIERS FOR THE SEVENTIES (A Panel Session-No Papers in this volume)
~VIINICOlVIPUTERS-THE PROFILE OF TO:.\'IORROW'S CONIPONENTS
A ne\v architecture for mini-computers-the DEC PDP-ll ... .
A systems approach to minicomputer I/O ... . A multiprogramming, virtual memory system for a small computer ..
Applications and implications of mini-computers ... . BUSINESS, COlVIPUTERS, AND PEOPLE?
Teleprocessing systems software for a large corporation information system ... ' ... . The selection and training of computer personnel at the Social Security Administration. . . . ... . PROCESS CONTROL
(A Panel Session-No Papers in this Volume)
657
677 683 691
697
711
G. Bell R. Cady H. NlcFarland B. Delagi J. O'Laughlin R. Noonan W. Wulf
F. Coury C. Christensen A. Hause G. Hendrie C. Ne\vport
H. Liu D. Holmes E. Coady
Editor's Note:
Due to the recent embargo of mail, several papers went to press without author and/or proofreader corrections.
An algorithm for producing half-tone computer graphics presentations with shadows and movable
light sources
by J. BOUKNIGHT and K. KELLEY University of Illinois
Urbana, Illinois
INTRODUCTION
In the years since the introduction of SKETCHPAD an increasing number of graphics systems for line draw- ing have been developed. Software packages are now available to do such things as picture definition, ro- tation and translation of picture data, and production of animated movies and microfilm. Automatic window- ing, three-dimensional figures, depth cueing by inten- sity, and even stereo line drawing are now feasible and in some cases, available in hardware.
Even with all these capabilities, however, represen- tation of three-dimensional data is not quite satis- factory. Representing a solid object by lines which define its edges leads to the computer generated un- reality of being able to see through solid objects. In recent years, research centered around means for com- puter graphical display of structural figures and data has begun to move from display of "wire-frame"
structures where the "wires" represent the edges of the surfaces of the structures, to the display of struc- tures using surface definition techniques to enhance the three-dimensional appearance of the final result.
Several efforts have been concentrated on producing graphical output which is similar to the half-tone commellCial printing process.
The work of Evans, et aI., at the University of Utah! established the feasibility of using a computer to produce half-tone images. Their algorithm processes structures whose surfaces are made up of planar tri- angles. The algorithm employs a raster scan and examines crossing points of the boundaries of the tri- angles by the scanning ray. A significant feature of their method is that the increase in computing time is linear as the resolution of the picture increases.
John Warnock's algorithm for half-tone picture repre- sentation employs a different technique.2 He divides the
1
scene recursively into quarters until all detail in a given square is known or the smallest size square is reached. The result is a set of "key squares", that is intensity change points, along the visible edges in the scene. The time required for this algorithm varies linearly as the total length of the visible edges in the picture, but varies also as the square of the raster size.
An important' feature of the Warnock algorithm is that it handles the occurrence of the intersection of two planes without having to precalculate the line of inter- section.
A t the General Electric Electronics Research Labora- tory in Syracuse, a system which combines both hard- ware and software to produce color half-tone image~ in real time has been developed for NASA as a simulator for rendezvous and docking training. This device can hold up a 600 X 600 raster point picture of up to 240 edges, in color, and change the picture as quickly as the beam scans the screen. 3
The work of the computer group at the Coordinated Science Laboratory began as an effort to add some realism to line drawings of structures being generated by R. Resch, who, while working in the laboratory, was also a member of the faculty of the Department
cif
Architecture. Through his acquaintance with J. Wa~
nock, we were able to implement a version of the Warnock algorithm which operates on the CDC 1604.
After several re.visions of the implementation and some fine tuning of the CRT display hardware, black and white half-tone images of the Resch structures were exhibited at the Computer Graphics Conference at the University of Illinois in April of 1969.
In discussions with J. Warnock and Robert Schu- macher of General Electric, we envisioned a hidden surface algorithm using a scanline technique combining the recursiveness of the Warnock algorithm with the hardware techniques used in the NASA simulator.
2 Spring Joint Computer Conference, 1970
These discussions were the impetus for the development of the LINESCAN algorithm.4 It was for this imple- mentation that laboratory engineers added a raster scan operation to the display hardware. As a result, the algorithm does not have to provide the scope with an item of data for each and every point. Only the location of an intensity change on the scanline and the new magnitude of the intensity are needed. In addition, the display hardware was modified to allow 256 levels of intensity under program control.
N either of the previously mentioned algorithms for half-tone images represented the picture with a light source located away from the observer position, al- though both regard it as a next step in development.
Moving the light source away from the observer po- sition presents the problem of cJ~st sgadows. Arthur Appel's work approaches the shadow problem and the hidden line or surface problem simultaneously.5 His algorithm also scans the picture description in a linescan manner. The question of which parts of which surfaces are visible is answered by a technique called "quanti- tative invisibility6". His structures are composed of planar polygonal surfaces. Appel also includes the ability to handle multiple illumination sources and the shadows cast due to those sources. His shadow boun- daries are computed by projecting points incrementally along the edge of a shading polygon to the surface which will be shaded.
The work of the Computer Group at the Coordinated Science Laboratory to move the ·light away from the observer began shortly after the completion of the LINES CAN algorithm. Augmentation of the original LINESCAN method with a dual scan for shadows cast upon the surfaces presents two questions.
First, the number of projected shadows to be calcu- lated must be kept to a minimum; but the technique for narrowing the set of polygon pairs must be simple.
For a single illumination source, we are constrained by the fact that for n polygons, there are n(n - 1) pairs to be considered. The method chosen to narrow the set of shadow casting and receiving polygons was to project the polygons onto a sphere centered at the light source and make some gross comparisons of maxi- mum and minimum Euclidean coordinates of the points so projected.7 The transformation to the sphere was so devised that no trigonometric functions or square roots were used. The comparisons used are not intended to discard all pairs that do not cause shadows. The point is to discard as possible shadow pairs all case~ in which it is obvious that a shadow is not cast on one by the other. Some nonshadow-producing pairs do slip through the first set of tests; this is allowed because the second set of tests can check these cases with less overall programming effort and execution time.
The second question which the algorithm answers is how to handle the most prevalent situation of shadows cast by one polygon only partially falling on another polygon. It is not necessary to compute the boundaries of the intersection of a polygon with a shadow cast upon its plane. The decision to reduce intensity as the scan enters the shadowed portion of a polygon is left to the final picture-producing stage of the process.
Also in the present version no computation is wasted to see if the cast shadow is visible to an observer.
Shadows are output with tags to tell which polygon is being shadowed and which polygon is casting the shadow. The final step of the process responds to shadow information by making appropriate intensity changes only in the case that the shadowed polygon is the same as the current visible polygon.
THE LINESCAN ALGORITHM AND ITS ADAPTATION FOR SOLVING THE SHADOW PROBLEM
The LINESCAN algorithm presents itself as a likely candidate for extension to a system for solving the shadow problem in half-tone image processing because of its speed of operation and because it is directly suited to processing a shadow-space which is structured in the same manner as the associated three-space poly- gonal surface structures. Shadows cast by one polygon onto another by point illumination sources are them-
Planar Polygon in Three
Space Projection of Square
on Polygon Plane
-~~+I--" Window on Viewing Plane
Observer Position
Figure I-Shadow and object projections
Light Source
Algorithm for Producing Half-Tone Computer Graphics 3
selves polygons in the same three-space. The resulting shadow three-space can be projected onto the viewing plane in the same way as the original three-space structure (see Figure 1). Thus, the extension of the LINES CAN algorithm involves only the addition of a second scanning process for keeping track of shadows on each scanline.
A brief description at this point will serve to orient the reader to the actual mechanisms of the LINESCAN algorithm. The LINES CAN algorithm processes a graphical image into a half-tone final image from two data sets derived from the three-space structure: (1) the set of all plane equation coefficients for the polygonal surfaces of the structure and (2) the perspective pro- jections of the edges of the surfaces on the viewing plane.
The construction of the final half-tone image is done in a television-like manner where a CRT beam scans across the image line-by-line and exposes a raster of points. As the beam moves across the scanline, the intersection points on the scanline corresponding to the viewable edges of the original structure will dictate changes in the tone (intensity) of the scanning beam from that point to the next intersection. These inter- section points, which are output to the final image pro- ducing routine as "key squares", are the primary output data produced by the LINESCAN algorithm.
"Key squares" are generated in two types of lo- cations on the viewing plane during a linescan oper- ation. The primary type of location is the intersection of the current scanline with the projection of an edge of the three-space structure. This location will cause a
"key square" to be produced only if the intersection is visible to the observer.
The second type of location on the viewing plane which can cause a "key square" to be produced is the intersection of an "implicitly defined line" and the current scanline. An "implicitly defined line" is the projection on the viewing plane of the intersection of two or more polygons in three-space. Polygon inter- sections are allowed in the theoretical world of the computer even though they violate the law of Nature that only one object may occupy a given amount of space. Because of the implicit nature of these inter- sections, special operations must be performed to detect and process them to produce the correct final result.
For any given scanline, a linked list is present con- taining all intersections of. projected edges with that scanline ordered in the direction of the scanning move- ment. The LINES CAN algorithm moves from inter- section to intersection keeping track of which polygon projections are entered and which ones are exited by the scanning ray. At each intersection, a "depth sort"
is performed on those polygons being pierced by the
scanning ray to find the closest or visible polygon at that intersection on the scanline.
The decision to produce a "key square" at a given intersection point is based primarily upon the relation of the depth of the edge associated with the point and the visible polygon determined by the "depth sort" at the intersection. If the edge is visible, then consideration is given to whether a polygon projection will be entered as this edge is· crossed or whether it will be exited.
For the e:ritering case, the "key square" will denote the new polygon for control of the CRT scanning beam at that intersection. For the exiting case, the
"depth sort" polygon will be denoted.
Two special problems arise concerning the output of multiple "key squares" for a given point on the final image raster. The first requires that constant checking be performed to see if the integer value of successive intersection points on the scanline are equal. If this occurs, any "key square" action which would be taken for any given intersection in the group will be deferred until the last member of the group has been processed.
Thus, only one "key square" will actually be produced.
The polygon to be denoted by the resulting "key square" may change from the beginning of the group to the end; but in any case, the last visible polygon will control the result.
The second special case of clos~ intersections occurs when coincident edges occur in th~pecification of the three-space structure. Performing a "depth sort" on the associated polygons at the common intersection would normally fail because their depths would be the same. Determination of the visible polygon of the group is performed by actually moving the scanning ray a small increment forward in the scanning direction and computing the "depth sort" at that point. This will yield the polygon which will be visible just after the scanning ray leaves the coincident intersection point.
"Implicitly defined lines" are detected when the visible polygon denoted at two successive intersection points is different. The procedure used in searching for the projected intersection involves finding which polygons are intersecting and using their plane equation coefficients to calculate their intersection's projection and its intersection with the scanline. An iterative pro- cedure is used in order to detect the possibility of multiple pairs of intersecting polygons which might yield more than one "implicitly defined line". "Key squares" will be produced for the calculated inter- section points on the scanline subject to the same con- straints about multiple "key squares" for the same raster points in the final image.
The extended version of the LINES CAN algorithm for solving the shadow problem includes two scanning
4 Spring Joint Computer Conference, 1970
operations. The primary scanning movement is the original scan operation where the three-space structure data is processed to provide the final image structure.
The additional or secondary scanning operation proc- esses in a parallel manner, the shadow three-space
stru~ture.to
produce data which will be combined with the primary scan data to form the scanline intensity data for the final image. The data output from the secondary scanning operation, which we call "shadow key squares", affects the intensity patterns of the final image only. Only the primary scan data defines the structure.In order to keep the changes in the LINESCAN algorithm to a minimum and for any changes made to have minimum influence in computation speed of the implementation, it was decided that as much of the processing operations for the final image as was possible would be shifted to the final output routine from the LINES CAN routine. This was because the original final output routine, PIXSCANR, had been input- output bound during the processing of the "key squares"
data file from the LINESCAN routine. The additional operation impressed on the new version of PIXSCANR was the keeping track of which shadow polygon pro- jections were being pierced by the scanning ray at any point in the processing of a scanline. Thus, the only change to the LINESCAN algorithm involved the ad- dition of the secondary scan which simply detected the crossings of the scanline by projected edges of the shadow three-space structure -and issued "shadow key squares" at every occurrence.
'The dichotomy imposed on the shadow processing responsibilities between the LINESCAN and PIX- SCANR routines has an additional advantage. There will always be the possibility of cast shadows falling outside the visible portions of the associated polygons.
Additionally, some polygonal surfaces of the original surface will not appear in the final image and therefore, neither will their shadows. We shall see in our dis- cussion of shadow pair detection that it is most economi- cal to allow shadow projections of these kinds to be processed in the same manner as all other shadow projections. Their data items will be passed on to the PIXSCANR routi:n,e where their occurrence will be duly noted. No effect will be registered on the final image, however, since the associated three-space surface polygon will not appear in the final image or at least not in conjunction with the projection of the extraneous shadow.
Once the mechanism for producing the proper final image of the half-tone presentation was established, it remained to develop the proper procedure for com- paring all possible pairs of polygons with respect to the illumination source, and in an economically feasible man-
ner discard as many extraneous shadow pairings as
pos~ible.
Economy of computation speed relative to total scanline processing time was the main concern.SHADOW DETECTION
The primary task· to be accomplished in shadow de- tection is not so much the actual projection of shadows as it is the elimination of the need for calculating pro- jections and storing shadow polygons unnecessarily.
The number of possible shadows cast is eqUal to the number of possible pairs of polygons in the structure.
Since this number increases rapidly as the complexity of the structure increases, it is extremely important to be able to identify useful shadow pairs with a minimum of computation and to store this information in a compact form.
The shadow pairs are stored in a chained list, with subchains linking all polygons that may shadow a given polygon. The procedure for narrowing the set of all possible pairs of polygons to a near minimal set of shadow producing pairs consists of. two distinct steps. In the first the polygons are projected onto. a sphere centered at the light source and are checked In an approximate fashion for interference with respect to the light source. In the second step, pairs of polygons which seem to occlude one another are further ex- amined to determine which polygons may shadow the others.
The light sphere projection is a device for culling out certain pairs of polygons which can in no way interfere with respect to a given light source. It is only a gross test, intended to ease the burden of com- puting projections of one polygon onto the plane of another. The test throws out polygon pairs only if it
Figure 2-Projection of polygon on sphere
Algorithm for Producing Half-Tone Computer Graphics 5
is obvious that no interference takes place. The light sphere projection is in no way used to compute inter- sections of polygon projections on the sphere, nor is it used to compute intersections of shadow polygons with the polygons being shadowed.
Every vertex of the three-space structure has to be projected onto the sphere centered at the light source in order to make initial interference tests. The sheer magnitude of the number of operations necessary re- stricts the projection in a number of ways. Namely, it would be preferred if the job could be done without computing any trigonometric functions and if possible, without computing very many square roots, since each of these requires much computer time. The projection is given by:
x
= sgn(Xl )*
Xl2*
K2s DELTA
Y = sgn(Yl )
*
Yl2*
K2S DELTA
Z _ sgn(Zl)
*
Z l2*
K2S - DELTA
where Xl, Yl, Zl are the coordinates of a point with respect to an origin at the light source, and DELTA is the square of the distance from the point to the light source (see Figure 2). This transformation to the light sphere is a composite of four transformations which are done algebraically to arrive at the final transformation:
(1) transform the points to an Euclidean 3-space with origin at the point of light;
(2) transform these coordinates to polar coordinates;
(3) map these points to the sphere by setting p to a constant for each point; and
(4) transform the points on the sphere back into the Euclidean 3-space with origin at the light source.
The algebraic derivation of these transforms yields a final form that involves some square roots in the numerator and denominator. However, since only the relative magnitude is used in the comparison operations, these results are all squared; and the sign is preserved, yielding the final transformation.
In order to use the transformed points to determine which polygons interfere with· each other with respect to the light source, the maximum and minimum of the Xs , Y s, Zs, and DELTA values are saved for each polygon, in addition to the transformed points. Also the coefficients of the equations of the planes in the light source space are computed and saved for possible shadow computation.
The first check made for each polygon is to see if it
is self-shadowed, that is, to see if the observer and light source are on opposite sides of the plane of the polygon. The procedure is to substitute both the light source point and the observer point into the equation of the plane. If the two results have different signs, the polygon is self-shadowed and no shadows cast on it will be computed. However, shadows cast by the self- shadowed polygon must still be considered.
If a polygon is not self-shadowed, then it is compared to each remaining polygon in the list to see if it is obvious that interference does not occur. The criterion is as follows:
For all pairs of polygons Pi and Ph if the points transformed to the sphere are separated in Xs , Ys,
or Zs, then the polygons do' not interfere with each other with respect to the light source.
This criterion amounts to simply examining the ortho- graphic projection of the points on the sphere onto the coordinate planes and looking for separation by com- paring maximums and minimums in each direction.
In the event that the projection of a polygon is so oriented on the sphere as to wrap around a coordinate axis, then the maximum· or minimum in some direction does not occur at a vertex. In this case, for the purpose of this comparison, the associated maximum or mini- mum is replaced by the absolute maximum or minimum coordinate value on the sphere.
When a pair of polygons are not separated enough for this test to detect the separation, then the maximum and minimum distances to the light source ·are com- pared .. If the maximum distance of the vertices of polygon I from the light source is less than the minimum such distance on polygon J, then it is clear that polygon I may cast a shadow on polygon J but not vice versa.
The tests of projections on the light source sphere eliminates many possible shadow pairs and thus reduces the total amount of storage and computing time re- quired. This set of tests, however, fails to eliminate certain other shadow pairings which will not affect the final image. Among these are shadow pairings of poly- gons with common vertices and of polygons which com- pletely overlap on the sphere. In neither case is there clear separation on the light source sphere. In the latter case the sizes of the polygons may be so disparate as to nullify the usefulness of vertex distance com- parisons.
Figure 3 illustrates one of the cases in which the projection of points of polygon I onto the plane of polygon J indicates the presence of a shadow, while the shadow cast in no way falls within the bounds of polygon J. Since there is no separation between the two polygons, both possible shadow pairings would be
6 Spring Joint Computer Conference, 1970
Light
,
Apparent Shadows on Extended Plane
Figure 3-0rientation of polygon pairs-Case 1
noted, and both would be computed, but neither would be present in the final picture.
We can eliminate this case and several others like it (see Figure 4) by defining and appropriately testing two relations:
I ~ J: "The planar polygon I is entirely on one side of the plane of planar polygon J."
I s J: "Each point of planar polygon I lies be- tween the light source and the plane of planar polygon J."
In the case if Figure 3 for example, we see that I ~ J, J ~ I, Is J, and J s I are all true, and therefore, the shadows are cast only upon the extended planes of the two polygons. As a result, neither shadow pairing is added to the list of. possible shadows.
All of the decisions about possible shadow pairs are computed in advance of the start of the LINESCAN operation. As the LINESCAN operates, it has a linked list for each polygon of all polygons which may cast a shadow upon it. It is at the point where the first line of a polygon is processed that the shadows cast upon it are computed and stored in a list. When the polygon is no longer active, we purge the shadow information from the list. Thus, shadow information is calculated only when it is first needed and discarded when the need for it ceases.
Shadows are computed by projecting the vertices of one polygon onto the plane of another. The parametric form of the equation of a line is used to calculate this projection. Given' two points Pl(Xl, Yl, Zl) and
;eLiQht
, /LiQht
Case 2 Case 3
.-1Il?
/ Light /Li9ht
Case 4 Case 5
•.. '"
/ LiQht
l
LightCase 6 Case 7 Case 8
Figure 4-Polygon orientations
P2(X2, Y2, Z2), the set of points P(X, Y, Z) that lie on a line joining PI and P2 is given by:
x -
Xl Y - Yl Z - Zl X2 - Xl Y2 - Yl Z2 - ZlSetting each of these ratios equal to a parameter r yields the parametric form:
X = Xl
+
r(X 2 - Xl) Y = Yl+
r(Y2 - Yl )Z
=
Zl+
r(Z2 - Zl)PI and P2_ are so chosen that PI is the light source position and thus the origin of the system. This reduces the equations to:
Algorithm for Producing Half-Tone Computer Graphics 7
The parameter T has the following useful properties:
T>1==> P is on the extension of P1P2
T=1==> P is identical to P2
T=O==> P is identical to PI P is between PI and P 2 P is on the extension of P 2P I
In addition to providing the coordinates of projected points, T can be used in establishing the truth value of the relations I s J and I ~ J. As we see in Figure 5, it is necessary to use the values of T for each vertex to see if the shadow makes sense. In this case polygon 7r i projects onto the plane of polygon 7rj as PI', P2', Pa', P/.
The routine has to check for such situations and instead use PI', P2', Pa", P/'. We do not, however, make any checks to see whether the shadow as cast is visible.
The fact that two or more polygons may cast shadows that overlap on a given polygon has no effect on the computation. The final stage of the process takes care of such contingencies.
We feel that in further implementations it would be useful to defer actual computation of "shadow key squares" until a complete scanline is processed. In this manner, it would be possible to introduce and compute shadows cast on a polygon only in the case that the
Figure 5-Shadow projection
polygon was, in fact, visible at sor;ne point on the scanline. This technique would eliminate a large number of "shadow key squares" that are, in fact, not needed at all in the production of the picture. Another extension being considered is to allow polygons to have a degree of translucency. However, self-shadowing polygons then would have shadows visible on them and this would cause a large increase in the number of shadow lines.
THE FINAL OUTPUT PROCESS
The final data set for the half-tone image consists of two parts. The first part contains the three-space plane equation coefficients for the surfaces of the three-space structure and the position data for the illumination source. The second part contains the linear string of scan control data items: "key squares", "shadow key squares" and "self-shadow key squares". It is the func- tion of the PIXSCANR routine to assimilate these two masses of data and to produce the final half-tone image.
In order to couple our results closely to the equipment that was available for our use, we modified the display hardware to provide a special raster scanning operation in which the equipment automatically performs the function of stepping across the raster, and our data input specifies what intensity levels will be used in various sections of the scan. The raster is plotted from left-to-right and bottom-to-top on the display screen.
A data item initializes the scan to the starting position and gives the initial intensity value for the CRT beam.
In addition, the stepping increment 0 is given. When the scanning operation comes to the end of a scanning line, the value of the x coordinate is reset to 0 and the y coordinate is incremented by
o.
The remaining data items presented to the display hardware consist of an x coordinate value and an intensity value. As the scanning operation proceeds, the current x coordinate value of the scan is compared to the x coordinate of the next data item. If agreement is achieved, then the intensity of the beam is adjusted to the new value and the scan continues. Once set, the beam intensity does not change.
This raster scan operation allows the final image to be exposed with a minimum number of actual data items being sent to the display hardware. A moderately complex picture might have, for example, an average of 20 intensity changes per scanline. If it were necessary to send display information for every point in the picture, each line would have 512, 1024, 2048, ... or more data items associated with each scanline. Another benefit gained from this condensed data format is that the amount of data needed per picture varies in a
8 Spring Joint Computer Conference, 1970
linear manner with the size of raster being used. Compu- tation speed also varies in a linear manner.
The section of PIXSCANR which processes the first part of the data file from the shadow-tone algorithm establishes the· intensity functions associated with the polygons of the three-space structure. A basic assump- tion made in our current implementation is that the intensity of light reflected from a given planar surface is uniform over the entire surface. Although this does not hold true in the physical world, it is close enough for our purposes.
We selected a cosine function for the intensity of the reflected light from a given surface. A ray emanating from the center of the illumination source and passing through the "centroid" of the surface defines the angle of incidence of the light for the entire plane. The
"centroid" is calculated by finding the average value of the x and y coordinates of the vertices of the polygon and solving for the corresponding z using the equation of the associated plane. The cosine of the angle between the surface of the polygon and the ray drawn to the illumination source is then given by:
I
Aa+
Bb+
CcI
cosO
=
vi
A 2+
B2+
C2va
2+
b2+
c2where the A, B, C are coefficients of the plane equation and a, b, c, are direction numbers of the ray. The intensity of the reflected light from the surface of a polygon not in shadow is given by:
Ii
= I
cos ()1*
Ri* RANGE+
IMINRANGE and IMIN are parameters controlled by the user which specify the total range of intensity to be used'in the half-tone image and a translation of that range along the scale of the display hardware. Ri is a pseudo-reflectivity coefficient specified by the user for each polygon surface to allow some differentiation be- tween surfaces. Those polygons indicated by "self- shadow key squares" are assigned a special intensity due to "ambient" light. This intensity is given by:
188 = 0.2
vi
A C RANGE+
IMIN2
+
B2+
C2where A, B, C are coeffiCients of the equation of the plane of the self-shadowed polygon.
Once the intensity functions have been calculated, the processing of the "key squares" data set begins.
In the original version of PIXSCANR used for non- shadow half-tone image presentations, it was a simple matter to transpose the "key squares" directly into data items to send to the display hardware. For the shadow half-tone system, the addition of the "shadow key squares" and the "self-shadow key squares" to the
data set complicates the process immensely. Recall that the function of keeping track of which shadows are being pierced by the scanning rayon a scanline is now a proper operation to be performed by PIXSCANR.
Shadow tracking is accomplished in an n X n binary array, in which the (i, j)th position is a 1 if polygon j is casting a shadow on polygon i. As the "shadow key squares" are processed from the data file, the associated positions in the binary array are flipped from the in- shadow state to the out-of-shadow state. When a struc- ture "key square" is processed, the intensity of the
Figure 6-Two present.ations of a three-space structure
Algorithm for Producing Half-Tone Computer Graphics 9
Figure 7a-A-Frame cottage with no shadows
Figure 7b-A-Frame cottage with shadows
beam will be set at that point. Otherwise, the shadow will be indicated by using the minimum value of in- tensity for the image (IMIN).
The remainder of the operations performed by the PIXSCANR routine are concerned with the outputting of the final image on various photographic media. At CSL, we have the option of photographic recording on either Polaroid 3000 speed black and white film or 70mm RAR type 2479 recording film. The PIXSCANR routine also provides for inversion of the image 'in a complementing operation on the intensity functions.
Further output capability is provided for making ani- mation sequences on a 16mm animation camera.
RESULTS OF THE ALGORITHM
The two photographs of Figure 6 compare the "wire- frame version" of a three-space structure with the shadow half-tone presentation of the same structure.
The object consists of three parts, all arranged to fit interlockingly within one another. The computation time for our implementation on the CDC 1604 com- puter was about 2 minutes, 20 seconds. Time for computation of the non-shadow half-tone presentation ran about 45 seconds.
Figure 7 shows the same view of an A-frame summer cottage, first with no cast shadows in part a. and then with cast shadows in part b. Non-shadow half-tone computation took 13.5 seconds and the shadow half- tone computation required about 27.0 seconds. Both cases indicate that time required for shadow half-tone computations is about twice the time required for the non-shadow case.
As an example of how the same scene appears with the light source in various locations, Figure 8 shows the A-frame cottage in three different appearances. When only the light source position changes, only the shadow
Figure 8-A-Frame with different light source positions
10 Spring Joint Computer Conference, 1970
pairings and their subsequent computations change.
Thus, future implementation of shadow half-tone al- gorithms may be able to save computation time by passing the "key square" data from scene to scene and computing only the "shadow key squares" and "self-<..
shadow key squares".
If the only change made from one presentation to another is a movement of the observer position, the converse of the above occurs. The shadow data does
Figure 9-Back-lighted Torus
not change and only the "key square" data must be computed. Both of these attempts to reduce compu- tation time by borrowing from past results will require increased amounts of storage and techniques for merging the old and new data sets to generate the final half-tone image.
Our final presentation of Figure 9 shows a torus in free space back-lighted with respect to the observer position. The torus is constructed of 225 planar poly- gons. The time for computation of the non-shadow case was one minute, 25 seconds. The shadow half-tone image required about three minutes of computation.
Approximately 700 shadow pairings were found to be useful by the detection stage of the algorithm. Only a small number were actually detected in the final image. In fact, only by back-lighting the torus could the complete image be. processed because the number of visible shadow exceeded the limits o( storage avail- able during execution of the program. Efficient compu- tation of the final image data will depend upon the availability of sufficient amounts of direct address core storage or an auxilliary storage medium which can be accessed in speeds approaching main memory access time.
BIBLIOGRAPHY
1 C WYLIE G ROMNEY D EVANS A ERDAHL Half-tone perspective drawings by computer
Proc of the Fall Joint Computer Conference Vol 31 49-58 1967
2 J WARNOCK
A hidden line algorithm for half-tone picture presentation Tech Report 4-5 University of Utah Salt Lake City Utah May 1969
3 BELSON
Color TV generated by computer to evaluate space borne systems Aviation Week and Space Technology October 1967 4 J BOUKNIGHT
An improved procedure for generation of half-tone computer graphics presentations
Report R-432 Coordinated Science Laboratory University of Illinois Urbana Illinois September 1969
5 A APPEL
Some techniques for shading machine renderings of solids Proc of the Spring Joint Computer Conference Vol 32 p 37-49 1968
6 A APPEL
The notion of quantitative invisibility and the machine rendering of solids
Proc ACM Vol 14 p 387-393 1967 7 M KNOWLES
A shadow algorithm for computer graphics
Department of Computer Science File No 811 University of Illinois Urbana Illinois 1969
The case for a generalized graphic problem solver*
by E. H. SIBLEY, R. W. TAYLOR, and W. L. ASH University of Michigan
Ann Arbor, Michigan
INTRODUCTION
Not so many years ago, SKETCHP ADI and DAC2 set the whole world of computing on a philosophical bender. People, who either knew little of the subject or else should have known better, started talking up a storm. The whole of engineering was about to be revolutionized and everyone should prepare now or be sunk, to drown in their own ignorance.
Unfortunately, even though we,in computation, have been regularly beset by super-salesmen who keep on telling us "how good its going to be," we still are suckers for a good line. We sat at the edge of our chairs listening to the prophets, and later scurried around trying to learn more about the wonders of the future, and bought expensive hardware (which we didn't yet know how to use) so that we should be ready.
Fortunately, some business managers finally asked why the expensive equipment was sitting there, and as a result, many people moved away from "research-like"
operations to a more reasonable "application" approach.
This meant that the people in graphics became divided into two camps (almost mutually exclusive) who either, tried rather unsuccessfully to implement a generalized graphic system, or else tried to produce a working application program. The latter set of investigators have produced many useful packages, or we should all have watched the graphics hardware being converted into TV sets. Why then has the well promoted "gener- alized graphic system package" proved so elusive? In this article, we shall try to show that this is due to lack of knowledge on the part of the prophets. That in fact they were proposing systems which needed, as their core a generalized problem solver, which is, after all, only asking for a really good artificial intelligence
*The work reported in this paper was supported in part by the Concomp Project, a University of Michigan Research Program Sponsored by the Advanced Research Projects Agency, under Contract Number DA-49-083 OSA-3050.
11
package, and that field has been having its own prob- lems for years, too.
The rest of this article focuses on what has been done, and what reasonably could soon be done towards providing a useful package for generalized graphic prob- lem solving. The techniques adopted in SKETCH- PAD's constraint satisfactions are discussed with con- clusions made about their generalization and their wider application in other fields.
Finally, some of those scientific, engineering, and mathematical modeling techniques which normally use graphics for either visualization, analysis, or numerical computation of the solution are examined in some detail. The conclusions suggest that there is still some- thing that can be achieved in the near future, although it is probably less than many of the early optimists had predicted.
BACKGROUND AND JUSTIFICATION
'Before starting a discussion on the merits or de- ficiencies of a generalized graphic problem solver, we must define that term. The use of graphics (other than symbols) for the solution of problems is common throughout much of engineering and science, and even in some fields of mathematics. The concept is often associated with the idea of a model which involves a topological or physically scaled picture from which the original problem is solved. Sometimes the picture itself is the solution (e.g., in the case of computer generated art, some phases of architecture, etc.), but more often the picture is either an immediate model from which algebraic or numeric equations are produced (these are solved to give the answer) or else the picture is later used to generate information (e.g., for architecture, the original drawings may later be examined to give ma- terial and cost information). Now if we consider a software computer system which aids the engineer, scientist, or mathematician in the formulation and
12 Spring Joint Computer Conference, 1970
analysis of a range of problems, using the heuristics of the man to formulate a reasonable model, and the computer to aid in and augment the analysis, etc., then this software could be termed a "generalized graphic problem solver".
At the other end of the scale from the generalized graphics processor, is the specialized graphic package.
Here the classical input-output devices (e.g., card reader and printer) are replaced by graphic devices (e.g., light pen and CRT) so that the user has an easier time stating his problem or understanding his solution, probably because it is two dimensional in form, or nearer to the engineers' medium, viz, pen and paper.
The first question must then be: "Is generalized graphics desirable?"
Obviously all the early graphic-systems/computer- aided design prophets thought that it was. To quote one:3
"In the near future-perhaps.Jwithin five and surely within 10 years-a handful of engineer-designers will be able to sit at individual consoles connected to a large computer complex. They will have the full power of the computer at their fingertips and will be able to perform with ease the innovative functions of design and the mathematical processes of analysis, and they will even be able to effect through the com- puter, the manufacture of the product of their efforts . ... "
Recently, there has been some retrenchment:4
"Suddenly a new wor~d seemed to have sprung into being, in which engineers and architects could sit in front of a screen ... and conjure up auto- mobiles or hospitals complete in every detail, in the course of an afternoon. Unfortunately, reality turned out to be more elusive than some people expected . ...
What emerges from the above is a requirement for a general system for building models, to which can be applied transformations and algorithmic pro- cedures . ... "
On the whole though, there is still much to be said for generalized graphics systems research. To begin, we can state the rather overoptimistic argument that:
there is bouIld to be some practi~al or more efficient fallout from research in general systems; thus we will have better specialized systems even if we never get a really generalized one. In this argument, we are prob- ably on reasonable ground, since the special systems of today have nearly all been- spin-offs from the past generalized systems. But th,is is not enough.
The important point seems to be that a reasonable research effort can and will produce further steps to- wards a generalized system, or at least a "less spe- cialized" system.
A second question is:
If we had a generalized graphic system today, could industry afford to use it? Unfortunately, with our best hopes, we still have to admit that the answer is NO.
This is mainly due to the fact that specialized systems are normally cheaper, and often easier to run than a generalized system. This could be compared to the difference between a "FORTRAN machine" which pro- vides a useful but ad hoc language, and a Turing ma- chine, which is certainly general, but is by no means as easy to use.
How, then, do we hope to succeed? The first way is by developing more powerful techniques, which, though general, are easy to use and well interfaced to the user.
The second is the normal effect of engineering progress and the economies of scale. As time goes on, we might hope to see both cheaper hardware and a ready pool of useful routines from a user community which can be integrated into a total, but generalized system.
THE SKETCHPAD METHOD OF CONSTRAINT SATISFACTION
Since picture meaning and solution will form the heart of any generalized system, we felt that a deeper understanding of the "graphical constraint problem"
was necessary. Naturally, we started with the SKETCHPAD approa,ch. We had the following ques- tions in mind:
1. Were SKETCHPAD's methods as general as some claimed or were people misconstruing some ex- citing beginnings?
2. Why hadn't further extensions of the graphical constraint problem appeared?
3. How might we extend the SKETCHPAD work on graphical constraints?
Some answers which led to our general conclusion will appear in the next few sections. It will. be helpful to consider the SKETCHPAD method in some detail for background purposes.
When SKETCHPAD was commanded to satisfy a set of constraints on a picture, it did so by using nu- merical measures of how much certain "variables"
(usually points) were "out of line" (our phrase). Con- straint satisfaction was therefore a matter of reducing the various numerical error measures to zero. The errors were computed by calling, for each constraint type and for each degree of freedom restricted by that constraint type, an error computing subroutine. Each subroutine would compute an error "nearly propor- tional to the distance by which a variable was removed from its proper position". Thus if the components of a
variable were displaced slightly and the error sub- routine called for each displacement, a set of linear equations could be found. These equations had the form
where Xi is a component of a variable, E is the computed error, and the subscript 0 denotes an initial value.
This set of equations could then be solved by Least- Mean-Squared Error Techniques to yield a new value for each component involved.
The general constraint procedure was thus based on this numerical measure, and the most general algorithm available was relaxation. Thus a variable was chosen and re-evaluated using the LMS technique such that the total error introduced by all constraints in the system was reduced. The process continued iteratively and eventually terminated when the total computed error became minimal.
Obviously, the relaxation method, with a set of equations to be computed and solved many times, was slow. Thus, before using relaxation, SKETCHPAD employed a heuristic, which will be discussed in some detail because we believe many similar techniques will be necessary. The object of the heuristic was to find an order in which a set of variables could be re-evaluated such that no subsequent re-evaluation would affect a former one. If this order could be found, then the con- straint satisfaction process could proceed much faster because the variables involved would need only one re-eval uation.
~o perform this search, the user picked a starting varIable. SKETCHPAD then considered the constraints on that variable and formed the set of all variables which participated with the starting variable in the constraints involved. If some of these variables had sufficient degrees of freedom to satisfy the constraints, then one could be sure that they would not affect previous constraint re-evaluations. Thus such con- straints could be removed from the constraint set on the starting variable, possibly allowing it to be easily re-evaluated. The technique was extended to build chains of constrained variables until sufficient free ones were found. Of course, such a se,t of free variables did not always exist, and it was necessary to have the relaxation method as a back-up.
COMMENTS ABOUT SUTHERLAND'S METHOD
In the conclusion to Reference 1, Sutherland stated
"It is worthwhile to make drawings on a compute;
Case for Generalized Graphic Problem Solver 13
only if you get more out of the drawing than just a drawing" (p. 67). While' this statement might arouse some debate (are plotters useless?), it nevertheless re- flects the key point that one must be able to associate meaning, and thus constraints, with a picture. When the Sketchpad method is evaluated relative to arbitrary picture semantics, several observations can be made.
First, all constraints in SKETCHP AD were eventu- ally related to a numerical error definition having to do with distance. This technique was clearly oriented to- ward the L1V[S equation solution method, but in ad- dition had several advantages. It allowed new con- straint types to be added quickly since all one had to do was write a new set of error computing subroutines;
the solution machinery was already present in the over- all system. The solution technique itself, though it involved a preliminary heuristic, could almost guarantee a solution in reasonable if not entirely pleasing time.
In addition, the numerical approach together with relaxation yielded results for a class of problems that were of particular interest in the author's field. The approach was therefore eminently successful for certain operations.
In a more general context, the approach has some drawbacks. The relaxation method depends critically on the results of a previous iteration. Thus once having applied it, it is a non-trivial matter to restore the pic- tUre to its previous status; one might have to make a copy of parts of storage, for instance. Design by trial and error, with recovery fr.om undesirable conditions, is thus hampered. Furthermore, the relaxation method is not generally selective in picking some priority in variable re-evaluation. One constraint is as strong as another and all are broken with equal abandon. This runs counter to most realistic concepts of a constraint.
These drawbacks were known to the author: "There is much room for improvement in the relaxation process and in making 'intelligent' generalizations that permit humans to capitalize on symmetry and eliminate re- dundancy" (p. 55).
A final criticism of the numerical definition of con- straints centers on the degree to which they are "picture oriented." A review of the available constraint types in SKETCHPAD (Appendix A) quickly reveals their obvious correlation with "picture transformations".
Certainly such picture transformations are a desirable part of man-machine communication. However, if the system is limited to constraint satisfaetion methods involving such simple picture transformations, the system capabilities are undoubtedly themselves limited.
Examples will be presented later. The point is that constraints are a function of picture semantics, and only incidentally of picture geometries.
It should be noted that the above criticisms are
