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COMMENT ⊗ VALID 00018 PAGES
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C00007 00003 ABSTRACT:
C00008 00004 1. IDEAS AND WORK ALREADY DONE.
C00016 00005 2. WHAT WE PROPOSE TO DO.
C00022 00006 The micro language is composed of a small set of primitive
C00028 00007 Besides language inputs, a geometric modeling system should
C00033 00008 An Itemized Shopping List.
C00036 00009 3. PREVIOUS WORK AT STANFORD.
C00039 00010 4. RELATION TO WORK DONE ELSEWHERE.
C00046 00011 5. FACILITIES AT STANFORD A.I. LAB
C00051 00013 8. BUDGET
C00054 00014 6. BIOGRAPHIES.
C00056 00015 Organized and directs Stanford Artificial Intelligence
C00058 00016 7. BIBLIOGRAPHY.
C00061 00017 11. "Time-Sharing Computer Systems" in Management and the
C00064 00018 23. (with J. Painter) "Correctness of a Compiler for
RESEARCH PROPOSAL SUBMITTED TO THE NATIONAL SCIENCE FOUNDATION
Computer Science Department
School of Humanities and Sciences
COMPUTER-AIDED MECHANICAL DRAWING OF THREE-DIMENSIONAL OBJECTS
Professor of Computer Science
Research Associate in Computer Science
This is a new request to NSF
The desired starting date is January 1, 1974.
The total amount requested for 24 months is $ 214,881
This is a request for a grant of $ 214,881 to support a two year
research program in computer aided mechanical drawing of three-
1. IDEAS AND WORK ALREADY DONE
2. WHAT WE PROPOSE TO DO
3. PREVIOUS WORK AT STANFORD
4. RELATION TO WORK DONE ELSEWHERE
5. FACILITIES AT STANFORD A.I. LAB
ENCLOSURE: (with orginal copy of Proposal only)
Flip book of mechanical arm animation.
1. IDEAS AND WORK ALREADY DONE.
The proposed work is based on the following ideas and work
i. Explicit 3-D Object Representation.
An effective way of obtaining 2-D mechanical drawings of a
three-dimensional object is to derive the drawings from an explicit
computer model of the three-dimensional object. The orthographic,
isometric and perspective projections of the object are obtained
automatically from the three-dimensional description, with the
hidden lines of the object either eliminated, dashed or thinned
and with the appropriate labels, dimensions, comments, and
arrowheads indicated. (Figure 1) (all figures follow this section).
ii. Object Generation from Physical Description.
A convenient way of making an explicit computer model of an
object is to simulate the process of building the object. That is,
the description of how to build an object is an implicit
representation of the object. For example it is easier to describe
Figure 2 as a dodecahedron with a regular five pointed star shaped
hole cut through it, than it is to draw the figure with a light pen
or to list the loci of its vertices.
iii. Language Extension.
Rather than developing new languages for geometric modeling
and mechanical drawing, we believe it is best to extend the old
languages: FORTRAN, ALGOL and LISP. The elements of language
extension include new data types for the language, general low
level primitives for manipulating the new data types, and a
convenient set of higher level operations. The division of the work
into high level operations defined in terms of low level primitives
is an important part of the design because it isolates the data
structure manipulating code.
iv. Object Representation from Physical Measurement,
Another way to get an explicit computer model of an object
is to derive it from measurements made on an actual physical object,
2-D drawing, or picture. For example, the physical object might be a
clay model of the thing being designed. We believe that only the
lack of appropriate software is preventing the use of television
cameras as an inexpensive, accurate, and automatic means of entering
graphical data into a computer. (Figure 3)
v. Prejudice against Pens for Interactive Graphics Control.
It has been our recent experience that a distinction should
be made between using a light pen (or sonic pen, Rand tablet, etc.)
for graphics input and using it for graphics editing and control. We
observe that when adequate keyboard edit, control and language
conventions are provided the use of the light pen diminishes to the
point where it is only demonstrated to visitors who expect graphics
to involve light pens. One reason for this is that when an operator
can do something exactly in a few keystrokes he does not bother with
picking up the pen, acquiring the pen tracker, and drawing. A second
reason is that a pen is necessarily based on 2-D screen coordinates
in which overlapping portions of a 3-D drawing can not be directly
distinguished with a light pen. Pen based editing systems require a
keyboard or button box in any event, so we argue that an operator
who can control and alter a drawing with his hands always in the
locality of the keyboard will be more efficient than an operator who
has to use both a keyboard and a pen. However, the use of a pen (or
Rand Tablet) for graphics input, such as tracing chromosome
photographs into the computer, is justifiable and expedient but not
directly relevant to editing a 3-D mechanical design. That is, pens
are functionally replaceable by either cameras or keyboards.
vi. Mechanical Simulation.
Information, such as the degrees of freedom of motion, is
included in the object description and can be used to get pictures
of objects in different positions. This is demonstrated in the
A.I.Laboratory's flip book animation of a mechanical arm turning a
block over. Mechanical information can also be used to constrain the
shape of a part in its desired place, or to find the space
potentially occupied by a moving part.
vii. Photometric Simulation.
Photometric information such as the location and nature of
light sources and the light scattering properties of the objects'
surfaces can be included in the model and used to compute the actual
appearance of solid opaque objects. (Figure 4)
2. WHAT WE PROPOSE TO DO.
We propose to represent and simulate solid objects in a
computer for the sake of mechanical design and mechanical drawing.
Our two year goal will be to automate as much as possible the task
of creating and altering three-dimensional data structures from
which mechanical drawings can be derived. The overall project to
date has been called "geometric modeling" a term which we use to
refer to our particular combination of computer graphics, physical
world modeling, image processing and geometry. Accordingly, the
details of the work we propose doing will be presented in terms of
the elements comprising a Geometric Modeling System.
Like a computer, the four main elements of a geometric
modeling system are memory, process, input and output. Starting with
memory, there are the problems of representation (how to describe a
physical object), accessing (how to find a particular description by
name, by location, or by whether it is currently in view), and
efficiency (how to keep the size of storage space down and how to
dynamically allocate fast and slow memory resources).
The presently implemented explicit object representation is
based on polyhedron models of solid rigid objects. A simple object
called a body is defined by a surface shell composed of vertices,
edges and faces that satisfy the Euler equation, V - E + F = 2.
Such polyhedron bodies are combined to form compound objects. At
present, curved objects are represented by approximating them using
a polyhedron composed of a sufficient number of flat polygonal
faces. We propose to further develop the appearance of curved
objects by automating the assignment of polygonal facets to a given
curved surface. Other current representation problems that we
propose working on include constructing efficient (and compatible)
object labelling, handling mechanical properties of an object, and
better representing compound and flexible objects.
A final representation issue we would study is that of a
format for communication of three-dimensional models between
modeling systems. Although we believe that it is too early to
propose a standard format, it is desirable to design and promulgate
a format as simple, but as inclusive as possible; it is also
desirable to develop formatible I/O routines so that new formats
can be sent or received.
The usual input devices to a geometric modeling system
include keyboards, light-pens, joy-sticks, buttons, cameras and
film scanners, of which the most important to this proposal is the
keyboard, because it is currently the best device for language input.
Indeed, we believe that we can demonstrate that a system based on
keyboards can do geometric control and editing better than a system
based on both a light pen and a keyboard. With respect to language,
we are proposing two projects: first, we would extend the programming
languages FORTRAN, ALGOL and LISP and second, we would continue
to develop our interactive edit and control language. The elements
of a language extension include new data types (the "memory" of our
system), a micro language of primitive operations and a macro
language of more complex operations.
The micro language is composed of a small set of primitive
functions that invoke the only subroutines allowed to directly
create and alter the data structure. All the geometric processors,
editors, input, output and higher language operations are
implemented in terms of these fewer than fifty primitives. The
reason for having a two-level system is to isolate and minimize the
amount of code that is necessarily dependent on the implementation
details of the particular higher level language. Furthermore, it is
possible to construct primitives that are complete and general with
respect to fundamental principles in polyhedron topology and
geometry. For example, we now have a set of Euler primitives that
can generate any Eulerian polyhedron (and only Eulerian polyhedra)
as well as a set of Euclidean primitives for applying the group of
Euclidean transformations. With more good luck, we intend to
isolate sets of primitives for mechanics and for image formation.
The macro level of language extension is comprised of
operations that make it convenient to simulate building a mechanical
model of an object. The present macro level includes an operation
for "sweeping" edges into faces, and faces into solids; an
operation for "glueing" surfaces together; an operation for passing
"cutting" planes thru an object; and a most powerful trio of
operations for forming the volume union, intersection and
difference of two given polyhedra. Since polyhedra can be taken as
either bounding a finite solid volume or a finite empty volume, we
have found it convenient to draw some objects indirectly by building
their holes and intersecting the holes with their simple outer
shape. Further macro operations we propose to code would include
more "imaginary" ones for bending, constraining, filling,
enveloping, and expanding upon a skeleton; as well as some more
"realistic" operations that would model regular machine shop tools
such as a lathe, punch and milling machine; as well as machine
building processes such as welding, fastening and assembly.
Our second language project is oriented towards edit and
control. The main differences between an interactive graphics
editor and a graphics programming language are that an editor
carries along its working context so that most arguments and data do
not have to be explicitly named (because they happen to be "at the
top of the stack") and that they are visibly intensified or
otherwise indicated on the display screen. The advantage of the
interactive editor is that the user is relieved of having to coin
and call names of things. However, the disadvantage is that he
cannot develop subroutines of the power available in a programming
language, which provides notation for procedures, arguments, and
variables. We plan to keep the programming language level distinct
from the control and edit language level; although it should be
clear that both language levels are calling the same primitive
Besides language inputs, a geometric modeling system should
have a way of reading data that is already in graphical form. For
such input, we propose using a television camera. For example, we
already have developed video intensity contouring to rapidly provide
the edges of an image in a form available for graphics editing.
Although video input per se is of secondary importance to this
proposal, we happen to have such hardware and software available at
Stanford and can make good use of it with little additional effort.
Furthermore, video (or visual) computer input has considerable
promise as a major input device of future computers.
The third element of a geometric modeling system is its
(software) processors. There are language processors, mechanical
simulators, locus solvers, image analysis and image synthesis, as
well as that process, quite central to three-dimensional drawing,
which is hidden line (and surface) elimination. We have a hidden
line eliminator which combines several of the existing techniques
and which can generate both line drawings and video images; also we
have reason to believe that further work on our design will yield a
hidden eliminator that can handle apparently curved objects,
generate shadows, use the coherence between successive images, and
still be fast without special purpose hardware. Since the purpose
of the processors just mentioned should be sufficiently clear, we
shall skip detailing their algorithms and implementation, although
this will comprise the bulk of the work and publication we propose
The fourth and final element of our modeling system is the
output, which includes dynamic CRT display, video display,
hardcopy printing, and magnetic tape. Although mundane, the
numerical object descriptions on conventional (nondisplay) computer
media like magnetic tape is important in making the output of an
interactive display system available for further automatic
processing or communication. On the other hand, a high quality CRT
that can display characters and vectors is now and shall remain the
primary tool requisite to developing interactive graphics software.
Consequently, nearly a third of the budget included with this
proposal is allocated to aquiring such a CRT to enhance our existing
display system. The most promising alternative to a CRT is a video
display. However, present day video display systems would require a
very large computer and fast memory to achieve the resolution and
speed of a CRT display.
An Itemized Shopping List.
Ignoring the overall system organization and fine details,
the goals of the proposed project are summarized in the following
Items partially in hand.
1. Representation of solid rigid three-dimensional polyhedra.
2. Language extension of geometric primitives.
3. Language extension of object building operations.
4. Polyhedron object hidden line (and surface) eliminator.
5. Geometric editor.
Items within one year's work.
6. Generation of mechanical drawings from geometric models.
7. Representation for the appearance of curved objects.
8. Representation for flexible objects.
9. Video acquisition of two-dimensional drawings.
10. Mechanical simulation and animation.
Second year and/or elective items.
11. Generation of high quality mechanical drawings.
12. Development of a remote display terminal version.
13. Development of a standard FORTRAN version.
14. Mechanical drawings for a special area of engineering
(pipefitting, screw threading, mining, or whatever).
Basic research items.
15. Video acquisition of three-dimensional objects.
16. Photometric simulation - shadows, multiple light sources
for generation of high quality video appearance.
Since substantial work has already been done on items one
through five, they would be included in the most conservative
estimate of our potential achievements over the next two years.
Intermediate expectations include making considerable progress and
original contribution with respect to items one through ten, as well
as doing one of the five items numbered eleven through fourteen. An
optimistic expectation would be to finish everything through item
3. PREVIOUS WORK AT STANFORD.
This proposal is based on work by Bruce G. Baumgart as a
graduate student. Mr. Baumgart expects to complete his dissertation
titled "Geometric Vision" in early 1974 and will continue as a
research associate upon receiving his degree.
This work includes GEOMED, a Geometric Editor, which would
be the prototype of the mechanical drawing system we propose to
build. GEOMED is a 3-D drawing program (controlled mostly by
keyboard) that can construct arbitrary polyhedral objects and
display them with hidden lines eliminated. GEOMED also accepts TV
images and can form polyhedron models consistent with such images.
The subroutines and data structures of GEOMED have been
embedded in LISP and SAIL (Stanford Algol) to provide geometric
languages for physical world modeling and physical action
simulation. The current embedded version of GEOMED falls short in
that adequate error recovery and memory allocation is currently
The image processing part of Mr. Baumgart's work lies in a
program named CRE, standing for Contour, Region, Edge image
representation. CRE converts a sequence of digital television
images into a contour edge data structure for interpretation by
other programs. Finally, there is TVFONT, which is a version of CRE
for making type font bit arrays from television images, or for
re-scaling existing fonts.
4. RELATION TO WORK DONE ELSEWHERE.
The work proposed here has been strongly influenced by the
pioneering computer graphics work of Larry Roberts, Steven Coons and
Ivan Sutherland done at the Massachusetts Institute of Technology,
Lincoln Laboratory, and Harvard University; as well as the more
recent work of Sutherland, Evans, Warnock, Watkins, Archuleta and
Gouraud at the University of Utah. In fact, Mr. Baumgart did his
undergraduate thesis (at Harvard, 1968) with Prof. Sutherland, on
development of a three-dimensional display system which was
subsequently moved to Utah. Another influence on the proposed work
has been the research in Artificial Intelligence, computer vision,
programming languages and time sharing done at Stanford University,
Massachusetts Institute of Technology and Stanford Research
In general, research work similar to that described in this
proposal is being conducted at the University of Utah and at IBM.
However, the recent research work at Utah has been mainly directed
toward the development of special purpose high quality display
hardware; whereas the work outlined in this proposal is directed
toward the problem of 3-D representation and graphics language
development. The relationship between our work and the work being
done at the University of Utah is like the relationship between
software and hardware, the two are overlapping but different.
The development and application of three-dimensional
computer design systems has also been underway for several years at
companies such as General Motors and Lockheed. The relation of our
work to the graphics done in industry is symbiotic and is, in fact,
accurately described by the hackneyed comparisons of a university
vs. a corporation, theory vs. practice, knowledge vs. production,
generality vs. practicality, etc. Thus, it is not too surprising
that the General Motors and Lockheed systems have produced
mechanical drawings of cars and airplanes. However, with the
exception of Appel's hidden line eliminator developed at IBM,
Yorktown, these systems have not produced new languages or
algorithms. For the most part the graphics software technology used
by industry began in university and government research.
Another area of related work is computerized 2-D mechanical
drawing. At present, there are several commercially available
automatic drafting systems (Cal Comp, Gerber, and so on) which allow
a mechanical drawing to be entered into a computer and to be edited
word for word and line for line. Such systems are indeed an advance
over manual drafting, however, the research work we are proposing
would be a further advance directed at producing many 2-D mechanical
drawings from the human design effort required to make one 3-D
Finally, there are many commercially available engineering
programs that generate mechanical drawings for particular
applications. For example, the Control Data Corporation has a
system that does structural steel detailing which produces graphics
in accord with the drawing standards of the American Steel
Association. Such special purpose drawing programs require input
decks specifying the exact shape, dimensions and location of each
steel beam. The input decks are prepared off line, largely by hand.
A three-dimensional design program, such as the one we propose
creating, would allow interactive design and specification of steel
structures and would allow easy interfacing (in effect, FORMAT
statements) for creating particular data required by an existing
program. Therefore, the relation of a 3-D design program to a 3-D
drafting program is simply sequential, the one would generate the
input of the other.
5. FACILITIES AT STANFORD A.I. LAB
The computer facilities at the Stanford Artificial Intelligence
Laboratory include the following:
Central Processors: Digital Equipment Corporation PDP-10 and PDP-6
Primary Store: 65K words of 1.7 microsecond DEC Core
65K words of 1 microsecond Ampex Core
131K words of 1.6 microsecond Ampex Core
Swapping Store: Librascope disk (5 million words, 22 million
bits/second transfer rate)
File Store: IBM 3330 disc file, 6 spindles (leased)
Peripherals: 4 DECtape drives, 2 mag tape drives (7 Chan. IBM),
line printer, Calcomp plotter, Xerox Graphics
Processor: BBN IMP (Honeywell DDP-516) connected to the
Terminals: 58 TV displays, 6 III displays, 3 IMLAC displays,
1 ARDS display, 15 Teletype terminals,
4 Texas Instrument terminals
Special Equipment: Audio input and output systems, hand-eye
equipment (4 TV cameras, 3 arms), remote-
The bulk of this equipment has been purchased through contract
research supported by the Advanced Research Projects Agency, with
some additional funds provided by the National Science Foundation and
the National Institutes of Mental Health. These facilities are
generally adequate, but lack precision display terminals of the sort
needed to support this project. Consequently, two such terminals
have been budgeted in this proposal.
1) Newman, W.M. and Sproull, R.F., "Principals of Interactive
Computer Graphics", McGraw-Hill Book Company, New York, 1973.
CO-PRINCIPAL CO-PRINCIPAL DEPARTMENT SPONSORED
INVESTIGATOR INVESTIGATOR HEAD PROJECTS
------------ ------------ ---------- ------------
NAME J. McCarthy B. Baumgart R. Floyd
SIGNATURE _____________ _____________ _____________ _____________
TITLE Professor, Research Chairman,
Computer Associate Computer
Science Dept. A.I. Lab. Science Dept.
TELEPHONE NO. (415) 321-2300 (415) 321-2300 (415) 321-2300 (415) 321-2300
Ext. 4430 Ext. 3824 Ext. 2273 Ext. 2883
Home: 321-7580 Home: 378-6038 Home: 493-5195
RESEARCH GRANT PROPOSAL BUDGET
TWO YEARS BEGINNING 1 JANUARY 1974
BUDGET CATEGORY YEAR 1 YEAR 2
I. SALARIES & WAGES:
McCarthy, John, $ 0 $ 0
Baumgart, Bruce G., 13,200 13,200
Mock, John S., 9,000 9,000
________, 5,070 5,304
Student Research Ass't.,
50% Acad. Yr., 100% Summer
Baur, Q., 1,834 1,834
Reserve For Salary Increases 1,601 3,316
@ 5.5% per year
TOTAL SALARIES $30,705 $32,654
II. STAFF BENEFITS:
1-1-74 to 8-31-74 @ 17.0% 3,480
9-1-74 to 8-31-75 @ 18.3% 1,873 3,984
9-1-75 thereafter @ 19.3% 2,101
East Coast 450
--- $600 $600
IV. CAPITAL EQUIPMENT:
(2) System Concepts Delta 1
Display Terminals or equivalent $75,000 0
V. EQUIPMENT RENTAL (IBM DISK) $7,500 $7,500
VI. EXPENDABLE MATERIALS & SERVICES:
A. Telephone Service 480
B. Office supplies 600
--- $1,080 $1,080
VII. PUBLICATION COSTS:
2 Papers @ 500ea $1,000 $1,000
VIII. TOTAL DIRECT COSTS:
(Items I thru VII less IV) $46,238 $48,919
IX. INDIRECT COSTS:
On Campus - 47% of NTDC $21,732 $22,992
X. TOTAL COSTS:
(Items IV+VIII+IX) $142,970 $71,911
BORN: September 4, 1927 in Boston, Massachusetts
B.S., (Mathematics) California Institute of Technology, 1948.
Ph.D. (Mathematics) Princeton University, 1951.
HONORS AND SOCIETIES:
American Mathematical Society
Association for Computing Machinery
Sloan Fellow in Physical Science, 1957-59
ACM National Lecturer, 1961
Proctor Fellow, Princeton University, 1950-51.
Higgins Research Instructor in Mathematics,
Princeton University, 1951,53.
Acting Assistant Professor of Mathematics,
Stanford University, Sept. 1953 - Jan. 1955.
Assistant Professor of Mathematics, Dartmouth
College, Feb. 1955 - June 1958.
Assistant Professor of Communication Science,
M.I.T., 1958 - 196l.
Associate Professor of Communication Science,
M.I.T., 1961 - 1962.
Professor of Computer Science
Stanford University, 1962 - present
PROFESSIONAL RESPONSIBILITIES AND SCIENTIFIC INTERESTS:
With Marvin Minsky organized and directed the Artificial
Intelligence Project at M.I.T.
Organized and directs Stanford Artificial Intelligence
Developed the LISP programming system for computing with
symbolic expressions, participated in the development
of the ALGOL 58 and the ALGOL 60 languages.
Present scientific work is in the fields of Artificial
Intelligence, Computation with Symbolic Expressions,
Mathematical Theory of Computation, Time-Sharing
BRUCE G. BAUMGART
BORN: August 7, 1946 in Chicago, Illinois
B.A. (Applied Math - Cum Laude) Harvard University, 1968.
Research Assistant, Harvard University, Physics Department,
1965 - 1968.
Research Programmer, Stanford Artificial Intelligence
Laboratory, 1968 - 1972.
Research Assistant, Stanford University, Computer Science
Department, Artificial Intelligence Laboratory, 1972 - present.
1. "Projection Operators and Partial Differential
Equations", Ph.d. Thesis, Princeton University,
2. "A Method for the Calculation of Limit Cycles by
Successive Approximation" in Contributions
to the Theory of Nonlinear Oscillations II,
Annals of Mathematics Study No. 29,
Princeton University, 1952, pp. 75-79.
3. "An Everywhere Continuous Nowhere Differentiable
Function", American Mathematical Monthly,
December 1953, p. 709.
4. "A Nuclear Reactor for Rockets", Jet Propulsion Lab,
5. "The Inversion of Functions Defined by Turing
Machines", in Automata Studies, Annals of
Mathematics Study No. 34., Princeton University
1956, pp. 177-181.
6. Coeditor with Dr. Claude E. Shannon of Automata
Studies, Annals of Mathematical Study No. 34,
Princeton University, 1956.
7. "Recursive Functions of Symbolic Expressions and
their Computation by Machine", Comm. ACM,
8. "Programs with Common Sense", Proc. Teddington Conf.
on Mechanization of Thought Processes", H.M.
Stationary Office, 1960.
9. (with 12 others) "ALGOL 60", Comm. ACM, May 1960
and Jan. 1963, and Numerische Mathematik,
10. "A Basis for Mathematical Theory of Computation",
Proc. Western Joint Computer Conf., May 1961,
pp. 225-238, and in Braffort and Hirschberg (eds.)
Computer Programming and Formal Systems, North-
Holland, Amsterdam, 1963.
11. "Time-Sharing Computer Systems" in Management and the
Computer of the Future (Greenberger, ed.), MIT
12. (with Abrahams, Edward, Hart, and Levin) LISP 1.5
Programmers Manual, MIT Press, 1962.
13. "Computer Programs for Checking Mathematical Proofs",
Amer. Math. Soc. Proc. Symposia in Pure Math.,
Vol. 5, 1962.
14. (with Boilen, Fredkin, and Licklider) "A Time-Sharing
Debugging System for a Small Computer", Proc.
AFIPS 1963 Spring Joint Computer Conf., Spartan,
15. (with F. Corbato and M. Daggett) "The Linking Segment
Subprogram Language and Linking Loader
Programming Languages", Comm. ACM, July 1963.
16. "Towards a Mathematical Theory of Computation", Proc.
IFIP Congress 62, North-Holland, Amsterdam, 1963.
17. "Problems in the Theory of Computation", Proc. IFIP
Congress 65, 1965.
18. "Time-Sharing Computer Systems" in Conversational
Computers (W. Orr, ed.), Wiley, 1966.
19. "Information", Scientific American, Sept. 1966.
20. "A Formal Description of a Subset of Algol", pp. l-12
of Formal Language Description Languages for
Computer Programming, T.B. Steel, Jr. (editor),
North-Holland Publishing Co., Amsterdam, 1966.
21. (with D. Brian, G. Feldman, and J. Allen) "THOR - A
Display Based Time-Sharing System", AFIPS Conf.
Proc., Vol. 30 (FJCC), Thompson, Washington, D.C.,
22. "Computer Control of a Hand and Eye", Proc. Third
All-Union Conference on Automatic Control
(Technical Cybernetics), Nauka, Moscow, Russia,
23. (with J. Painter) "Correctness of a Compiler for
Arithmetic Expressions", in Amer. Math. Soc.
Proceedings of Symposia in Applied Mathematics,
Mathematical Aspects of Computer Science, New
24. "Programs with Common Sense", in Semantic Information
Processing (M. Minsky, ed.), MIT Press, 1968.
25. (with Earnest, Reddy, and Vicens) "A Computer with
Hands, Eyes and Ears", Proc. AFIPS Conf., 1968
26. (with P. Hayes) "Some Philosophical Problems from
the Standpoint of Artificial Intelligence",
in Machine Intelligence 4 (D. Michie, ed.),
American Elsevier, New York, 1969.
27. (with Z. Manna and A. Pneuli) "Formalization of
Properties of Recursively Defined Functions",
Proc. ACM Symposium on Computing Theory, May 1969.
Also appeared in the Journal of the ACM, July 1970.
28. (with Z. Manna) "Properties of Programs and Partial
Function Logic", in Machine Intelligence 5,
Edinburgh University Press, 1970.
BRUCE G. BAUMGART
1. "GEOMED -- A Geometric Editor", Stanford Artificial
Intelligence Laboratory Operating Note,
No. SAILON-68, May 1972.
2. "Winged Edge Polyhedron Representation", Stanford
Artificial Intelligence Laboratory Memo No. AIM-179,
3. "Image Contouring and Comparing", Stanford Artificial
Intelligence Laboratory Memo No. AIM-199, June 1973.