Reprinted from proceedings of the AFIPS Spring Joint Computer Conference,
Detroit, Michigan, May 21-23, 1963, pp. 329-346.
The Sketchpad system makes it possible for a man and a computer to converse rapidly
through the medium of line drawings. Heretofore, most interaction between man and
computers has been slowed down by the need to reduce all communication to written
statements that can be typed; in the past, we have been writing letters to rather
than conferring with our computers. For many types of communication, such as describing the
shape of a mechanical part or the connections of an electrical circuit, typed statements
can prove cumbersome. The Sketchpad system, by eliminating typed statements (except for
legends) in favor of line drawings, opens up a new area of man-machine communication.
|Figure 1. TX-2 operating area – Sketchpad in use. On the display can be seen part of a bridge similar to those of Figure 15. The Author is holding the light pen. The push buttons “draw,” “move,” etc., are on the box in front of the Author. Part of the bank of toggle switches can be seen behind the Author. The size and position of the part of the total picture seen on the display are controlled by the four black knobs just above the tables.|
An introductory example
To understand what is possible with the system at present let us consider using it to
draw the hexagonal pattern in Figure 4. We will issue specific commands with
a set of push buttons, turn functions on and off with switches, indicate position information
and point to existing drawing parts with the light pen, rotate and magnify picture
parts by turning knobs, and observe the drawing on the display system. This equipment
as provided at Lincoln Laboratory’s TX-2 computer1 is
shown in Figure 1. When our drawing is complete it may be inked on paper, as
were all the drawings in this paper, by a PACE plotter.15
If we point the light pen at the display system and press a button called “draw,”
the computer will construct a straight line segment which stretches like a rubber band
from the initial to the present location of the pen as shown in Figure 2. Additional
presses of the button will produce additional lines, leaving the closed irregular hexagon
shown in Figure 3A.
|Figure 2. Steps for drawing straight lines and circle arcs.|
To make the hexagon regular, we can inscribe it in a circle. To draw the circle we
place the light pen where the center is to be and press the button “circle center,”
leaving behind a center point. Now, choosing a point on the circle (which fixes the
radius) we press the button “draw” again, this time getting a circle arc
whose angular length only is controlled by light pen position as shown in Figure 2.
|Figure 3. Illustrative example, see text.|
Next we move the hexagon into the circle by pointing to a corner of the hexagon and
pressing the button “move” so that the corner follows the light pen, stretching
two rubber band line segments behind it. By pointing to the circle and terminating, we
indicate that the corner is to lie on the circle. Each corner is in this way moved onto
the circle at roughly equal spacing as shown in Figure 3D.
We have indicated that the vertices of the hexagon are to lie on the circle, and they
will remain on the circle throughout our further manipulations. If we also insist
that the sides of the hexagon be of equal length, a regular hexagon will be
With Sketchpad we can say, in effect, make this line equal in length to
that line, pointing to the lines with the light pen. The computer satisfies
all existing conditions (if it is possible) whenever we turn on a toggle switch. This
done, we have a complete regular hexagon inscribed in a circle. We can erase the entire
circle by pointing to any part of it and pressing the “delete” button. T
he completed hexagon is shown in Figure 3F.
To make the hexagonal pattern in Figure 4 we wish to attach a large number of
hexagons together by their corners, and so we designate the six corners of our
hexagon as attachment points by pointing to each and pressing a button. We now
file away the basic hexagon and begin work on a fresh “sheet of paper” by
changing a switch setting. On the new sheet we assemble, by pressing a button
to create each hexagon as an “instance” or subpicture, six hexagons around a
central seventh in approximate position as shown in Figure 3G. A subpicture may
be positioned with the light pen, rotated or scaled by turning the knobs, or
fixed in position by a termination signal, but its internal shape is fixed.
|Figure 4. Hexagonal lattice with half hexagon and semicircle as basic elements.|
By pointing to the corner of one hexagon, pressing a button, and then pointing to
the corner of another hexagon, we can fasten those corners together, because these corners
have been designated as attachment points. If we attach two corners of each outer
hexagon to the appropriate corners of the inner hexagon, the seven are uniquely
related, and the computer will reposition them as shown in Figure 3H. An entire
group of hexagons, once assembled, can be treated as a symbol. An “instance”
of the entire group can be called up on another “sheet of paper” as
a subpicture and assembled with other groups or with single hexagons to make a
very large pattern.
Interpretation of introductory example
In the introductory example above we used the light pen both to position parts
of the drawing and to point to existing parts. We also saw in action the very
general subpicture, constraint, and definition copying
capabilities of the system.
Subpicture: The original hexagon might just as well have been anything else:
a picture of a transistor, a roller bearing, or an airplane wing. Any
number of different symbols may be drawn, in terms of other simpler symbols if
desired, and any symbol may be used as often as desired.
Constraint: When we asked that the vertices of the hexagon lie on the
circle we were making use of a basic relationship between picture parts that is built
into the system. Basic relationships (atomic constraints) to make lines vertical,
horizontal, parallel, or perpendicular; to make points lie on lines or circles; to
make symbols appear upright, vertically above one another or be of equal size;
and to relate symbols to other drawing parts such as points and lines have been included
in the system. Specialized constraint types may be added as needed.
Definition copying: We made the sides of the hexagon be equal in length by pressing
a button while pointing to the side in question. Had we defined a composite operation
such as to make two lines both parallel and equal in length, we could have applied
it just as easily.
Implications of introductory example
As we have seen, a Sketchpad drawing is entirely different from the trail of carbon
left on a piece of paper. Information about how the drawing is tied together is stored
in the computer as well as the information which gives the drawing its particular
appearance. Since the drawing is tied together, it will keep a useful appearance
even when parts of it are moved. For example, when we moved the corners of the
hexagon onto the circle, the lines next to each corner were automatically moved so that
the closed topology of the hexagon was preserved. Again, since we indicated that
the corners of the hexagon were to lie on the circle, they remained on the circle
throughout our further manipulations.
As well as storing how the various parts of the drawing are related, Sketchpad stores
the structure of the subpictures used. For example, the storage for the hexagonal
pattern of Figure 4 indicates that this pattern is made of smaller patterns which
are in turn made of smaller patterns which are composed of single hexagons. If the
master hexagon is changed, the entire appearance but not the structure of the hexagonal
pattern will be changed. For example, if we change the basic hexagon into
a semicircle, the fish scale pattern shown in Figure 4 instantly results.
Sketchpad and the design process
Construction of a drawing with Sketchpad is itself a model of the design
process. The locations of the points and lines of the drawing model the variables
of a design, and the geometric constraints applied to the points and lines of
the drawing model the design constraints which limit the values of
design variables. The ability of Sketchpad to satisfy the geometric constraints
applied to the parts of a drawing models the ability of a good designer to satisfy
all the design conditions imposed by the limitations of his materials, cost, etc.
In fact, since designers in many fields produce nothing themselves but a drawing of
a part, design conditions may well be thought of as applying to the drawing of
a part rather than to the part itself. When such design conditions are added to
Sketchpad’s vocabulary of constraints, the computer will be able to assist a
user not only in arriving at a nice looking drawing, but also in arriving at a sound design.
As more and more applications have been made, it has become clear that the properties
of Sketchpad drawings make them most useful in four broad areas:
For storing and updating drawings: Each time a drawing is made, a description of
that drawing is stored in the computer in a form that is readily transferred to magnetic
tape. A library of drawings will thus develop, parts of which may be used in
other drawings at only a fraction of the investment of time that was put into the
For gaining scientific or engineering understanding of operations that can be
described graphically: A drawing in the Sketchpad system may contain explicit
statements about the relations between its parts so that as one part is changed the
implications of this change become evident throughout the drawing. For instance,
Sketchpad makes it easy to study mechanical linkages, observing the path of some
parts when others are moved.
As a topological input device for circuit simulators, etc.: Since the storage
structure of Sketchpad reflects the topology of any circuit or diagram, it can
serve as an input for many network or circuit simulating programs. The additional
effort required to draw a circuit completely from scratch with the Sketchpad system
may well be recompensed if the properties of the circuit are obtainable through simulation
of the circuit drawn.
For highly repetitive drawings: The ability of the computer to reproduce any
drawn symbol anywhere at the press of a button, and to recursively include subpictures
within subpictures makes it easy to produce drawings which are composed of huge numbers of
parts all similar in shape.
II. Ring structure
The basic n-component element structure described by Ross10
has been somewhat expanded in the implementation of Sketchpad so that all references made to
a particular n-component element or block are collected together by a string of
pointers which originates within that block. For example, not only may the end
points of a line segment be found by following pointers in the line block (n-component
element), but also all the line segments which terminate on a particular point
may be found by following a string of pointers which starts within the point block.
This string of pointers closes on itself; the last pointer points back to the
first, hence the name “ring.” The ring points both ways to make it
easy to find both the next and the previous member of the ring in case, as
when deleting, some change must be made to them.
The basic ring structure operations are:
- Inserting a new member into a ring at some specified location on it, usually first or last.
- Removing a member from a ring.
- Putting all the members of one ring, in order, into another at some specified location
in it, usually first or last.
- Performing some auxiliary operation on each member of a ring in either forward
or reverse order.
These basic ring structure operations are implemented by short sections of program
defined as MACRO instructions in the compiler language. By suitable treatment of zero
and one member rings, the basic programs operate without making special cases.
Subroutines are used for setting up new n-component elements in free spaces in
the storage structure. As parts of the drawing are deleted, the registers which
were used to represent them become free. New components are set up at the end of the
storage area, lengthening it, while free blocks are allowed to accumulate. Garbage collection
periodically compacts the storage structure by removal of the free blocks.
Generic structure, hierarchies
The main part of Sketchpad can perform basic operations on any drawing part, calling
for help from routines specific to particular types of parts when that is necessary.
For example, the main program can show any part on the display system by calling
the appropriate display subroutine. The big power of the clear-cut separation of the
general and the specific is that it is easy to change the details of specific parts
of the program to get quite different results without any need to change the general
In the data storage structure the separation of general and specific is accomplished by
collecting all things of one type together in a ring under a generic heading.
The generic heading contains all the information which makes this type of thing different
from all other types of things. Thus the data storage structure itself contains all
the specific information. The generic blocks are further gathered together under
super-generic or generic-generic blocks, as shown in Figure 5.
|Figure 5. Generic structure. The n-component elements for each point or line, etc., are collected under the generic blocks “lines,” “points,” etc., shown.|
Addition of new types of things to the Sketchpad system’s vocabulary of picture
parts requires only the construction of a new generic block (about 20 registers) and
the writing of appropriate subroutines for the new type. The subroutines might be
easy to write, as they usually are for new constraints, or difficult to write, as
for adding ellipse capability, but at least a finite, well-defined task faces one to
add a new ability to the system. Without a generic structure it would be
almost impossible to add the instructions required to handle a new type of element.
III. Light pen
In Sketchpad the light pen* is time shared between the
functions of coordinate input for positioning picture parts on the drawing and
demonstrative input for pointing to existing picture parts to make changes. Although almost
any kind of coordinate input device could be used instead of the light pen for
positioning, the demonstrative input uses the light pen optics as a sort of
analog computer to remove from consideration all but a very few picture parts which
happen to fall within its field of view, saving considerable program time. Drawing
systems using storage display devices of the Memotron type may not be practical because
of the loss of this analog computation feature.
To initially establish pen tracking, the Sketchpad user must inform the computer
of an initial pen location. This has come to be known as “inking-up” and
is done by “touching” any existing line or spot on the display, whereupon
the tracking cross appears. If no picture has yet been drawn, the letters INK
are always displayed for this purpose. Sketchpad uses loss of tracking as
a “termination signal” to stop drawing. The user signals that he
is finished drawing by flicking the pen too fast for the tracking program
Demonstrative use of pen
During the 90% of the time that the light pen and display system are free from the
tracking chore, spots are very rapidly displayed to exhibit the drawing being built,
and thus the lines and circles of the drawing appear. The light pen is sensitive
to these spots and reports any which fall within its field of view. Thus, a
table of the picture parts seen by the light pen is assembled during each complete display
cycle. At the end of a display cycle this table contains all the picture parts
that could even remotely be considered as being “aimed at.”
The one-half inch diameter field of view of the light pen, although well suited to
tracking, is relatively large for pointing. Therefore, the Sketchpad system will
reject any seen part which is further from the center of the light pen than
some small minimum distance; about 1/8 inch was found to be suitable. For every
kind of picture part some method must be provided for computing its distance from
the light pen center or indicating that this computation cannot be made.
After eliminating all parts seen by the pen which lie outside the smaller effective
field of view, the Sketchpad system considers objects topologically related to the ones
actually seen. End points of lines and attachment points of instances (subpictures)
are especially important. One can thus aim at the end point of a line even though
only the line is displayed. Figure 6 outlines the various regions within which the
pen must lie to be considered aimed at a line segment, a circle arc, their end
points, or their intersection.
|Figure 6. Areas in which pen must lie to “aim at” existing drawing parts (solid lines).|
Pseudo pen location
When the light pen is aimed at a picture part, the exact location of the light pen
is ignored in favor of a “pseudo pen location” exactly on the part aimed
at. If no object is aimed at, the pseudo pen location is taken to be the actual
pen location. The pseudo pen location is displayed as a bright dot which is used
as the “point of the pencil” in all drawing operations. As the light pen is
moved into the areas outlined in Figure 6 the dot will lock onto the existing
parts of the drawing, and any moving picture parts will jump to their new locations
as the pseudo pen location moves to lie on the appropriate picture part.
With just the basic drawing creation and manipulation functions of “draw,”
“move,” and “delete,” and the power of the pseudo pen
location and demonstrative language programs, it is possible to make fairly extensive
drawings. Most of the constructions normally provided by straight edge and compass are
available in highly accurate form. Most important, however, the pseudo pen
location and demonstrative language give the means for entering the topological properties
of a drawing into the machine.
IV. Display generation
The display system, or “scope,” on the TX-2 is a ten bit per axis
electrostatic deflection system able to display spots at a maximum rate of
about 100,000 per second. The coordinates of the spots which are to be seen on
the display are stored in a large table so that computation and display may proceed
independently. If, instead of displaying each spot successively, the
display program displays them in a random order or with interlace, the flicker of
the display is reduced greatly.
Marking of display file
Of the 36 bits available to store each display spot in the display file, 20 give
the coordinates of that spot for the display system, and the remaining 16 give
the address of the n-component element which is responsible for adding that spot
to the display. Thus, all the spots in a line are tagged with the ring structure address
of that line, and all the spots in an instance (subpicture) are tagged as
belonging to that instance. The tags are used to identify the particular part
of the drawing being aimed at by the light pen.
If a part of the drawing is being moved by the light pen, its display spots will
be recomputed as quickly as possible to show it in successive positions. The
display spots for such moving parts are stored at the end of the display file so
that the display of the many non-moving parts need not be disturbed. Moving parts
are made invisible to the light pen.
Magnification of pictures
The shaft position encoder knobs below the scope (see Figure 1) are used to
tell the program to change the display scale factor or the portion of the
page displayed. The range of magnification of 2000 available makes it possible to
work, in effect, on a 7-inch square portion of a drawing about ¼ mile on a side.
For a magnified picture, Sketchpad computes which portion(s) of a curve will appear
on the display and generates display spots for those portions only.
The “edge detection” problem is the problem of finding suitable end
points for the portion of a curve which appears on the display.
In concept the edge detection problem is trivial. In terms of program time for
lines and circles the problem is a small fraction of the total computational load
of the system, but in terms of program logical complexity the edge detection
problem is a difficult one. For example, the computation of the intersection of
a circle with any of the edges of the scope is easy, but computation of the
intersection of a circle with all four edges may result in as many as eight
intersections, some pairs of which may be identical, the scope corners. Now
which of these intersections are actually to be used as starts of circle arcs?
Line and circle generation
All of Sketchpad’s displays are generated from straight line segments, circle
arcs, and single points. The generation of the lines and circles is accomplished
by means of the difference equations:
for lines, and
for circles, where subscripts i indicate successive display spots,
subscript c indicates the circle center, and R is the radius of
the circle in Scope Units. In implementing these difference equations in the program,
the fullest possible use is made of the coordinate arithmetic capability of the
TX-2 so that both the x and y equation computations are performed in parallel
on 18 bit subwords. Even so, about ¾ of the total Sketchpad computation time is
spent in line and circle generation. A vector and circle generating display would
materially reduce the computational load of Sketchpad.
For computers which do only one addition at a time, the difference equations:
should be used to generate circles. Equations (3) approximate a circle well enough and
are known to close exactly both in theory and when implemented, because the x
and y equations are dissimilar.
Digits and text
Text, to put legends on a drawing, is displayed by means of special tables which
indicate the locations of line and circle segments to make up the letters and
numbers. Each piece of text appears as a single line of not more than 36 equally
spaced characters which can be changed by typing. Digits to display the value
of an indicated scalar at any position and in any size and rotation are formed from
the same type face as text. It is possible to display up to five decimal digits with
sign; binary to decimal conversion is provided, and leading zeros are suppressed.
Subpictures, whose use was seen in the introductory example above, are each represented
in storage as a single n-component element. A subpicture is said to be an
“instance” of its “master picture.” To display an instance,
all of the lines, text, etc. of its master picture must be shown in miniature
on the display. The instance display program makes use of the line, circle,
number, and text display programs and itself to expand the internal structure
of the instance.
Display of abstractions
The usual picture for human consumption displays only lines, circles, text, digits,
and instances. However, certain very useful abstractions which give the drawing
the properties desired by the user are represented in the ring structure storage.
For example, the fact that the start and end points of a circle arc should be
equidistant from the circle’s center point is represented in storage by
a “constraint” block. To make it possible for a user to manipulate
these abstractions, each abstraction must be able to be seen on the display
if desired. Not only does displaying abstractions make it possible for the human
user to know that they exist, but also makes it possible for him to aim at them
with the light pen and, for example, erase them. To avoid confusion, the display
for particular types of objects may be turned on or off selectively by toggle
switches. Thus, for example, one can turn on display of constraints as well as
or instead of the lines and circles which are normally seen.
If their selection toggle switch is on, constraints are displayed as shown
in Figure 7. The central circle and code letter are located at the
average location of the variables constrained. The four arms of a constraint extend
from the top, right side, bottom, and left side of the circle to the first,
second, third, and fourth variables constrained, respectively. If fewer than four
variables are constrained, excess arms are omitted. In Figure 7 the constraints
are shown applied to “dummy variables” each of which shows as an X.
|Figure 7. Display of constraints.|
Another abstraction that can be displayed if desired is the value of a set
of digits. For example, in Figure 8 are shown three sets of digits all displaying
the same scalar value, -5978. The digits themselves may be moved, rotated,
or changed in size, without changing the value displayed. If we wish to change
the value, we point at its abstract display, the # seen in Figure 8. The three sets
of digits in Figure 8 all display the same value, as indicated by the lines connecting them
to the #; changing this value would make all three sets of digits change. Constraints
may be applied independently to either the position of the digits or their value
as indicated by the two constraints in the figure.
|Figure 8. Three sets of digits displaying the same scalar value.|
V. Recursive functions
In the process of making the Sketchpad system operate, a few very general functions
were developed which make no reference at all to the specific types of entities
on which they operate. These general functions give the Sketchpad system the ability
to operate on a wide range of problems. The motivation for making the functions as
general as possible came from the desire to get as much result as possible from the
programming effort involved. For example, the general function for expanding instances
makes it possible for Sketchpad to handle any fixed geometry subpicture. The power
obtained from the small set of generalized functions in Sketchpad is one of the
most important results of the research.
In order of historical development, the recursive functions in use in
the Sketchpad system are:
- Expansion of instances, making it possible to have subpictures within subpictures
to as many levels as desired.
- Recursive deletion, whereby removal of certain picture parts will remove other picture
parts in order to maintain consistency in the ring structure.
- Recursive merging, whereby combination of two similar picture parts forces
combination of similarly related other picture parts, making possible application
of complex definitions to an object picture.
If a thing upon which other things depend is deleted, the dependent things must
be deleted also. For example, if a point is to be deleted, all lines which
terminate on the point must also be deleted. Otherwise, since the n-component elements
for lines contain no positional information, where would these lines end? Similarly,
deletion of a variable requires deletion of all constraints on that variable;
a constraint must have variables to act on.
If two things of the same type which are independent are merged, a single
thing of that type results, and all things which depended on either of the
merged things depend on the result* of the merger. For example, if two points are
merged, all lines which previously terminated on either point now terminate on
the single resulting point. In Sketchpad, if a thing is being moved with the
light pen and the termination flick of the pen is given while aiming at another thing
of the same type, the two things will merge. Thus, if one moves a point to
another point and terminates, the points will merge, connecting all lines which
formerly terminated on either. This makes it possible to draw closed polygons.
If two things of the same type which do depend on other things are merged,
the things depended on by one will be forced to merge, respectively, with the things
depended on by the other. The result* of merging two
dependent things depends, respectively, on the results*
of the mergers it forces. For example, if two lines are merged, the resultant line
must refer to only two end points, the results of merging the pairs of end
points of the original lines. All lines which terminated on any of the four
original end points now terminate on the appropriate one of the remaining pair.
More important and useful, all constraints which applied to any of the four
original end points now apply to the appropriate one of the remaining pair. This
makes it possible to speak of line segments as being parallel even though (because
line segments contain no numerical information to be constrained) the parallelism
constraint must apply to their end points and not to the line segments themselves.
If we wish to make two lines both parallel and equal in length, the steps outlined
in Figure 9 make it possible. More obscure relationships between dependent
things may be easily defined and applied. For example, constraint complexes can
be defined to make line segments be collinear, to make a line be tangent to
a circle, or to make the values represented by two sets of digits be equal.
|Figure 9. Applying a two-constraint definition to turn a quadrilateral into a parallelogram.|
Recursive display of instances
The block of registers which represents an instance is remarkably small considering
that it may generate a display of any complexity. For the purposes of display,
the instance block makes reference to its master picture. The instance will appear
on the display as a figure geometrically similar to its master picture at a
location, size, and rotation indicated by the four numbers which constitute the
“value” of the instance. The value of an instance is considered numerically
as a four dimensional vector. The components of this vector are the coordinates
of the center of the instance and its actual size as it appears on the drawing times
the sine and cosine of the rotation angle involved.
In displaying an instance of a picture, reference is made to the master picture
to find out what picture parts are to be shown. The master picture referred to
may contain instances, however, requiring further reference, and so on until a
picture is found which contains no instances. At each stage in the recursion, any
picture parts displayed must be relocated so that they will appear at the correct
position, size and rotation on the display. Thus, at each stage of the recursion,
some transformation is applied to all picture parts before displaying them. If an
instance is encountered, the transformation represented by its value must be adjoined
to the existing transformation for display of parts within it. When the expansion
of an instance within an instance is finished, the transformation must be restored
for continuation at the higher level.
Attachers and instances
Many symbols must be integrated into the rest of the drawing by attaching lines to
the symbols at appropriate points, or by attaching the symbols directly to each
other. For example, circuit symbols must be wired up, geometric patterns made by fitting
shapes together, or mechanisms composed of links tied together appropriately. An
instance may have any number of attachment points, and a point may serve as
attacher for any number of instances. The light pen has the same affinity for the
attachers of an instance that it has for the end point of a line.
An “instance-point” constraint, shown with code T in Figure 10C,
is used to relate an instance to each of its attachment points. An instance-point constraint
is satisfied only when the point bears the same relationship to the instance that
a master point in the master picture for that instance bears to the master
picture coordinate system.
|Figure 10. Definition pictures to be copied, see text.|
Any point may be an attacher of an instance, but the point must be designated as
an attacher in the master drawing of the instance. For example, when one first
draws a resistor, the ends of the resistor must be designated as attachers if wiring
is to be attached to instances of it. At each level of building complex pictures,
the attachers must be designated anew. Thus of the three attachers of a
transistor it is possible to select one or two to be the attachers of a flip-flop.
VI. Building a drawing, the copy function
At the start of the Sketchpad effort certain ad hoc drawing functions were
programmed as the atomic operations of the system. Each such operation, controlled
by a push button, creates in the ring structure a specific set of new drawing
parts. For example, the “draw” button creates a line segment and two
new end points (unless the light pen happens to be aimed at a point in which case
only one new point need be created). Similarly, there are atomic operations for drawing
circles, applying a horizontal or vertical constraint to the end points of a
line aimed at, and for adding a “point-on-line” constraint whenever
a point is moved onto a line and left there.
The atomic operations described above make it possible to create in the ring structure
new picture components and relate them topologically. The atomic operations are,
of course, limited to creating points, lines, circles, and two or three types
of constraints. Since implementation of the copy function it has become possible to
create in the ring structure any predefined combination of picture parts and constraints
at the press of a button. The recursive merging function makes it possible to
relate the copied set of picture parts to any existing parts. For example, if
a line segment and its two end points are copied into the object picture, the action
of the “draw” button may be exactly duplicated in every respect.
Along with the copied line, however, one might copy as well a constraint, Code H,
to make the line horizontal as shown in Figure 10A, or two constraints to make
the line both horizontal and three inches long, or any other variation one cares to
put into the ring structure to be copied.
When one draws a definition picture to be copied, certain portions of it to be
used in relating it to other object picture parts are designated as “attachers.”
Anything at all may be designated: for example, points, lines, circles, text, even
constraints! The rules used for combining points when the “draw” button
is pressed are generalized so that:
For copying a picture, the last-designated attacher is left moving with the light
pen. The next-to-last-designated attacher is recursively merged with whatever object the
pen is aimed at when the copying occurs, if that object is of like type. Previously
designated attachers are recursively merged with previously designated object picture
parts, if of like type, until either the supply of designated attachers or the
supply of designated object picture parts is exhausted. The last-designated attacher
may be recursively merged with any other object of like type when the termination flick
is given. Normally only two designated attachers are used because it is hard
to keep track of additional ones.
If the definition picture consists of two line segments, their four end points,
and a constraint, Code M, on the points which makes the lines equal in length, with
the two lines designated as attachers as shown in Figure 10B, copying enables the
user to make any two lines equal in length. If the pen is aimed at a line
when “copy” is pushed, the first of the two copied lines merges with
it (taking its position and never actually being seen). The other copied line is left
moving with the light pen and will merge with whatever other line the pen is aimed
at when termination occurs. Since merging is recursive, the copied equal-length
constraint, Code M, will apply to the end points of the desired pair of
object picture lines.
As we have seen above, the internal structure of an instance is entirely fixed. The
internal structure of a copy, however, is entirely variable. An instance always
retains its identity as a single part of the drawing; one can only delete an entire
instance. Once a definition picture is copied, however, the copy loses all identity
as a unit; individual parts of it may be deleted at will.
One might expect that there was intermediate ground between the fixed-internal-structure
instance and the loose-internal-structure copy. One might wish to produce
a collection of picture parts, some of which were fixed internally and some of
which were not. The entire range of variation between the instance and the copy can
be constructed by copying instances.
For example, the arrow shown in Figure 10C can be copied into an object picture
to result in a fixed-internal-structure diamond arrowhead with a flexible tail. As
the definition in Figure 10C is set up, drawing diamond-arrowheaded lines is
just like drawing ordinary lines. One aims the light pen where the tail is to end,
presses “copy,” and moves off with an arrowhead following the pen.
The diamond arrowhead in this case will not rotate (constraint Code E), and will
not change size (constraint Code F).
Copying pre-joined instances can produce vast numbers of joined instances very
easily. For example, the definition in Figure 10D, when repetitively copied, will
result in a row of joined, equal size (constraint Code S) diamonds. In this case
the instances themselves are attachers. Although each press of the “copy”
button copies two new instances into the object picture, one of these is merged
with the last instance in the growing row. In the final row, therefore, each instance
carries all constraints which are applied to either of the instances in the
definition. This is why only one of the instances in Figure 10D carries the erect
constraint, Code E.
VII. Constraint satisfaction
The major feature which distinguishes a Sketchpad drawing from a paper and pencil
drawing is the user’s ability to specify to Sketchpad mathematical conditions on
already drawn parts of his drawing which will be automatically satisfied by the computer
to make the drawing take the exact shape desired. The process of fixing up a drawing
to meet new conditions applied to it after it is already partially complete is very
much like the process a designer goes through in turning a basic idea into a finished
design. As new requirements on the various parts of the design are thought of, small
changes are made to the size or other properties of parts to meet the new conditions.
By making Sketchpad able to find new values for variables which satisfy the conditions
imposed, it is hoped that designers can be relieved of the need of much
mathematical detail. The effort expended in making the definition of constraint types as
general as possible was aimed at making design constraints as well as geometric
constraints equally easy to add to the system.
Definition of a constraint type
Each constraint type is entered into the system as a generic block indicating the
various properties of that particular constraint type. The generic block tells how many
variables are constrained, which of these variables may be changed in order to
satisfy the constraint, how many degrees of freedom are removed from the constrained
variables, and a code letter for human reference to this constraint type.
The definition of what a constraint type does is a subroutine which will compute,
for the existing values of the variables of a particular constraint of that type,
the error introduced into the system by that particular constraint. For example, the
defining subroutine for making points have the same x coordinate (to make a line between
them vertical) computes the difference in their x coordinates. What could be
simpler? The computed error is a scalar which the constraint satisfaction routine will
attempt to reduce to zero by manipulation of the constrained variables. The
computation of the error may be non-linear or time dependent, or it may
involve parameters not a part of the drawing such as the setting of
toggle switches, etc.
When the one pass method of satisfying constraints to be described later on fails,
the Sketchpad system falls back on the reliable but slow method of relaxation11
to reduce the errors indicated by various computation subroutines to smaller and smaller
values. For simple constructions such as the hexagon illustrated in Figure 3,
the relaxation procedure is sufficiently fast to be useful. However, for complex
systems of variables, especially directly connected instances, relaxation is unacceptably
slow. Fortunately it is for just such directly connected instances that the one pass method
shows the most striking success.
One pass method
Sketchpad can often find an order in which the variables of a drawing may be re-evaluated
to completely satisfy all the conditions on them in just one pass. For the cases in
which the one pass method works, it is far better than relaxation: it gives correct
answers at once; relaxation may not give a correct solution in any finite time.
Sketchpad can find an order in which to re-evaluate the variables of a drawing for
most of the common geometric constructions. Ordering is also found easily for
the mechanical linkages shown in Figures 13 and 14. Ordering cannot be found
for the bridge truss problem in Figure 15.
The way in which the one pass method works is simple in principle and was
easy to implement as soon as the nuances of the ring structure manipulations
were understood. To visualize the one pass method, consider the variables of
the drawing as places and the constraints relating variables as passages through which
one might pass from one variable to another. Variables are adjacent to each other in
the maze formed by the constraints if there is a single constraint which constrains them
both. Variables are totally unrelated if there is no path through the constraints by
which to pass from one to the other.
Suppose that some variable can be found which has so few constraints applying
to it that it can be re-evaluated to completely satisfy all of them. Such a variable
we shall call a “free” variable. As soon as a variable is recognized
as free, the constraints which apply to it are removed from further consideration, because
the free variable can be used to satisfy them. Removing these constraints, however,
may make adjacent variables free. Recognition of these new variables as free
removes further constraints from consideration and may make other adjacent variables
free, and so on throughout the maze of constraints. The manner in which freedom
spreads is much like the method used in Moore’s algorithm8
to find the shortest path through a maze. Having found that a collection of variables
is free, Sketchpad will re-evaluate them in reverse order, saving the first-found
free variable until last. In re-evaluating any particular variable, Sketchpad uses
only those constraints which were present when that variable was found to be free.
VIII. Examples and conclusions
The examples in this section were all taken from the library tape and thus serve to
illustrate not only how the Sketchpad system can be used, but also how it
actually has been used so far. We conclude from these examples that Sketchpad drawings
can bring invaluable understanding to a user. For drawings where motion of the
drawing, or analysis of a drawn problem is of value to the user, Sketchpad excels.
For highly repetitive drawings or drawings where accuracy is required, Sketchpad is
sufficiently faster than conventional techniques to be worthwhile. For drawings which
merely communicate with shops, it is probably better to use conventional
paper and pencil.
The instance facility enables one to draw any symbol and duplicate its appearance
anywhere on an object drawing at the push of a button. This facility made the
hexagonal pattern we saw in Figure 4 easy to draw. It took about one half hour
to generate 900 hexagons, including the time taken to figure out how to do it.
Plotting them takes about 25 minutes. The drafting department estimated it would take
two days to produce a similar pattern.
The instance facility also made it easy to produce long lengths of the zig-zag pattern
shown in Figure 11. As the figure shows, a single “zig” was duplicated
in multiples of five and three, etc. Five hundred zigs were generated in a
single row. Four such rows were plotted one-half inch apart to be used for producing a
printed circuit delay line. Total time taken was about 45 minutes for constructing
the figure and about 15 minutes to plot it.
|Figure 11. Zig-Zag for delay line.|
A somewhat less repetitive pattern to be used for encoding the time in a digital clock
is shown in Figure 12. Each cross in the figure marks the position of a hole.
The holes are placed so that a binary coded decimal (BCD) number will indicate the time.
Total time for placing crosses was 20 minutes, most of which was spent trying
to interpret a pencil sketch of their positions.
|Figure 12. Binary coded decimal encoder for clock. Encoder was plotted exactly 12 inches in diameter for direct use as a layout.|
By far the most interesting application of Sketchpad so far has been drawing and moving
linkages. The ability to draw and then move linkages opens up a new field of graphical
manipulation that has never before been available. It is remarkable how even a simple
linkage can generate complex motions. For example, the linkage of Figure 13 has
only three moving parts. In this linkage a central ⊥ link is suspended between
two links of different lengths. As the shorter link rotates, the longer one oscillates
as can be seen in the multiple exposure. The ⊥ link is not shown in Figure 13 so
that the motion of four points on the upright part of the ⊥ may be seen. These are
the four curves at the top of the figure.
|Figure 13. Three bar linkage. The paths of four points on the central link are traced. This is a 15 second time exposure of a moving Sketchpad drawing.|
To make the three bar linkage, an instance shaped like the ⊥ was drawn and given 6
attachers, two at its joints with the other links and four at the places whose paths
were to be observed. Connecting the ⊥ shaped subpicture onto a linkage composed of three
lines with fixed length created the picture shown. The driving link was rotated by
turning a knob below the scope. Total time to construct the linkage was less than
5 minutes, but over an hour was spent playing with it.
A linkage that would be difficult to build physically is shown in Figure 14A.
This linkage is based on the complete quadrilateral. The three circled points and
the two lines which extend out of the top of the picture to the right and left
are fixed. Two moving lines are drawn from the lower circled points to the intersections
of the long fixed lines with the driving lever. The intersection of these two
moving lines (one must be extended) has a box around it. It can be shown theoretically
that this linkage produces a conic section which passes through the place
labeled “point on curve” and is tangent to the two lines
marked “tangent.” Figure 14B shows a time exposure of the moving point
in many positions. At first, this linkage was drawn and working in 15 minutes. Since then
we have rebuilt it time and again until now we can produce it from scratch in
about 3 minutes.
|Figure 14. Conic drawing linkage. As the “driving lever” is moved, the point shown with a box around it (in A) traces a conic section. This conic can be seen in the time exposure (B).|
To make it possible to have an absolute scale in drawings, a constraint is provided
which forces the value displayed by a set of digits to indicate the distance between
two points on the drawing. This distance-indicating constraint is used to make the
number in a dimension line correspond to its length. Putting in a dimension line
is as easy as drawing any other line. One points to where one end is to be left, copies
the definition of the dimension line by pressing the “copy” button, and
then moves the light pen to where the other end of the dimension line is to be.
The first dimension line took about 15 minutes to construct, but that need never
be repeated since it is a part of the library.
One of the largest untapped fields for application of Sketchpad is as an input program
for other computation programs. The ability to place lines and circles graphically, when
coupled with the ability to get accurately computed results pictorially displayed,
should bring about a revolution in computer application. By using Sketchpad’s
relaxation procedure we were to demonstrate analysis of the force distribution in the
members of a pin connected truss.
A bridge is first drawn with enough constraints to make it geometrically accurate.
These constraints are then deleted and each member is made to behave like a bridge beam.
A bridge beam is constrained to maintain constant length, but any change in length
is indicated by an associated number. Under the assumption that each bridge beam
has a cross-sectional area proportional to its length, the numbers represent the forces
in the beams. The basic bridge beam definition (consisting of two constraints and a
number) may be copied and applied to any desired line in a bridge picture by pointing
to the line and pressing the “copy” button.
Having drawn a basic bridge shape, one can experiment with various loading conditions
and supports to see what the effect of making minor modifications is. For example,
an arch bridge is shown in Figure 15 supported both as a three-hinged arch (two
supports) and as a cantilever (four supports). For nearly identical loading conditions
the distribution of forces is markedly different in these two cases.
|Figure 15. Cantilever and arch bridges. The numbers indicate the forces in the various members as computed by Sketchpad. Central load is not exactly vertical.|
Sketchpad need not be applied exclusively to engineering drawings. For example,
the girl “Nefertite” shown in Figure 16 can be made to wink by
changing which of the three types of eyes is placed in position on her otherwise
eyeless face. In the same way that linkages can be made to move, a stick
figure could be made to pedal a bicycle or Nefertite’s hair could be made to
swing. The ability to make moving drawings suggests that Sketchpad might be used for making
|Figure 16. Winking girl, “Nefertite,” and her component parts.|
Electrical circuit diagrams
Unfortunately, electrical circuits require a great many symbols which have not
yet been drawn properly with Sketchpad and therefore are not in the library. After
some time is spent working on the basic electrical symbols it may be easier to
draw circuits. So far, however, circuit drawing has proven difficult.
The circuits of Figure 17 are parts of an analog switching scheme. You can
see in the figure that the more complicated circuits are made up of simpler symbols
and circuits. It is very difficult, however, to plan far enough ahead to
know what composites of circuit symbols will be useful as subpictures of the final
circuit. The simple circuits shown in Figure 17 were compounded into a big
circuit involving about 40 transistors. Including much trial and error, the time
taken by a new user (for the big circuit not shown) was ten hours. At the end of
that time the circuit was still not complete in every detail and he decided it would be
better to draw it by hand after all.
|Figure 17. Circuit diagram. These are parts of the large circuit mentioned in the text.|
The circuit experience points out the most important fact about Sketchpad drawings.
It is only worthwhile to make drawings on the computer if you get something more out
of the drawing than just a drawing. In the repetitive
patterns we saw in the first examples, precision and ease of constructing great
numbers of parts were valuable. In the linkage examples, we were able to gain
an understanding of the behavior of a linkage as well as its appearance. In the
bridge examples we got design answers which were worth far more than the computer time
put into them. If we had had a circuit simulation program connected to Sketchpad so
that we would have known whether the circuit we drew worked, it would have
been worth our while to use the computer to draw it. We are as yet a long way from
being able to produce routine drawings economically with the computer.
The methods outlined in this paper generalize nicely to three dimensional drawing. In
fact, the work reported in “Sketchpad III” by Timothy Johnson3
will let the user communicate solid objects to the computer. Johnson is
completely bypassing the problem of converting several two dimensional drawings into
a three dimensional shape. Drawing will be directly in three dimensions from the
start. No two dimensional representation will ever be stored.
Work is also proceeding in direct conversion of photographs into line drawings.
Roberts reports a computer program9 able to recognize
simple objects in photographs well enough to produce three dimensional line drawings
for them. Roberts is storing his drawings in the ring structure described here
so that his results will be compatible with the three dimensional version
Major improvements to Sketchpad of the same order and power as the existing
definition copying capability can be foreseen. At present Sketchpad is able to
add defined relationships to an existing object drawing. A method should be
devised for defining and applying changes which involve removing some parts of the
object drawing as well as adding new ones. Such a capability would permit one
to define, for example, what rounding off a corner means. Then, one could round
off any corner by pointing to it and applying the definition.
The author is indebted to Professors Claude E. Shannon, Marvin Minsky and
Steven A. Coons of the Massachusetts Institute of Technology for their help and
advice throughout the course of this research.
The author also wishes to thank Douglas T. Ross and Lawrence G. Roberts for their
help and answers to his many questions.
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