The Number Wheel.
A Tablet Based V a l u a t o r
for Interactive Three-Dimensional Positioning
Robert W. Thornton 1
Carneg,e-Mellon
Umverslty
Pittsburgh, Pennsylvania
A logical valuator device which provides
i n t e r a c t i v e g r a p h i c a l i n p u t o f numeric values is
p r e s e n t e d . This d e v i c e , c a l l e d t h e Number Wheel,
w a s d e v e l o p e d f o r I n t e r a c t i v e control of highly
d y n a m i c t h r e e - d i m e n s i o n a l d i s p l a y s b u t is not limited
t o t h i s u s e : It Is a g e n e r a l p u r p o s e v a l u a t o r d e v i c e .
T h e I m p l e m e n t a t i o n o f t h e Number Wheel d e s c r i b e d
h e r e Is b a s e d upon a d i g i t i z e r t a b l e t as t h e p h y s i c a l
Input device.
1. Introduction
The Number Wheel Is a graphic Input device whose
d e v e l o p m e n t w a s m o t i v a t e d by the need for accurate
and c o n v e n i e n t I n t e r a c t i v e control over dynamic
d i s p l a y s o f t h r e e - d i m e n s i o n a l shapes such as rotation
o r o t h e r a n i m a t e d motion. The Number Wheel Is a
l o g i c a l valuator d e v i c e (allowing Input of a numerical
v a l u e ) w h o s e implementation is based upon a Iocator
d e v i c e ( w h i c h allows Input of locations In a space of
o n e o r more dimensions) 2. A group of Number Wheels
Is u s e d t o control the three-dimensional display by
a s s o c i a t i n g a particular Number Wheel's value with
e a c h o f t h e v i e w parameters under control such as
a n g l e s of rotation, location of viewpoint, angle of view,
e t c . : as t h e user changes a Number Wheel's value the
t h r e e - d i m e n s i o n a l display Is updated In conjunction
w i t h t h e n e w value of the associated v i e w parameter.
T h e c h a r a c t e r o f t h e Number Wheel is b e s t
e x p l a i n e d b y d e v e l o p i n g an a n a l o g y w i t h a
h y p o t h e t i c a l p h y s i c a l d e v i c e . The Number Wheel
c a n b e t h o u g h t o f as a w h e e l w h i c h has a portion o f
i t s c i r c u m f e r e n c e , o r t r e a d , p r o t r u d i n g through a
s l o t on t h e s u r f a c e o f t h e t a b l e t , s o m e w h a t like a
g i a n t t h u m b w h e e l . Each value in t h e d e s i r e d r a n g e
o f t h e v a l u a t o r Is r e p r e s e n t e d b y a point on t h e
c i r c u m f e r e n c e o f t h e w h e e l w i t h the value of t h e
d e v i c e a t a n y g i v e n t i m e being t h e point at t h e t o p
o f t h e w h e e l . T h e v a l u a t o r is c h a n g e d b y p u t t i n g
t h e p e n on t h e w h e e l w h e r e it p r o t r u d e s t h r o u g h t h e
t a b l e t a n d m o v i n g It b a c k o r f o r t h In t h e d i r e c t i o n o f
r o t a t i o n . W h e n e v e r t h e pen leaves the rim of t h e
w h e e l w h i l e s t i l l m o v i n g , t h e Number Wheel
m a i n t a i n s t h e s a m e s p e e d o f r o t a t i o n until t h e pen
r e t u r n s t o t h e w h e e l In o r d e r t o c h a n g e o r stop its
movement.
As s t a t e d b e f o r e , the Number Wheel Is based on a
I o c a t o r d e v i c e . This Iocator may be either the relative
p o s i t i o n i n g t y p e , such as a "mouse" (see [ 5 ] ) , or the
a b s o l u t e t y p e , such as a digitizer tablet.
Most
m u l t i - d i m e n s i o n a l Iocators such as two-dimensional
t a b l e t s , t h e mostly o n e - o f - a - k i n d three-dimensional
d i g i t i z e r s ( s e e [ 4 ] for mechanical, [ 1 ] for sonic, or [ 3 ]
f o r LED b a s e d e x a m p l e s ) , or many-dimensioned remote
m a n i p u l a t o r s might be used e f f e c t i v e l y for controlling
sets
of
Number Wheels.
The only additional
r e q u i r e m e n t s for t h e Iocator are that updated locations
m u s t b e a v a i l a b l e many times per second ( 6 0 per
s e c o n d is commonly used, 20 per second Is adequate)
and t h e r e must be a s w i t c h for the user to turn this
s t r e a m o f l o c a t i o n s on or o f f (such as a function button
on a " m o u s e " or t h e pen-point switch found on many
Key Words and Phrases~ g r a p h i c display, g r a p h i c
I n p u t , I n t e r a c t i v e g r a p h i c s , i n t e r a c t i v e input, logical
I n p u t d e v i c e , n u m e r i c v a l u e input, r e a l - t i m e
g r a p h i c s , t a b l e t input, v a l u a t o r Input d e v i c e , 3-D
dynamic graphics
CR Categorles~ 3.9, 4.41, 6.35, 8.2
1Mailing address: Robert W. Thornton, Carnegie-MellonUniversity,
SUPA - Schenley Park, Pittsburgh,PA 15213, USA.
2For a discussion of logical graphic input devices and a descriptionof
various classes of such devices, see, for example,[8, g],
© 1979 ACM O-89791-004--4/79/0800--102 $00.75
See Copyright Pg.
102
tablets).
The description of the Number Wheel as
p r e s e n t e d here will assume the use of a t a b l e t - p e n
I o c a t o r . This input d e v i c e has the ability to provide
m a n y forms of Input through a single physical device
and Is a v a i l a b l e a t a r e l a t i v e l y low cost.
2. Functionality
t h e s i z e ( d i a m e t e r ) s e l e c t e d for the hypothetical
w h e e l . Since t h e wheel has no mass (and hence no
m o m e n t u m ) and Is mounted on frlctlonless bearings, It Is
v e r y e a s y t o push the wheel and s t a r t It rotating v e r y
q u i c k l y . It can also be s t o p p e d "on a dtme" when a
d e s i r e d v a l u e Is reached. Thus It Is possible to make
g r o s s c h a n g e s In a Number Wheel's value very quickly
y e t also perform p r e c i s e selections of value st the
l e v e l o f t h e v a l u a t o r ' s p r e - d e t e r m l n e d resolution.
F i g u r e 1 : Hypothetical physical analogy of
the Number Wheel
F i g u r e 2: Analogical Number Wheel with different
size and orientation.
The c h a r a c t e r of the Number Wheel Is b e s t
e x p l a i n e d w i t h t h e use of a physical analogy: by
d e s c r i b i n g a h y p o t h e t i c a l device which operates In s
f a s h i o n similar t o the logical Number Wheel device. It
Is from this physical analogy that the name "Number
W h e e l " Is d e r i v e d .
W h e r e t h e Number Wheel Illustrated In Fig. 1 Is
m a n i p u l a t e d b y moving the pen forward and backward
o v e r e n a r r o w w i n d o w on the tablet, the size, shape,
and l o c a t i o n of t h e window through which s Number
W h e e l p r o t r u d e s may v a r y for different uses. Figure 2
I l l u s t r a t e s a Number Wheel which covers the entire
s u r f a c e of t h e t a b l e t in addition to having a different
d i r e c t i o n of rotatlon: It is changed by moving the pen
l e f t and right. Other alternatives might Include several
s e p a r a t e Number Wheel's each accessible through
s e p a r a t e w i n d o w s on the t a b l e t at the same time, or
even
more
than
one Number Wheel available
s i m u l t a n e o u s l y through the same t a b l e t window, each
w i t h a d i f f e r e n t direction of rotation.
The Number Wheel can be thought of as a wheel
w h i c h has s portion of Its circumference protruding
t h r o u g h a slot on the surface of the tablet, somewhat
like s g i a n t thumb wheel, as Illustrated in Fig. 1. Each
v a l u e In t h e desired range of the valuator Is
r e p r e s e n t e d by a point on the circumference of the
w h e e l w i t h t h e value of the device at any given time
b e i n g t h e point at the top of the wheel. The valuator
Is c h a n g e d b y putting the pen on the wheel where It
p r o t r u d e s through the t a b l e t and moving It back or
f o r t h In t h e direction of rotation. Whenever the pen
l e a v e s t h e rim of the wheel while still moving, the
Number Wheel mslntalns the same speed of rotation
(I.e. r a t e of change In value) until the pen returns to
t h e w h e e l In o r d e r to change or stop Its movement.
3. Examples
An e x a m p l e of how Number Wheels might be used
w i l l b e d e v e l o p e d by continuing with the physical
a n a l o g y Just p r e s e n t e d .
Going back to the original
n e e d e x p r e s s e d for developing the Number Wheel, one
c a n b e c o n f i g u r e d for Interactlvely controlling the
r o t a t i o n of a three-dimensional o b j e c t being displayed.
Using t h e Number Wheel Illustrated In Fig. 2 and
a s s i g n i n g t h e values from zero to 359 around the
c i r c u m f e r e n c e of It, the current value (the number at
t h e t o p ) of this Number Wheel can be used to Indicate
The number of d i s c r e t e values possible for the
p o r t i o n o f t h e Number Wheel's rim which Is accessible
t h r o u g h t h e s u r f a c e of the t a b l e t at a given Instant Is
l i m i t e d b y t h e resolution of the tablet. However, the
r e s o l u t i o n o f the Number Wheel over Its entire range Is
n o t l i m i t e d b y t h e t a b l e t and Is adjustable by varying
103
the
angle
of
rotation,
In
degrees,
of
the
t h r e e - d i m e n s i o n a l o b j e c t on display about the y - a x i s .
F l g u r e 4; H y p o t h e t l c a l mechanlsm controlllng
x - a x l s rotatlon.
F i g u r e 3: Number Wheel used to control rotation
of o b j e c t about y - a x i s .
The h y p o t h e t i c a l physical mechanism which w e are
m o d e l i n g for tills application Is Illustrated In Fig. 3.
T h e r e Is a t h r e e - d i m e n s i o n a l o b j e c t In front of us which
is c o n n e c t e d w i t h the Number Wheel by a f l e x i b l e
c a b l e through Its y - a x i s . As the wheel Is r o t a t e d with
a l e f t or right movement of the pen, the o b j e c t rotates
In a d i r e c t i o n and s p e e d corresponding to the
m o v e m e n t s of t h e pen.
In a similar manner, a Number Wheel with Its axis
turned
9 0 d e g r e e s so that it rotates with a
f o r w a r d / b a c k w a r d motion might be used to control the
r o t a t i o n o f t h e three-dimensional o b j e c t about the
x-axis.
Another hypothetical mechanism which
i l l u s t r a t e s this action Is shown In Fig. 4. This could be
c a r d e d f u r t h e r b y placing both of these Number Wheels
In t h e same t a b l e t w i n d o w at the same time so that
a n y c o m b i n a t i o n of f o r w a r d / b a c k w a r d and l e f t / r i g h t
m o v e m e n t s can provide a desired combination of
r o t a t i o n s a b o u t t h e x and y a x e s (Illustrated In Fig. 5).
F i g u r e 5 : Hypothetical mechanism controlling
combined x and y a x e s rotations.
Similarly, o t h e r Number Wheels may be defined which
c o n t r o l o t h e r p a r a m e t e r s of the display transformation,
s u c h as t r a n s l a t i o n s In various directions, angle of
vision, positioning of section planes, or for the arbitrary
a x i s r o t a t i o n s as p r e s e n t e d In [ 2 ] .
4. Implementation
This s e c t i o n d e s c r i b e s one particular w a y of
I m p l e m e n t i n g Number Wheels which has been found t o
104
d e t e r m i n e which Number Wheel (or gang of Number
Wheels,
If t w o or more are to be controlled
s i m u l t a n e o u s l y In the same area of the t a b l e t ) the pen
Is c u r r e n t l y controlling, and/or switches to control
w h i c h s e t o f Number Wheels is available through the
s u r f a c e o f t h e t a b l e t at any given time.
b e c a p a b l e and f l e x i b l e . There are, however, many
o t h e r a p p r o a c h e s which could be taken to provide
d i f f e r e n t f e a t u r e s . A following section suggests some
o f t h e s e varlat=ons and extensions.
Implementing a particular Number Wheel Is fairly
straight forward.
A procedure to update an active
Number Wheel must be performed at each time interval
( e . g . 1 / 6 0 s e c o n d ) . If the pen Is down on the rim of
t h e w h e e l (I.e. surface of the tablet) then the
incremental change for the Number Wheel must be
r e c a l c u l a t e d b y taking the relative change In position
o f t h e pen since the last time period (If the pen was
a l s o d o w n last time) and scaling It by a value which
p r o v i d e s t h e d e s i r e d amount of resolution over the
Number W h e e l ' s range.
The current Incremental
c h a n g e ( p o s s i b l y zero) Is then added to the current
v a l u e o f t h e Number Wheel. At this time the value must
a l s o b e t e s t e d to s e e If It has reached one of the
limits o f t h e v a l u a t o r ' s defined range. If It has, there
a r e a t l e a s t t w o possible courses of action:
To make tt ~'asy to Implement Number Wheels for
d i f f e r e n t programs and make It a simple process to add
Number Wheels or dynamically change existing Number
Wheels
(perhaps
with
another
Number Wheel
c o n t r o l l i n g one of Its parameters!) in a running program,
t h i s I m p l e m e n t a t i o n has a generalized design. A table
Is u t i l i z e d t o hold the parameters which define the
c h a r a c t e r i s t i c s of the Individual valuators, In addition
t o t h e f e w v a r i a b l e s required In the operation of each,
s u c h as t h e current value of the Number Wheel,
w h e t h e r It Is c u r r e n t l y a c t i v e (at the surface of the
t a b l e t ) or not, the Incremental change, etc. All that is
r e q u i r e d t o add a n e w Number Wheel or change the
c h a r a c t e r of an e x i s t i n g one Is to add or change an
e n t r y In this t a b l e .
R e s e t t h e Number WheePs value to Its
o p p o s i t e limit and allow It to continue
changing In the same direction (wrap
around).
This Is similar in result to a
continuous-turn
rotary
type
p o t e n t l o m e t e r . This t y p e of action might
b e u s e d for a valuator which controls the
a n g l e of rotation about a particular axis
o f an o b j e c t on display. The maximum
end minimum might be 3 5 g degrees and
z e r o d e g r e e s so when the Number Wheel
Is pushed up to and past 3 5 g degrees,
t h e o b j e c t will continue rotating In the
same manner as the valuator wraps
around to zero.
A s e t o f s i x p a r a m e t e r s has been s e l e c t e d which
a l l o w simple s p e c i f i c a t i o n of a large class of d i f f e r e n t
Number Wheels. They are:
- The minimum value allowed for the range
o f t h e Number Wheel.
- The maximum value In the range.
The number of units of resolution In the
valuator's
range
or
distinct
steps
between
t h e minimum and maximum
values.
It should be noted that the
resolution of the physical Input device
d o e s not limit this parameter or the t w o
p r e v i o u s ones: t h e y are only limited by
t h e numerical representation used In the
calculations.
Simply s t o p changing the value of the
Number Wheel; leaving it at the limit until
such time t h a t it is turned back In the
o p p o s i t e direction. This t y p e of action
might be used for a valuator which Is
controlling the angle of vision for a
t h r e e - d i m e n s i o n a l display. For example,
t h e maximum and minimum values might be
1 7 g d e g r e e s and one degree. When the
u s e r pushes the Number Wheel to zoom in
on t h e o b j e c t , it stops upon reaching one
d e g r e e and t h e only available action is to
zoom b a c k out.
The number of units of resolution on the
Input d o v l c e which are to correspond to
one of t h e above defined units of
resolution of the logical valuator. This
parameter,
In conjunction with the
previous
one
establishes the ratio
b e t w e e n the physical distance the pen Is
m o v e d and t h e amount that the valuator
changes.
The c u r r e n t value of the Number Wheel may be used as
r e q u i r e d In calculating a display update or otherwise.
The t y p e of limit condition desired. The
c h o i c e s for this are either "wrap around"
o r " s t o p " , e x p l a i n e d earlier In this
section.
For most applications, more than one Number Wheel
w i l l b e u s e d . Additional logic must then be provided to
105
- An indication of whtch controlling variable
Is t o be used. This variable controls the
I n c r e m e n t a l change used In updating the
Number Wheel and will normally be the
c h a n g e In the pen's location, from one
time p e r i o d t o the n e x t , In either the x or
y direction.
An additional definitional parameter could
b e used t o apply braking to a freely
r o t a t i n g Number Wheel.
This might be
t h o u g h t of as specifying the amount of
f r i c t i o n In the bearings of the wheel,
going b a c k to the previously made
p h y s i c a l analogy of the Number Wheel.
This w o u l d control the amount of time
r e q u i r e d for a Number Wheel to slow to a
s t o p w h e n l e f t rotating.
It might also be desirable to Identify a particular
w i n d o w or s u b - a r e a of the t a b l e t through which each
particular
Number
Wheel
appears.
However,
experience
has shown t h a t It Is usually more
c o n v e n i e n t for each Number Wheel to cover the entire
s u r f a c e o f t h e t a b l e t w i t h the added provision of a s e t
o f logical b u t t o n s w i t h which the user may s e l e c t one
o r t w o of a s e t of Number Wheels to be available on
t h e t a b l e t a t any given time. This frees a user of the
n e e d t o p u t t h e pen down on a particular area of the
t a b l e t w h i l e using a Number Wheel; allowing one to
c o n c e n t r a t e on viewing the display as opposed to
w o r r y i n g a b o u t t h e location of the pen on the tablet.
This might seem a small point but it adds to the ease of
u s e or h a b i t a b i l i t y of the system and thus Improves the
a b i l i t y t o quickly gain a complete perception of the
t h r e e - d i m e n s i o n a l forms being displayed.
In
addition
to
the
above
friction
p a r a m e t e r , It might be des&able to have a
spring return which pulls the valuator
b a c k t o a "home" posltlon when released.
Additional
alternative
responses
to
r e a c h i n g a Number Wheel's range limit
might be provided, such as switching the
d i r e c t i o n of change, or "bouncing back" In
t h e o p p o s i t e direction when a limit Is
reached.
Finally, for some applications It might
.even be helpful to be able to define a
n o n - c o n t i n u o u s range over which the
v a l u a t o r may o p e r a t e .
Additional d e t a i l s and more complete descriptions of
u s e o f t h e Number Wheel may be found In [ 7 ] .
6. Summary
For t h e i n t e r a c t i v e control of three-dimensional
p o s i t i o n i n g , for which the Number Wheel was originally
d e s i g n e d , It has proven to be a very convenient and
f l e x i b l e d e v i c e , overcoming many of the limitations
f o u n d in p r e v i o u s l y used logical valuators (such as
l o g i c a l slide p o t e n t l o m e t e r s , rate controls, or the well
k n o w n " L i g h t Handle" [ 6 ] ) and physical valuators (such
a s p o t e n t l o m e t e r s or j o y s t i c k s ) , Characteristics of the
N u m b e r W h e e l contributing to its success Include:
5. Extensions
In
addition
to
Its
application
to
dynamic
t h r e e - d i m e n s i o n a l positioning, the Number Wheel will
f u n c t i o n w e l l for many other uses as a general
I n t e r a c t i v e v a l u a t o r device. An even larger class of
v a l u a t o r s Is possible using the same basic logic
d e s c r i b e d here for the Number Wheel by expanding the
d i m e n s i o n s of variation described earlier. Examples of
t h e s e v a r i a t i o n s are;
-The
resolution is limited only
numerical r e p r e s e n t a t i o n used.
Use o f controlling variables other than
t h e c h a n g e In x or y position of a pen on
tablet
to
calculate the incremental
c h a n g e for the valuator.
These might
Include t h e absolute pen coordinates (as
o p p o s e d to r e l a t i v e to the previous
position), 'the change in x or y position
m o d i f i e d b y some non-linear function to
p r o v i d e a w i d e r range of velocities of
c h a n g e , or values obtained from other
physical
devices
such
as
remote
manipulators, rotary potentlometers, or
Joysticks:
providing an e x t r a level of
f l e x i b i l i t y o v e r the physical devices.
by
the
-Gross changes In value can be made
q u i c k l y and easily.
T h e r e is a c a p a c i t y for easy "fine tuning"
o f s p e c i f i c values at the level of the
Number W h e e l ' s resolution.
Smooth and continuous change of value
many times per second are provided for
controlling u p d a t e s of a dynamic display.
- T h e r e Is s choice of how the limit
c o n d i t i o n Is handled, something not found
106
in most physical devices.
References
A p a r t i c u l a r r a t e of change may be s e t
initially which Is automatically continued
I n d e f i n i t e l y w i t h o u t further action from
t h e user.
1. Brenner, A. E. and de Bruyne, P. A sonic pen: a
d i g i t a l s t y l u s s y s t e m . IEEE EC-19, 6 (June l g 7 0 ) ,
546.
2. Britton, E. G., Llpscomb, J. S., and Pique, M. E.
M a k i n g n e s t e d rotations convenient for the user.
P r o c e e d i n g s SIGGRAPH 78: Fifth Annual Conference on
C o m p u t e r Graphics and I n t e r a c t i v e Techniques, ACM SIGGRAPH, August, 1978, pp. 2 2 2 - 2 2 7 .
There
;s
a
close
correspondence
between
the
numerical value being
c h a n g e d and the physical movements
r e q u i r e d by a user to control such
change.
This Is provided In three
manners: when the pen Is on the t a b l e t
t h e value changes when the pen moves
and not when it Is still (as Is done In
t a b l e t b a s e d valuators which control the
r a t e of change), the value can change in
a d i r e c t i o n which corresponds to the
d i r e c t i o n of pen movement, and the value
c h a n g e s at a s p e e d relative to the speed
o f t h e Initiating pen movement.
3. Burton, R. P. Real-t/me measurement of multiple
t h r e e - d / m e n s / o n a l p o s i t i o n s . Ph.D. Th., University of
Utah, 1 9 7 3 .
4. Clark, J. H. Designing surfaces In 3-D. Comm. ACM
1 9, 8 (August 1 9 7 6 ) , 4 5 4 - 4 6 0 .
5. English, W. K., Englebart, and D. C., Berman, M. L.
D i s p l a y - s e l e c t i o n techniques for t e x t manipulation.
IEEE T r a n s a c t i o n s on Human Factors HFE-8, 1 ( 1 9 6 7 ) ,
5.
I n t e r a c t i v e control of a dynamic numeric
v a l u e does not require the constant
a t t e n t i o n of the user to the f a c t that he
Is controlling a numeric value as such.
6. Newman, W. M. A graphical technique for numerical
Input. C o m p u t e r J o u r n a l 11 (May 1968), 6 3 - 6 4 .
7. Thornton, R. W. MODEL - Interactive modelling In
t h r e e dimensions through two-dimensional windows.
M a s t e r Th., Cornell Unlversit;y, January 197F.
The use of Number Wheel controls Is
e a s i l y learned and feels "natural" to the
user: d e s i r e d results are obtained with
s p e e d and ease.
8. T r a m b a c z , U. Towards device Independent graphics
s y s t e m s . Proceedings SIGGRAPH 75: Second Annual
C o n f e r e n c e on Computer Graphics and Interactive
T e c h n i q u e s , ACM - SIGGRAPH, Spring, 1075, pp. 4 9 - 5 2 .
Many
uses of computer graphics to display
p r o j e c t i o n s of three-dimensional shapes are to Impart
some
additional
perception
of
the
actual
t h r e e - d i m e n s i o n a l form to a human user. It is common
t o use s e v e r a l cues In trying to enhance this
t h r e e - d i m e n s i o n a l perception, such as p e r s p e c t i v e
p r o j e c t i o n , d e c r e a s i n g Intensity of lines with their
d i s t a n c e from the o b s e r v e r position, removing hidden
lines, and s h a d e d surface displays. Even with all of
9. W a l l a c e , V. L. The semantics of graphic input
d e v i c e s . Proceedings ACM Symposium on Graphic
L a n g u a g e s , ACM - SIGGRAPH/SIGPLAN, Spring, 1976,
pp. 01-65.
t h e s e s t a t i c three-dimensional cues, the single most
e f f e c t i v e aid t o spatial perception is a user's ability to
I n t e r a c t i v e l y animate movement of the o b j e c t as he
might desire.
The e x t e n t to which the user can
a c c u r a t e l y and naturally control such motion can have
a l a r g e e f f e c t upon the user% complete perception of
t h e t h r e e - d i m e n s i o n a l space. The use of the Number
Wheel
can help shorten this step to complete
perception.
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