Method of and apparatus for touch-input computer and related display employing touch force location external to the display

A method of and apparatus for determination of touch location on a display screen or the like or other surface embodying a force-sensing platform or surface supporting or otherwise externally contacting the display screen monitor apparatus, and responding to the forces created by the thrust of touching a point of the display screen, to sense and calculate the location of the touching point. The underlying technique employs force-sensing means responsive to all six degrees of freedom of applied (touching) force and torque, achieving force location away from the plane of the sensors and in spite of tangential force components by calculating the point of least magnitude of the three-dimensional torque vector from among all points within the screen or surface, and outputting this point as an estimate of the intersection point of the screen or surface with the thrust line of the touching or other contact force.

The present invention relates to touch screen cathode-ray tube and similar 
displays, as for use in computers and other video systems and the like, 
being more particularly directed to novel methods of and apparatus for 
determining the touch force location on the display from apparatus 
disposed external to and remote from the display, as distinguished from 
force sensors applied to the periphery and/or over or adjacent the display 
surface itself. 
More generally, still, the invention relates to novel three-dimensional 
force locating techniques adapted for measurement of forces applied 
outside the plane or surfaces of force-sensing elements. 
BACKGROUND OF INVENTION 
Though thus more general in application, one of the important uses of the 
invention is in the field of computer or related display screen systems, 
such as cathode-ray tube displays (or LCD, LED, electroluminescent or 
other electro-optical displays or the like); and it is therefore to this 
exemplary use that the invention will hereinafter be described as an 
important illustration. 
A modern computer typically presents its user with such a display screen on 
which may be presented descriptions or pictoral representations of various 
choices or selections which the user may make. In many cases, the 
quickest, easiest, and most intuitive way for the user to respond is by 
physically finger-touching the areas of the screen which show the desired 
selections. 
To allow this, the computer must be equipped with an input device which 
permits the program on which it is operating to determine the fact and 
location of such touch events. For present purposes, any input device of 
this sort will be termed a "touch screen". 
A desirable touch screen input device should be inexpensive, rugged, 
reliable, and sufficiently accurate. It is also very desirable that a 
single model work with a wide range of different display devices, and that 
it be susceptible to easy field installation by untrained users, either on 
new or on existing equipment. 
Unfortunately, existing touch screens, such as those later described, are 
of relatively low manufacture volume and thus very expensive by the 
standards of their natural market, being therefore precluded in major 
usage from integration at the time a display is manufactured. In addition, 
they require great effort, expense, and manufacturing expertise to 
retrofit. Since each model is more-or-less unique to a specific screen 
geometry, different models must be made in great profusion, or would-be 
users must be restricted in their display choice. For a combination of 
functional and cosmetic reasons, thus, certain prior art touch screens are 
indeed built into the display device, such as a cathode-ray tube, at 
initial manufacture (though expensive, due to low volume), and others 
require an awkward retrofit (also expensive). Such prior touch screens, 
moreover, are closely tied to the design of the display device with which 
they are to be used, and must be provided in a profusion of different 
types to find wide application. Many, furthermore, have inherently 
expensive sensor structures tightly constrained by the geometry, 
compatibility, and packaging constraints of the associated display, so 
that sensor structures cannot often be optimized for cost. 
Turning to such prior art techniques for determining touch location on a 
cathode-ray tube or similar display screen, they involve some combination 
of distributing sensors around the periphery of, or over the surface of, 
the actual displaying surface or screen. Such known methods employing 
force sensing to locate the point at which a force is applied to a surface 
generally embody three or more force sensors placed in a plane, but not 
allowed to lie along a single line. The axis of sensitivity of each is 
oriented perpendicular to this plane, and the outputs of the sensors are 
used to compute the location of contact forces which are applied in this 
same plane. If and when the contacted surface is allowed to depart from 
this plane, the unpredictable tangential components of the contact force 
must necessarily cause errors in the reported location. If the contact 
surface lies far from the plane of the sensors (or is severely 
non-planar), prior methods are ineffective. 
Specifically, a first system of this nature is adapted for the front 
portion of cathode-ray tube screen displays, being provided with various 
additions to enable touch localization, including both resistive and 
capacitive sensing technologies, in which an extra sensor plate is applied 
over the face of the display screen. The plate bears one or two layers of 
transparent conductor patterns which develop and convey touch location 
information to conductors at the edge of the overlay plate. While efforts 
are made to keep all components transparent, losses in practice are 
sufficient substantially to reduce image brightness and clarity. Examples 
of such touch screen sensors may be found in U.S. Pat. Nos. 4,198,539; 
4,293,734; 4,353,552; 4,371,746; 4,806,709; and 4,821,029. 
A second approach involves surface acoustic wave (SAW) technology in which 
a glass overlay plate carries acoustic energy generated, redirected, and 
sensed by transducer and reflector means disposed about the periphery. 
Touching the plate damps this energy in a manner particular to the contact 
location, as described, for example, in Eleographics 1987 flier "Surface 
Acoustic Wave". 
Another technique has involved a planar force sensing technology in which 
piezoelectric force transducers support a glass overlay plate, attaching 
it to a mounting. The intersection of a finger-touch thrust line with the 
transducer plane occurs at a point which is associated with a specific 
ratio of transducer outputs, allowing the position of this point within 
the plane to be computed. When curved, phosphor-bearing screen surfaces 
must necessarily deviate from the plane, creating a particular form of 
parallax error in which the user, expecting response at a particular 
point, instead actually receives response at another point. Sensor 
techniques and signal processing suitable for such an approach are 
described, for example, in U.S. Pat. Nos. 4,340,777; 4,355,202 (and prior 
art strain gauge sensors described therein including U.S. Pat. No. 
3,657,475 and "One-Point Touch Input of Vector Information for Computer 
Displays," C. Herot et al., Computer Graphics, Vol, 12, No. 3, pp. 
210-216); and U.S. Pat. No. 4,675,569. 
Still another approach uses planar force-sensing technology in which steel 
beam springs with strain gauge transducers constitute force sensors 
bearing the entire weight of, for example, the cathode-ray tube assembly. 
This technology avoids the image degradation of an overlay plate, but at 
the cost of requiring greater sensor dynamic range and problems of 
rejection of stray signals from sway and vibration. Its function is 
otherwise substantially identical to the above-described piezoelectric 
system. U.S. Pat. Nos. 4,918,262 and 5,038,142 describe such a system, 
citing, also, earlier piezoelectric and related sensors. 
Infrared light technology has also been proposed in which many separate 
beams travelling from emitters to detectors define a plane. When the 
user's finger (or other probe of sufficient width) crosses this plane, the 
identity of interrupted beams locates the "touch". Again, a transverse 
component to the touch motion can lead to a parallax error in which 
response at the expected location is replaced by response at an unexpected 
location. Parallax errors for this technology tend to be particularly 
severe, since the response surface cannot be positioned to intersect the 
phosphor surface, nor be shaped to conform to it. Additionally, such 
apparatus may require obtrusive bezels. An example of such a system is 
described in pages 12-44 of a text entitled "Caroll Touch", which also 
summarizes the before-described resistive-capacitive sensor overlay 
systems, surface acoustic wave systems and piezoelectric systems, as well. 
Each of the above methods has an effective response surface which, 
unfortunately, fails to be coincident with the active surface of the 
display, leading to the universal prior performance imperfection of 
parallax. 
The before-described resistance, capacitance and acoustic plate sensors 
have a response surface which conforms to the actual physical surface of 
touch contact, such lying visually about 1/2 inch in front of the phosphor 
surface in the case of a cathode-ray tube display. An operator whose eye 
is somewhat to the side, will therefore perceive an error in the touch 
system response unless touching a surface point that lies directly over 
the desired target point, rather than the target point itself. 
The piezoelectric and other planar force-sensing systems above-described, 
on the other hand, do not actually report an actual location of surface 
contact, but rather provide what may be called an "indicated point" on a 
"virtual response surface". The indicated point is at the intersection of 
the thrust line and the plane of the force sensors. For the described 
infrared beam system, such an indicated point is where the finger breaks 
the plane of the infrared beams. Since the glowing phosphors are not 
located in such plane, the virtual surface does not correspond to anything 
visible or intuitive, making the parallax error of these devices 
particularly troublesome. 
Underlying the present invention, however, is the discovery of a novel 
method of and apparatus for enabling a wide variety of cathode-ray tube or 
other screen display systems, as in computers, monitors and other video 
systems and the like, to be placed upon or in touch with a common, 
universal force-sensing platform, the sensors of which are thus external 
to the plane of the display screen and remote even from the display 
equipment itself, but nonetheless provide a novel three-dimensional force 
locating technique for forces, such as the finger-touching of the display 
screen, while obviating all of the above-described limitations and 
disadvantages of the prior art techniques, including the total elimination 
of parallax. 
Other distinguishing features of the invention from the above-described and 
other prior art approaches will be more fully addressed hereinafter. 
OBJECTS OF INVENTION 
A principal object of the present invention, accordingly, is to provide 
such a new and improved method of and apparatus for touch screen sensing, 
void of the limitations of prior art systems, and, to the contrary, 
adapted for unobtrusive location of the sensing external to the display, 
preferably beneath or in back of it, and universally employable with a 
wide variety of display systems of many different configurations and 
types. 
A further object is to provide such a novel touch-locating input device for 
use in conjunction with a computer display, to locate touches directed at 
features of the displayed image; and which, in addition to unobtrusive 
location external to the display, can easily be field installed, with one 
or a very few types or sizes adaptable to all displays. Such design, 
furthermore, which can be optimized for low cost, since unconstrained by 
internal design aspects of the display, is robust, long-lived, and immune 
to wear, providing parallax-free response for any display surface, and 
without degrading the displayed image. 
Additionally, it is a further and more general object of the invention to 
provide a novel method of fully locating the thrust line of a force in 
three-dimensional space, or the line of minimum torque, accurately 
determining the location of a force applied to a surface, or the location 
at which a force is directed through a surface. Such surface may be far 
removed from the plane of the sensors, may be substantially different from 
a flat plane surface, and is not constrained by device design to have a 
particular relationship in space to the device. 
In accordance with the invention, moreover, a device embodying the same may 
be programmed or calibrated in use to project a virtual response surface 
of any shape to any location, subject only to certain natural limitations. 
Such limitations are that the thrust lines of the forces to be localized 
shall intersect the response surface with positive polarity at but a 
single point (or more precisely that the lines of minimum torque magnitude 
do so), and that the object bearing the physical surfaces to be matched by 
the virtual projection, shall be appropriately coupled to or supported by 
the measuring device, with the distances and forces involved falling 
within the dynamic range and sensitivity of the particular measuring 
device. 
Other and further objects will be explained hereinafter and are more 
particularly delineated in the appended claims. 
SUMMARY OF THE INVENTION 
In summary, however, in one of its important applications, the invention 
embraces a method of determination of touch location on a display surface 
apparatus, that comprises, contacting the display surface apparatus 
against or in touching relationship to a force-sensing platform having 
sufficient degrees of freedom and sensing sensitivity to develop and 
encode, in response to the thrust of touching a point of the display 
surface, the coordinate components of the resulting thrust vector and the 
components of the accompanying torque vector; calculating from the 
encoding, a location on a line of minimum torque to provide an 
intersection of the display surface; and outputting the resulting sensed 
location as an estimate of said touching point. 
In the best mode and preferred form of the invention, a six-degree force 
platform or plate is employed upon which any monitor or other display 
device may be placed, receiving line power and sending a single parallel 
or serial port cable to the host computing device--say, for example, an 
IBM PC (personal computer) or the like. The format may be something like 
an electronic bathroom weight scale, but reading out six numbers at once 
instead of one. These encode the same information as is contained in the 
x, y, and z coordinate components of thrust, and the roll, pitch, and yaw 
components of torque. For convenience, the actual numbers are an 
equivalent linear transformation of these. 
The challenge in recovering a touch position from such a remote sensor 
platform or surface lies in the fact that the direction of touch force on 
the display screen can vary greatly from one instance to the next, even 
when exactly the same point on the screen is touched. When the sensors 
cannot be confined to the same effective plane as the touch (as is done 
with, and indeed required by prior art devices, as before explained), 
different touches at the same point of the screen may produce different 
sets of numbers. 
The present invention admirably obviates these problems, however, by taking 
two important considerations into account, the appreciation and 
application of which are at the heart of the invention. 
First, the force at the point of contact can be described quite accurately 
as a pure thrust. For present purposes, the torque components referenced 
to this point are negligible--partly because the area of contact is small, 
and in part, because the finger is not attached to the screen. This kind 
of force is referred to herein as a "simple contact force", defining the 
"thrust line" as the locus of points obtained by extending the thrust 
vector through the point of contact. For a simple contact force then, the 
line in space of points with minimum (in this case, zero) magnitude of the 
three dimensional torque vector is coincident with the thrust line of the 
force. 
Secondly, a measurement of the thrust and torque occasioned by the touch at 
some remote reference point is sufficient to reconstruct the line of 
minimum torque, and therefore the thrust line. (For simplicity, in the 
discussion that follows, the term "thrust line" is sometimes used to refer 
to the line of minimum torque which approximates it. The method of the 
invention, however, deals directly with the latter.) Although the theory 
and practice of this will be more fully developed below, consider first a 
brief outline of the principle involved. 
The thrust (or perhaps more intuitively, the reaction thrust to maintain 
static equilibrium) is an invariant of position, but the torque is not. 
The torque vector is perpendicular to the plane containing the thrust line 
and the reference point, and has a magnitude equal to the product of the 
thrust magnitude times the distance at closest approach of the thrust line 
to the reference point. Since the directions and magnitudes of the thrust 
and torque vectors are obtained by measurement, one can, in summary, 
calculate backwards as follows: (1) Find the direction perpendicular to 
the plane containing the thrust and torque vectors (which direction of two 
is determined by consistent use of some handedness rule); (2) Proceed in 
this direction a distance equal to the magnitude of the torque vector 
divided by the magnitude of the thrust vector, ending up at the point on 
the thrust line which is closest to the reference point; (3) Extend the 
(known) thrust vector through this point to obtain the thrust line which, 
of course, intersects the surface of the display screen in a single point. 
The contour of this surface either is known, or is conveyed to the 
computer through an appropriate calibration procedure enabling the 
location of the touch point. 
Other details of best mode design and construction are more fully described 
hereinafter. 
DRAWINGS 
The invention will now be described in connection with the accompanying 
drawings, FIG. 1 of which is a side elevation depicting the use of the 
force-sensing platform of the invention as a remote touch screen system 
for a computer or similar monitor with a cathode-ray tube display screen 
supported on the platform; 
FIG. 2 is a top elevation of the platform sensor of FIG. 1 depicting a 
simple means for reproducibly locating the supported monitor upon the 
force sensing platform of the embodiment of FIG. 1; 
FIG. 3 is an isometric view of the major components and the construction of 
the force sensing platform, showing the same in open position; 
FIGS. 4 and 5 illustrate a design for the springs used in the platform; 
FIG. 6 is a cross-sectional view of the details of a suitable pair of 
capacitive displacement sensors for the platform; 
FIG. 7 is a simplified schematic circuit diagram of electronic conversion 
and calculating circuitry for the system; and 
FIGS. 8-10 provide graphical depictions of the force vectors and geometry 
of the force locating operation for a force of the kind made locatable by 
the invention, and which is applied out of the plane of the platform 
sensors.

DESCRIPTION OF PREFERRED EMBODIMENT(S) 
A six degree-of-freedom force sensing platform 32, FIG. 1, is used to 
provide information sufficient for the calculation of an "Effective Thrust 
Line" resulting from a "Simple Contact Force" arising where the monitor 
display screen 31 (or other object, in general) supported upon the 
platform, is touched or contacted by another object, as by the finger F. 
The platform also contains electronic signal conversion and calculating 
means suitable to prepare and deliver desired output results to external 
devices, as over, for example, a simple RS-232 serial communication link 
38. 
Force Locating Platform Construction 
FIG. 1 depicts the platform embodiment 32 of the remote force-locating 
device constructed in accordance with a preferred form of the present 
invention, contacting or touching, indeed supporting, the base surface of 
the cathode-ray tube monitor 31 on support surface 33 to provide a touch 
screen function, though remote from the cathode-ray tube screen itself 
which is touched by the user. The force locating device 32 receives power 
through an AC adapter cable 35, and communicates location information to a 
computer (typically a personal computer, or "PC", not shown) through, for 
example, the cable 38. 
Since the calibration of the locating function depends upon the position of 
moniter 31 with respect to the platform 32, the platform is provided with 
a stop 39 (see also FIG. 2), which is an "L" shaped strap or land of 
material protruding above the platform surface. The monitor 31 is slid 
back and to the right against the stop 39, giving an accurately and 
rapidly reproducible position. Dashed-circle sets 40 and 41 illustrate two 
possible patterns of foot location for two possible monitor styles. 
In FIG. 3, the platform 32 is shown separated or opened into an upper plate 
assembly 50 and a lower plate assembly 51. When brought together and 
fastened with screws 53 and washers 54 (only one set shown), a flange 55 
overlaps flange 56, so that the four steel beam springs 52 in the corners 
carry the entire weight of the upper assembly and all supported objects. 
Only under conditions of overload, do the flanges contact each other or 
the opposing plate, so as to protect the beam springs 52 and hereinafter 
discussed capacitor sensors 57 (having upper and lower segments 57a and 
57b) from damage. The upper capacitor elements 57a face and align within 
the lower capacitor elements 57b to provide linearly independent 
measurements responsive to all six components of plate-to-plate 
displacement. These capacitance sensors are shown provided substantially 
midway along the front of, and toward the rear of the two sides of the 
platform plates. Six wires 58a provide connection of the upper elements to 
printed circuit board 60 through connector halves 58b and 58c. Similarly, 
59a, 59b, and 59c provide connection to the lower elements. Connector 61 
provides power, allowing the printed circuit board electronics (not shown) 
to compute force location data which is then outputted through connector 
62. 
The beam spring 52 is shown enlarged in FIG. 5. It may be produced from a 
double-L flat 70 of FIG. 4, folded, as shown, and provided with press-fit 
threaded inserts 71. 
FIG. 6 shows details of a pair of suitable and preferred capacitor 
displacement sensors 57 in section. The plates may be formed from 
rectangles of unetched printed circuit board material, for example, about 
3 square inches in area. Foil capacitor plates 72 are supported on 
insulating laminates 73, which in turn are attached by adhesive to an 
upper bracket 74 and a lower bracket 75. The brackets 75 and 74 are 
nesting brackets, which are shown flattened parallel to the platform 
plates 50 and 51 to which they are respectively secured. The free arms of 
the brackets are bent outwardly (for 74) and correspondingly inwardly (for 
75) to mount the pair of capacitor plates 72, oriented at matching angles 
(shown as 45.degree.) to the platform. Capacitor 76a, formed of the 
right-hand capacitor plates 72, FIG. 6, is sensitive to relative capacitor 
plate displacements along axis 76b orthogonal to the capacitor plates; 
while capacitor 77a, formed of the left-hand capacitor plates 72, is 
sensitive along orthogonal axis 77b. The two sensitive axes themselves are 
thus at right angles. 
Operating Circuit Explanation 
FIG. 7 provides a simplified schematic diagram of the electronic conversion 
and calculating means incorporated in a successfully operated platform 
force sensing device 32. Microprocessor system 80 may be one of many 
different standard designs, such as the Intel Type 80188 with associated 
components, physically comprising one to several integrated circuits, and 
logically comprising a processing unit, read/write memory, firmware 
program memory, a small non-volatile read/write memory for storage of 
calibration and operating mode data, an asynchronous serial I/O capability 
for driving output cable 38, a digital input capability for receiving the 
output of analog-to-digital (A/D) converter 81, and a digital output 
capability for setting the input selection of a multiplexer 82. 
Timing circuit 83 divides a 20 MHz clock by 128 to give 156 KHz 5 V square 
wave signal 84 for sensor drive, and by 65,536 to drive converter 81 to 
provide one 16-bit conversion every 3.3 ms. 
Signal 84 is connected to each of six identical capacitor impedance 
measuring circuits 85. An operational amplifier 86 generates a signal 87, 
which transfers charge through the sensor capacitor 57 exactly equal and 
opposite to the charge flowing through fixed capacitor 88, thus 
maintaining virtual ground at its summing junction 89. The peak-to-peak 
amplitude of signal 87 is thus linearly proportional to the capacitor 
plate separation of sensor 57. A resistor 90 of high value (22 MOhm, for 
example) provides a return path for input leakage, keeping signal 87 
within the operating range of amplifier 86. The value of capacitor 88 (5 
pF, for example) is chosen approximately to match the value shown by the 
sensor capacitors under conditions of no platform load. A synchronous 
amplitude detection circuit 91 converts AC signal 87 to DC signal 92, 
which, in turn, is admitted through multiplexer 82 to A/D converter 81 
when processor 80 selects this channel for measurement. Connections 94 
lead to other circuits similar to 85. A complete set of measurements 
across all six inputs may be completed about fifty times each second. 
To achieve the desired accuracy, the force platform 32 must be able to 
measure contact forces of a few ounces to a relative accuracy of about 1%. 
These must be measured in the presence of a large but unpredictable static 
load: i.e., monitors commonly weigh as little as twenty pounds to as much 
as eighty pounds or more. It is necessary, therefore, to find a design in 
which wide load range does not compromise either economy or the necessary 
sensitivity. 
Since the smallest practical gap for capacitor sensor 57 is about 20% of 
the no-load opening, the amplitude of signal 87 may vary from about 5 V 
P--P (peak-to-peak) down to about 1 V P--P at the maximum monitor weight 
of 100 lbs. Circuits 91 and 82 being unity gain, the working input range 
of converter 81 is roughly 1 to 5 VDC. With appropriate operating margins 
allowed, this provides a sensitivity of about 500 counts/lb. Since the RMS 
noise is about 1 count, force changes of 3 ounces and larger can be 
resolved with 1% or better accuracy, based on a single conversion value 
difference from baseline. As the typical touch force determination is 
based upon a weighted average of a number of measurements, the actual 
minimum force is somewhat less. 
Single-slope A/D converters may be of known design which can combine high 
resolution with low cost. Converter 81, as indicated, may have 16-bit 
resolution; but as a counterpart of its very inexpensive design, it has 
nowhere near the linearity or freedom from drift required for 16 bit 
absolute accuracy. Its non-linearity, however, is considerably less than 
1%, and its worst case drift is less than a count per minute. As the 
firmware in processor 80 re-calculates baseline every few seconds or less, 
drift is thus obviated as a source of error. Since, moreover, it is the 
relative error of small changes that is of concern, not absolute error, 
the linearity is entirely adequate. 
Analysis 
The desired remote three-dimensional force locating (finger-touching) 
function is achieved by the above exemplary embodiment in the following 
manner. 
In one mode, data specifying the Effective Thrust Line itself (or, more 
particularly, the effective line of minimum torque) may be the desired 
output. 
In another, the intersection of the Effective Thrust Line with a known 
surface contour may be computed, and the coordinates of this point within 
the surface outputted, perhaps in combination with other detected 
characteristics, such as force magnitude. The known surface contour may 
match the actual physical exterior of the supported monitor or other 
object, or of a portion of it, in which case the coordinates identify the 
actual point of physical contact. 
The force-sensing platform 32, in its most basic form, thus comprises two 
rigid plates 50,51 supported and separated by at least three springs 52 
placed around the periphery. These springs, as above indicated, are 
preferably securely fastened at both ends so as to prevent all pivoting or 
sliding motions which might introduce mechanical hysterisis through 
friction. They are designed to offer (when so mounted) roughly equal 
spring rates in both compression and shear; such rates typically being in 
the range of a few one-thousandths of an inch per pound for each spring 
and in each direction. The overall spring rate is chosen as a trade-off 
between the greater sensitivities which can be achieved with a softer 
mounting, and the greater freedom from dynamical errors achieved when a 
stiffer mounting raises the resonant frequencies of the supported mass. 
The capacitance displacement sensors 57 are mounted between the plates with 
positions and directions of sensitivity chosen effectively to encode all 
six degrees of freedom of rigid motion. These sensors, having the 
preferably variable geometry achieved through their previously described 
construction are inexpensive and sensitive. In another embodiment, each of 
the six sensors may comprise an optical emitter-detector pair mounted to 
one of the platform plates, the beam of each being variably attenuated by 
a small piece of graded transparency film supported from the opposing 
plate (not shown). 
The sensor outputs are detected, scaled, and multiplexed to form the input 
to the A/D converter of FIG. 7. This, as earlier stated, may be of very 
inexpensive single-slope design while still providing the required wide 
dynamic range, since neither high stability non-perfect linearity is 
required. Digitized values sensitive to the various displacements are fed 
to the standard microprocessor system 80, which performs the necessary 
calculations and formats output as required by the application. In the 
case of this touch screen application, this may include emulation of other 
touch screen devices, as well. 
Thus, the touching of a point P on the display screen 31 of FIG. 8, will 
result in a thrust mechanically conveyed to the remote force-sensing 
platform 32, that, through the six degrees of freedom and sensing 
sensitivity thereof, will sense and develop encoding signals corresponding 
to (or corresponding to linear transformations of) the x, y and z 
coordinate components of the resulting thrust vector, FIG. 9, and the 
accompanying torque vector roll, pitch and yaw components. As shown in 
FIG. 10, as hereinafter more fully explained, the before-described 
microprocessor calculations will derive the remotely sensed location of 
the touching point, and output this at 38. 
Theory of Use of Force Data 
While FIG. 8 depicts the display device 31 resting upon the force sensing 
platform 32, FIGS. 9 and 10 re-represent this same system, but with the 
display and platform replaced by a transparent cube for diagrammatic 
clarity. For concreteness, a specific reference point "R" is shown, with a 
particular coordinate system illustrated at 104 in FIG. 9. Thrust and 
translation vectors may consist of an x, y, z enumeration of pound or inch 
values, and torque and rotation vectors may consist of a pitch, yaw, roll 
enumeration of pound-inch or radian values. Although centering and 
aligning the coordinates on the axes of symmetry in the manner suggested 
by FIG. 9 would make numerical examples of the matrices discussed below 
look simpler, this choice is otherwise arbitrary. For simplicity, 
moreover, force and sensor outputs will be discussed as though only 
time-varying components existed, since carrying through such constants as 
the display weight or the baseline sensor outputs would unnecessarily 
clutter the description without altering the results. 
In FIG. 10, thus, a thrust vector THRUST.sub.-- P is diagrammed at its 
point of application P. The "thrust line" of the force applied at P is 
defined to be the locus of points reached by the infinite extension of 
THRUST.sub.-- P through touch point P. The actual area of contact between 
the user's finger and the display screen actually consists of many points 
close to P, through which infinitesimal contributions to the total thrust 
pass in directions roughly parallel to THRUST.sub.-- P. This means that 
the torque exerted by finger pressure about P, and indeed about all points 
on the thrust line, is negligible. Since the torque magnitude of the force 
referenced to other points rises in proportion to their distance from the 
thrust line, there exists a well defined line of minimum torque magnitude 
which is virtually coincident with the thrust line for a force of this 
kind--called a "simple contact force". (Note that were the hand, instead 
of using finger touch, inserting a peg into a pegboard, the contact force 
might not be simple; the mechanical interlock of peg in hole would allow a 
substantial uncontrolled torque to be transmitted through the "point" of 
contact. Indeed, if the peg and hole were square, there would not need to 
be any relationship at all between the thrust line and the line of minimum 
torque). 
As will be seen, the force measurements made by the platform are sufficient 
to compute the line of minimum torque. The external surface of the 
display, however, is also required to remain in fixed relationship to the 
force plate since the last performance of a user calibration procedure. 
(This procedure is, in effect, a way of letting the platform know where 
the screen is). The sensor data, therefore, is logically sufficient to 
locate the contact point of a simple contact force in three dimensional 
space, and, given appropriate calibration data, any two dimensional grid 
imagined on the surface. 
Returning to FIG. 10, the reference point R has been selected to express 
the aggregate effect of the time-varying forces on the system. For greater 
clarity, the plane containing thrust line 102 and reference point R is 
made visible by rectangular segment 105, with sides parallel or 
perpendicular to the thrust line, and by the intersection 106, where this 
plane passes through the boundary of the cube representing the display and 
force platform. 
The particular total force, later discussed, referenced as "TF.sub.-- P@R", 
comprises THRUST.sub.-- R and TORQUE.sub.-- R taken together, and which, 
applied at point R in FIG. 10, would produce the same motions and 
displacements of the top plate of the platform as does the touch force at 
P. It is a known result, in fact, that there is always a unique equivalent 
total force of this kind for any reference point chosen. For present 
purposes, it is convenient to imagine R located at the center of symmetry 
of the suspension system inside the force sensing platform. (Since this is 
a point in empty space, one must imagine it connected to a massless rigid 
extension of the top plate). 
The force at R equivalent to that at P is expressed by the relations: 
EQU THRUST.sub.-- R=THRUST.sub.-- P (1a. 
EQU TORQUE.sub.-- R=TORQUE.sub.-- P+R-&gt;P cross THRUST.sub.-- P (1b. 
where "R-&gt;P" is the displacement vector from point R to point P, and 
"cross" refers to the vector cross product. Since, for a simple contact 
force, TORQUE.sub.-- P is effectively zero, TORQUE.sub.-- R is 
perpendicular to plane 105 and has a magnitude given by the produce of the 
magnitude of THRUST.sub.-- P times the length of vector R-&gt;Q. (Q is found 
by dropping a perpendicular 107 to the thrust line). Consider the 
following equation for the location vector "R-&gt;T" of a point "T": 
EQU R-&gt;T=Lambda*THRUST.sub. -- R +(THRUST.sub.-- R cross TORQUE.sub.-- 
R)/.vertline.THRUST.sub.-- P.vertline. 2, (2. 2 
where paired vertical bars are understood to return the magnitude of the 
vector between them, and where the symbols represent the appropriate forms 
of multiplication, division, and exponentiation, respectively, and where 
"Lambda" represents a scalar parameter. The cross product in the second 
term on the right constructs a vector in the direction of R-&gt;Q, with 
magnitude of .vertline.-&gt;Q.vertline.*.vertline.THRUST.sub.-- 
R.vertline.*.vertline.TORQUE.sub.-- R.vertline., such that the whole 
second term can be seen to locate the point Q with respect to the 
reference. Since the first term represents an aribtrary length vector in 
the direction of THRUST.sub.-- R, which is also the direction of 
THRUST.sub.-- P, T takes on the identity of each and every point on the 
thrust line for some value of Lambda. In the more general case, it can be 
shown that the equation for T generates the line of minimum torque; but 
given the constraint that TORQUE.sub.-- P be zero, this is indeed the same 
as the thrust line. 
It has thus been shown that the point of contact can be calculated from 
information sufficient to determine the total force vector acting on the 
system as seen at some reference point, such as R. Let us now turn to the 
relationship between this total force vector and the values measured by 
the platform sensors. 
Aquisition of Force Data 
The thrust and torque on the system produce a displacement of the top plate 
which may be expressed as a combination of a rotation about R, followed by 
a translation. The three component rotation vector is represented as 
"ROTATION.sub.-- R", and the three component translation vector as 
"TRANSLATION.sub.-- R". The total displacement vector "D.sub.-- R" is also 
defined as consisting of the components of translation followed by the 
components of rotation. 
In the range where Hooke's law applies, the deflection is described by 
flexure matrix "FLEXMAT.sub.-- R": 
EQU D.sub.-- R=FLEXMAT.sub.-- R*TF.sub.-- R.sub.-- MEASURED, (3. 
where "TF.sub.-- R.sub.-- MEASURED" is the sum of all forces, referred to 
R, except for the non-baseline spring forces. It is distinguished from 
TF.sub.-- P@R in recognition of the non-equilibrium effects to be 
discussed in the next section. 
Consider one particular sensor located at a point "S", the response of 
which is characterized by a sensitivity vector "SENSITIVITY.sub.-- S". 
When the rigid extension of the top plate at S moves in the direction of 
SENSITIVITY.sub.-- S, the sensor gives a maximum positive response which 
is equal to the product of the distance moved times the magnitude of 
SENSITIVITY.sub.-- S. When the motion is perpendicular to this line, there 
is no response; that is: 
EQU Response.sub.-- S=SENSITIVITY.sub.-- S dot TRANSLATION.sub.-- S, (4. 
where "Response.sub.-- S" is that one of the six components of the sensor 
data vector "RESPONSE" due to the sensor at S. (The operator "dot" is the 
vector dot product). In the limit of small rotations, the geometry of the 
system gives: 
EQU TRANSLATION.sub.-- S=TRANSLATION.sub.-- R +ROTATION.sub.-- R cross R-&gt;S(5. 
The error is about one-half the rotation magnitude, in radians, times the 
result. Since the rotations of interest are less than one thousandth of a 
radian, the error is insignificant compared to desired accuracy. Taken 
together, the previous two relationships imply that the response is a 
linear transformation of the total displacement, the dependence being 
summarized in a 6 by 6 matrix "SENSMAT.sub.-- R": 
EQU RESPONSE=SENSMAT.sub.-- R*D.sub.-- R (6. 
If, by definition, a 6 by 6 calibration matrix "CALMAT.sub.-- R" is given 
by: 
EQU CALMAT.sub.-- R=inverse (SENSMAT.sub.-- R * FLEXMAT.sub.-- R),(7. 
there results: 
EQU TF.sub.-- R.sub.-- MEASURED=CALMAT.sub.-- R * RESPONSE. (8. 
That CALMAT R be tractable requires that both FLEXMAT.sub.-- R and 
SENSMAT.sub.-- R be reasonably far from singular. For FLEXMAT.sub.-- R, 
this means that the springs should have roughly comparable compliance in 
both compression and shear. They also should be spread apart a distance 
something like the size of the touch surface, to give a reasonable balance 
between torsional and translational stiffness. For SENSMAT.sub.-- R, it 
means that sensors should be placed and oriented to respond as 
independently as possible. Again, how spread apart they are determines the 
relationship of rotational to translational sensitivities, the desirable 
balance being set by the touch surface size. 
Interference from Intertial Effects 
To this point, it has been assumed that forces are applied slowly and 
smoothly enough closely to approximate static equilibrium. In reality, the 
non-zero compliance of the display and platform imply a difference between 
"TF.sub.-- R.sub.-- MEASURED", the actual force sensed by the platform, 
and TF.sub.-- R, the total force mathematically projected from point P. 
This difference may be represented as: 
EQU TF.sub.-- R.sub.-- MEASURED=TF.sub.-- P@R+TF.sub.-- R.sub.-- INERTIAL.(9. 
"TF.sub.-- R.sub.-- INERTIAL" is the reaction force of the display and top 
plate mass referred to R. It consists of excitations of the normal modes 
of vibration of this mass. It has power spectrum confined almost entirely 
to frequencies above a value somewhat below the lowest normal mode 
frequency. 
It would be desirable to use standard linear filtering techniques to remove 
the corrupting influence of TF.sub.-- R.sub.-- INERTIAL. These techniques 
comprise taking various time-weighted averages of the measured data. It 
must first be demonstrated, however, that such averages will not disrupt 
the accuracy of contact localization in some other way. 
Consider the time evolution of a typical touch force. It not only rises and 
falls, but constantly changes direction. As the fan shape swept out by the 
instantaneous thrust line will usually have some conical cupping to it, 
the thrust line of a summary average force does not necessarily lie close 
to any of the instantaneous values. Given that P itself does not move, 
however, (R-&gt;P in equation 1b is constant), it can be seen that a time 
weighted average of the total force components at R, or of any linear 
transformation of those components, corresponds to the components (or 
transformed components) of a similarly time-weighted average of the 
instantaneous forces at P. But any sum of forces applied at P totals to a 
force at P, so the thrust line computed from the time weighted components 
("effective thrust line") must pass through P. 
Now a linear filter applied to TF.sub.-- R.sub.-- MEASURED will produce a 
response which is the sum of TF.sub.-- P@R filtered and TF.sub.-- R.sub.-- 
INERTIAL filtered. The latter is close to zero for an appropriate filter, 
and, as above shown, the first term provides values which compute to the 
correct contact location, thus yielding the desired result. 
An effective filter may be of known lowpass and/or notch design, preferably 
implemented digitally within the microprocessor system 80. Such a filter 
can have a group delay as low as 0.5 to 1 times the cycle time of the 
lowest normal mode of vibration, or something in the range of 0.1 second. 
As this is shorter than the typical touch duration, good measurement 
amplitude is maintained (i.e., the power spectrum of the touch lies in 
substantial part in frequencies lower than those of TF.sub.-- R.sub.-- 
INERTIAL), and reasonable response speed is achieved. Note in particular 
that this group delay is often much shorter than the damping time of the 
system--the excited vibrations may ring for many cycles before something 
approximating static equilibrium is achieved. 
The Planar Model 
There are many situations where a contact surface may be adequately 
approximated by a properly located flat plane. It is found that good 
results may be achieved in applying this special case to a touch 
application, if the maximum deviation of the surface from the plane does 
not exceed about 3 times the required accuracy; i.e., for most touches, 
the tangential component of the contact force is one-third or less of the 
normal one. Although practical difficulties in the placement of sensors 
within this same plane may elevate the cost and limit the applicability of 
the before-described prior art techniques in many such applications, the 
method of the invention for calculating an electrical model that results 
in remotely sensing the location of the touching point on the display 
surface provides a good solution. 
Consider that the contact surface is to be labeled by a two-dimensional 
grid with coordinates "u" and "v". The origin of this grid is at point "O" 
in three-dimensional space, with which we associate the three dimensional 
basis vectors EU and EV. If the point of contact "P" is at coordinates 
&lt;u,v&gt; within the grid, we may write: 
EQU R-&gt;P=R-&gt;O+u*EU+v*EV. (10. 
Now it can be shown that there exist three sets of six numbers, represented 
by the six component vectors U.sub.-- CAL, V.sub.-- CAL, and W.sub.-- CAL, 
such that (in the static limit): 
EQU u=(U.sub.-- CAL dot RESPONSE) / (W.sub.-- CAL dot RESPONSE)(11a. 
EQU v=(V.sub.-- CAL dot RESPONSE) / (W.sub.-- CAL dot RESPONSE)(11a. 
and "W.sub.-- CAL dot RESPONSE" is proportional to the normal component of 
the contact force. For brevity, define: 
EQU us=U.sub.-- CAL dot RESPONSE 12a 
EQU vs=V.sub.-- CAL dot RESPONSE (12b. 
EQU w=W.sub.-- CAL dot RESPONSE (12c. 
As "us", "vs", and "w" ultimately are just linear transformations of 
TF.sub.-- R.sub.-- MEASURED, the filtering described above may be applied 
to these derived data streams. Then the equations: 
EQU u=(filtered us) / (filtered ws) (13a. 
EQU v=(filtered vs) / (filtered ws) (13b. 
closely approximate u and v without requiring static equilibrium. The 
"filtered w" may be monitored to determine the presence of contact; and 
well defined values of u and v may be calculated from the above equations 
whenever "filtered w" is large enough. 
Consider now how values for U.sub.-- CAL, V.sub.-- CAL, and W.sub.-- CAL 
can be obtained. After placing the display device in its position on the 
force-sensing platform, the user runs software which takes the user 
through a calibration procedure. This software may run on the host 
computer, if desired, rather than on microprocessor system 80. After the 
procedure is completed, the calibration values are downloaded via 
communication link 38 for storage in a small non-volatile memory which is 
part of 80. The system is then ready for use. 
For convenience, let it be assumed that the grid which is to be used on the 
display screen has coordinates &lt;u,v&gt;=&lt;0,0&gt; at the lower left corner, and 
u.v&gt;=&lt;1,1&gt; at the upper right. The calibration itself can be performed as 
follows: The four points at the four corners of the screen, &lt;0,0&gt;, 
&lt;0,1&gt;&lt;1,0&gt; and &lt;1,1&gt;, are successively illuminated, and the user is 
instructed to press each one, three separate times as it appears. The user 
may be further instructed to deliver touches with an intentional and 
varying direction of sideways force, as this allows for more accurate 
calibration of the response to tangential components. The exact force and 
direction of each touch is not important, however; only that each is 
placed carefully at the indicated point. 
For each of the six measurements made with u=0, it must be that "U.sub.-- 
CAL dot RESPONSE" is also 0, since "w" is certainly not infinity. Thus 
U.sub.-- CAL is a vector in the null space of the matrix made by 
collecting together these six measurements, and a scalar multiple of this 
can be extracted by standard methods, called "U.sub.-- CAL.sub.-- A". A 
similar multiple of V.sub.-- CAL, "V.sub.-- CAL.sub.-- B", can be 
determined from the touches with v=0. While any arbitrary multiple of the 
calibration vectors taken together suffices, the relative scaling must be 
consistent. Define: 
EQU a=U.sub.-- CAL.sub.-- A/UCAL (14a. 
EQU b=V.sub.-- CAL.sub.-- B/VCAL (14b. 
Dividing 11a by 11b, then multiplying both sides by a/b, we get for the 
touches at &lt;1,1&gt;: 
EQU a/b=(U.sub.-- CAL.sub.-- A dot RESPONSE)/(V.sub. -- CAL.sub.-- B dot 
RESPONSE) 
The value of a/b is determined from one such touch, or as the average of 
the ratios so derived. Then, 
EQU V.sub.-- CAL.sub.-- A=(a/b)*V.sub.-- CAL.sub.-- B (16. 
Using equation 11a, for each of the six touches with u=1: 
EQU W.sub.-- CAL.sub.-- A dot RESPONSE=U.sub.-- CAL.sub.-- A dot RESPONSE.(17. 
Collecting together the six numbers computed from the six right hand sides, 
and pre-multiplying this vector by the inverse of the matrix of the 
corresponding measurements, (a5 ROWS) W.sub.-- CAL.sub.-- A is extracted 
and the process completed. 
A Non-Planar Model 
Now to consider briefly an approach to the more general non-planar case. 
At the factory, each platform can be pre-calibrated in a specially designed 
fixture which supplies a set of six precisely known forces. The forces are 
chosen such that the matrix of these forces, each expressed in terms of a 
specific reference point and coordinate system, such as R and 104, is 
readily invertible. The matrix of measurements is then multiplied by this 
inverse, yielding the desired calibration matrix (CALMAT.sub.-- R, above), 
which is stored in the non-volatile memory. 
In the field, the user calibration procedure presents the user with a point 
at the center of the display, and each of the four points centered along 
one edge. Two differently directed touches are requested for each point, 
and the point locations in space determined from the points of 
intersection of the thrust line pairs. Since the line will not precisely 
intersect, the mid-point of the segment is used which is perpendicular to 
both as a surrogate "intersection". If the segment is too long, or the 
lines of the pair are too close to parallel, the user will be prompted to 
repeat the point. That plane, vertically oriented cylinder, and sphere are 
now determined which best fit (in the RMS sense) the 5 test points. The 
quality of fit for each is compared and the shape passing closest to all 
the points is retained for use. (These three families tried here are by 
far the predominant geometries for display surfaces). 
In application, the factory calibration matrix may be used to compute the 
thrust line in accordance with equation 2, above, with the use of 
appropriate filtering of the sensor data. The information from the user 
calibration is then employed for calculating the point of surface 
intersection in three space, which is reported via 38 in terms of the 
two-dimensional coordinates of that rectangular plane grid, which when 
orthogonally projected onto the postulated surface, places the 5 test 
points in the right place. 
To recapitulate, in the application just described, explicit use is made 
within the embodiment itself of such entities as the thrust line, and the 
components of the total force at R, which were developed in the analysis. 
In the application to the planar case, however, they need not appear 
within the embodiment, although they were used to develop it. Thus, it may 
be seen that two different types of embodiments within the scope of the 
invention may employ calculations that may differ radically as to both 
structure and detail. What they do have in common, in accordance with the 
invention, is: 
(1) Use of force-sensing means responsive to all six degrees of rigid 
motion; and 
(2) Calculating means which from the output of said force-sensing means, 
computes the location of a contact force; such computed location being 
substantially free of error caused by the presence of an unpredictable 
tangential component of the contact force, for all potential contact 
points of interest, including those well removed from the plane of the 
sensors. 
The information provided by the proposed out-of-plane sensors of the 
invention is in fact theoretically sufficient to eliminate errors from the 
before-described tangential force component. While particular practical 
techniques for performing each stage of the required calculations have 
been presented, it is to be understood, however, that there are many 
different ways in which these calculations may be performed, and many 
variations in such matters as the location and orientation of sensors, 
type of sensor, type of support, etc. 
Recapitulation of Distinguishment from Prior Art 
In summary, thus, there are at least three major ways in which the 
methodology underlying the present invention distinguishes it from the 
previously described and other prior art techniques and which are 
responsible for the novel results attained with the invention. 
First, the invention employs force-sensing means responsive to all six 
degrees of freedom of applied force and torque. Prior art methods, on the 
other hand, go out of their way to be sure that they are not responsive to 
tangential components. 
Secondly, the present invention achieves force location away from the plane 
of the sensors, in spite of such tangential components. 
Thirdly, the invention computes the point of least magnitude of the 
three-dimensional torque vector from among all points within the surface 
of interest, and then outputs this point as an estimate of the 
intersection point of the surface of interest with the thrust line of a 
contact force. 
That this is, for all dispositions of this surface, distinct from prior art 
methods of sensing or calculating, is further explained below. 
Each of the above characteristics clearly distinguishes the present 
invention from the before-described prior art and the results obtainable 
thereby. 
Prior art methods, before explained, on the other hand, report the position 
within the flat plane of the sensors at which the magnitude of a certain 
two dimensional torque vector is zero. This vector may be viewed as the 
projection onto the plane of the sensors, at each point in space lying on 
that plane, of the true three dimensional torque vector at that point. Not 
only is the method of the invention far more general, in allowing the 
surface of interest even to be curved, and indeed remote from the plane of 
the sensors, but it is also conceptually and numerically distinct from 
prior art when applied to a flat plane which may contain the sensors. 
To clarify this, consider the following: support a flat board at its 
corners with sensors operated in accordance with prior art. Place this 
whole apparatus in turn upon a device of the invention, so that locations 
of contact upon the board may simultaneously be read out by both methods. 
Drive a screw into the board at 45 degrees to the surface (or at any angle 
that is not perfectly perpendicular). Again, press the screwdriver, also 
at 45 degrees, against the screw head, but without twisting. At this 
point, both methods will report the correct contact location. 
Both two- and three-dimensional torque vectors are zero at the point of 
contact. The field of the three dimensional torque vector can be 
visualized as cylinders of equal length arrows centered on the thrust 
line, the arrow length for each cylinder rising in proportion to the 
cylinder's radius. The individual arrows lie perpendicular to the thrust 
line and pursue each other around it in a circular pattern. 
Now, as the screwdriver is twisted to the right, a non-zero torque vector 
appears at the point of contact which points into the board parallel to 
the thrust line. This component appears uniformly added throughout the 
field, lengthening the arrows everywhere and bending them to point 
somewhat in the direction of the thrust (they now appear to pursue each 
other in right-handed helices). 
Since the minimum magnitude still lies along the thrust line, where only 
the parallel component is present, the method of the invention alone 
continues to report the correct contact point. The two-dimensional 
projection of the parallel component at the point of contact cannot be 
zero, since it is inclined to the surface normal (as it must always be, to 
at least some extent, for any real force). Away from the thrust line, 
however, the helical inclination of the torque field causes the 
two-dimensional projection of some particular vector to vanish at an 
extraneous point. 
Imagine the board horizontal and the screwdriver inclined toward the user, 
with a line drawn on the board through the point of contact, extending to 
the right at right angles to the thrust line. Pick a point on this line, 
say, 2 inches from the screw. Press on the screw with a 1 pound force, 
while applying 2 pound inches clockwise torque with the screwdriver. The 
torque component occasioned (at the point just cited) by the thrust has 
magnitude 2 pound inches and points into the board inclined 45 degrees 
toward the user. The torque component occasioned by the twisting has 
magnitude 2 pound inches and points into the board inclined 45 degrees 
away from the user. The resultant has magnitude 2.818 pound inches, 
directly normal to the board. Its projection into the surface, therefore, 
has zero magnitude; this is the location of the extraneous point reported 
as the contact location by the prior art methods. 
Note that the previously described calibration methods do not necessarily 
define a surface of interest which is coincident with the external surface 
of the display device. When the user directs touches "through" the 
illuminated point of the screen from two or more different directions, the 
user may well be touching physically different points on the surface. 
Thus, when using a cathode-ray tube monitor with a thick glass faceplate, 
the surface of interest is located where the phosphors appear to be; and 
this may be defined implicitly in the application through the effect of 
the calibration procedure, allowing the device to project a virtual 
response surface to match. The point of intersection of the thrust line 
with this response surface is closely approximated by finding the point 
within the virtual response surface having the least magnitude of the 
three-dimensional torque vector. 
The method of the invention is distinguished from the prior art in that it 
reports the location within a surface of interest at which the 
three-dimensional torque vector takes on minimum magnitude (i.e. has 
shortest length). Indeed, this may be taken as a description of the sole 
calculational requirement of the invention. 
Further modifications will also occur to those skilled in this art 
including, for example, other types of similarly functioning springs and 
sensors, as desired; and other locations of the external force-sensing 
platform contacting or abutting or otherwise touching the monitor or other 
apparatus carrying the surface upon which touch or other contact events 
are to be located, including for more general applications, placement 
internally of or behind the supported apparatus. All such supporting or 
abutting platforms or objects for a surface of interest of whatever shape, 
are generically termed herein as a "display surface portion" or similar 
term for generically termed "display apparatus". Other, more general 
"surfaces of interest" may be imagined. Consider the force applied to a 
glass window on a vending machine when a customer presses and points to a 
desired object far inside. The surface of each object is then a "surface 
of interest", potentially intersecting the line of minimum torque. A 
medical student, for example, may point to invisible organs within the 
torso of an opaque human model; the model may be quite hollow, yet 
mathematical descriptions may be found for the surfaces of interest 
corresponding to the organs that would be there were the model real. Those 
skilled in the art will readily see how such surfaces might be adequately 
described within the overall calculating means to be employed, and how the 
method of the invention can be applied to such and other particular cases. 
Thus the "surface(s) of interest", and the corresponding desired "virtual 
response surface(s)", are defined by the application and the intent of the 
user, without being restricted by the specific illustrated particulars of 
the described mode of the invention. It is also to be understood, as 
before stated, that the invention is useful with other types of 
electro-optical display surfaces than cathode-ray tubes, including, but 
not limited to, LCD and LED displays. Such and other indicated 
modifications are deemed to fall within the spirit and scope of the 
invention as defined in the appended claims.