Digitizer Technology:
`Performance
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`® active drawing area
`data rate (time resolution in points per second)
`spatial resolution (in physical distance)
`worst case position accuracy (from absolute
`position)
`®@ pointer type (pen stylus or puck)
`
`L. the commercial world, tablets are usually described
`
`with the following performancespecifications:
`
`Mutability of tablet performance
`Most designers incorporating a digitizing tablet into
`a system are not so familiar with signal processing tech-
`niques as with computer graphics technology. They
`often overlook the possibility of trading performance in
`one dimension for performance in another. We have
`found that commondigitizers typically have in one or
`more domainsexcessquality (relative to the needsof the
`application) that can be manipulated to improve quality
`markedly in domains wherethedigitizer is deficient.
`For example, if a tablet samples the position of the
`pointerfaster thanis actually needed, averaging several
`inputvaluestogetherwill substantially reduce the mag-
`nitude of any randompositionalerrors. Differentfilter-
`ing or averaging algorithms can correct for Gaussian
`noise, wild data, and slew rate errors. The effective result
`will be a digitizer with much better accuracy, but a some-
`what lower samplingrate.
`Conversely, an application might require a higher sam-
`pling rate, but not involve the tracking of sudden, small
`changes in position. An example is human-generated
`animation input, which needs smooth, nonjerking
`motion morethantheability to read sudden changesin
`Valve Exhibit 1064
`Valve Exhibit 1064|31
`0272-1716/87/0400-0031$01.00 © 1987 IEEE
`April 1987
`Valve v. Immersion
`Valve v. Immersion
`
`Thefirst four are usually measured with a puck pointer
`held stationary. For a pen stylus, sometimes the worst
`case positionerror fromtilting the stylus will be given,
`but frequently this is ignored.
`These specifications can fail to show how well (or
`badly) the tablet performsfor a given user action for two
`reasons.First, the specifications have been measured for
`onetypeof action, but perhapsnotfor the action thatis
`importantin a given application. Second,the specifica-
`tions do not describe the nature ofthe error, only its mag-
`nitude. The nature of the error may be important in a
`specific user action, since it may determine whether the
`useror the application can overcomeit by some means
`of correction.
`
`

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`the need to capture small features
`the need to keepupwith ahigh continuouswrit.
`ing speed
`the requirerrenttowrite withapen stylus,notthe
`larger, moreaccurate puck
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`Background: tablet sensing
`technologies
`Manyperformanceproblemsofdigitizer tablets result
`from the particular designof the tablet. Most tablets use
`electromagnetic/electrostatic or resistive sheet sensing
`technology. Other methodsare acoustic sensingin air,”
`surface acoustic wave sensing,’ and mechanical sens-
`ing.*° Each design is prone to certain performance
`problems. Before we discuss particular performance
`characteristics, we will review the commontechnologies.
`
`Electromagnetic /electrostatic tablets
`Electronic sensing tablets typically have an x/y grid
`of conductors underthetablet surface, spaced from 0.1”
`to 0.5” apart, and a loop ofwire within the pointer. The
`position of the pointer is determinedby exciting either
`the grid or the loop with an electromagnetic pulse, and
`sensing the inducedvoltage, current, or spatially depen-
`dent phase’of a sinusoidalsignalin the other. The tab-
`let conductors are scannedtofind the conductor closest
`to the loop (rough position), and the sensed pulse meas-
`uredto interpolate the precise position between conduc-
`tors. Usually several pulses are sensed and averaged to
`give a better final value.”
`Either the loop can be the transmitter andthetablet
`grid the receiver,’ or vice versa.° If the pointer is the
`receiver, it is harder to shield and is morelikely to suf-
`fer when putnear sourcesofelectromagnetic noise (such
`as a color VDT), causing it to report spurious or inac-
`curate position data.
`
`Resistive sheet tablets
`Another group of technologies is based on measuring
`the voltage gradientacrossa resistive sheet. One design
`uses layers of conductive andresistive material with a
`spacing between the layers.*°"1 A voltage gradient is
`applied across oneofthe layers in one coordinate direc-
`tion. Whena pentip or otherobject presses on thelayers,
`the conductive layer gets the voltage at that point in the
`resistive layer. The voltage can be measuredto determine
`the pointof contact along that ordinate. The design has
`the advantagethat it can use an ordinary penorfinger-
`tip. One disadvantageis that a “light touch” can give bad
`position data due to contactresistance;a ‘‘broad touch”’
`(such as a wholefingertip) will give some variable cen-
`troid value.
`A similar technique is to vacuum deposit a resistive
`layer ona hard surface and inducea voltage gradient by
`applying a voltage with thetip of the writing stylus. At
`least one design uses capacitive coupling to a signal in
`the stylus” instead of dc voltage.
`The most notable feature of these designsis that trans-
`parent materials can be used to makea ‘‘see-through”’
`digitizer. We have found that the performance can be
`limited by the manufacturing uniformity of a resistive
`
`position. Digitizer data could be interpolated between
`points by different methodsto “improve” the sampling
`rate: Straight-line interpolationis a very simple method,
`and produces points only in integer multiples of the
`input data rate. Other algorithms have much better
`“tracking,”’ and can simulate any desired data rate. The
`result is “smoother” positioning from more intermedi-
`ate points, with a loss of sudden-movementdetail.
`In general, there are methodsto overcomeanyspecific
`deficiency of a digitizing system. The questionsfor the
`applications designer are what characteristics are
`important, and howdifferent characteristics should be
`traded off against each other.
`
`32
`
`IEEE CG&A
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`

`

`layer of material, whetherit is rolled and pressed, or
`vacuum deposited on a hard surface.
`Onenote: Several applications in recent years involve
`mounting a digitizer directly on a display, resulting in
`muchbetterresolution thanthat ofeither a light pen or
`most capacitive or infrared touch screens. But this can
`introduce new problems. The application involves point-
`ing to featuresor objects on the display. The display posi-
`tion can changewith line voltage or the display can be
`stretched in portions as muchas 10 percent, introduc-
`ing errors much worsethan thoseof the lowest accuracy
`digitizer we have ever seen. LCD and plasmapaneldis-
`plays are “‘flatter,” but some generate strong electrical
`noise and hurt digitizer performance.
`
`Acoustic tablets
`Acoustic tablets use eitherthe travel time or the phase
`of a standing wave for a sound pulse from a transducer
`to a sensing microphone to compute the position of a
`pointer.This is perhaps the easiest technology for
`digitizing in three-space, since each transmitter/micro-
`phonelink can be designedto workwell in any direction.
`Aside from the obvious environmental problems in
`nonbenignsettings(two digitizers operating next to each
`other, for example),
`the nonuniformity of air as a
`medium can also cause substantial performance var-
`iation.
`For high accuracy, these tablets have to be calibrated
`for local air temperature andaltitude pressure. Local var-
`iances, such asa draft? or the heat from a cigarette or
`electrical equipment, can affect accuracy. A 5° C change
`in temperature near 20° C changesthe speed of sound
`in air by 0.8 percent." If applied to an 11” sensingdis-
`tance, this produces anerror of 0.08”, whichis larger
`than the nominalerror of mosttablets.
`
`True characteristics of digitizer
`performance
`Since the usual performance measures usedby ven-
`dors ontheirtablets are not adequate,in this section we
`show whatthetrue characteristics are. We also describe
`the parts of a digitizer design that could cause problems,
`the applications that they might affect, and ways the
`application designer can correct them. Wethinkthat the
`most important performance measures are the fol-
`lowing:
`
`@ missing coordinates
`monotonicity
`output continuity
`slew rate
`rectilinear displacement
`scaling error
`orthogonality
`differential error
`
`April 1987
`
`
`
`Figure 1. Density map of the coordinates reported by
`acommercialtablet: actual coordinates reported with
`“‘missing’’ coordinates.
`
`static error (periodic and nonperiodic)
`hysteresis
`noise and repeatability
`proximity range
`tilt error
`stylus transducereccentricity
`accuracy at drawing pressure
`
`Each of these deservesa brief discussion.
`
`Missing coordinates
`Sometablets that we have examined do not produce
`every coordinate intheir active area. For example, a tab-
`let with an 11”x11” active area at a resolution of 200
`points per inch should produceevery coordinate value
`from zero to 2199 in both the x- and y-axes. A tablet may
`fail
`to produce every coordinate because the fine-
`position interpolation method used doesnotinterpolate
`far enough between rough-position sensing points. The
`resulting “‘under-interpolation” leaves an apparent gap
`between the reference points.
`This does not meanthereis an actualgap in the phys-
`ical positions that can be sensed. The reported coor-
`dinates might be uniformly spaced, but the controlling
`firmwarereports only nine distinct points for every 10
`physical points on thetablet.
`If the application requiresfine positioning of a display
`crosshair, and the pixel range of the display is approxi-
`mately the sameas the coordinate range ofthetablet,
`there maybe display pixels corresponding to the miss-
`ing tablet coordinates that cannotbe “pointed to.”’
`Figure 1 showsa “density map” of the coordinates
`actually reported by one commercial tablet. The input
`
`33
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`

`

`Tasks performedby digitizing tablets
`Nota lot has been written about thelimits ofdigitizer
`performance and how the characteristics affect differ-
`ent applications. A limited amount of material is avail-
`able describing aspects of digitizer design, mostly
`tutorial information on functional design (transparent
`versus opaque, electromagnetic versus electrostatic,
`etc.), with somediscussion of what characteristics are
`most commonly given in vendor specifications.‘
`These presentations do not discuss applications in
`detail.
`Foley, Wallace, and Chan give a comprehensive over-
`data includes every nominally reportable point. Note the
`view of the interaction tasks in graphics applications
`regular x/y pattern of the missing coordinates.
`using digitizers and other pointing devices, but say very
`little about the devices’ performance characteristics.®
`Theeffect is that the tablet hasless resolution for the
`They dolist six kinds of graphical interaction tasks for
`locations near the missing coordinates: You cannot
`the user: select, position, orient, path, quantify, and text
`“point” into the gaps.If the application needsonly the
`input. They describe the possible methods for each
`lowerresolution, this may not be a problem. Mostappli-
`interaction for many kinds of devices.
`cations for screen-oriented positioningfall into this cat-
`For digitizer tablets, we find it useful to divide the
`egory, since a typical high-resolution display (that is,
`physical acts required for the interaction tasks into
`1000x1200 pixels) is much grainier than even a low-
`three basic categories: coarse selection, fine position-
`resolution tablet (200 points per inch on an 11”x11”
`ing, and dynamic graphical entry. Some short defini-
`tions follow.
`area).
`If the application emphasizes dynamicentry, such as
`Coarse selection—Commandsoriconsare selected
`by pointing and touching the tablet surface to make a
`markingthe path an image should movein an animation
`selection. The feedback for this process can beeither
`system, the slight displacementof one pointinaset of
`screen- or tablet-oriented, with slightly different require-
`widely spaced pointsis notlikely to affect the applica-
`ments for each.
`tion. Low-passfiltering of the digitizer data could be used
`Screen-oriented selection refers to selection of digi-
`to interpolate data into the gaps as the pointer is moved
`tized points using feedback from a cursor on the
`over them.For applications involvingfine detail, a more
`screen. In these applications, the resolution of the
`serious problem is the loss of resolution for small fea-
`screen is often much lower than the resolution of the
`tures.
`digitizer.
`An exampleof tablet-oriented selection is “function
`boxes” on a tablet overlay. The requirements for such
`a system are minimal, since the selection targets are
`
`
`
`which cannotbe corrected,is visible when watching the
`positions for a movingstylus, becausethestylus is not
`likely actually to jerk discontinuously. However,if the sty-
`lus is not moving, there is no indication of which side
`of the error it is on. The areas wheretheerror occurs are
`less accurate thantherest of the tablet.
`
`Output continuity
`Mostdigitizing tablets support a ‘“‘stream” mode of
`input, wherethe position of the pointer is reported con-
`tinuously. The state of the pointer’s contact switch
`(touching/closed or up/open)is included with eachset
`of coordinates, either explicitly or implicitly by not trans-
`mitting data whenthe pointeris “‘off tablet.”” We have
`observedseveral tablets that send spurious“‘off”’ points
`in the middle of a data stream.
`Forelectronic tablets, one possible sourceof the prob-
`lem is the scanning method usedto locate the pointer
`loop. Scanning the entire grid can take longer than the
`available time betweenpoints. For example, the control-
`
`IEEE CG&A
`
`
`
`Figure 2. Straight line with nonmonotonicity errors.
`
`Monotonicity
`Sometablets will occasionally report a slight jump
`backwardas the pointer is moved acrossthetablet. In
`electronic tablets, this is usually caused by overcompen-
`sation in the interpolation between sensed positions
`from the conductor grid. As the pointer moves from a
`position near one conductorto the next, the interpola-
`tion relative to the new conductorresults in a coordinate
`too far away from the new conductor. In resistive sheet
`tablets this can be caused by nonuniformitiesin the elec-
`trical properties of the materials. When the user must
`trace small features, the resulting ‘‘noise’—which can be
`seen only when the pointer is moving across the
`transition—distorts the digitized image.
`For the electromagnetic tablets we have examined,
`theseerrors are consistent from onetablet to another of
`the same design with the samefirmware.Theerror can-
`not be detected without knowledgeof the pointer’s com-
`plete dynamicpath. Therefore, the only straightforward
`correctionis to scale the coordinates to reducethereso-
`lution so that it becomescoarser than the magnitude of
`the errors.
`Figure 2 showsthe theeffects of a simple, periodic
`nonmonotonicity on a straight diagonal line. Theeffect,
`
`34
`
`

`

`
`
`_
`
`large, if only to make them readable and easily acces-
`_ sible to the user. Most selections are made closeto the
`_ center of the function box, so that absolute accuracy
`usually is not necessary.
`Fine positioning—tThe user must point precisely to
`a specific point, either relative to the screen, or toa
`drawing onthetablet.
`An exampleis the manualtask of digitizing points
`from an existing blueprint or engineering drawing to
`enter the drawing into a computer database. Each point
`must be accurate, but the data rate (numberof digitized
`points entered per minute) is low, and thedigitizer sty-
`lus is held stationary whenentering a point.
`Dynamic graphical entry—The user traces out a
`(complicated) curved path with the digitizer in real time.
`Typical usesof this technique include on-line charac-
`ter recognition, signature verification, and graphical
`entry for human-generated animation. In these applica-
`tions, the pen, in general, will not be stationary. To cap-
`ture the path written in a signature, for example, the
`digitize rate must be continuous and fast (over 100
`points per second). The details to captured are small
`(someless than 0.05”).
`
`References
`
`
`
`Figure 3. Discontinuities in a resistive sheet tablet: (a)
`“I”? as written, (b) ‘‘I’’ as digitized.
`
`
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`The problem can be reduced,butnot eliminated, by
`extrapolating the nextlikely position of the pointer based
`on its travel, not just its previous position. This change
`must be madein thetablet designitself. The application
`can reduce the error somewhatbyfiltering out short
`“pointer-up” periodsfrom thetablet’s data stream. This
`1. D.J. Grover, “Graphics Tablets—AReview,” Displays, July
`helps only if the pointer does not continue to move too
`1979, pp. 83-93.
`fast for the tablet to catch up.
`2. “Digitizer Terminology and Comparability,” Science
`Accessories Corp., Southpark, Conn., 1982.
`In one designfora resistive sheet tablet, a sheet of con-
`
`
`3.
`Ilvaschenizoetal., ‘Inductive Transducers for Graphical
`ductive material is separated fromaresistive sheet by
`Input Devices,” SovietJ. of Instrumentation and Control,
`
`small spacing “bumps” at regular intervals.'® Thetablet
`Aug. 1969, pp. 22-25.
`
`is effectively “‘pressure sensitive,” since it reads the posi-
`4. K. Dunn, “Choose Digitizer Technology and Features to
`
`tion where the twosheets get pressed together. When the
`Suit Applications,’ Computer Technology Review,
`
`Fall/Winter 1981, pp. 171-175.
`stylus tip crosses a spacing bump,the twosheets lose
`
`5. J.D. Foley, V.L. Wallace, and P. Chan, “The HumanFactors
`
`contact with each other, producing a spurious “pen-up”’
`of Computer Graphics Interaction Techniques,” /EEE
`
`point.
`CG&A, Nov. 1984, pp. 13-48.
`In our application (dynamic character recognition),
`the effect of these discontinuities is to make quickly writ-
`ten strokes in a character look like a series of shorter
`ler on a tablet with a 10” square active area and conduc-
`strokes. Since the numberofstrokes in a character is one
`tors ona 0.1”grid may needto scan 200 conductors (100
`feature used in the recognition process, the characteris
`each in x andy) to locate the pointer. If the controller
`made“unrecognizable,” even thougha plotted image of
`averages five measurementsto get good accuracy and
`the data mightstill be legible to a humanreader(see Fig-
`must supportadigitizing rate of 100 points per second,
`this represents a scanningrate of 200*5*100,or 100 kHz,
`ure 3).
`Someapplications usea digitizer to control the posi-
`a very fast rate for the typeof circuitry commonly used
`tion of a mechanical object, such as a robotic arm,or to
`in low-cost digitizers.
`“drag” a graphicalobject, such as an imagein a display.
`Acommon method usedto reduce the required scan-
`If the application uses the stylus switch to ‘‘drop’” the
`ning speed is to scan only the small area of thetablet
`dragged objectat a final position, the discontinuities can
`nearest the last knownposition ofthe pointer.’® A com-
`cause the object to be dropped partway along the
`plete scan is necessary only whenthepointerisfirst
`intendedpath.
`brought into sensing range. This may causea delay in
`reportingthefirst point after the pointer is in range.
`Theproblemhereis that with its restricted scan the
`tablet may notfind the pointerif it has moved rapidly
`awayfrom thelast reported position. Whenthe pointer
`cannot be found, the tablet electronics cannot distin-
`guishthis case from thatof the pointer not being on the
`tabletatall.
`
`Slew rate
`Wedefine slew rate as the maximum travelrate of the
`stylus that the tablet can report with a specified posi-
`tional accuracy. Slew rate accuracy can be limited by low-
`pass filtering, time delays in measuring the x and y
`ordinates, and wild data.
`
`April 1987
`
`35
`
`

`

`Whowrote the specifications?
`
`applications resolution is notcritical.
`
`We have found that many vendors play a game of
`“Specs-manship” when quoting performanceon their
`digitizers. We give several examples:
`
`@ One vendor quoted an 11”« 11” active area, but
`quoted accuracy only for a region bounded one inch
`from the edges of the active area, or 9”x9” Testing
`showed large sloping errors near the right and bottom
`edges of the 11” 11” active area.
`@ We were shipped onetablet that, according to the
`vendor, had aresolution of 0.001” (1000 points per inch)
`and an accuracyof 0.01” The tablet turned outto be the
`vendor’s standard 200-points-per-inch tablet with the
`firmware modified to multiply all coordinatesby five to
`simulate 1000 points per inch. The discrete valuesof
`0.005”, 0.01”, 0.015”, 0.02”, etc., were within the
`“accuracy” specification of 0.01”
`@ All vendors that we have checked offering a
`choice of apen stylus or a puck quote accuracyonly for
`the puck. A puck on an electromagnetictabletis inher-
`ently more accurate, since a puck generally has a larger
`sensing/transmitting loop,is always perfectly horizon-
`tal at a constant height above the tablet surface, and
`is usually held stationary.
`@ Some vendors quote accuracyrelative to an abso-
`lute physical point on the tablet, while others quoteit
`relative to the “first” reference point digitized, covering
`up any offseterrors.
`@ The quoted datarate for one tablet was “up to 100
`points/second,” but the tablet used an ASCII format
`that took up to 14 charactersper point, on a 9600-baud
`line. For most values (more than twodigits for x and for
`y), the extra characters limited the maximum possible
`reported data rate to about 63 points per second.
`All vendors want to showthe bestside of their prod-
`uct. The figures given in each caseare correct and true.
`The pointis that different characteristics are critical
`dependingon the application ofthe digitizer. For exam-
`ple, many digitizers are sold based on one high-
`performancecharacteristic—resolution—but for many
`
`@eeoee 688
`
`Figure 4. Theresults of “drag’’: written “‘Z’’ digitized
`as ‘‘2.”? Note how the uppercornerin thedigitized ‘‘Z”’
`(center) has been roundedby excessive drag.
`
`If the tablet firmware averages several measurements
`to get good accuracy,it will send a series of interpolated
`points that “drag behind” the motion of a quickly mov-
`ing pointer. Theresultis that rapidly drawn, angularfea-
`tures in dynamic graphical entry are roundedout, and
`small, quickly drawn loops maybecollapsedinto single
`points. For our character recognition application, the
`results can change the appearance of one character
`shapeto another, as shownin Figure 4. This phenome-
`non would also affect applications such as signature cap-
`ture and artistic drawing.
`Somedigitizer designs perform separate cycles of
`processing for each coordinatepair:first a measurement
`in x, thenin y.If the time for each cycle is significant,
`the apparentposition will “bow” in one ordinate direc-
`tion if the stylus is moved at varying speeds along a
`diagonalline.”
`If the time between the x and y measurementsis
`known,the error can be substantially corrected by geo-
`metric projection, such as the algorithm given by
`Carau.’®
`
`Rectilinear displacement
`Rectilinear displacementis the difference between the
`nominal coordinatesof a baseline homeposition on the
`tablet, and the actual coordinates transmitted for that
`location.
`Digitizer applications in whichthe userinputs exact
`points from a fixed menu (possibly permanently
`mounted onthetablet), or from photographs, may need
`the precise physicallocation of the data,notjust the rela-
`tive positionsof the different input locations. Sometab-
`let designs have a raised borderor other hardware guide
`for positioning a sheet of paper or a photograph on the
`tablet.
`A fixed offset in the input coordinatesforall tablets of
`one modelcan be seenas a discrepancyin the manufac-
`turing of the tablet. The error should befixedin the tab-
`let firmware,sinceit is the sameonall tablets. A varying
`displacement error amongtablets of the same design
`occursif the mounting of the sensinggrid in thetablet
`
`“‘skin” is not machinedto be precise. Imprecise mount-
`ing can also lead toerrors in orthogonality (see below).
`The varying displacementerror can be corrected by
`computing the displacements in x and in y from the
`baseline value for a reference point on the image and
`adding these to offset the coordinates of every input
`point. Some manufacturersincludethis one-pointcali-
`bration procedure in the firmware for their tablets."
`The procedurecanjust as easily be addedto the appli-
`cations codeby havingtheuserpointto a specified refer-
`ence point whose correct position is known.
`Any application wherethe user mustdigitally “tran-
`scribe” an image requires accurate absolute physical
`
`36
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`IEEE CG&A
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`

`

`positioning. Commoncasesarethe digitization of exist-
`ing engineering drawingsthat predate the direct use of
`CADin an organization, and medical analysis of X-ray
`images.
`
`Scaling error
`For large displacements, scaling error is the ratio
`between the measured physical distance between two
`points parallel to eitherthe x- or the y-axis, and the actual
`distance. The most likely causein electronictablets is an
`improperor inaccurate scaling operation on the sensed
`position to a “normalized” scale (such as converting 0.1”
`grid spacing to metric units). In resistive sheet tablets,
`the mostlikely cause is variations in componentproper-
`ties in the analog electronics.
`The error can be introducedin the applicationitself,
`as whentheuseris digitizing an imagethat itself has
`scaling errors. Images from office copiers, for example,
`typically have up to +3 percent scaling distortion
`separately in x andin y. This distortion is enoughtoshift
`text the height of an entire text line. Scaling error on pho-
`tographs, too, caused severe problems when published
`curves for a control system weretranscribed from pho-
`tocopies.”°
`If the error is simple, it can be corrected by adding an
`“aspect ratio calibration” to the application.”!
`
`Orthogonality
`Weconsider twoseparate characteristics for orthogo-
`nality in a digitizer: the relative angle in physical space
`between the digitized x- and y-axes, and the absolute
`angle to the physical baseline of the tablet. Some
`digitizers have a raised edgeor frameto makesure that
`the paper on thetablet is laid down square to prevent
`misalignment.
`For electronic digitizers using an x/y grid of conduc-
`tors, an absolute error in the angle of an axis is proba-
`bly a result of improperor imprecise mounting of the x/y
`grid relative to the tablet skins. At least one commercial
`tablet has this sort of design.”
`Anerrorin the relative angle of the two axesis a result
`of mechanical distortion in the x/y grid. The same
`apparent phenomenonresults whenthetablet is nomi-
`nally “‘precise,” but the image being digitizedisitself
`subject to orthogonality errors. We have observed errors
`of as muchas 3 degrees in nominally “square” alignment
`on a printed form produced with commercial offset
`pressesor office copiers.
`Absolute error in one axis can be measured using two
`reference points along the “physical” axis. Measuring
`relative error requiresat least three-point calibration,??
`where onepointis the vertex of a fixed angle formed by
`the three points. The trigonometric calculations for the
`correction have been described.” To reduceerror in the
`measuredangle from small changesin the placementof
`one or moreofthe points, all other positioning errors
`
`April 1987
`
`Figure 5. Nonrandom differential error reflects
`underlying tablet structure. The space between the
`two vertical lines reflects the spacing of the tablet
`sensing grid.
`
`mustbe correctedfirst, and the reference points should
`be spaced widely apart in the active area of the tablet.
`
`Differential error
`The positioningerrorfor a tablet can also be measured
`differentially; that is, the maximumerrorfor a smallrela-
`tive change in position is measured, regardless of the
`absolute error. An example would be a small-scale saw-
`tooth error in one axis as the pointer is moved slowly
`along the axis (see Figure 5).
`An application requiring the correct ‘‘imaging’’ of
`small features maybeableto tolerate a large cumulative
`error acrossthetotal area of the tablet, but may not be
`able to tolerate “noisy” data around the area of the
`pointer tip. For example, a handwritten signature may
`still be acceptable with a large but well-behaveddistor-
`tion to the image. The features that makethe signature
`uniquely recognizable are the small hooks and corners
`of each individual character.
`Differential errors can be causedbytransition between
`grid lines on an electromagnetictablet, local nonlinear-
`ities in the materialofa resistive sheet tablet, or thresh-
`old crossings in the A/D measurement circuitry.
`Visually, the effects of this type of error may bedifficult
`to distinguish from random noise. However, true Gaus-
`sian noise can be compensatedfor by trading perform-
`ance in temporal sampling rate for spatial accuracy.
`Fixed differential errors cannot be compensatedfor in
`this way.
`Differential error can be an especially pernicious form
`of static error in the tablet. Confusing its symptoms with
`noise is easy, but differential error is much harder to
`correct.
`
`37
`
`

`

`=10.2”
`
`Figure 6. ‘‘Hockey-stick’’ static error showing edge
`distortion.
`
`Static error
`Static erroris the fixed error remaining in the reported
`tablet coordinatesafter all corrections for scaling, rec-
`tilinear displacement, andothererrors have been made.
`If the errorsare identicalforall tablets of a given model,
`wesay theerroris predictable, regardless of the nature
`or the sourceofthe error.If the errors are not identical
`for different tablets of the same model, wesay the errors
`are unpredictable. With many applications, the predict-
`able errors can be compensatedfor.
`Different mechanisms can produce a spatially peri-
`odic error, or a well-behaved but nonperiodic error.
`Sometablets exhibit a geometrically regular but varying
`positionerroras the pointer loop is moved acrossthe tab-
`let. The most frequent cause is that the interpolation
`used to compute the position between grid conductors
`doesnot correctly model the changein the sensed pulse
`as the pointerloopis at different distances from the grid
`conductors.
`A nonperiodicerror is typical near the boundaries of
`the active areaof a digitizer. It may be caused by the prox-
`imity of the pointer to electromagnetic fields from the
`tablet electronics, poor algorithmsfor the transition from
`interpolation to extrapolation, or merely the lack of a
`suitable “infinite” plane for the tablet grid. Figure 6
`showsthe actual error we measured for one commercial
`tablet with an 11”x11” active area.
`Mostresistive sheet digitizer designs are very sensitive
`to nonuniformities in the resistive sheet. Here the errors
`in x and y tendto beinterrelatedin different spots on the
`tablet. A regionthatis electrically thicker or thinner than
`the rest of the sheet affects the resistance paths to the
`edgesfor the entire sheet, not just in one direction.
`The most general wayto fix static, continuouserrors
`is to measure the actual position versus the reported
`
`38
`
`position for every point on thetablet, put the results in
`a correction matrix, and look up the correcting offset
`every timea position is read from thetablet. In practice,
`the size of the correcting matrix hasto be limited to avoid
`taking up too much memory.At least one vendor uses
`this techniqueona resistive sheet tablet, where each tab-
`let hasto be “‘calibrated”’ individually to correct for the
`variations in resistance in the sheet.
`Note that piecewise continuousfactors should be used:
`You haveto interpolate betweenthe pointsin the correc-
`tion matrix, not just add or subtract and offset in each
`small correction patch. One vendordid notinterpolate,
`andthe result was discontinuities at the edges ofthe cor-
`rections patches.
`
`Hysteresis
`A broad class of characteristics can be described as
`“memoryerrors”: The reported valuefor the position of
`the pointer depends on thespatial and temporal path
`taken to putit there. The most well-known property in
`this class is hysteresis.
`Manydigitizers have an explicit hysteresis incorpo-
`rated into th