A PARAMETRIC GRAPHICAL DISPLAY TECHNIQUE FOR ON-LINE USE. M. L. Dertouzos and H. L. Graham

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1 A PARAMETRIC GRAPHICAL DISPLAY TECHNIQUE FOR ON-LINE USE M. L. Dertouzos and H. L. Graham Massachusetts Institute of Technology Cambridge, Massachusetts INTRODUCTION Graphical displays are gaining unquestioned importance 1 in the growing field of communication between man and digital computers. The development of time-shared digital computers 2 further accentuates the need for widely-used graphical interaction within the framework of certain economic constraints. Typically, these constraints involve the use of relatively low telephone-channel data rates and the temporary storage of graphical data at the' display site. User requirements dictate both an input and output ability of alphanumeric and graphical data * for. typical. applications. A typical time-shared application, WhICh gave rise to the technique and prototype described in this paper, involves the online design ~f electronic circuits. 3, 4 Here, a designer c?mmumcates graphically a circuit to the computer, VIsually observes circuit-analysis results in the form of curves, and modifies on-line circuit parameters and topology in order to improve circuit performance. The display technique to be presented involves only ~he ou.tput of graphical data. It is normally combmed with a device such as a teletypewriter or * T~is distinction between alphanumeric and graphical data ~s one of efficiency, since character generation and graphlcal-segi?ent generation could be accomplished by the same mechamsm: 201 a light-pen for graphical data input. Main objectives in developing this approach have been the display of complex curves in terms of relatively few computer commands, and the evolution of a display system sufficiently simple and inexpensive to accompany a typer of a time-shared installation. First, the principle of operation is described. Discussion of certain system-design decisions is followed by the way in which the experimental prototype was implemented. Experimental results, relevant software, and conclusions complete the paper. PRINCIPLE OF OPERATION A block diagram of the basic elements used in t~is technique is shown in Fig. 1. Visual data is pro VIded by an x-y graphical display device such as a storage-type cathode ray tube driven by waveforms x(t) and y(t), where t is time. These waveforms are the outputs of two linear networks, Tx and T y, char- COMpm~ ( WORD XDi Pi YD j Figure 1. Basic configuration.

2 202 PROCEEDINGS-FALL JOINT COMPUTER CONFERENCE, 1966 acterized by unit-step responses T x (t) and T y (t), respectively, which are constrained to have unity steady-state gain, that is T x ( 00) = 1 and T y ( 00 ) = 1. Signals XA (t) and Y A (t) are the outputs of digital-to-analog converters which convert two parts, XD i and YD i, of the computer output from digital into analog form. A third part, Pi, of the computer output controls the parameters of networks T x and Ty. Assume that at time, tk, the linear networks have attained steady state. As a consequence, outputs of Tx and Ty will be X(tk) = XA (tk) and y(tk) = Y A (tk), thus establishing at time, tk, a point [XA(tk), YA(tk)] on the CRT: Suppose that at t = tk the computer output changes, so that XA (t) = XA (tk) + AXU-1(t - tk) (1) Y A (t) = Y A (tk) + AYU-1(t - tk) (2) for t > tk, where U-1 (t) is the unit step. Signals x(t) and y (t) will then be, by the linearity of T x and T y, for t ~ t1\ x(t) = XA (tk) + AX Tx(t - tk) (3) yet) = YA(h) + AY Ty(t - tk) (4) Since T x and T yare constrained to have unity steady-stage gain, the final values of x(t) and y(t) at some time tk+1, where tk+1 - tk is much greater than the time constants of Tc and T y, will be ~(tk+1) = XA (td + AX (5) y(tk+1) = Y A (fk) +b..y (6) thus, establishing a point [XA (tk) +b..x, Y A (tk) + b..y] at time tk+1 on the CRT. What is of interest here is the trajectory I(x, y) = O-resulting from elimination of t in Eqs. (3) and (4 )-between these two points. This trajectory will depend upon the nature of networks T x and T y and on the way in which their internal parameters are controlled by Pi. For instance, in the special case where TIlJ is identical to T y, Eqs. (3) and (4) give the following trajectory: y = Y(tk) + - AY b..x (x- X(fk)) (7) which is, as expected, a straight line. In general, when Tx and Ty are not identical, the trajectory will be some type of curve segment dependent upon the class and parameters of Tx and T y. It is, therefore, desirable that T x and T y be properly chosen, so that a large and useful class of curve segments will be available through appropriate control of network parameters with Pi. A complex curve may then be synthesized as a composition of these basic curve segments. SELECTION OF NETWORKS Tx AND Ty Let Tx and T11 have step responses which are rising exponentials, i.e., Tx{t) = (1 - e-uxt)u_l{t) (8) T 11 (t) = (1-e- Uyt )u_1(t) (9) where Ux, U y are positive and U- l (t) is the unit step. If XA(tk) = X o, YA(tk) = Yo,.b..X = (Xl - X{)), and b..y = (Yl - Yo), then by Eqs. (3) and (4), signals x(t) and yet) will be x{t) = (Xl + (Xo - Xl)e-UX(t-tk»)U_l(t - tk) (10) yet) = (Y l + (Yo - Yl)e-Uy<t-tk»)U_l(t - tk) (11) for t > fr.. Eliminating time between Eqs. (10) and (11) gives, between points (Xo, Yo) and (Xl, Y l ), the following trajectory: By varying the ratio of natural frequencies, Uy/ ux, the class of curve segments connecting points (Xo, Yo) and (Xl, Y l ) is given by Eq. (12). Various members of this class are shown in Fig. 2, for X 0 = Yo = 0 and Xl = Y l = 1. As shown, it is possible to obtain a large, well-spaced family of curves by properly varying U1J/ ux. This set of curve segments, however, has a major disadvantage. The final slope of a segment is easily shown to be: r 0 dy I i (Yo - Yl)/(X O - Xl) dx I x=x l L 00 for for for U!J > u,c Uy = Ux U!I < U x (13) That is, the final slope is either zero or infinity except for the special case when the segment is a straight line. This constraint imposes the severe limitation of slope discontinuities between adjacent curve segments. It appears, then, that besides the determination of steady-state coordinates, the selected networks should have at least two degrees of freedom in order

3 A PARAMETRIC GRAPHICAL DISPLAY TECHNIQUE C = (Q+Yc)/Xc-2Xl(2Q+MoXc-Yc) / X2 + 3X2 (Q-Y c + MoX c) / X3 C 1 C (20) x- Figure 2. Family of curves obtained from simple exponential realization. to specify either initial or final slope, and in order to yield, for each such slope, a class of varying-curvature segments. On this basis, two alternative realizations of T x and T yare investigated next. Polynomial Realization Let Tx(t) and T1f(t) be of the form Tx(t) = (1 - e- at ) U- l (t) (14) Ty(t) = (a + (3e- fjt + ye- 2fJt + Be- 3CJt )u_ l (t) (15) where a + (3 + y + B is constrained to be the initial value of y, in this case 0, and a is constrained to be the final value, in this case 1. The initial slope of the resulting trajectory from (Xo, Yo) to (Xl, Yl ) is D = YI-XI(Q+ Yc)/Xc+X~ (2Q+MoXc-Y c) /X2_Xl3(Q- Y c+m O X c)/x3 (21) where Xc = Xl - Xo and Y c = Y I ' - yo. Some representative curves generated by varying M 0 and Q are shown in Figs. 3 and 4. As seen from these figures, this approach permits specification of initial slope of a given curve segment to match the final slope of the previous, segment. A good "fit" to the desired curve can then be obtained by varying Q. Values of a, (3, y and B are determined by the computer, and are converted into appropriate commands through Pi. More degrees of freedom are available by varying y and B independently instead of attempting to match slopes. Exponential Approach An alternative realization is given by -fjot -fjxt Tx(t) = (1-(axe + (1-a.r)e )) U- 1 (t) Mo= 1 xo~o XI = 1 Yo=o Y I =1 (22) dy I = f3 + 2y + 38 dx x=x Xo - Xl o (16) and the resulting trajectory curve is a third-order polynomial of the form y(x) = Ax 3 + BX2 + Cx + D (17) Defining initial slope Mo and class index Q = y + B, 0.2 yields for the coefficients of Eq. (17) the following: A = (Q - Y c + M O X c)/x3 C (18) o~-l B = (2Q + MoXc-Yc) x- /X2-3XI(Q-Yc+MoXc) /X3 c c (19) ~ L--J -L ~~~-L ~~ o Figure 3. Curve segments from polynomial realization.

4 204 PROCEEDINGS-FALL JOINT COMPUTER CONFERENCE, 1966 Some typical members of this class are shown in Figs. 5 and 6. The final slope mf of any such segment is 1.0 MO=2 XO= 0 XI = I YO = 0 YI ~ I 0.8 (FI NAL SLOPE =Q+I) t 0.6 ~ ol-~--~--~~---l--~--~~--~~ o Figure 4. under the constraints x- Curve segments from polynomial realization. 0:::::; ax :::::; 1 o :::::; ay :::::; 1 ax < 1= all = 1 all < 1= ax = 1 (1'm > (1'0 and (1'11 > (1'0 (26) From Eq. (26), final slope is determined only by parameter ax or ay and by coordinate values. Therefore, a large family of curves with a given final slope can be obtained by fixing x and Y and by varying the ratio of natural frequencies as shown in Fig. 6. Both of the above realizations can display complex curves with smoothly connected segments. While the first realization yields a larger class of curve segments, it has two distinct disadvantages when compared to the latter: ( 1 ) computing time necessary to select an optimum set of segments to match a given curve is far greater, and (2) implementation is much more complicated and expensive. For example, the order of three times as much equipment is required, and there exist timing problems and an increased tolerance sensitivity. The prototype was, therefore, implemented with two exponential-type networks, capable of slope matching and class indexing, given by Eqs. (22) and (23). Further implementation considerations follow oy = 2eT o xo=y o = 0 XI = Y I = I x = Xl + (XO-X I ) ( ax(y-yi) + (l-ay) ( Y-YI ) :: ) YO-YI YO-YI for ay = 1 and ax :::::; 1 (25) O~~ ~ L-~ -L ~ L-~ -L~ o x- Figure 5. Curve segments obtained from exponential realization.

5 A PARAMETRIC GRAPHICAL DISPLAY TECHNIQUE Xo = YO = 0 XI = Y I = I ax: I a y = 114 O~~---L--~--~--L-~--~--~--~~ o x- Figure 6. IMPLEMENTATION :: I Curve segments with the same final slope. The experimental prototype was designed for use in co'njunction with a remote teletypewriter console O'f the time-shared computer facilities at Project MAC. Digital info'rmation specifying a curve segment is available at the console in series-parallel form, as four* bits per character. Bit requirements of each curve segment are as follows: six bits each for XD and YD, six bits for ax and fx. y, five bits for y ( the ratio of natural frequencies), and a single bit for designating whether the beam' is to' be ON O'r OFF. Thus, 24 bits, or 6 characters are needed to specify each curve segment. The basic components of the system are shown in the block diagram O'f Fig. 7. Functions O'f the major components are as follows. The interface has three functions: (1) It converts bit information from the co'nsole to signal levels compatible with the system logic. (2) It generates a strobe pulse coincident with the co'nsole signals for sampling purposes. (3) It recognizes the delimiter signal (which defines the completion of a segment description) and generates a delimiter pulse coincident with this signal. The storage registers retain the curve parameters supplied by the computer. The word designator "points" to that por- * Actually, 8 bits are sent to the teletypewriter for each character. However, all combinations of only 4 bits are available. COMPUTER LINE BEAM --;-}SZgPE figure 7. Block diagram of complete system.

6 206 PROCEEDINGS~FALL JOINT COMPUTER CONFERENCE, 1966 tion of the storage register which is to be filled by each set of bits. It is advanced to sequential portions of the storage register by the strobe pulse and is reset by the delimiter pulse. The D / A converters along with their associated storage, convert the coordinate value to analog form. These converters are loaded by the delimiter pulse. If the beam-intensity bit is ON, the intensity control increases the intensity of the trace while the curve segment is being plotted. A Tektronix type 564 storage oscilloscope is used as the display device. Implementation of Tc and T lj follows the configuration decided upon in the previous section, and is shown in Fig. 8. Note that due to the constraints on ax anday only one of the variable resistors of Fig. 8 is in use for plotting any given segment. Likewise, only one set of the multipliers is used for plotting any segment. Thus, the variable resistor, an a multiplier and a (1-0'.) multiplier are time-shared between Tc and T y as shown in Fig. 9. The switch control,as, which is one of the bits used to specify a, differentiates between the two cases (ax = l,ay S 1) and (ay = 1, ax S 1). The multipliers are realized with a resistive divider scheme, and have variable' "gain" from 0 to 1 in steps of 1/16. The buffers and the adder are differential amplifiers with unity feedback. XA(t) YA(t) Ro Rx Co ~ RoCo Ry Co ~ Ro Co Figure 8. Configuration of T x and T y. I----)((t) )----y(t) As shown in Fig. 9, the variable resistance is obtained by operating switches across resistors in a series string. For reasons of economy, magnetic reed switches were used here and whenever a floating switch was needed. These switches have a switching time of 1 msec which is adequate for present data rates. Solid-state switches may be easily substituted if the device is to be used with a higher data-rate channel. SOFTWARE TRANSLATOR The process of converting a desired curve from point-by-point description to a series of segments within the class, realizable by T J' and T y, is the task of a software translator. In the case of online design of electronic circuits.'1 the curve to be displayed is available within the computer as a set of closely spaced points or ordered pairs (X'i, Yd. The translator software converts this set of points to a set of ordered quadruples (XD-i, YD i, a, y), which are display commands. A chosen performance index matches the given curve with the minimum possible number of segments within a given maximum allowable error. Wherever possible, slopes of connecting segments are matched. For simplicity, the translator algorithm has been divided into several steps. 1. Initially the curve is scanned to locate all local maximum and minimum points in both the x and y directions. Since all segments are single-valued in both x and y (except for the trivial cases of vertical and horizontal lines), no single segment can contain such a maximum or minimum. Thus the curve is matched between successive pairs of these points with a minimum number of segments. All these points are stored in an array, P. 2. Next, a search is conducted for curve segments with the realizable class that match successive points in P with minimum error. This search, which is binary, locates the smallest number of segments that will match the curve between each pair of points in P within a maximum specified error. * For each * Absolute value of the error in the x(y) direction is used as error measure for segments that are functions of y(x).

A PARAMETRIC GRAPHICAL DISPLAY TECHNIQUE 207 x (t) XA (t) ---... - 10K... N'v--... -----l Figure 9. Schematic of reduced Tx and Ty.

7 A PARAMETRIC GRAPHICAL DISPLAY TECHNIQUE 207 x (t) XA (t) K... N'v l Figure 9. Schematic of reduced Tx and Ty. segment a is set to match the slope of the previous segment or, if this is not possible, to match the slope of the given curve. 3. The computer words found in Step 2 above are then mapped into the corresponding symbols to be sent to the console. This algorithm was implemented in the AED version of Algol as used by Project MAC. EXPERIMENTAL RESULTS Used in connection with CIRCAL/ the language for on-line design of electronic circuits, the prototype hardware and the translator software gave rise to results shown in Figs. 10, 11, 12, and 13. Figure 10 shows output voltage versus time for a tunnel diode circuit. Four segments were used to compose this curve. No display time was spent in labeling and dimensioning curves. If necessary, this information can be supplied by the typewriter upon Figure 10. Voltage response of tunnel diode circuit (0.5% fit). Figure 11. Voltage response of tunnel diode circuit (3 % fit).

208 PROCEEDINGS-FALL JOINT COMPUTER CONFERENCE, 1966 Figure 12. Step response of a damped L-C circuit. Figure 14. Automobile silhouette. request. The translator operated for a fit of 0.5%.

8 208 PROCEEDINGS-FALL JOINT COMPUTER CONFERENCE, 1966 Figure 12. Step response of a damped L-C circuit. Figure 14. Automobile silhouette. request. The translator operated for a fit of 0.5%. "Fit" here is the ratio of error measure, defined in the preceding section, to full scale. Decreasing the desired accuracy of fit to 3% reduced the number of segments to three as shown in Fig. 11 for the same curve. Computing time spent in translation was 0.5 seconds for a 0.5% fit and 0.3 seconds for the 3% fit. Figures 13 and 14 show other curves resulting from this display. Observe that in Fig. 13 the storage property of the scope permits the superposition of any number of curves for comparative study. Figure 14 shows an automobile silhouette drawn with 26 segments. These segments are shown in Fig. 15. This number of segments can be contrasted with possibly a few hundred points necessary for a piecewise-linear approximation or a point-by-point plot of the same drawing. CONCLUSIONS The main feature of this display technique is the utilization of few computer words for the display of a complex curve. Advantages resulting from this feature are small storage requirements for the translated curves and a relatively fast display time. The main penalty is the computational effort necessary for translation of a given curve into appropriate display commands. One obvious conclusion is that the display should be more advantageous in cases where standard parts are repeatedly used. In such cases, an initial translation would be successfully justified after repeated use of the translated data. Besides the above class of applications, the prototype has proven to be useful in cases of one-time curve plotting. Used in the on-line design of electronic circuits, the fraction of a second spent in curve translating can be justified both economically and temporally, since it represents but a small fraction of the computation effort allocated to circuit design. The advantage of having a visual display of the analyzed data in a typical display time interval of 2-3 seconds by far overrides the inconvenience of using the teletypewriter as a plotting tool at the expense of 3-.:.4 minutes of plotting time and significant accuracy. Figure 13. Superimposed voltage responses. ACKNOWLEDGMENT This research was sponsored in part by the National Aeronautics and Space Administration under contract number NsG-496 (Part). Work reported herein was supported (in part) by Project MAC, an M.LT. research program sponsored by the Advanced Research Projects Agency, Department of Defense, under Office of Naval Research Contract Number Nonr-4102(01). Reproduction in whole or in part is permitted for any purpose of the United States Government.

9 A PARAMETRIC GRAPHICAL DISPLAY TECHNIQUE ,14-- _7 t Figure 15. Command points for plot of Jaguar. / 10 REFERENCES 1. Nilo Lindgren, "Human Factors in Engineering," IEEE Spectrum, vol. 3, no. 4 (Apr. 1966). 2. MIT Project MAC Progress Report, July J. F. Reintjes, and M. L. DertollZos, "Computer Aided Design of Electronic Circuits," Wincon Conference, Feb. 1966, Los Angeles, Calif. 4. M. L. Dertouzos and C. W. Therrien, "CIR CAL: On-Line Analysis of Electronic Networks," Report ESL-R-248, MIT Electronic Systems Laboratory (Oct. 1965).

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