United States Patent 3696391

A variety of graphic symbols, to be displayed on the screen of a cathode- tube under the control of a computer, are synthesized from a store of basic elements which can be selectively combined into groups, the latter in turn being assembled into figures. Digital instructions regarding the nature, size, orientation and location of any selected configuration in each of these three denominations (element, group, figure) are transmitted by the computer, via a memory containing the necessary data, to an analog processor which includes a function generator and several function modifiers in the sweep circuit of the cathode-ray tube to project successively the several elements defining a group, the several groups forming a figure, and the several figures constituting the display, with individual treatment of each higher-order configuration as to overall positioning and size. A function generator capable of producing different conic sections includes two cross-connected integrating amplifiers in the signal paths for the control of the horizontal and the vertical scan. A coincidence circuit may be activated to detect the traverse of the boundaries of a selected rectangular screen area by any elemental trace for instructing the computer to suppress all parts of the display outside that area for the purpose of distinctive visualization of the framed portion.

Application Number:
Publication Date:
Filing Date:
Primary Class:
Other Classes:
345/27, 708/849
International Classes:
G09G1/08; G06F3/023; G06F3/033; G06F3/048; G06G7/26; G09G1/12; H03M1/00; (IPC1-7): G06F3/14
Field of Search:
340/324A 235
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Primary Examiner:
Caldwell, John W.
Assistant Examiner:
Curtis, Marhsall M.
I claim

1. A system for the visualization of graphic symbols on the screen of a cathode-ray tube provided with scanning means for controlling the position of its beam, said symbols being composed of groupings of basic elements, comprising:

2. A system as defined in claim 1 wherein said first set of registers are duplicated for preserving instructions relating to one element during readout of instructions relating to the next element.

3. A system as defined in claim 1 wherein said function-generating means include size and shape generators, said function-modifying means including transformation generators.

4. A system as defined in claim 3 wherein said function-generating means includes other transformation generators controllable by certain of said first set of registers.

5. A system for the visualization of graphic symbols on the screen of a cathode-ray tube provided with scanning means including a pair of orthogonally related sweep circuits for controlling the position of its beam, comprising:

6. A system as defined in claim 5 wherein said switch means includes sign-inverting means in at least one of said cross-connections for the selective generation of trigonometric and hyperbolic functions.

7. A system as defined in claim 5 wherein said function-modifying means includes bypass switches for selectively cutting out the first integrating stage of either of said amplifier means.

8. A system as defined in claim 5 wherein said multiplication networks are hybrid networks with a multiplicand input for analog voltages and a multiplier input for digital signals.

9. A system as defined in claim 8 wherein each of said hybrid networks comprises a ladder-type resistance network with a plurality of shunt branches connected in parallel to said multiplicand input and individual gates between said multiplicand input and said shunt branches having control leads connected to said multiplier input.

10. A system as defined in claim 9 wherein said shunt branches are resistors of identical magnitude and are separated by series resistors of half said magnitude bracketed between two terminal resistors of said magnitude.

11. A system as defined in claim 5 wherein one set of said instructions relates to basic elements of a symbol to be displayed whereas another set of said instructions relates to groups of such basic elements arrayed in selected combinations, said function-modifying means including circuitry divided into a first subsection for the processing of individual elements and at least one other subsection for the processing of higher-order groupings.

12. A system as defined in claim 11 wherein said control unit comprises a first set of registers for the control of said function-generating means and said first subsection, and a second set of registers for the control of said other subsection, said first set of registers being duplicated for controlling said processor to trace an element to be visualized and for simultaneously registering information relating to a subsequent element.

13. A system as defined in claim 11 wherein said control unit includes respective address registers for the temporary identification of the element and the group represented by the last instructions read out from said memory means, said address registers being provided with feedback connections to said memory means for enabling same to deliver instructions for successive elements in consecutive groups in a predetermined order.

14. A system as defined in claim 5, further comprising selector means for establishing two limiting values for each signal voltage and comparison means connected to said channels and to said selector means for transmitting a marker pulse to said computer means upon coincidence of either of said signal voltages with either of the two limiting values established therefor.

15. A system as defined in claim 14 wherein said comparison means comprises two pairs of coincidence circuits and two pairs of shift registers respectively connected to said coincidence circuits for emitting a marker pulse any time a trace of said beam, produced under the control of said processor, reaches the outline of a rectangular area defined by said limiting values.

The present invention relates to a system for displaying graphic symbols on the screen of a cathode-ray tube under the control of a computer.

Modern computers are capable of converting stored or instantly generated input data into scan-control signals for the sweep circuits of a cathode-ray tube whose beam thereupon traces a more or less complex figure visualizing the information received. The analog voltages or currents used to deflect the beam are derived from the digital output of a calculating section which may form part of the principal computer or constitute an ancillary unit. The binary words delivered by this calculating section must be stored in a buffer memory to enable the tracing of different shapes, in response to corresponding sets of instructions from the computer, to be generated repeatedly and in rapid succession so as to create a visual impression of a unitary picture.

With increasing complexity of the symbols to be so displayed, the computer must be capable of performing a large number of calculations in a short period of time. Moreover, though in many instances these symbols consist but of a relatively small number of different basic elements varying only as to size, relative position and orientation with reference to a given co-ordinate system, the computer must individually recalculate the law of each basic element in a time-consuming severely severly taxing the available facilities.

It is, therefore, the general object of my present invention to provide a display system of the character set forth which avoids the aforestated disadvantages and greatly accelerates the visual synthesis of complex shapes, to be traced on a CRT screen, from a limited number of basic elements.

A more particular object is to provide a system of this type which can be used, if desired, for direct communication between the machine and a human operator, i.e. for the creation or modification of a display by the actuation of a keyboard, a stylus or similar manual input means.

Still more specifically, my invention aims at providing a relatively simple yet highly versatile electronic function generator and associated circuitry for shifting, rotating and homothetically modifying (enlarging or reducing) any shape representating a function of the first or the second order, i.e. straight lines and conic sections (the former, of course, representing a limiting case of the latter).

To realize the general object stated above, a system according to my invention essentially comprises an analog processor including one or more function generators for the control of a CRT beam in response to characterization and modification commands from a service memory in which the information delivered to it by the computer is stored in digital form, the computer having access to the memory for calling out any word stored therein to specify both the shape (e.g. line, ellipse, hyperbola) and the parameters (size, position, orientation) of a basic element to be traced.

According to another advantageous feature of the invention, several such elements traced in sufficiently rapid succession to give the impression of a higher-order configuration are modified (displaced or changed in size) as a group, in response to special group-instruction words called out from the service memory by the computer, so that only the relative positions and orientations of the several elements within a given group need be taken into account in the individual processing of each element. The same principle can be extended to additional classes of higher-order groupings, e.g. "figures" formed from "groups" composed of "elements."

In this manner, it is possible to synthesize even an involved symbol from various combinations of only a few basic elements and, in turn, to bodily modify such symbol with the aid of only a few additional instructions called out from the service memory. This characteristic can be utilized, pursuant to a further feature of the invention, for isolating and distinctively visualizing -- e.g. magnifying -- a selected portion of an overall display. This can be done, as more fully described hereinafter, by establishing two limiting values for each of a pair of signal voltages issuing from the processor for the control of the two mutually orthogonal sweep circuits of the cathode-ray tube (conventionally referred to as "horizontal" and "vertical" , respectively) and, upon either of these signal voltages reaching one of the limiting values chosen for it, transmitting to the computer a marker pulse indicating that the element being traced on instructions from the computer touches or intersects one of the boundaries of a rectangular frame defined by these limiting values. The computer, by evaluating this information in light of the programmed position, size and shape of the element, can then give rise to special command d signals (not necessarily relayed through the service memory), to be stored for an indefinite number of cycles, which cause the suppression of the trace outside the selected frame area, the visible remainder of the trace being then subject to the same modifications as any original element or combination of elements regarding size and position. Thus, the operator may preselect the boundaries of that area by the setting of two potentiometers or the like and, by depressing a special "cropping" key of an associated keyboard may cut off all the external portions of the picture, thereafter manipulating his size, location and orientation controls to register the remaining details in a desired manner.

A function generator especially adapted to produce sweep voltages for the selective tracing of a variety of conic sections includes, in accordance with another feature of this invention, a pair of integrating amplifiers connected in a pair of parallel branches in the output of the processor, these amplifiers being provided with cross-connections for generating conjugate complex functions of time. Given a zero input voltage in one branch and a finite input voltage in the other branch, such a pair of amplifiers will generate trigonometric (sine and cosine) functions if the two cross-connections are of relatively inverted sign, i.e. if one is positive while the other is negative, and will produce hyperbolic functions (sinh and cosh) if the signs are equal. Without cross-connections, the resulting function will be linear after integration in a first amplifier stage and parabolic after similar integration in a second stage.

The above and other features of the invention will be described in detail hereinafter with reference to the accompanying drawing in which:

FIG. 1 is a block diagram of the principal components of a visualization system embodying the invention;

FIG. 2 is a more detailed circuit diagram of some of the components shown in Fig. 1 ;

FIG. 3 is a schematic representation of a composite instruction code delivered to a service memory shown in Fig. 2;

FIG. 4 is a circuit diagram of an analog function generator included in the system;

FIG. 5 is a somewhat simplified circuit diagram of a hybrid multiplier forming part of a processor included in the system;

FIG. 6 is a block diagram of another part of the processor;

FIG. 7 is a graph showing a selected frame area of a CRT screen for the cropping of a picture displayed by the system; and

FIG. 8 is a block diagram of a comparison circuit serving to determine the intersections of a trace with the boundaries of the frame area shown in Fig. 7.

In Fig. 1 I have shown a main computer 1 exchanging information with an ancillary computer 3, the latter co-operating with a service memory 4 storing data for a digital control unit 5. This controller, which also has input connections from a marker 8 and a keyboard 9, coacts with an analog processor comprising two sections 6, 7. Section 6 establishes the fundamental shape of a basic element to be traced by the beam of a cathode-ray tube 2 whose horizontal and vertical sweep circuits receive respective input voltages from section 7 which specifies the variable parameters defining the position of the trace with reference to the sweep axes. The size of the trace, included among several variables transmitted in digital form to the analog processor 6, 7 from the control unit 5, is communicated to generator section 6 via a channel 60 also carrying the signals which determine the algorithm of such shape (e.g. linear, elliptical or hyperbolic). Another channel 70, whose individual leads are partly illustrated in Fig. 2 described below, conveys the positioning signals to several subsections of section 7 shown in Fig. 2 at 7E (for the basic elements), 7G (for the groups) and 7F (for the figures).

Thus, a typical code word delivered in binary form from ancillary computer 3 to memory 4 may be divided into three parts as illustrated in Fig. 3, i.e. a classification part Eijk denoting the ith element of the ith group of the kth figure, a characterization part N identifying the geometrical shape, and a modification part LT giving original size (L) as well as transformation (T) including commands for translational and/or rotational displacement with reference to the origin as well as possible enlargement or reduction.

Calculating unit 3, which generates the code word of Fig. 3, may be physically separated from the main computer 1 and could, in fact, be linked to it (or to some other source of binary data) via a transmission line or radio channel.

The construction of units 5- 7 will now be described in greater detail with reference to Fig. 2.

Fig. 2 shows an input register 10 and an output register 11 associated with memory 4, together with a transfer register 12 in unit 5 receiving the instructions called out from the memory and distributing them through a gating network 13 pursuant to the directions contained in the classification part of the code work shown in Fig. 3. (It should be noted in this connection that instructions relating to groups and figures, rather than to basic elements, lack the second part N and the portion L of the third part of the code.) The timing and programming of the readout of memory 4 is controlled by conventional circuits not further illustrated.

The output of memory 4, as emitted by gating network 13, is channeled over a multiplicity of leads collectively designated 50 delivering the binary information L, N (Fig. 3) to correspondingly designated registers via respective leads 51, 52 and to elemental, group and figure transformation registers T1 E ... Tn E, T1 G ... Tn G, T1 F ... Tn F by way of leads 53- 58. Registers L, N and T1... Tn E are duplicated at (L)v , (N)v,(T1 E)v ... (Tn E)v to provide for the storage of a new set of elemental instructions while digital commands for the tracing of a previously selected element are transmitted to analog processor 6, 7 by way of corresponding output leads 61, 62, 73, 74. The output leads of registers T1 G ... Tn G and T1 F ... Tn F, also carrying digital commands, have been designated 75- 78.

Unit 5 further comprises three address registers AE (element), AG (group) and AF (figure), the first of these being again duplicated at (AE) for dealing with consecutively called-out elements. These address registers receive their information from input register 10 over leads collectively designated St and feed it back to calculator 3 and also, via a signal path SR, to register 10 for conditioning same to switch to the next group or figure after all the constituents of such higher-order grouping have been processed; lead SR does not serve the register AE.

The several registers shown in Fig. 2 may be conventionally provided with ferrite cores or the like for the storage of the individual bits of each message or word received. Registers 10 and 11 may be included in the associated memory 4. This memory may also store various commands for controlling the intensity of the beam of tube 2 (Fig. 1) and performing other ancillary functions, under the control of computer 3 and/or an associated programmer not shown, in a manner only peripherally relevant to the present improvement.

All the data relating to a given display, received from computer 3, may be stored in register 10 for an indefinite period to facilitate repetitive reproduction of the same image at rates fast enough to create the impression of a persistent image. This image may be subject to modification with the aid of, for example, the manually operable units 8, 9 of Fig. 1 as more fully described hereinafter. Unit 8 may comprise a conventional tracker ball or any other means for marking a selected part of the display in order to make the computer 3 receptive to new information (e.g. fed in via keyboard 9) concerning this part. Reference may be made in this connection to two copending U.S. Pat. applications filed by me jointly with others; i.e. Ser. No. 692,026, dated 20Jan. 1967 and Ser. No. 20,369 dated 17 Mar. 1970. The first of these two applications, now Pat. No. 3,559,182, disclosed an electronic stylus or pointer with photoelectric means for picking up the luminous spot of a CRT beam on the screen of the tube to give a signal at the precise instant when that beam traverses a selected location; the second application describes the generation of voltages corresponding to the co-ordinates of a selected point by an electric transducer responsive to mechanical pressure locally applied to the screen.

I shall now describe the operation of the system to the extent that it is performed automatically, without the intervention of a local operator, under the control of calculator 3 receiving its digital input from main computer 1 (Fig. 1) either directly or after storage on a tape or the like.

Thus, at the instant when the programmer signals the beginning of a display cycle, memory 4 may contain in its register 10 a number of code words Fk Tfk indicating one or more transformations to which each figure of the display is to be individually subjected; a number of code words Gjk Tgjk specifying the transformations to be undergone by any group Gj of any figure Fk ; and a number of composite code words of the type shown in Fig. 3, relating to all the elements Ei of each group Gj of any figure Fk . Advantageously, this memory is programmed to read out first the instructions F1 Tf1 , F1 Tf1 , F1 Tf1 pertaining to the first figure; when all these instructions are decoded by gating network 13 and routed to the proper buffer registers T1 F ... Tn F in the "figures" set, register 10 generates an identification signal on multiple St to enter in register AF the address (here "1" ) of the figure being processed. Register AF , via multiple SR , reports this address to register 10 while gating network 13, upon decoding a switchover command issuing from memory 4 at that point, energizes a lead Sa to cause a shift within register 10 from figure processing to group processing with readout of the instructions G11 Tg11, G11 Tg11 ,etc. relating to the first group of the first figure. It should be noted that all instructions concerning a particular configuration (element, group or figure) are transferred in parallel from memory 4 via buffer registers 11, 12 to network 13.

In a manner analogous to that described above with reference to the processing of figures, the completion of the loading of any register or combination or register in "group" set T1 G ... Tn G causes entry of the address of this group in register AG with feedback to register 10. In response to another switchover command, network 13 again energizes the lead Sa to initiate a shift to element treatment with readout of the corresponding instructions. The "N" part of the code word shown in Fig. 3 is merely a progressively increasing numerical value that steps the "element" section of memory 10 , essentially a binary counter, to call forth the several elements of the group in a predetermined sequence from a roster stored in a section of memory 4. Thus, for example, N=1 may signify a straight line, N=2may be a circle, N=3 may designate a parabola, whereas two multiplicities of values of N may be assigned to ellipses and hyperbolas with different axial ratios.

Again, the identity of each element read out is stored on address register AE as soon as registers L, N, T1 E - Tn E have been loaded. During the time slot immediately following the one in which the first element was read out (the number of such time slots in a display cycle or frame varying according to the complexity of the picture); the second element of the first group of the first figure is called forth; to make room for the corresponding information, the data heretofore stored in registers T1 E ... Tn E, N, L and AE are transferred at this point to the respective companion registers (T1 E)v, ... Tn E)v, (N)v, (L)vand (AE)v for the control of processor stages 6 and 7E as well as the reporting to calculator 3 of the identity of the element being traced. This duplication of registers, therefore, considerably accelerates the translation of coded instructions into a visual display.

When the entire roster of elemental shapes has been scanned in the synthesis of the first group of the first figure, network 13 responds to another (reverse) switchover command to instruct register 10 to shift back to group selection but to read out the data pertaining to the group immediately following the group just processed, i.e. the one whose address (here "2") is greater by 1than the address now stored in register AG. That second group is then treated in the same manner as the group preceding it, and the completed processing of all the groups of the first figure gives rise to another "reverse" switchover command for restarting the same sequence of operations on the groups and elements of the next figure, i.e. the second one of the display as determined from the address stored in register AF. When all the figures have been thus displayed, the system starts a new frame by shifting back to the first figure.

If an operator wishes to alter or replace any element of the display, he may identify it to the computer by his marker 8 with the aid of the information available to calculator 3 from address registers AF , AG and (AE)v. To change the geometric law of the trace, for example, he may depress a modification key and one or more alphanumerical keys on keyboard 9 (Fig. 1) so as to substitute another "N" value for the original one, that new value being then read out by the register 10 in its proper numerical place but with the same position-indicating parameters to make it appear at the location previously occupied by the former shape. The modified data then remain stored in register 10 until a new modification occurs or the entire display is canceled.

Processor section 6 may include, ahead of a function generator proper, a digital/analog converter operating on the binary codes transmitted via the multiple represented by lead 61. Multiple 62 may control a variety of switches as described hereinafter with reference to Fig. 4. Modification sections 7E, 7G, 7F may include hybrid multipliers, advantageously of the type described below in connection with Fig. 5, to form the product between the analog values (i.e. voltages) issuing from section 6 and the digital magnitudes transmitted by way of leads 73 - 78.

The sweep xc Xc and yc appearing in the outputs of the two signal channels X and Y of Fig. 2 are fed to the horizontal and vertical scanning circuits, respectively, of cathode-ray tube 2 (Fig. 1). Though the final magnitudes of these output voltages are determined by the cascaded modifiers 7E, 7G and 7F following the processor section 6, their law of variation (within a time slot allotted to the tracing of a graphic element) is established by the function generator or generators in that section which could be selectively switched in and out under the control of register N(v) and multiple 62. In accordance with an important feature of the invention, however, it is preferable to use for this purpose a single amplifier unit adapted to generate all the functions discussed above, i.e. straight lines and conic sections. Such a universal function generator, shown in Fig. 4, has two parallel branches designed to convert a pair of fixed input voltages vx and vy into the desired output voltages xc and yc. Voltages vx and vy are the analog equivalents of the digitized values transmitted from register (L)v over multiple 61 (Fig. 2).

The "x" branch of the function generator comprises an operational amplifier Ax of the feedback-stabilized type, a first integrating amplifier I1x with a differentiating feedback circuit including a capacitor Cx and a resistor Rx, and a similarly designed second integrating amplifier I2x ; amplifier Ax feeds amplifier I1x through an electronic switch 21 and is connected to the output of the latter through a feedback loop including a resistor R'x. Another electronic switch 25 enables selective energization of the second-stage integrator I2x from either the first integrating stage I1x or amplifier Ax. All the switches shown in Fig. 4 are controlled by commands transmitted via multiple 62 (Fig. 2).

The "y" branch of the function generator of Fig. 4 is identical with the "x" branch and comprises an operational amplifier Ay, two integrating amplifiers T1y, I2y, a feedback capacitor Cy, resistors Ry, R'y, and switches 22, 26. The two branches are connected by a first path, extending from the output of amplifier I1x through a multiplier M1 and a resistor R1 to the input of amplifier I1y, and a second path, analogously extending from the output of amplifier I1y through a multiplier M2 and a resistor R2 to the input of amplifier Ix1 . The two cross-connecting circuits may be broken with the aid of switches 23, 24. Multipliers M1 and M2, which are advantageously of the hybrid type described hereinafter, receive respective factors K1 and K2 o from unit 5 via lead 62 (Fig. 2).

Switches 21, 22 open and close periodically, in response to clock pulses from a timer feeding the lead 50 of Fig. 2, to allow for the establishment of the selected starting conditions in the outputs of amplifiers Ax and Ay before the function generator is made operational for the remainder of the corresponding time slot. Generally, the following choices are possible:

(a) Generation of straight line. Switches 25 and 26 are reversed to cut out the first integrating stages I1x and I1y ; the output voltages of stages I2x and I2y are linear functions of time t given by

ti xc = px t + q

xy = py t + qy

with the parameters px, py determined by the applied voltages vx, vy and with the constants qx, qy additively (or subtractively) superimposed in the outputs of amplifiers I2x, I2y. Circuit breakers 23 and 24 remain open.

(b) Generation of parabolic segment. Circuit breakers 23 and 24 are still open whereas one of the two switches 25, 26 is in its illustrated position, with cascading of the corresponding integrating stages. If, for example, switch 26 is in that normal position, output voltage xx has the value given above whereas voltage vy follows the law

vy = py t2 + qy t + ry

where, again, the parameters py, qy and ry are independently determined.

(c) Generation of hyperbolic segment. The time the circuit breakers 23, 24 are closed and the switches 25, 26 are in their illustrated normal position. A sinh (or cosh) function appearing in the output of either integrator I1x, I1y returns to its input as the conjugate of that function while a like conjugate is added thereto over the cross-connection from the companion stage. So long as the amplifiers do not become overloaded within the allotted time slot, the system in this and the preceding cases may be regarded as stable (i.e. nonoscillatory).

(d) Generation of ellipse or segment thereof. The stable system of the preceding paragraph is modified by relatively inverting the signs of the cross-fed voltages. For this purpose, a sign inverter 27 has been diagrammatically illustrated in Fig. 4 together with a switch 28 adapted to insert it in the circuit leading from amplifier I1x to amplifier I2y. This causes oscillations at a frequency determined by the fixed circuit parameters and by the selected input voltages, vx, vy as well as magnification factors K1, K2. The immediate output voltages of integrator stages I2x, I2y are conjugate trigonometric functions (sine and cosine or vice versa) of ωt (ωbeing the pulsatance of the oscillation) of equal amplitudes, thus defining a circle as a special case of an ellipse. Further multipliers (not shown) in the outputs of integrating amplifiers I2x and I2y may then individually modify these amplitudes in order to provide an ellipse of desired axial ratio; in the same manner the hyperbolic function referred to in the preceding paragraph may be altered.

The postulated generation of circular and hyperbolic traces under the conditions described above may be verified by the following considerations:

If amplifiers I1x and I1y have identical forward gains and feedback factors of absolute magnitudes α and β, respectively, and if (with inverter 27 disconnected by switch 28) the input voltages vox, voy of stages I1x, I1y are considered to satisfy the relationships vox = A sinh zt and voy = A cosh zt, then amplifier I1x has an output v1x = A/z α cosh zt whereas amplifier I1y supplies an output voltage v1y = A/z α sinh zt. Input voltage vox must equal the sum of its own feedback voltage, applied through condenser Cx, and the cross-fed voltage K2 v1y from the output of multiplier M2. Similarly, input voltage must equal the sum of its own feedback voltage from condenser Cy and the cross-feed voltage K1 v1x from multiplier M1. We therefore obtain the relationships

A sinh zt = A α β sinh zt + A/z(K2) α sinh zt (1).


A A cosh zt = A α β cosh zt + A/z(K1) α cosh zt (2).


z =K2 α/(1 -αβ) = K1 α/(1 -αβ) 3.

so that the system is in equilibrium if K1 = K2 = K and

z = K α/(1 -αβ). 4.

at t = 0,i.e. upon closure of switches 21 and 22, vox must be zero if the sinh function is to develop in the "x" branch. The initial magnitude A of voltage voy then represents the half-axis of an equilateral hyperbola. The double integration in stages I1x and I1y preserves the sinh function in the output xc so that, in the absence of subsequent shifting or rotation, the vertex of the hyperbola comes to lie on the vertical axis of the screen.

Let us now assume that the input voltages of amplifiers I1x and I1y satisfy the relationships vox = A α sin ωt and voy = A α cos ωt. The corresponding output voltages then have the form v1x = - (A)/(ω)α cos ωt and v1y = (A)/(ω) α sin ωt, respectively.

The foregoing equations now become

A sin ωt = Aα β sin ωt + (A/ω) (K2) α sin ωt 1'.


A cos ωt = Aα β cos ωt - A/ω (K1) α cos ωt 2'.


ω= K2 α/(1 - αβ) = - K1 α/(1 - αβ) 3'.

so that the system is in equilibrium if K1 = - K2 or K2 = K, K1 = - K with

ω = K α/(1 - α β). 4'.

The insertion of inverter 27 (or an equivalent modification of multiplier M1 therefore creates the requisite conditions for such oscillatory operation.

As before, the amplitudes of the two conjugate functions in the outputs of the two-stage integrators will be the same so that the trace, if not modified in the signal paths beyond stages I2x and I2y, will be a circle. The sine function develops in the branch having the starting voltage 0 applied to it, the magnitude A of the other input voltage representing the radius of the circle.

It is desirable to make the peripheral tracing speed independent of radius, in order to simply the task of the computer in measuring a desired length of arc. Since, in a circle, this tracing speed equals the radius times the angular velocity ω , K,since the latter varies directly with the multiplication factor K , this constancy can be achieved by making the amplitude A inversely proportional to K so that the finite input voltage, e.g. vy , is increased with decreasing multiplication factors and vice versa. Since the second integration at I2x , I2y again introduces the magnitude of ω and therefore of K into the denominator of the voltage function v2x , v2y generated by the system of Fig. 4, the final radius still depends on the choice of K. Similar considerations apply to the tracing of ellipses and hyperbolae. On the CRT screen itself, of course, the tracing speed will depend on the chosen parameters, yet the computer need only take into consideration the magnifications or reductions, if any, occurring beyond stages I1x , I1y .

Other exponential functions may be established, for example, by operating the system of Fig. 4 with equal starting voltages vx , vy and with inverter 27 disconnected, there being no finite values of t for which the cosh and sinh functions are identical.

In Fig. 5 I show a hybrid multiplier suitable for use in the function generator of Fig. 4 as well as in any of the modifying subsections 7E, 7G, 7F of processor section 7. A ladder-type resistance network 38 is connected between a terminal 34 of fixed reference potential (here ground) and the input 35 of an operational amplifier 36 having an output 39. Network 38 has two terminal sections of magnitude R separated by a multiplicity of series arms of half that magnitude, the junctions of these series arms with one another and with the two terminal sections being connected to respective shunt arms also of magnitude R . Each shunt arm is connected to a pair of input terminals 32, 33, by way of respective gating elements here shown as field-effect transistors FET1 , FET2 , the gates of these transistors being tied to the output of an associated AND gate 30 with interposition of an inverter 31 in the case of transistor FET2. All the AND gates 30 have one terminal tied to a source of blocking potential (here positive) represented by a terminal 37. The other input of each AND gate is tied to an individual conductor of a multiple carrying a multidigit binary value M, such as the multiples illustrated as leads 73- 78 in Fig. 2. These conductors have been labeled 20 , 21, 22 , ... 2n-1 , 2n , according to their denominational ranks in the binary code.

Input terminal 32 is assumed to be held at a fixed potential equal to that of terminal 34 (ground) so that an input voltage applied to network 38 at any point between amplifier 36 and one of the network junctions is reduced in a predetermined ratio, consistent with the digital position of the corresponding shunt arm, when the respective AND gate 30 is nonconductive whereby field-effect transistor FET1 is saturated and represents a negligible resistance. An analog voltage Ve to be multiplied by the magnitude of number M appears on terminal 33 but cannot pass the companion transistor FET2 under these conditions, that transistor being cut off by the inversion of the AND gate output at circuit 31. Conversely, if the second input of any AND gate 30 is energized, the associated transistor FET1 is blocked while the companion transistor FET2 is saturated so as to give passage to voltage Ve . With only the lowest-order conductor 20 energized, for example, the magnification factor is unity; thus, the gain of amplifier 36 should be so chosen that the potential of terminal 39 equals that of terminal 33 under these conditions. With other digital inputs energized, the output voltage at terminal 39 is then a multiple M:Ve of the analog input voltage Ve .

The network of Fig. 5 can be easily adapted for use with complementary binary codes (i.e. with designation of a bit by the absence rather than presence of voltage on the correspondingly conductor 20 - 2n by the simple expedient of reversing the input connections by grounding the terminal 33 and applying the potential Ve to terminal 32.

Moreover, if a voltage of unity value is applied to the live terminal 33 (or 32), this system will operate as a digital/analog converter. As such it may be used, for example, in processor section 6 ahead of the function generator described with reference to Fig. 4.

As compared with conventional voltage-dividing networks using weighted resistances, the circuit arrangement of Fig. 5 offers the additional advantages of simplified manufacture (requiring only two calibrated resistance values R and R/2), operativeness with resistors of relatively low magnitudes, and a constant input resistance as seen from voltage source Ve.

Fig. 6 shows a circuit, adapted to be used in any of the processor subsections 7E, 7G, 7F, for selectively displacing a generated trace by translation and/or rotation. This circuit includes four multipliers 40, 41, 43, 44, each preferably of the hybrid type just described, and two conventional adders 42, 45. An analog voltage x'c from a preceding stage is applied to the analog inputs (32, 33 in Fig. 5) of multipliers 40 and 44 in parallel, a companion voltage y'C being similarly applied to multiplier 41 and 43. If the trace is to be rotated through an angle θ , multipliers 40 and 44 receive at their binary inputs (M, Fig. 5) the digitized magnitudes of cos θ while the other two multipliers similarly receive the magnitude of sin θ . Adders 42 and 45, respectively receiving the outputs of multipliers 40, 41 and multipliers 43, 44 perform the operations

x"c = x'c cos θ - y'c sin θ

y"c = x'c sin θ + y'c cos θ

which represents the desired inclination of the co-ordinate system by the angle θ . A translational shift, such as those needed to add a constant in the above-discussed formulas for straight lines and conic sections, may be carried out with the aid of further voltages xT and yT applied to additional inputs of adders 42 and 45 , respectively. A simple shift occurs with θ = 0 , i.e. zero voltages at the binary inputs of multipliers 41 and 44 along with unit voltages at the corresponding inputs of the other two multipliers.

The circuitry of Fig. 6 allows for the original plotting of straight lines along one or the other co-ordinate axis, followed by a suitable rotation, which further simplifies the task of the calculator.

Fig. 7 illustrates part of the screen of a cathode-ray tube on which an elemental trace 100 is being displayed. By depressing special keys on the keyboard 9 of Fig. 1, and by the use of some numerical keys thereof in selected combinations, the operator has chosen two pairs of constant potentials X1 , X2 , Y1 and Y2 (Fig. 8) corresponding to specific values of the deflecting voltages for the sweep circuits of the tube, thereby establishing two imaginary vertical lines V1 , V2 with abscissae x1 , x2 and horizontal lines H1 , H2 with ordinates y1 , y2 as measured along axes x and y . The part of trace 100 within the area framed by these four lines is to be explored in detail, the remaining portions being of no interest.

Points P1 , P2 , P3 , P4 mark the intersections of the trace with the boundaries of the desired area. It will be seen that, in this example, trace 100 cuts the line V1 once (at P1) from without, the line H1 once (at P4) from within, the line H2 twice (at P2, P3) and the line V2 not at all.

As shown in Fig. 8, the selected potentials X1, X2, Y1, Y2 are fed to respective digital/analog converters, such as that described with reference to Fig. 5, respectively designated 101, 102, 103, 104 and working into associated comparators 201, 202, 203, 204. The first two comparators also receive the sweep voltage xc from the channel X (Fig. 2) while the two other comparators receive the companion voltage yc . The output of each comparator is transmitted to a two-stage shift register 301, 302, 303, 304, this number of stages being sufficient inasmuch as no second-order curve can intersect a given line more than twice.

When the sweep voltage yc matches the analog equivalent of the limiting voltage X1 or X2 , comparator 201 or 202 responds and trips the associated shift register 301 or 302. Similarly, a coincidence of voltage yc with either limiting voltage Y1 , Y2 actuates the comparator 203 or 204 to step the corresponding shift register 303 or 304. In the outputs of these shift registers there are thus generated up to eight possible signal pulses S1,1 , S1,2 , S2,1 , S2,2 , S3,1 , S3,2 , S4,1 , S4,2 which mark the intersections between the trace 100 and the frame in Fig. 7. Thus, point P1 gives rise to a marker pulse S1,1 from register 301, points P2 and P3 trigger the register 304 to generate marker pulses S4,1 and S4,2 , and point P4 causes the emission of a marker pulse S3,1 by register 303. All these registers are, of course, automatically reset at the end of each time slot so that similar information can be obtained on other elements crossing or touching the boundaries of the frame.

In this manner, the calculator 3 receiving the marker pulses can ascertain from the contents of address registers (AE)v, AG, AF the identity of such an element; having available all the data relating to the nature and position of that element, it may then compute the extent to which it falls within the selected frame area and give instructions to memory 4 (Fig. 2) for the suppression of the remainder in subsequent cycles. The cropped picture within that area may then be magnified (and shifted, if necessary) by the aforedescribed modification circuits without extensive recalculation.

The system of Fig. 8 is illustrative of a variety of means enabling an operator to communicate with the computer, through the intermediary of the control unit 5, in producing or changing a display. Such communication is also possible with the aid of various marking implements, e.g. the photoelectric stylus of U.S. Pat. No. 3,559,182 enabling the free-hand tracing of pictures on a conventionally illuminated screen with transformation of the data into digital information by the main computer 1.

Of course, the invention is not limited to the embodiments described and shown which has been given solely by way of example.