US3721810A - Display system utilizing one or more conic sections - Google Patents
Display system utilizing one or more conic sections Download PDFInfo
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- US3721810A US3721810A US00106108A US3721810DA US3721810A US 3721810 A US3721810 A US 3721810A US 00106108 A US00106108 A US 00106108A US 3721810D A US3721810D A US 3721810DA US 3721810 A US3721810 A US 3721810A
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06G—ANALOGUE COMPUTERS
- G06G7/00—Devices in which the computing operation is performed by varying electric or magnetic quantities
- G06G7/12—Arrangements for performing computing operations, e.g. operational amplifiers
- G06G7/22—Arrangements for performing computing operations, e.g. operational amplifiers for evaluating trigonometric functions; for conversion of co-ordinates; for computations involving vector quantities
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B19/00—Programme-control systems
- G05B19/02—Programme-control systems electric
- G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
- G05B19/41—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by interpolation, e.g. the computation of intermediate points between programmed end points to define the path to be followed and the rate of travel along that path
- G05B19/4103—Digital interpolation
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06G—ANALOGUE COMPUTERS
- G06G7/00—Devices in which the computing operation is performed by varying electric or magnetic quantities
- G06G7/12—Arrangements for performing computing operations, e.g. operational amplifiers
- G06G7/26—Arbitrary function generators
- G06G7/28—Arbitrary function generators for synthesising functions by piecewise approximation
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- G—PHYSICS
- G09—EDUCATION; CRYPTOGRAPHY; DISPLAY; ADVERTISING; SEALS
- G09G—ARRANGEMENTS OR CIRCUITS FOR CONTROL OF INDICATING DEVICES USING STATIC MEANS TO PRESENT VARIABLE INFORMATION
- G09G1/00—Control arrangements or circuits, of interest only in connection with cathode-ray tube indicators; General aspects or details, e.g. selection emphasis on particular characters, dashed line or dotted line generation; Preprocessing of data
- G09G1/06—Control arrangements or circuits, of interest only in connection with cathode-ray tube indicators; General aspects or details, e.g. selection emphasis on particular characters, dashed line or dotted line generation; Preprocessing of data using single beam tubes, e.g. three-dimensional or perspective representation, rotation or translation of display pattern, hidden lines, shadows
- G09G1/08—Control arrangements or circuits, of interest only in connection with cathode-ray tube indicators; General aspects or details, e.g. selection emphasis on particular characters, dashed line or dotted line generation; Preprocessing of data using single beam tubes, e.g. three-dimensional or perspective representation, rotation or translation of display pattern, hidden lines, shadows the beam directly tracing characters, the information to be displayed controlling the deflection and the intensity as a function of time in two spatial co-ordinates, e.g. according to a cartesian co-ordinate system
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- G—PHYSICS
- G09—EDUCATION; CRYPTOGRAPHY; DISPLAY; ADVERTISING; SEALS
- G09G—ARRANGEMENTS OR CIRCUITS FOR CONTROL OF INDICATING DEVICES USING STATIC MEANS TO PRESENT VARIABLE INFORMATION
- G09G1/00—Control arrangements or circuits, of interest only in connection with cathode-ray tube indicators; General aspects or details, e.g. selection emphasis on particular characters, dashed line or dotted line generation; Preprocessing of data
- G09G1/06—Control arrangements or circuits, of interest only in connection with cathode-ray tube indicators; General aspects or details, e.g. selection emphasis on particular characters, dashed line or dotted line generation; Preprocessing of data using single beam tubes, e.g. three-dimensional or perspective representation, rotation or translation of display pattern, hidden lines, shadows
- G09G1/08—Control arrangements or circuits, of interest only in connection with cathode-ray tube indicators; General aspects or details, e.g. selection emphasis on particular characters, dashed line or dotted line generation; Preprocessing of data using single beam tubes, e.g. three-dimensional or perspective representation, rotation or translation of display pattern, hidden lines, shadows the beam directly tracing characters, the information to be displayed controlling the deflection and the intensity as a function of time in two spatial co-ordinates, e.g. according to a cartesian co-ordinate system
- G09G1/12—Control arrangements or circuits, of interest only in connection with cathode-ray tube indicators; General aspects or details, e.g. selection emphasis on particular characters, dashed line or dotted line generation; Preprocessing of data using single beam tubes, e.g. three-dimensional or perspective representation, rotation or translation of display pattern, hidden lines, shadows the beam directly tracing characters, the information to be displayed controlling the deflection and the intensity as a function of time in two spatial co-ordinates, e.g. according to a cartesian co-ordinate system the deflection signals being produced by essentially analogue means
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B2219/00—Program-control systems
- G05B2219/30—Nc systems
- G05B2219/34—Director, elements to supervisory
- G05B2219/34136—Ellipse, hyperbola
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B2219/00—Program-control systems
- G05B2219/30—Nc systems
- G05B2219/35—Nc in input of data, input till input file format
- G05B2219/35554—Mirror, other conversions
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B2219/00—Program-control systems
- G05B2219/30—Nc systems
- G05B2219/49—Nc machine tool, till multiple
- G05B2219/49221—Control of scale
Definitions
- Means are prov ded to compensate for variations in the display intensity produced by varia 3,488,483 1/1970 Freedman ..340/324 A X tions in cathode-ray-tube Writing Speed. 3,205,349 9/1965 Bryan et al.
- This invention relates to display systems and more particularly to a computer controlled system for the display of graphic, alpha-numeric, symbolic and other data utilizing a sequence of elliptical curve sections.
- the computer controlled display system functions to produce a generally continuous image.
- the display image can include for example alpha-numeric data for conveying work information, pictorial or diagrammatic representation of design and engineering data inputs, or graphical representations of data inputs.
- the actual images displayed will result from data entered by the user from a variety of sources including digitizers, keyboards, and various controls.
- the input data may or may not be further processed by a computer to produce a given result which is to be displayed.
- a display generator From the actual information to be displayed, a display generator must operate so as to create a curve which conforms to the information for display, be it an alphanumeric character or a graphical or pictorial image. The characteristics of the display generator determine how accurate, flexible, and efficient display images can be generated and later manipulated.
- a curve or other figure to be displayed is formed from data by a series of closely spaced points or short line segments which are of a size and spacing to present to a viewer an effectively continuous representation of a curve or figure.
- Such a system is shown, for example, in U.S. Pat. No. 3,205,344.
- a major disadvantage of such systems is that a large number of point or line elements must be employed to accurately represent the data, and a correspondingly large amount of computer storage and display time must be used to generate all necessary elements. Display manipulation is likewise difficult and time consuming. Where display data must be conveyed over a telephone line or communication channel of limited capacity, as is common with most display systems operating on a time shared basis, the resulting process of curve display is rather slow.
- a more recent type of display system employs curve segments which are selectively combined to display a curve which approximately fits the original data within a prescribed tolerance.
- a sequence of sections of a specific kind of electrically realizable curve, such as an exponential or conic section is generated with each section approximating a portion of the original data.
- Prior art systems for displaying alpha-numeric data and specialized characters such as transistor symbols include dot matrices, light or electron beam masks and selected line and curve strokes.
- Dot matrices exemplified by U.S. Pat. No. 3,255,443, operate to illuminate specified dots which in combination approximate, usually not very closely, certain characters and symbols.
- Masks provide only a limited repertory of characters and symbols and to display other characters and symbols requires physical replacement of the mask.
- Characters and symbols formed from selected line or curve strokes such as described in U.S. Pats Nos. 3,394,367; 3,335,416; and 3,283,317, fail to provide sufficient flexibility in adapting to the many different characters or symbols needed in a modern display or to different styles of individual characters.
- slight position alterations for characters, as in subscripts and superscripts have been awkward or impossible due to inflexibility of placement of individual strokes, masks or dot patterns.
- a display system in which a plurality of elliptic sections are employed with each section specified by a minimum of easily calculated parameters and selectively combined to cause accurate display representations of graphic or alpha-numeric data and subsequent ease of manipulation. Any segment of any ellipse or circle or any vector is simply and quickly displayable at any orientation. Any segment or vector can be drawn for display by starting at either end.
- a display system apparatus for generating time varying X and Y electrical signals representing the orthogonal coordinates of an elliptical curve section.
- the X and Y electrical signals are preferably the combinations of quarter cycle sine and cosine electrical functions, the manner of combination being specified in accordance with four parameters presented to the display system for each elliptical section.
- a fifth parameter specifies the duration of the sine and cosine functions.
- the X and Y signals when applied to a display device in the nature of CRT display or X-Y plotter produce the desired image, be it graphic or alpha-numeric.
- the five parameters necessary for specifying the curve are communicated to the display system from a computer where they are calculated from original data to provide constraints for the elliptical sections casing them to trace the desired image.
- Manipulation, including rotation, perspective control, etc., of the image is easily achieved by transformations of the five parameters directly without the need for recalculation from original data.
- the computer may be remote and accessible in timeshared fashion over telephone lines or not as desired.
- a digital control unit associated with the display stores parameters for commonly used curves, symbols, characters and figures.
- each image is readily constructed by a succession of curve segments under instructions normally stored in electronic memory and activated by a character code, scale, and starting point. Position alternations are easily achieved by simply specifying a new starting point for the entire character or symbol, all subsequent segments stemming for the initial point. New characters or symbols or different forms can be easily placed into memory by the computer.
- means are provided for compensating for the variation in display intensity produced by variations in writing speed.
- This writing speed or velocity compensation can be used to control the mark intensity as with an oscilloscope or to control the writing speed ofa moving pen at or near a selected velocity.
- FIG. 1 is a graph in X and Y coordinates of a curve showing points and parameters of the curve used in computing the A and B coefficients;
- FIG. 2 and FIG. 2a are block diagrams of a display system according to the invention.
- FIG. 3 is a block diagram and partial schematic of velocity compensation circuitry useful in the invention.
- FIG. 4 is a block diagram of modified and simplified circuitry for accomplishing a part of the function of velocity compensation as in FIG. 3;
- FIG. 5 is a block diagram of circuitry including details of the digital control unit of FIG. 2 indicating its operation.
- a curve 12 is shown for purposes of illustration between orthogonal X-Y axes.
- a curve section 14 is bounded by end points 16 and 18, point 18 being an inflection point of curve 12.
- the slope at the end points is respectively indicated by lines 20 and 22.
- a straight line 24 connects the two end points 16 and 18.
- a point, 26, represents the point on the section 14 of curve 12 where the section 14 is at a maximum perpendicular distance from the straight line 24.
- Two additional points, 28 and 30, are marked on the section 14 between the end points 16 and 18.
- a line 32 indicates the slope of the section 14 at the point 30.
- orthogonal X and Y time varying signals are generated from the data of FIG. 1 and applied to X and Y orthogonal controls of, for example, a cathode-raytube oscilloscope or an X-Y plotter with the result that an elliptical section is traced closely resembling the section 14.
- Generating the X and Y time varying signals from the curve data of FIG. 1 normally involves many mathematical computations which, even through normally performed by a computer, require considerable computation time, storage, and/or transmission time when a multiplicity of sections 14 are connected together to trace a total curve 12.
- the X and Y time varying signals are formed as the following functions:
- the sine and cosine functions are generated by an electronic function generator.
- the X, and Y, signals are initial point values which are determined by the values of the end point from the previous section or any other desired starting point.
- the A and 8 parameters along with the range of t, defining the portion of the sine and cosine periods and consequently the portion of the ellipse used for drawing the curve section, are the remaining parameters to be specified from the data of FIG. 1.
- the data for the curve section 14 in FIG. 1 may be assembled from various sources including a pointer or digitizer such as an X-Y movable arm which electrically encodes points and slopes on the original curve section 14 as the arm is placed at the points on curve 14. Slope information may be entered from arm motions or directly through a keyboard or other data entry device.
- the data for curve 14 may also be entered directly from other sources containing graph data, or, in the case where the curve is known in terms of an algebraic expression, a computer may be used to establish the necessary data.
- the parameters may be stored in memory facilities of a digital control unit associated with the function generator.
- equations relate the A and B coefficients to the curve parameters:
- S and S are the respective slopes of the curve to be traced at the points 16 and 18 respectively, and are given by Defining S, and S further:
- X is the X difference between points 16 and 26;
- AX is the X difference between points 16 and 18;
- Y is the Ydifference between points 16 and 26.
- AY is the Y difference between points 16 and 18.
- the A and B coefficients are the same for the same ellipse segment so that the constraints from any computational method or case all apply to one set of A and B coefficients and are manipulated by the same transformation of the A s and Bs.
- a straight line or vector can be produced by setting either the A or B coefficients at zero and adjusting the non-zero coefficients to define slope.
- a sincos function generator 34 outputs on lines 36 and 38 respectively a cosine and sine function electrical signal.
- the values of these signals correspond to the functions cos X(t) and sin X(t) where x can be varied to alter the speed at which the curve is traced.
- the cosine function electrical signal is conducted byline 36 to multiplier inputs of multipliers 40 and 42 while the sine function electrical signal is conducted byline 38 to multiplier inputs of multipliers 44 and 46.
- An Ax constant electrical signal is conducted to a multiplicand input of multiplier 40 from a digital control unit 48, over line 50.
- the multipliers 40, 42, 44 and 46 are analog multipliers.
- the multipliers 40, 42, 44, and 46 can be multiplying digital to analog converters.
- the product outputs of the multipliers 40 and 44 are fed to noninverting inputs of a variable gain summing amplifier 58.
- the output of amplifier 58 is fed to a summing input of a summing amplifier 60 along with an X,,-A, offset signal from the digital control unit 48.
- a digital to analog converter 62 is interposed between the summing amplifier 60 and digital control unit 48 to convert the X,,A offset electrical signal form a digital to an analog signal.
- the output of the summing amplifier 60 is an X(t) electrical signal whose value is Ax (cos (t)-l Bx sin (l)+ X
- An analog scaling signal 63 is conducted from the digital control unit 48 and fed to a gain control input of summing amplifier 58 to control the amplification of the sum of the inputs to the amplifier 58.
- the Ax signal can be applied directly to an inverting input of summing amplifier 58, and the offset signal to amplifier 60 is an analog X, signal as indicated in FIG. 2a.
- the outputs of multipliers 42 and 46 are fed to noninverting inputs of a variable gain summing amplifier 64.
- the output of amplifier 64 is fed to one noninverting input of a summing amplifier 66 which has on an other noninverting input a Y,,A,, constant electrical signal from the digital control unit 48.
- a digital to analog converter 68 is provided for the Y,,A,, signal between the digital control unit 48 and the amplifier 66 to produce an analog equivalent of the Y,A,, signal.
- the output of the summing amplifier 66 is a Y (t) electrical signal whose value is Ay (cos (I) l)+ By sin (t)+Y,,.
- Scaling signal 63 is fed to a gain control input of summing amplifier 64 to adjust gain as indicated above.
- an Ay analog signal is fed to an inverting input of amplifier 64, and an analog Y signal is fed to a noninverting input of amplifier 66, similar to the system indicated in FIG. 2a.
- OUtputs of the amplifiers 60 and 66 are fed to the digital control unit 48 over respective X and Y termination point electrical signal lines 70 and 72, to X and Y input terminals of a display 74, and to the inputs of a velocity compensator 76.
- the display 74 may be, for example, either a cathode-ray-tube oscilloscope or an X-Y plotter. In either case, a visible mark is produced at X and Y coordinates on the display surface representative of the value of the X and Y input signals to the display 74.
- the velocity compensator 76 has an output to Z-axis control of the display 74 to control the intensity of the visible mark for constant brightness and for alternative use, an output to the sine-cosine function generator 34 to control its frequency. Since the rate of motion of the visible mark produced by the display 74 affects the apparent intensity of the mark, the velocity compensator 76 is provided to compensate for varying mark velocities and to produce a more even intensity in the mark. In one embodiment, the velocity compensator 76, after detecting the mark velocity from the signals at the outputs of amplifiers 60 and 66, controls the intensity of the mark produced by the display 74 by sending an intensity control signal to the Z-axis input of the display 74. In another embodiment, the velocity compensator 76 keeps the mark velocity constant by controlling the frequency of the sine-cosine function generator 34. Further details of the structure and function of the velocity compensator 76 are indicated below.
- the cosine and sine function electrical signal output on lines 36 and 38 of the sine-cosine function generator 34 are fed to a phase detection circuit 78 which feeds the digital control unit 48 over lines 80 information on phase, polarity and level of the sine and cosine electrical signals.
- a display control signal 82 is outputted from the digital control unit 48 to a mark inhibit circuit 84 cooperating with the display 74 to allow the display to produce a visible mark only when the digital control unit 48 commands that a visible mark be made by a signal on line 82.
- the marked curve corresponds to selected portions of the sin-cos function electrical signal cycle.
- the data input to the digital control unit 48 is provided from a computer 90 which in turn may receive raw information from any of a number of sources including a curve data generator 92, a data source 94 and a digitizer 96.
- the computer 90 receives curve section data from any of the sources including the curve data generator 92, data source 94, and curve follower 96. From this data the computer 90 makes a number of decisions including: (1) How to divide the original curve into sections to be approximated by one elliptical segment or section with a unique set of A and B coefficients. Normally the computer 90 will exclude inflection points from each section, making inflection points a convenient dividing point between sections. (2) What portion of an elliptical period to use. Normally a quarter period is used unless specific circumstances of the curve being copied particularly suit it to being matched by an elliptical segment of greater cyclical period.
- the computer 90 establishes the A and B coefficients and outputs them to the digital control unit 48 for each section to be displayed.
- the digital control unit 48 also receives instructions from the computer 90 on the portion of an elliptical period to be used for each segment.
- the outputs of the amplifiers 60 and 66 correspond to the Equations (1) and (2). They have values representing the X and Y coordinates over the selected portion of the cycle of the elliptical section or segment which closely matches the original data for that section as inputted to the computer 90.
- the digital control unit 48 determines the values of the end points for each segment from the initial points X and Y, and from the values of AX and AY as determined from the A and B coefficients supplied through the digital control unit 48.
- the endpoints can alter-natively be determined by sampling the X and Y function signals on lines 72 and 70.
- the termination point for each segment provides the coordinates for the initial points X, and Y of the next segment, or the end point may be offset by computer specified coordinate changes to produce the next segment in nonattached relationship relative to its preceeding segment. This insures that each curve section begins exactly where the previous section ended, or a preselected distance therefrom if a discontinuous curve is intended.
- FIGS. 3 and 4 there is shown an ex emplary preferred embodiment and modification for a velocity compensation system for use in the FIG. 2 display system.
- the X and Y signals from amplifiers 58 and 64 of FIG. 2 are fed to respective differentiators 112 and 114.
- the output of the differentiators 112 and 114 is respectively the time derivative of the X and Y function electrical signals.
- the differentiators 112 and 114 may be operational amplifiers connected in a conventional manner to take the time derivative of the input to them or simply high-pass filters which approximate the time derivative of the input to them as in capacitive coupling circuits.
- Each output of the differentiators 113 and 114 is fed to both the multiplier and multiplicand inputs of respective multipliers 116 and 118.
- the outputs of the multipliers 116 and 118 are thus respectively the square of the derivative of the X and Y function signals.
- a summer 120 receives these squared derivatives as inputs and outputs their sum. The output of summer 120 is thus proportional to the square of the velocity, V, of the trace in display 74.
- a square rooter 121 after the summer 120 produces an output proportional to V which can be fed into the Z axis control 122 of the display, 74.
- the output of summing amplifier 120 can be fed into one input of a regulator 124.
- the other input to the regulator 124 is a reference 126.
- the regulator 124 is typically a high gain amplifier differencing its two inputs.
- the sine-cosine function generator 34 is composed of a selective gating network 130 alternately feeding inverting and noninverting inputs of an amplifier 128.
- One input to the gating network 130 is the output of regulator 124, while a control input 131, is derived in the digital control unit 48 from the levels of the sine and cosine function signals detected by phase detector circuit 78.
- the gating network 130 switches in response to DCU control signal 131 to supply the output of the regulator 124 to the amplifier 128 on the opposite input, or to the input specified by the polarity of the sine function electrical signal.
- the output of the amplifier 128 is fed to an integrator 132 which produces at its output an integration of the positive or negative signals from amplifier 128.
- the control signal 131 into gate 130 causes the output of the integrator 152 to increase from zero during the periods t 11/2 and 'Tr t (31r/2), and to decrease toward zero during the periods 1r/2 5 [5 1r and (3 1r/2) t s 2 11.
- the slope of the output of the integrator 132 reverses every 1r/2
- the output of the integrator 132 is a positive value, variable slope triangle wave varying between zero and a positive level.
- variable slope triangle wave is fed to two different diode approximating networks 136 and 137 to produce the sine and cosine functions respectively.
- the sine function approximator 136 through the use of a plurality of break points generates a zero to 180 sine function from the first zero-to-peak-to-zero section of the triangle wave, and thereafter, by the inversion of a selectively inverting circuit 138 controlled by a gate 139 responding to the zero crossover of the output of approximator 136, produces a negative half 180 to 360 portion.
- the cosine diode approximator 137 receives the triangle wave through an inverter 140 for inversion of the triangle wave so that the zero level becomes the positive level and the positive slope of the original triangle wave becomes negative and produces a zero to 90 portion of the cosine function.
- a zero crossing at 90 causes switching of a selective inverting amplifier 142 at the output of approximator 137 by a gate 143 and the positive to zero portion of the original triangle wave generates a 90 to 180 degree portion of the cosine function.
- the next zero to positive level portion of the original triangle wave produces the l80 to 270 part of the cosine function.
- Zero crossing at 270 switches back the inverting amplifier 142, and the subsequent positive to zero portion of the triangle wave creates the 270 to 360 portion of the cosine wave.
- the break points in the approximators 136 and 137 are provided so that not only do the resulting signals fit well to sine and cosine functions but their sums, as required in Equations (1) and (2), fit well to summed sine and cosine signals.
- the break points in the approximators 136 and 137 are concentrated over the upper half of the range of output signal levels where the slope is changing most rapidly, between 45 and for the sine function and between 0 and 45 for the cosine function.
- Some break points are distributed in the lower half of the range of input signal levels to compensate for vertical errors in the sine and cosine function signals at points of near maximum steepness.
- Differentiators 112 and 114 receive respectively the X and Y signals.
- the differentiators 112 and 114 respectively feed full-wave rectifiers 148 and 150 which output a signal having a level equal to the magnitude of the differentiated X and Y signals.
- the outputs of the full-wave rectifiers 148 and 150 are summed by summer amplifier 152 to yield an output signal which can be used in place of the output from the amplifier or square rooter 121 of FIG. 3 as an approximation to the velocity or rate of change of the vector sum of the X and Y signals.
- the function generator 34 can be replaced by a free running oscillator directly providing a sine function output and providing a cosine function output through an integrator.
- phase detection circuit 78 provides similar detection of the period of the sine and cosine function electrical signals and enables the display 74 for a preselected period of time after the positive slope zero crossing of the sine function signal.
- the preselected time corresponding to 1r/2, qr, (31r/2), 211' or other portions of the sine and cosine functions, is terminated by detecting subsequent zero crossings or reference levels of the sine and cosine function signals or, alternatively, by counts in a counter.
- a counter is used, it is run at a high frequency from which the output frequency of the generator 34 is taken by count down techniques to insure accurate synchronization of the counter and sine and cosine cycles. In this case, any portion of a cycle can be used as the preselected time by specifying a corresponding count.
- the digital control unit 48 may receive computed coefficient data from a computer interface 160, data line 162 and computer 90, or may generate the computation itself if associated with a small computer.
- the digital control unit 48 receives directly data input from a graphic input 164 and manual data entry keyboard 166 among other input sources.
- a data bus 168 provides data communication among the inputs and outputs of the digital control unit 48 and internal units including curve transformation 170, mode generator 172.
- the internal units further include random access and ROM memory 174, plus output registers 176, 178, 180, 182, 184, 186 for Ax, Bx, Ay, By, Y, and X (or Y ,Ay and X,,Ax) signals respectively.
- An enable control 188 provides time and duration control for the portion of period used for marking at display 74 from phase, and level information provided by the phase detection circuit 78 over line 80.
- the mode generator 172 allows selection of a variety of display orientations and modes. in point mode a single point is displayed. Increment mode provides display of sequential contiguous points or lines.
- Vector relative and absolute allows straight lines drawn at absolute or relative position by setting either the A or B coefficients at zero and using X and Y, signals for position. The non-zero coefficients are scaled and set in a ratio to define slope.
- Curve increment provides elliptical fitted sections in contiguous display.
- Curve relative and absolute provides for display of curve sections at selected positions.
- Figure relative and absolute, character and symbol generate displays of figures and alpha-numeric characters and symbols.
- the parameters for specific curves, vectors, figures, characters, and symbols can be stored in memory 174 for use without the necessity of recalculation.
- Computer 90 can supply special parameters to memory 174 where special user needs demand unusual displays such as transistor symbols.
- Memory 174 also provides storage of parameters for all portions of a complete display for illumination of a CRT Display to give the appearance of
- each character or symbol When alpha-numeric characters and symbols are to be generated, each character or symbol is initially generated on a scale substantially larger than its ultimate scale on the display surface. It is subsequently reduced a predetermined amount and positioned for proper size and placement according to data received from computer 90.
- the mode generator 172 in response to data specifying alpha-numeric information from computer 90 obtains from memory 172 the parameters of the strokes necessary for displaying each character and symbol in a size larger than the ultimate display by the predetermined reduction. This allows the initial point for each character to be specified from an array of a great many initial points rather than a very limited number of points possible if small size (e.g., typewriter scale) characters and symbols were initially generated to scale. The limited number of initial points would result in character distortion or misalignment.
- mode generator 172 With generation of the X and Y function signals in a large scale for each character, mode generator 172 provides the scaling signal 63 to the gain control inputs of the summing amplifiers 58 and 64 to adjust the scale of the X and Y function signals to produce the character size specified by computer 90 or keyboard 166. Positioning is accomplished by the X and Y signals after reduction of the Ax and Ay signals. For non-alpha-numeric displays scaling signal 63 is set at a value for no reduction.
- Digital control unit 48 also provides for various transformations on the curves through operations of curve transformation 170.
- a 3-D transformation varies display intensity and/or perspective projections to give the effect of a 3-D curve projected on the display surface. Rotation provides a selected angular displacement. Scaling" alters the relative size of sections. Scissoring” and windowing" expands selected portions. Sub-routining effectively allows for any other preprogrammed transformation. All these transformations and manipulations are achieved through mathematical manipulations directly on the A and B parameters by known mathematical techniques without the need for recalculation from original data.
- a data flow controller 190 provides data sequencing and organization in the well known manner of digital control implementation to deliver appropriate data to the proper location at the right moment.
- a system for controlling the rate of change of the vector sum of said separate electrical signals comprising:
- means for producing single polarity signals in response to and varying with the magnitude of the derivative of said separate electrical signals; means for summing said single polarity signals; and means for controlling the rate of change of the output of said developing means to maintain the summation of said single polarity signals at least approximately at a value representative of a predetermined rate of change of said vector sum.
- said means for producing single polarity signals comprises a squarer.
- controllable means for generating two electrical signals phase separated by a quarter cycle to provide a sine and cosine function electrical signal
- the system for generating X and Y function electrical signals of claim 3 further including:
- the system for generating X and Y function electrical signals of claim 4 further including:
- the system for generating X and Y function electrical signals of claim 3 further including:
- constraints are the position and slope in orthogonal coordinates of each endpoint of said section of said curve.
- constraints are in orthogonal coordinates the position of each endpoint and one intermediate point and the slope of one of said three points on said section of said curve.
- constraints are in orthogonal coordinates, the position on said section of said curve of the endpoints and a third point which is at the maximum perpendicular distance from a straight line between said endpoints.
- the system of claim 3 further comprising means for controlling the rate of change of said X and Y function electrical signals to maintain the vector sum of the rates of change with respect to time of said X and Y function electrical signals substantially equal to a preselected value.
- controlling means is characterized by including means to adjust the frequency of the sine and cosine function electrical signals as generated by said generating means to control the vector sum of the rates of change of said X and Y function electrical signals.
- break points being distributed so as to occur at substantially even spacing in said X and Y function electrical signals.
- the system of claim 3 further including:
- controllable intensity means for displaying images in response to said X and Y function electrical signals
- a system for displaying curve sections comprising:
- display means operative to receive said first and second control signals on orthogonally reacting inputs thereof to produce quarter cycle elliptical curve sections in response to said control signals; said first, second, third, and fourth independent parameters representing point and slope constraints for quarter cycle elliptical curve sections.
- the system of claim 16 further including means to maintain the brightness of display of said display means in response to variations in the writing speed of said display means from variations in the rates of change of said output control signals.
- the system of claim 15 further including means for compensating for display brightness variations due to changes in the writing speed of said display means from variations in the rates of change of said output control signals.
- a system for generating orthogonal control signals for use in producing a curve section between first and second points said system including:
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- Computer Hardware Design (AREA)
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- Computing Systems (AREA)
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- Mathematical Optimization (AREA)
- Pure & Applied Mathematics (AREA)
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Abstract
Description
Claims (24)
Applications Claiming Priority (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
US10610871A | 1971-01-13 | 1971-01-13 |
Publications (1)
Publication Number | Publication Date |
---|---|
US3721810A true US3721810A (en) | 1973-03-20 |
Family
ID=22309538
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
US00106108A Expired - Lifetime US3721810A (en) | 1971-01-13 | 1971-01-13 | Display system utilizing one or more conic sections |
Country Status (5)
Country | Link |
---|---|
US (1) | US3721810A (en) |
JP (1) | JPS5213890B1 (en) |
CA (1) | CA973637A (en) |
GB (1) | GB1371935A (en) |
IT (1) | IT948170B (en) |
Cited By (1)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US4371933A (en) * | 1980-10-06 | 1983-02-01 | International Business Machines Corporation | Bi-directional display of circular arcs |
Citations (8)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US3205349A (en) * | 1961-10-02 | 1965-09-07 | Electronic Associates | Function generator |
US3283317A (en) * | 1963-06-14 | 1966-11-01 | Sperry Rand Corp | Symbol generators |
US3335416A (en) * | 1963-08-07 | 1967-08-08 | Ferranti Ltd | Character display systems |
US3422305A (en) * | 1967-10-12 | 1969-01-14 | Tektronix Inc | Geometry and focus correcting circuit |
US3476974A (en) * | 1968-01-22 | 1969-11-04 | Stromberg Datagraphix Inc | Digital controlled elliptical display |
US3488483A (en) * | 1967-06-30 | 1970-01-06 | Raytheon Co | Constant writing rate vector generator |
US3519876A (en) * | 1968-07-26 | 1970-07-07 | Harris Intertype Corp | Alphanumeric character display |
US3539860A (en) * | 1969-04-01 | 1970-11-10 | Adage Inc | Vector generator |
-
1971
- 1971-01-13 US US00106108A patent/US3721810A/en not_active Expired - Lifetime
-
1972
- 1972-01-10 IT IT47649/72A patent/IT948170B/en active
- 1972-01-12 GB GB147372A patent/GB1371935A/en not_active Expired
- 1972-01-12 CA CA132,246A patent/CA973637A/en not_active Expired
- 1972-01-13 JP JP47006109A patent/JPS5213890B1/ja active Pending
Patent Citations (8)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US3205349A (en) * | 1961-10-02 | 1965-09-07 | Electronic Associates | Function generator |
US3283317A (en) * | 1963-06-14 | 1966-11-01 | Sperry Rand Corp | Symbol generators |
US3335416A (en) * | 1963-08-07 | 1967-08-08 | Ferranti Ltd | Character display systems |
US3488483A (en) * | 1967-06-30 | 1970-01-06 | Raytheon Co | Constant writing rate vector generator |
US3422305A (en) * | 1967-10-12 | 1969-01-14 | Tektronix Inc | Geometry and focus correcting circuit |
US3476974A (en) * | 1968-01-22 | 1969-11-04 | Stromberg Datagraphix Inc | Digital controlled elliptical display |
US3519876A (en) * | 1968-07-26 | 1970-07-07 | Harris Intertype Corp | Alphanumeric character display |
US3539860A (en) * | 1969-04-01 | 1970-11-10 | Adage Inc | Vector generator |
Cited By (1)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US4371933A (en) * | 1980-10-06 | 1983-02-01 | International Business Machines Corporation | Bi-directional display of circular arcs |
Also Published As
Publication number | Publication date |
---|---|
DE2201535A1 (en) | 1972-08-10 |
IT948170B (en) | 1973-05-30 |
CA973637A (en) | 1975-08-26 |
DE2201535B2 (en) | 1976-08-12 |
JPS5213890B1 (en) | 1977-04-18 |
GB1371935A (en) | 1974-10-30 |
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Owner name: HARVIL CORPORATION, MASSACHUSETTS Free format text: ASSIGNMENT OF ASSIGNORS INTEREST;ASSIGNOR:HUGHES AIRCRAFT COMPANY;REEL/FRAME:003962/0708 Effective date: 19801107 Owner name: HARVIL CORPORATION, 60 STATE ST., BOSTON, MA. 0210 Free format text: ASSIGNMENT OF ASSIGNORS INTEREST.;ASSIGNOR:HUGHES AIRCRAFT COMPANY;REEL/FRAME:003962/0708 Effective date: 19801107 |