U.S. patent number 3,746,912 [Application Number 05/054,938] was granted by the patent office on 1973-07-17 for method of and means for recording line drawings on the screen of a cathode ray tube under computer control.
This patent grant is currently assigned to Dr.-Ing. Rudolf Hell. Invention is credited to Friedrich Redecker, Ruediger Sommer.
United States Patent |
3,746,912 |
Redecker , et al. |
July 17, 1973 |
METHOD OF AND MEANS FOR RECORDING LINE DRAWINGS ON THE SCREEN OF A
CATHODE RAY TUBE UNDER COMPUTER CONTROL
Abstract
Curves are plotted and displayed on the screen of a cathode ray
tube by deriving control voltages from the differences between the
coordinates of adjacent points of a curve, controlling the plotting
of line portions with the derived voltages, maintaining the speed
and current of the recording electron beam of the CRT constant and
maintaining a uniform brightness of the several portions of a
trace.
Inventors: |
Redecker; Friedrich (Kiel,
DT), Sommer; Ruediger (Raisdorf, DT) |
Assignee: |
Dr.-Ing. Rudolf Hell (Kiel,
DT)
|
Family
ID: |
5739911 |
Appl.
No.: |
05/054,938 |
Filed: |
July 15, 1970 |
Foreign Application Priority Data
|
|
|
|
|
Jul 16, 1969 [DT] |
|
|
P 19 36 051.1 |
|
Current U.S.
Class: |
315/386; 315/379;
315/391; 345/15 |
Current CPC
Class: |
G09G
1/10 (20130101); G06G 7/30 (20130101) |
Current International
Class: |
G09G
1/06 (20060101); G06G 7/00 (20060101); G09G
1/10 (20060101); G06G 7/30 (20060101); H01j
029/72 () |
Field of
Search: |
;315/26,21R,21MR,18,22,24 ;235/61,61.7,61PK,61.11G ;340/324A |
References Cited
[Referenced By]
U.S. Patent Documents
Primary Examiner: Quarforth; Carl D.
Assistant Examiner: Lehmann; E. E.
Claims
We claim:
1. Apparatus for recording line drawings on the screen of a CRT
which has horizontal and vertical deflection circuits, a horizontal
and a vertical deflection coil, a recording beam emission circuit,
the line drawings represented by a plurality of individually spaced
coordinate points, each line drawing recorded by the recording beam
connecting an initial coordinate point and an end coordinate point,
means to produce deflection voltages representing the initial
coordinate point, means to produce deflection voltages for
connecting the initial coordinate point with the end coordinate
point, and means to produce difference voltages representing the
difference between initial coordinate point and the end coordinate
point comprising:
adding means for adding the deflection voltages to the deflection
coils, said adding means connected between the deflection coils and
the means to produce the deflection voltages which represent the
initial coordinate point and the means to produce the deflection
voltages for connecting the individual coordinate point with the
end coordinate point,
sawtooth generating means producing constant slope sawtooth
voltages which represent the deflection voltages for connecting the
initial coordinate point and the end coordinate point, said slope
being dependent upon the difference voltages derived from the
initial coordinate point and the end coordinate point of the line
drawing,
comparator means having an output and a pair of inputs for
receiving respective horizontal and vertical difference signals and
operable to provide a first signal at its said output when the
horizontal difference voltage is less than the vertical difference
voltage and a second signal at its said output when the horizontal
difference voltage is greater than the vertical difference
voltage,
dividing amplifier means having a pair of inputs and an output and
operable to provide at its said output the quotient of the voltage
on a first of said pair of inputs divided by the voltage on a
second of said pair of inputs,
first switching means having a first input for receiving the
horizontal difference voltages and a second input for receiving the
vertical difference voltage, a pair of outputs connected to said
pair of inputs of said dividing amplifier means, and a control
input connected to said output of said comparator means and
operable in response to said first and second signals to
selectively connect said horizontal and vertical difference
voltages to the input of said dividing amplifier means, and
second switching means having a pair of inputs for receiving said
sawtooth voltages, a pair of outputs connected to said deflection
circuits and a control input connected to said comparator means and
operable in response to said first and second signals to
selectively connect said horizontal and vertical sawtooth voltages
to the horizontal and vertical deflection circuits.
2. Apparatus according to claim 1, comprising function amplifier
means connected between said output of said dividing means and said
saw-tooth voltage generating means for selectively operating said
sawtooth generating means in accordance with sin arc tg and cos arc
tg functions.
3. Apparatus according to claim 1 comprising means for dividing
said difference voltages by one another to provide quotients that
are less than unity and means for forming sin arc tg and cos arc tg
functions from said quotients, and wherein said sawtooth generator
means is linearly responsive to said sin arc tg and cos arc tg
functions to control the deflection circuits.
4. Apparatus for recording line drawings on a screen of a CRT which
has horizontal and vertical deflection circuits, a horizontal and a
vertical deflection coil, a recording beam emission circuit, the
line drawings represented by a plurality of individually spaced
coordinate points, each line drawing recorded by the recording beam
connecting an initial coordinate point and an end coordinate point,
means to produce deflection voltages representing the initial
coordinate point, means to produce deflection voltages for
connecting the initial coordinate point to the end coordinate
point, and means to produce difference voltages representing the
difference between the initial coordinate point and the end
coordinate point comprising:
adding means for adding the deflection voltages to the deflection
coils, said adding means connected between the deflection coils and
the means to produce the deflection voltages which represent the
initial coordinate point and the means to produce the deflection
voltages for connecting the individual coordinate point with the
end coordinate point,
sawtooth generating means producing constant slope sawtooth
voltages which represent the deflection voltages for connecting the
initial coordinate point and the end coordinate point, said slope
being dependent upon the difference voltages derived from the
initial coordinate point and the end coordinate point of the line
drawing,
a timing pulse generator for producing repetitive pulses,
said sawtooth generating means including timing pulse input
connections connected to said timing pulse generator, said sawtooth
generating means being responsive to successive timing pulses to
turn on and off,
means for controlling beam current of the CRT including means for
squaring said difference voltages, means for adding the squared
voltages, means for extracting the square root of the added square
voltages, and means for distoring the square root voltage connected
to the recording beam emission circuit, means for adding the
difference voltages, means for subtracting the difference voltages
including means for rendering the subtraction effective without
regard to sign, means for adding the sum and difference of said
difference voltages connected to said means for distorting for
distortion of said difference voltages.
5. Apparatus according to claim 4 comprising at least one voltage
divider connected to the output of said means for adding the
difference voltages, a second means for subtracting connected to
the first mentioned means for subtracting and to said voltage
divider for subtracting to provide the absolute value difference
between the voltages provided by said voltage divider and said
first-mentioned means for subtracting, said second means for
subtracting also connected to said means for adding the sum and
difference of said difference voltages.
6. Apparatus for recording line drawings on the screen of a CRT
which has horizontal and vertical deflection circuits, a horizontal
and a vertical deflection coil, a recording beam emission circuit,
the line drawings represented by a plurality of individually spaced
coordinate points, each line drawing recorded by the recording beam
connecting an initial coordinate point and an end coordinate point,
means to produce deflection voltages representing the initial
coordinate point, means to produce deflection voltages for
connecting the initial coordinate point with the end coordinate
point, and means to produce difference voltages representing the
difference between the initial coordinate point and the end
coordinate point comprising:
adding means for adding the deflection voltages to the deflection
coils, said adding means connected between the deflection coils and
the means to produce the deflection voltages which represent the
initial coordinate point and the means to produce the deflection
voltages for connecting the initial coordinate point with the end
coordinate point,
sawtooth generating means producing constant slope sawtooth
voltages which represent the deflection voltages for connecting the
initial coordinate point to the end coordinate point, said slope
being dependent upon the difference voltages derived from the
initial coordinate point and the end coordinate point of the line
drawing,
two variable gain amplifier means each having an input for
simultaneously receiving the difference voltages, a control input,
and an output connected to said sawtooth generators,
two function amplifiers, each of said function amplifiers including
an input connected to the output of one of said variable gain
amplifier means, said function amplifiers operable to square the
output voltages of said variable gain amplifier means,
an adjustable voltage source representing the desired value of the
drawing speed of the recording beam between adjacent points of the
drawing, and
an adder circuit including an output connected to said gain control
inputs of said variable gain amplifier means, and a plurality of
inputs connected to said adjustable voltage source and said outputs
of said function amplifier means for adding said squared output
voltages and comparing such voltages with the voltage of said
adjustable voltage source to provide control voltages to said
variable gain amplifier means, whereby said variable gain amplifier
means regulates the slope of a sawtooth voltage of said sawtooth
generating means for each difference voltage with respect to both
difference voltages and the voltage of the adjustable voltage
source.
Description
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to a method of and means for
recording line drawings on the screen of a cathode ray tube under
computer control, the coordinates of individual points on the lines
of the drawings being spaced at differing intervals and continuous
line series being represented by straight lines connecting these
points, said lines approximating the line drawing.
2. Description of the Prior Art
Cathode ray tubes are frequently used to display information
calculated by a computer. Such illustrations are generally
constructed from a limited number of symbols, i.e., numbers,
letters and characters, whose recording data are distributed in an
electronic memory of the recording apparatus or in the computer.
These data consist of binary numbers of coordinates for positioning
on the screen of the cathode ray tube and of binary coded numbers
giving details of the length pieces of the individual picture lines
from which the symbols are constructed. Each picture line piece is
built up from a whole multiple of a minimum piece whose size is
barely preceivable by the eye. The symbols thus have a raster
structure. The data from the symbols are distributed under certain
addresses in the memories. Upon call-up of this address they
control, by means of the computer, the recording of the symbols on
the screen of the cathode ray tube.
Often it is desired to plot not only symbols but also so-called
"line drawings," i.e. drawings that are made up of continuous
series of lines of the same line thickness and shape. For example,
a weather map can be used which, in addition to the symbols and
meteorological signs, also contain continuous series of lines of
varying shapes, i.e., coastlines and iso-lines. Apparatus which
plot weather maps are referred to as "plotters." Also during
scientific computer calculations, functions often result which can
be advantageously recorded with the aid of the plotter so that they
are directly visible as curves and can be photographically fixed
for evaluation.
The plotting of such curves can be particularly simply effected by
plotting rows of points close to one another so that the eye
observes a continuous solid line. Plotting of this kind has the
disadvantage that a large number of points have to be displayed on
the screen of the cathode ray tube. Each point has to be determined
by an X- and a Y-coordinate which, in turn, have to be determined
in a plurality of individual calculations and possibly stored in
some form of memory.
In order to decrease this large amount of data, in an improved
method of plotting, small lines of fixed length are employed
instead of points. A definite number of line units having various
angles of inclination is fixed. By lining up a plurality of these
lines of appropriate inclination in any series and amount,
approximation to the required curve can be attained.
However, it has been obligatory to compromise in the case of line
plotting. If the continuous series of lines has to be plotted with
few line units of greater length, then less information and storage
room is necessary, however, a rectangular, rugged and unpleasant
series of lines was obtained. If the lines are, however,
sufficiently small to overcome this disadvantage, then the amount
of data which has to be plotted, addressed and stored increases
proportionally.
In an advantageous method of recording, as small as possible a
number of points on the continuous series of lines is determined,
at differently sized and advantageously chosen spacings, and these
points are connected to one another by straight line portions. This
gives rise to a polygonal trace approximating the actual curve
required. In order to achieve as good as possible an approximation,
many points must be laid down close to one another in curved pieces
having small radii of curvature, fewer points being necessary in
curved pieces having a large radius of curvature and in straight
members, and these need be provided only on the periphery and end.
The line drawings thus produced have a smooth effect despite the
enormously varying spacing between the points making up these
lines. with a relative small number of points they satisfy the
requirements for accuracy and satisfy the requirements to take up
as little data and storage space as possible.
One improtant requirement is, however, not fulfilled. The line
thickness must be uniform over the total length of the line series,
if the latter is to have a satisfactory appearance. It is very
difficult to achieve such uniformity, due to the vary great
difference in length of the part pieces, and the recording times,
so that uniform illumination is not achieved and thus there is no
equality in the line thickness. Two falts arise: firstly, the speed
and brightness of the scanning point is not constant between the
points delineating the line so that line pieces appear as commas,
i.e., thicker to one side; and secondly, the brightness of the
total line series is also not uniform due to the varying basic
brightness of the individual line pieces. Therefore, the appearance
of the line series is poor.
SUMMARY OF THE INVENTION
The straight union a of two points on the curve determined by the
coordinates x.sub.1 ;y.sub.1 and x.sub.2 ;y.sub.2 is:
a = .sqroot.(x.sub.2 - x.sub.1).sup.2 + (y.sub.2 - y.sub.1).sup.2 =
.sqroot..DELTA.x.sup.2 + .DELTA.y.sup.2
The electron beam has to move over this path a during plotting of
the curved piece. In order to achieve equally bright recording of
the whole line series, each individual piece of the trace must be
recorded at constant speed and beam intensity, and the beam
intensity must be such that a uniform brightness is attained.
To this end, and according to the invention, voltages are derived
from the differences between the coordinates of adjacent points and
these voltages are fed to control means operative during plotting
of individual line pieces, to keep the speed and current of the
recording electron beam constant, and during the plotting of all
the line members, to achieve uniform brightness on the screen of
the recording tube.
BRIEF DESCRIPTION OF THE DRAWINGS
Other objects, features and advantages of the invention, its
organization, construction and operation will be best understood
from the following detailed description, taken in conjunction with
the accompanying drawings which show some embodiments of the
invention by way of example, and in which:
FIG. 1 shows a polygon, which is approximated to a curved path;
FIG. 2 shows a circuit diagram of a first proposal providing a
uniform and constant speed and constant current of the electron
beam for all the line pieces;
FIGS.3 and 4 show graphical illustrations for developing the
following circuit arrangement of FIG. 5;
FIG. 5 shows a circuit diagram of a second proposal providing
constant speed and constant electron beam current;
FIG. 6 shows a circuit diagram of a first proposal for recording
line pieces of different length in equal times and at controlled
speed and beam current;
FIG. 7 shows a graphical illustration for an approximation method
for solving the problem referred to in connection with the circuit
of FIG. 6;
FIG. 8 shows a circuit diagram for carrying out the approximation
method of FIG. 7;
FIG. 9 shows graphical illustrations for a further method according
to FIG. 7; and
FIG. 10 shows a circuit diagram for carrying out the further
approximation method of FIG. 9.
DESCRIPTION OF THE PREFERRED EMBODIMENT
The plotting of any representations on the screen of a cathode ray
tube is conventionally carried out by deflecting an electron beam,
focussed to a point, in two orthogonal coordinate directions and
preferably horizontally (x-direction) and vertically (y-direction),
and at the same time the beam intensity is appropriately
controlled. By establishing a pair of coordinates x and y, the
position of a point on the screen is determined and can be
controlled by deflection currents or voltages which are allocated
to these coordinates.
If a definite point on the screen is to be controlled by a computer
or memory, then this is achieved by the numerical values of the
coordinates x and y of the point, which are offered in binary
numbers depends on the degree of resolution which the electron beam
point is to attain on the screen. The following numbers are of
interest as a practical example. The usable diameter of this screen
should amount to approximately 210 mm. so that a square field of
150 mm, can be used. The electron beam point should have a diameter
of 0.05 mm. Then for instance 3,000 positions are possible in each
coordinate direction, in the whole field 9 .times. 10.sup.6. For
detailing the position of, or expressed in data technique parlance,
"addressing" a point in the field, a twelve-digit binary number is
required for x and y.
Referring now to the drawings, FIG. 1 represents any curved path
which is to be plotted on the screen.
In order to be able to use as little control data as possible, a
few points P.sub.1, P.sub.2 . . . . P.sub.n are selected on the
curved path. The spaces are of different sizes and chosen so that
straight connecting pieces between adjacent points (shown dashed)
offer as good as possible an approximation to the real curve.
The curved piece P.sub.1 - P.sub.2 is determined by the coordinates
x.sub.1 ;y.sub.1 for point P.sub.1 and x.sub.2 ;y.sub.2 for point
P.sub.2. In order visibly to plot the connecting line P.sub.1 -
P.sub.2, the electron beam must follow the path from P.sub.1 -
P.sub.2 at a finite speed and a fixed constant brightness.
The path which the beam is to take is the hypotenuse of the
right-angled triangle having the short sides .DELTA.x and .DELTA.y,
wherein: .DELTA.x = x.sub.2 - x.sub.1 and .DELTA.y = y.sub.2 31
y.sub.1.
In order to move the electron beam along the straight path a
uniformly from P.sub.1 to P.sub.2, the deflection voltages for both
the coordinates must change uniformly at the same time from x.sub.1
to x.sub.2 or from y.sub.1 to y.sub.2. With a constant electron
beam current, the line portion is recorded at an even
brightness.
The line portions P.sub.2 - P.sub.3 ; P.sub.3 - P.sub.4 ...(P.sub.n
- 1) - P.sub.n, succeed the line portion P.sub.1 - P.sub.2. They
form a continuous line which adapts itself closely to the curved
path. So that the whole continuous line shall have an even line
thickness, the individual line portions must be recorded at an even
brightness. If the concession is made that large line pieces be
recorded at the same speed as small ones, then the point brightness
will also be equal for all the line pieces and the whole line
series is evenly recorded. Corresponding to a second proposed
solution the time for recording the individual line portions is to
be equal. From the criteria of constant time intervals, which are
given by a timing pulse generator, the control values for the beam
speed and current can be derived by the distance between two points
determined by the differences in the coordinates.
For implementing the first of the alternatives the following
equation is to be fulfilled:
V = R .sqroot. .DELTA.x.sup.2 +.DELTA.y.sup.2 = constant (a)
ps V signifying speed, and R a normal size, by which a constant
real speed is adjusted.
FIG. 2 shows a circuit diagram of an electronic arrangement with
whose assistance the above function of expression a is simulated.
The circuit design implements the function obtained by squaring the
expression a
V.sup.2 = R.sup.2. .DELTA. x.sup.2 + R.sup.2. .DELTA. y.sup.2.
(b)
It is assumed that the differences .DELTA.x and .DELTA.y of the x
and y coordinates of both the points between which the curved
portion is recorded have already been calculated and are available
as proportional difference voltages, .delta.x and .delta. y. These
difference voltages reach input terminals 1 and 2 of the circuit
arrangement. Firstly, they pass variable gain amplifiers 3 and 4
without change and, via circuit connections 5 and 6, arrive at
function amplifiers 7 and 8 which square the voltages according to
the equation b. The output voltages at conductors 9 and 10 are
added in an adder 11, simultaneously compared with a control
voltage supplied via line 12 It originates from a controllable
voltage source 13 and represents the value V.sup.2. The voltage
simultaneously amplified and obtained in the adder 11 passes over a
line 14 simultaneously to the control inputs of the variable gain
amplifiers 3 and 4 and so regulates these latter that in the
regulating system the adjusted and regulated values are equal to
one another.
The voltages appearing in lines 5 and 6 control a saw-tooth
generator 16 for horizontal deflection and a saw-tooth generator 26
for vertical deflections, in such a manner that voltages arise in
lines 17 and 18, whose differential quotient is proportional to the
control voltages in lines 5 and 6. These voltages pass via adders
19 and 20 to deflection coils 21 of a cathode ray tube 22 and
effect movement of the electron beam from one point P.sub.z to its
adjacent point P.sub.z .sub.+ 1. The movement therefore emanates
from a basic position which is determined by the coordinates of the
point P.sub.z, namely x(P.sub.z) and y(P.sub.z). Voltages
corresponding to these coordinate values pass via lines 23 and 24
to second inputs of the adders 19 and 20 and determine the initial
position for the movement of the electron beam. The adders 19 and
20 in the example shown also simultaneously transform the
controlling voltages into deflecting currents. The brightness of
the electron beam is adjusted to a desired value by means of an
adjustable voltage source 25 and the deflection time of the
individual saw-tooth phases is proportional to the line portions to
be recorded. A suitable switch (not shown) is provided for this
purpose.
A second solution of the object of recording line series at a
constant recording speed and constant brightness is shown in FIG.
5. This arrangement avoids electronic control (feedback) loops and
is therefore free from any tendency to set up interfering control
oscillations. The circuit design is modeled on the equation a as in
the aforementioned example.
In the triangle formed in FIG. 3 from .DELTA.x and .DELTA.y,
.DELTA.y/.DELTA.x is the tangent of the angle formed by .DELTA.x
and .sqroot.x.sup.2 + y.sup.2
.phi. = arc tg .DELTA.y/.DELTA.x (c)
The speed at which the electron beam moves in the x-direction
is:
V.sub.(x) = V.sub.S .sup.. cos .phi. =(cos arc tg
.DELTA.y/.DELTA.x).sup.. V.sub.s (d)
and in the y-direction:
V.sub.(y) = V.sub.s .sup.. sin .phi. =(sin arc tg
.DELTA.y/.DELTA.x).sup.. V.sub.s (e)
V.sub.S being the desired constant beam speed in the reproducing
direction S.
Both the functions can be simulated electronically. It is, however,
advantageous to limit the range of the variables .DELTA.y/.DELTA.x
to be used to the region between 0 and 1, because the functions in
this interval are approximately rectilinear and can be simulated
electronically more easily than in the total area from 1 to
.infin.. The range .DELTA.y/.DELTA.x>1 is considered, cos arc
tg.DELTA.y/.DELTA.x being replaced by sin arc tg .DELTA.x/.DELTA.y
and sin arc tg.DELTA.y/.DELTA.x being replaced by cos arc
tg.DELTA.x/.DELTA.y.
FIG. 4 shows in the two curves 26 and 27, the functions sin arc
tg.DELTA.y/.DELTA.x and cos arc tg.DELTA.y/.DELTA.x. In the range
from 0 to 1, sin arc tg increases from the point 28 along the
branch of the curve 26 to point 29. One point, e.g., 30 on the
branch of the curve in the region of 1 to .infin. corresponds to
the point 30' of the curve 27 for the range 1 to 0. The whole
branch of the curve 26 in the range of 1 to .infin. can be replaced
by the branch 27 in the range of 1 to 0 between point 29 and 32.
The same also applies inversely. The point 31 on the branch of the
curve 27 in the range of 1 to .infin. corresponds to point 31' on
the branch 26 in the range of 1 to 0 between the points 29 and 28.
The functions sin arc tg .DELTA.y/.DELTA.x are therefore replaced
by cos arc tg .DELTA.x/.DELTA.y and cos arc tg .DELTA.y/.DELTA.x
are replaced by sin arc tg.DELTA. x/.DELTA.y when sin arc tg
.DELTA.y/.DELTA.x is greater than cos arc tg .DELTA.y/.DELTA.x so
the branches of the curve are avoided in the range of 1 to.infin.
shown hatched.
This exchange of functions in the electronic production of the
proposed solution occurs after comparison in size between .DELTA.x
and .DELTA.y by simple switching.
FIG. 5 shows a suitable circuit arrangement to accomplish the
foregoing proposal. The difference voltages .delta.x and .delta.y
pass from the input terminals 1 and 2 simultaneously to a
comparator 33 and a switch 34. If .delta.x < .delta. y, the
switch 34 remains in the position shown. The voltage .delta.x is
applied to a line 36 and the voltage .delta.y to a line 37. If,
however, .delta.x > .delta.y, the switch 34 is reversed. The
voltage .delta.y reaches the line 36 and the voltage .delta.x the
line 37. The voltage on the line 36 is therefore always smaller
than that on the line 37.
A dividing circuit 38 divides the voltage at its one input 36 by
the voltage applied to its other input 37. The quotient voltage on
the output line 39 is simultaneously fed to two function generators
40 and 41. The function generator 40 forms the function sin arc tg
and the function generator 41 the function cos arc tg. The output
voltage on lines 42 and 43 control the saw-tooth generators 44 and
45 which supply the currents for deflection of the electron beam in
the cathode ray tube. The deflection currents are, however, fed
through a switch 48 which is simultaneously with and similarly to
the switch 34, controlled by the comparator 33 via line 35. If,
therefore, .delta.x < .delta.y, then the connection shown
exists, and the deflection current passes through a line 47 to a
terminal 50 of the deflection coils for horizontal deflection.
Thus, the current controls the vertical deflection via a terminal
49 through a line 46. The horizontal deflection follows the
function cos arc tg and the vertical deflection the function sin
arc tg.
If .delta.x > .delta.y, the comparator 33 responds and actuates
the switches 34 and 48. As a result, 1 is connected to 37 and 2 to
36 at the input, furthermore 46 is connected to 50 and 47 to 49.
The horizontal deflection now follows the function sin arc tg and
the vertical deflection the function cos arc tg.
For adjusting a desired brightness of the electron beam an
adjustable voltage source 25 is also used in this case. A basic
positioning is required, which details the initial point during the
recording of each line member. These basic deflection currents have
the same function as is described in FIG. 2 and was shown at the
lines 23 and 24 and are mixed with the deflection currents in the
lines 49 and 50. Re-representation is therefore in this case
unnecessary.
The switches 34 and 48 shown in the drawings as mechanical contacts
for case of illustration, are actually constructed from logic
components including diodes or transistors.
The second alternative solution of the invention consists in
plotting the connecting lines between adjacent points always in the
same time. This solution has the result that the recording speed
differs very greatly and the brightness of the light spot i.e., the
intensity of the electron beam has to be controlled so that all the
line pieces are plotted equally brightly or approximately equally
brightly. The beam current I.sub.S is therefore dependent upon the
deflection speed:
I.sub.S = E .sqroot..DELTA.x.sup.2 + .DELTA.y.sup.2 . f.sub.lin
(f)
where E is an adjustment constant and f.sub.lin a function for
correcting the non-linearity between control voltage and beam
current as well as between beam current and spot brightness on the
screen.
Simulation of the function f is made possible with the aid of the
arrangement shown in FIG. 6. The difference voltages .delta.x and
.delta.y are applied to the terminals 1 and 2 and pass to function
generators 53 and 54, which form the squares .delta.x.sup.2 and
.delta.y.sup.2. The resultant voltages on lines 55 and 56 are added
by means of adder 57, and the square root is extracted from the
total be means of a function generator 59 so that at the output
from a line 60 there is produced a voltage proportional to the size
.sqroot..delta.x.sup.2 + .delta.y.sup.2. This voltage is to control
the beam current of the cathode ray tube 22 and therefore the
brightness of the light spot to be plotted. In this way,
proportionality remains guaranteed. The control voltage is
predistorted by the correcting member 61 = f.sub.lin in such a
manner that non-linear distortions are compensated between the
control voltage and beam current, as well as between beam current
and light intensity of the tube. The pre-distorted voltage passes
via a line 62 to the control electrode of the tube.
Simultaneous with the function generators 53 and 54, saw-tooth
generators 63 and 64 are controlled by .delta.x and .delta.y. The
slopes of the saw-tooth currents supplied to lines 67 and 68 are
proportional to the voltages .delta.x or .delta.y. A timing pulse
generator 65 supplies start- and stop-pulses at regularly equal
intervals simultaneously to both the deflection amplifiers over a
line 66. During each interval, a line piece is plotted between two
adjacent points. The deflection currents for the basic position are
also added in this case in the manner already described, to lines
67 and 68.
This aforementioned proposal can lead to technical difficulties in
cases at the limits. If the ratio between the maximum and minimum
possible beam speed is very great then it is difficult to simulate
the expression f with sufficient precision. When electronically
squaring and subsequently forming the square root, considerable
errors can occur more particularly at low beam speeds. The
following proposal avoids these calculation operations by using an
approximation method. It offers, using only additative calculation
operations and with minimal electronics, a sufficiently
satisfactory result. The following reasons lead to the new
solution.
It should be V.about.F.sqroot..DELTA.x.sup.2 +.DELTA.y.sup.2 in the
following all expressions .DELTA.x, .DELTA.y, .delta.x and .delta.y
are absolute values that means their signs are always positive
(g)
The constant F is attributed to the value 1.sqroot.2 for
standardizing the calculation. With a constant .DELTA.y, .DELTA.x
increases from 0 to .DELTA.x = .DELTA.y. V then follows the path
shown in FIG. 7 at curve 70. Its smallest value is
.DELTA.y/.sqroot.2 .congruent.0.7.DELTA.y at .DELTA.x = 0, its
greatest .DELTA.y at .DELTA.x = .DELTA.y. The curve 70 is
applicable for any value from .DELTA.x and .DELTA.y, .DELTA.x and
.DELTA.y being interchangeable.
A straight line 71 is laid through the curve 70 in such a manner
that as good as possible approximation to the curve 70 is achieved.
For example, the straight line 71 is located by the point .DELTA.x
= .DELTA.y = 1. It intersects the ordinate at 0.68.
The straight line 71 can be obtained by adding straight lines 72
and 73. The straight line 72 is represented by the equation:
A = r.sub.1 (.DELTA.x + .DELTA.y) (h)
whereby r.sub.1 = 0.5, and the straight line 73 by the
equation:
B = r.sub.2 .vertline..DELTA.x - .DELTA.y.vertline. (i)
where r.sub.2 is equal to the amount r.sub.2 enclosed on the
ordinate between the straight lines 71 and 72, namely
.about.0.18.
The electronic execution of the addition of both the equations h
and i is shown in the circuit arrangement according to FIG. 8.
The difference voltages .delta.x and .delta.y are applied to the
inputs 1 and 2. .delta.x is simultaneously fed to a first input of
an adder 74, a subtractor 75 and the saw-tooth generator 63 for
horizontal deflection, and .delta.y is fed to the second input of
the adder 74 and the subtractor 75 as well as to the saw-tooth
generator 64 for vertical deflection. In the device 74 a simple
adder, the total .delta.x + .delta.y is formed and fed to an adding
device 77. The difference .delta.x - .delta.y is formed in the
substractor 75, and is passed via a line 78, a rectifier 79 and a
conductor 80 to the second input of the adder 77. The rectifier 79
is provided to make the difference .delta.x - .delta.y effective
according to their amount.
Correction of the non-linearity between the control voltage and
brightness of the cathode ray tube occurs, as already described,
with the aid of the correction amplifier 61. The saw-tooth
generators 63 and 64 supply the current for the horizontal and
vertical deflection via lines 67 and 68. They are, as already
explained in the description of FIG. 6, steadily increasing (or
falling) currents, whose rates of change dI/dt are proportional to
.delta.x or .delta.y. The timing pulse generator 65 supplies start-
and stop- pulses to the saw-tooth generator at regularly equal
intervals via line 66. During each interval, one line piece is
plotted between two adjacent points.
The approximation achieved with the straight line 71 is sufficient
in many cases because it is controlled according to the brightness
of the electron beam, and the eye is not very sensitive to depth or
width deviations of the lines recorded. Nevertheless a requirement
for better approximation to the real curve 70 can be fulfilled.
Instead of the straight line 71, a continuous line is produced from
two ro more smaller straight pieces which adapt themselves as a
polygonal path to the real curve with increasing exactitude as the
number of pieces increases.
FIG. 9 shows the improvement when using two straight pieces, namely
81 and 82. The knee 83 at which the members meet, is located for
example at .DELTA.x = 0.5.DELTA.y.
The line series 81/82 is, as apparent from the drawing, obtained by
the addition of the straight lines 72, 84, and 85, the negative
branch of straight line 85 (shown by dots) having to be suppressed.
The addition of the straight lines 72 and 84 is effected in the
same manner as has been described in FIG. 8 in connection with
straight lines 72 and 73. In addition an equation j (below) of the
straight line 85 has to be added. For the equation h the factor
r.sub.1 = 0.5, for equation i the factor K.sub.1 = 0.1 and equation
j receives the factor K.sub.2 = 0.12. These values are divided on
the ordinate.
The equation for the straight line 85 is as follows:
C = K.sub.2 .vertline..DELTA.y - 2.DELTA.x.vertline. (j)
For this it is necessary that its value from K.sub.2 = 0.12 at
.DELTA.x = 0 takes off with an increasing .DELTA.x until, at
.DELTA.x= 0.5.DELTA.y, the value nil is obtained. With further
increasing .DELTA.x values the sign changes until at .DELTA.x = 1
the value becomes C = -K.sub.2. This negative (shown in dots)
branch is not to be used.
The straight line 85 therefore intersects the ordinate at .DELTA.x
= 0.5.DELTA.y= 0.5. The knee of the polygonal path is located above
this point. The knee is given by the equation:
Z =.vertline..DELTA.x - .DELTA.y.vertline./.DELTA.x + .DELTA.y
(k)
In the case of our example it should be located at .DELTA.x = 1/2
.DELTA.y,
Z = 1 - 1/2/1 + 1/2 = 1/3
For the practical execution of the operation by electronic means it
is advantageous to transform the equation k as follows:
.vertline..DELTA.x - .DELTA.y.vertline.- Z(.DELTA.x + .DELTA.y) =
0, (1)
receiving the equation of the straight line 85 intersecting the
zero line in the knee .DELTA.x - 1/2 .DELTA.y. Only the left hand
positive branch located above the zero line is to be used. The
right hand branch (not used) having a negative value is blocked in
electronically by a diode.
FIG. 10 shows an electronic circuit arrangement which implements
the improved approximation method explained with reference to FIG.
9. The adders 74, 75, the rectifier 79, as well as the summing
device 77 and the correcting device 61 are understood from FIG. 8.
The equations of additional lines are to be added to the sum A + B
which is formed in the adding device 77. The polygonal path of the
approximation curve consists of the total sum of the equations of
the additional lines and the sum A + B. These equations are C,
C.sub.1 . . . C.sub.n. Firstly, we satisfy ourselves with C; that
means an approximation according to FIG. 9 having only one knee.
The factors calculated and assumed from the drawing (FIG. 9)
are:
r.sub.1 = 0.5; K.sub.1 = 0.1; K.sub.2 = 0.12 and Z = 1/3
The terms of a sum r.sub.1 (.DELTA.x + .DELTA.y) and K.sub.1
.vertline..DELTA.x - .DELTA.y.vertline.are available at lines 76
and 80 as electric potentials. A corresponding voltage passes
through the voltage divider 86, which forms the factor Z/K.sub.1,
to the second negative input of the subtractor 88, at whose first
input the unipolar voltage .vertline..DELTA.x -
.DELTA.y.vertline.is applied, via the line 80. The resultant
voltage on the line 89 can be positive or negative. However, only
the positive value is to be used corresponding to the left hand
positive branch of the straight line 85 in FIG. 9. The negative
voltage is blocked by means of the blocking diode 90. The positive
voltage passes over line 91 to the summing device 77. The sum
voltage on the line 60 subsequently passes through the correcting
member 61 and controls in a known manner the beam current from the
cathode ray tube. Deflection of the beam occurs at always the same
times by means of the deflecting amplifiers 63 and 64, as already
described.
The circuit may be developed to achieve ever greater precision, in
any desired fashion. At each knee at which the polygonal path
increased, the number of aggregates 86, 88 and 90 is increased by
one. The factors K.sub.1 . . . K.sub.n and also the values for
Z.sub.1 . . . Z.sub.n, are advantageously determined graphically.
In addition, a drawing is to be prepared which must be extended
logically with respect to FIG. 9. The individual line portions of
the polygonal path are extended up to the intersection point with
the ordinate. The lengths divided up on the ordinate, result in
corresponding scale in the values K... . The projections of the
knees to the abscissa give the values for Z.... .
Two modifications of the embodiments according to the invention
will now be described. If the differences between the points become
too large, it is advantageous to change the adjustment values,
namely the recording speed and the associated beam brightness
according to FIGS. 2 and 5, or the recording time and the beam
current according to the circuits of FIGS. 6 and 10 in matched
stages; criteria for these inversions are the difference voltages
.delta.x and .delta.y.
A predetermined beam speed and beam current is adjusted in the
first case up to a fixed limit value .delta.x or .delta.y. If one
of the values .delta.x or .delta.y or both exceed this limit at
greater point distances, the saw-tooth generators 15 and 16 in FIG.
2 or 44 and 45 in FIG. 5 and in addition the beam current control
25 in FIG. 5 are switched over to the next fixed operational range.
It is also possible to extend this switching over to more than only
two ranges.
In the second case which is implemented by the circuit arrangement
in FIGS. 6 and 8 and 10, swtiching over effects upon exceeding the
distance limit that the intervals between the start- and
stop-pulses from the timing pulse generator 65 become larger, so
that with larger point spacings, the recording time is not
disporportionally small and the beam current is not too great. In
addition, the difference voltage values .delta.x .delta.y at the
input terminals 1 and 2 are reduced by one factor or if more
operational ranges are desired, selectively by additional factors.
The time intervals supplied by the generator 65 are increased by
the same factor.
However, the switching over of the operational range within one
these described methods is only one of the possible modifications.
Cases can be conceived in which it is advantageous, dependent of
the point spacings between which the line member is to be plotted,
to change the arrangement or even the method. Very large line
pieces are advantageously plotted at constant speed, whilst with
short pieces constant recording time is at least preferable.
Although we have described our invention by reference to specific
examples, many changes and modifications of the invention may be
made by one skilled in the art without departing from the true
spirit and scope of the invention, and it is to be understood that
we intent to include within the patent warranted on this invention
all such changes and modifications as may reasonably and properly
be included within the scope of our contribution to the art.
* * * * *