JPH04134285A - Coordinate conversion device - Google Patents

Abstract

PURPOSE:To reduce the magnitude of a circuit to a great extent and embody it at a low cost by executing all processings through computation of rotational motions without use of the triangular relationship, and thereby eliminating necessity for provision of any large memory circuit. CONSTITUTION:Because and adding device 5 works a certain specified procedures and sends theta.xn+1+yn to the output terminal SIGMA1 a timing signal generator 4 generates simultaneously the timing signals XCLK-2 and YCLK at a certain timing after an X-register 2 has emitted a new coordinate value xn+1, and another X-register 3 and a Y-register 6 will output new coordinate values xn+1 and yn+1 (yn+1= .xn+1+yn), respectively. Repeating these procedures in the same manner permits determining new coordinates one by one. When the converting operation for example on the whole circumference having a radius (r) is finished, initial values xs+1, ys+1 corresponding to the new radius r+1 are given, and a selector 7 (8) is actuated to select the change over terminal S side, and processing for the next circumference of 360 deg. is conducted. Through repetitions of these motions, the addresses of picture elements on orthogonal coordinates are specified corresponding to all picture elements in a polar coordinate display screen having a certain area specified by polar coordinate signal, and thereby the polar coordinate signal can be written in an orthogonal coordi nate memory.

Description

DETAILED DESCRIPTION OF THE INVENTION (Field of Industrial Application) The present invention relates to a coordinate converter that converts polar coordinates to rectangular coordinates.

(Prior Art) As is well known, for example, in a color scanning sonar, the acquired received signal is a polar coordinate signal used on a PPI scanning system polar coordinate display screen, but this is converted into a rectangular coordinate memory using a coordinate converter. The information is written and displayed on a rectangular coordinate display screen using a raster scanning method such as a television.

Second, the conventional coordinate converter is mainly constructed with a conversion ROM that generates address signals for the orthogonal coordinate memory. That is,
As shown in Figure 5, the polar coordinate point (r, θ) defined by the circumferential angle θ to the radius is the rectangular coordinate point (Xθ, yθ).
, and are related by the following equation (1).

Xθ ””rcosθ, yθ=rsimouthθ
(1) Therefore, set the values of Xθ and yθ determined in advance in the conversion ROM so that the address signal of the orthogonal coordinate memory can be directly obtained, or
The triangular function value for each angle θ is set in the conversion ROM, and the address signal of the orthogonal coordinate memory is obtained by multiplying it by the radius r.

(Problem to be solved by the invention) The conventional coordinate converter described above has the following problems.

First, when the polar coordinate display screen and the orthogonal coordinate display screen have a relationship as shown in FIG. 6, the polar coordinate pixel a is the same as the orthogonal coordinate pixel (X3 y3) (X4, y3)
, and a pixel in polar coordinates is a pixel in orthogonal coordinates (X
3, 'y'3) and (X4.co13), it corresponds to one polar coordinate pixel or two orthogonal coordinate pixels, which is inconvenient.

Therefore, the division of polar coordinates must be made more finely. Moreover, since the polar coordinate system expands as it goes outward as shown in the figure, the division must be even finer.

In short, the position of each pixel in rectangular coordinates corresponding to each pixel in polar coordinates is stored for each pixel, but since all pixels in each coordinate system do not have a simple one-to-one correspondence, the position of each pixel in each coordinate system is stored. It is necessary to store data according to the unique characteristics, and the setting method for conversion ROMs becomes extremely complicated, and the amount of information to be stored increases, resulting in a large capacity. In particular, with the recent advances in technology, the resolution of images has increased and the number of pixels in orthogonal coordinates has also tended to increase, causing the problem that the conversion ROM becomes considerably large.

Therefore, in the past, as a measure to reduce the capacity of this conversion ROM, for example, instead of storing all the information on one screen, that is, in polar coordinates, a 360 degree circle,
A method is used in which the whole is divided into four parts for each quadrant and applied to the whole by changing only the polarity.

However, this method also requires a large amount of original information, so even if it is 1/
Even if only the 4 part is stored, a considerable amount of storage capacity is still required, and there is a way to further divide it into 1/8.1/16, but this time, the polarity switching circuit becomes complicated,
There is a problem in that the number of peripheral circuits increases in inverse proportion to the decrease in storage capacity.

In addition, as another reduction measure, instead of storing the entire circle as described above, only the circumference information is stored as trigonometric function information, the radius information is calculated by calculation, and the multiplier is used to Find the product of circumference information and radius information,
There is a way to find the coordinates of the entire circle. However, this method has the problem of requiring expensive high-speed multipliers.

The present invention has been made in view of such problems, and an object of the present invention is to provide a coordinate converter that can calculate orthogonal coordinates corresponding to polar coordinates by calculation without using trigonometric functions.

(Means for Solving the Problems) In order to achieve the above object, the coordinate converter of the present invention has the following configuration.

That is, the coordinate converter of the present invention converts the orthogonal coordinates (X,
This coordinate converter calculates the value of Y) as a value for each minute angle Δθ on the circumference of the radius; this coordinate converter converts the initial value of the externally set X coordinate axis and each subsequent X coordinate value a first switch that selects and outputs according to the switching signal; an X register of a predetermined bit length that sequentially stores and outputs the output of the first switch according to the X-coordinate axis timing signal; a second switch that selects and outputs each Y coordinate value according to a switching signal; a Y register of a predetermined bit length that sequentially stores and outputs the output of the second switch according to a Y coordinate axis timing signal; and: of the outputs of the Y register. The complement of the output consisting of several bits corresponding to the shift by the minute angle Δθ, which is a constant value of a power of 2, is added to the output of the X register, and the output is generated by each of the X coordinate values. A first adder and an output consisting of several bits corresponding to the output of the X register shifted by the minute angle Δθ and the output of the Y register are added together to generate and output each Y coordinate value. 2 adder; and a timing signal generation circuit that generates the switching signal and the various timing signals.

(Function) Next, the function of the coordinate converter of the present invention configured as described above will be explained.

The coordinate converter of the present invention attempts to generate orthogonal coordinates from polar coordinates by a method of drawing a circle without using trigonometric functions, that is, by a well-known calculation of rotational movement. First, the conversion is performed with reference to FIG. Explain the principle.

In Figure 1, the coordinates of a point P on the circumference (x n
, y a) by θ rotationally moving the point p n+
If the coordinates of 1 are (X n+I+ y n++), x
O”l=X ncO5θ −y, sinθ
・・・・・・・・・ (2) 3'll11""X
(ISjllθ+yIICO5θ ・・・・・・・・・
(3), or considering a small angle Δθ that approximates sl[lθ−θ, co5θ−1, equations (2) and (3)
is XO+1=xI, -△θ y, ...
...(4) ya++-△θ・x, l+ y n-
--(5). However, if left as is, it will not become a perfect circle but will become a spiral. However, it is known that a correct circle can be drawn if Xfi+1 obtained by equation (4) is used in place of X in equation (5). That is, Xn+1−xIl−△θ・y n −・−−(6)
yIl+1=Δθ・x,,+1+yゎ...
...(7).

Then, Δθ・yll and Δθ・Xn+1 are not determined by a multiplier, but by setting Δθ to a constant value of a power of 2.
Moreover, the purpose is achieved by making the multiplicand a binary number and shifting the multiplicand by a minute angle Δθ. Here, digit movement is realized by wiring.

Specifically, the output of the X register becomes one input of the first adder, but the minute angle △θ
The output consisting of several bits corresponding to the shifted value becomes the other input of the second adder. In addition, the output of the Y register becomes one input of the second adder as it is, but the complement of the output consisting of several bits corresponding to the shift by 0 to the minute angle is the complement of the output of the second adder. This becomes the other input of the adder.

Thus, the current value of the X register is xIl, and the current value of the Y register is y. Then, in the first adder, (X
, -Δθ·yfi) is performed, a new X coordinate value X11+4 is obtained, this is taken into the X register, and the next subtraction operation is performed.

On the other hand, the second adder uses the new X coordinate value X 6 + 1 to perform the addition operation of (Δθ・xfi+□+yゎ) in equation (7) to obtain a new Y coordinate value 3'll+1, which is It is taken into the Y register and the process moves to the next addition operation. Here, the X-coordinate axis timing signal and the Y-coordinate axis timing signal are generated to control the intake and output timing of the X register and Y register so that the addition operations of equations (6) and (7) can be performed without any problems. ing.

In short, according to the coordinate converter of the present invention, all processing is performed by rotational movement calculations without using trigonometric functions, so there is no need for a large memory circuit to store trigonometric function data. Furthermore, the high-speed multiplier required to reduce the data storage capacity is no longer necessary, and this has the effect of making it possible to significantly reduce the circuit scale and reduce the cost.

In addition, since calculations are performed only by fixed additions and subtractions and digit shifts realized by wiring, calculation speed is extremely fast.
It also has the effect of being able to be used for images with high resolution, which is the case these days.

(Example) Embodiments of the present invention will be described below with reference to the drawings.

FIG. 2 shows a coordinate converter according to an embodiment of the present invention. In FIG. 2, the timing signal generator 4 connects the switch 7 (8) based on the reference clock CLK given from the outside.
switching signal for X register 2 (3), timing signal XCLK1 (XCLK-2>, Y register 6
A timing signal YCLK is generated for each.

The switch 7 (8) sets one switching terminal S to an initial value x s (
y g) is input, and the adder 1 (
5) is input, and upon receiving the switching signal from the timing signal generator 4, one of the two
(Y register 6).

Here, the initial value x a (y s) gives the X value (y value) of the orthogonal coordinates corresponding to the starting point at one radius of the polar coordinates, and is set from the outside for each radius r.

This switch 7<8) initially selects and outputs the switching terminal S (I!!l).The timing signal generator 4 simultaneously generates the timing signal XCLK-1 (YCLK), and initial values x, ( ys) into the X register 2 (Y register 6), the switch 7 (8) is immediately controlled to selectively output the switching terminal N side, and the conversion operation for the specified radius r is completed. to maintain the switching state.

The X registers 2, 3, and Y registers 6 each input and output data of a predetermined bit length in parallel. The X register 2 takes in the output (parallel data) of the switch 7 according to the timing signal XCLK-1 and outputs it in parallel as it is, but its output terminal corresponds to the input terminal of the However, the input terminal B of the adder 5 is connected to an output terminal of several bits corresponding to the output of the X register 2 shifted by a minute angle Δθ.

The X register 3 takes in the parallel output of the X register 2 according to the timing signal XCLK-2 and outputs it as an X coordinate value. Timing signal XCLK-2 is generated immediately following timing signal XCLK-1 when X register 2 outputs the initial value Xs, so X register 3 and Y register 6 output the initial value at approximately the same time. X,, same y
3 are output respectively.

The Y register 6 takes in the output (parallel data) of the switch 8 in accordance with the timing signal YCLK and outputs it in parallel as it is, and its output terminal is connected to the input terminal A of the adder 5 in a bit-corresponding manner. However, at the input terminal B of the adder 1, the output terminals of several bits corresponding to the output of the Y register 6 shifted by a minute angle Δθ are connected via the inverter 9, and "1" is A two's complement number is generated. In short, the adder 1 operates as a subtraction circuit.

Now, assume that the output of the X register 2 is the initial value xs, and the output of the Y register 6 is the initial value y. In adder 1, input terminal A receives the initial value X, and input terminal B receives the initial value y.
Since the complement of Δθ·y3 is generated by shifting 8 by a minute angle Δθ, X, −Δθ y6 is output to the output terminal Σ.

This is applied to the input terminal of the X register 2 via the switch 7. Therefore, the timing signal generator 4 generates the timing signal XCLK-1 after an appropriate time delay from the timing signal XCLK-2 output to cause the X register 3 to take in the initial value X. As a result, the contents of X register 2 change from the initial value x3 to the next new coordinate value x.
n(xゎ=X6−Δθ・ys). At this point, the Y register 6 is outputting the initial value y. The same applies to the X register 3.

Therefore, the input terminal A of the adder 5 has the initial value y.

is input, and input terminal B receives the new X coordinate value X. Since Δθ·xn, which is obtained by shifting Δθ by a minute angle Δθ, is directly input, Δθ·X n + 3′ s is output to the output terminal Σ. This is applied to the input terminal of the Y register 6 via the switch 8.

Therefore, the timing signal generator 4 simultaneously generates the timing signal XCLK-2 and the same YCLK at an appropriate time delay after the X register 2 outputs the coordinate value Xn. As a result, the X output of the X register 3 is X n (X
n '' Moving on to P n (X n, 3' n).

Next, since the output of the X register 2 is xo, the adder 1 applies the output terminal Σ with X, , -Δθ
3'n, the timing signal generator 4 outputs
The timing signal XCLK-1 is output at an appropriate time after the register 3 outputs Xn, and the output (X, ,
-Δθ·3' n -X n and 1) are taken into the X register 2. Then, the adder 5 sends ΔθX n+ + + 3' fi to the output terminal Σ according to the above procedure, so the timing signal generator 4 outputs the new coordinate value X114-1 at an appropriate time after the X register 2 outputs the new coordinate value X114-1. The timing signal XCLK-2 and the same YCLK are generated at the same time, and
New coordinate values x, 1, 3 in register 3 and Y register 6
Similarly, new coordinates can be obtained one after another by repeating the above operation. After completing the conversion operation for the entire circumference, for example, the initial value X corresponding to the new radius r+1,
+□, y, , +□ to switch terminal S to switch 7 (8)
The user selects the side and processes the next 360° rotation.

In this way, by repeatedly performing the above operations, the address of the orthogonal coordinate pixel corresponding to all the pixels of the polar coordinate display screen of a predetermined area defined by the polar coordinate signal is specified, and the polar coordinate signal is written into the orthogonal coordinate memory. I can do it.

Note that X register 3 is basically not necessary, but
This is provided for reasons such as making the output timing of the value and the Y value the same.

Next, FIG. 3 shows a laser scanning sonar using the coordinate converter of the present invention.

This color scanning sonar operates in synchronization with a timing signal output from a timing generator 15. First, the transmission signal generator 19 is connected to the timing generator 15.
In synchronization with the TX pulse from the sensor, a burst pulse of the frequency of an ultrasonic signal necessary for detecting a target such as a school of fish is generated.

This burst pulse is sent to the power amplifier 18, where the power is amplified to an output power that matches the detection capability, and sent to the transducer 11 via the automatic transmission/reception switch 12. This transducer 11 converts this electrical signal into ultrasonic vibrations and radiates them into, for example, seawater.

The emitted ultrasonic waves hit a target such as a school of fish, are reflected, and return to the transducer 11 again. Transducer/receiver 1
1 converts the returned ultrasonic signal from mechanical to electrical, and this electrical signal, ie, the received signal, is sent to the receiver 13 via the automatic transmission/reception switch 12 . The receiver 13 receives and processes the received signal scanned by the transducer 11 defined in polar coordinate format in accordance with the timing signal sent from the timing generator 15 to generate a predetermined polar coordinate signal. This is applied to the data input of the video memory 20, which is digitized by the A/D converter 14.

On the other hand, the timing generator 15 is connected to the range signal generator 17.
The coordinate converter 16 according to the present invention provides pulses and pulse trains necessary for generating a range signal corresponding to a predetermined received signal range.
The operating clock pulse CLK output from the range signal generator 17 and the range information output from the range signal generator 17 (the initial value
, roar), and the Cartesian coordinate address (
X, Y) and outputs it to the address switch 21 as a write address. Here, the initial value Y1 of Y is GN
Since it is connected to D, it is always O.

The range signal generator 17 generates the range value r immediately after transmission.
is output with X. The first value of X is usually O. Now, when the range value is rfi, rfi, which is the output of the range signal generator 17, is taken into the coordinate converter 16 as xs in synchronization with the clock pulse CLK, which is the output of the timing generator 15. This situation can be seen in the second
This will be explained using FIG. 4, which shows the diagram and the coordinate situation. In FIG. 2, the switch 7 (8) is connected to the switching terminal S side, and the X register 2 has r and I, and the Y register 6 has 0.
are taken in in synchronization with the timing signals XCLK-1 and YCLK, respectively, and immediately the switch 7 (8) is reconnected to the switching terminal N side. Thereafter, the clock pulse CLK input from the timing generator 15 in FIG.
The orthogonal coordinates (X, Y
) is calculated using equations (6) and (7), and a circle with radius rn as shown in FIG. 4 is drawn.

If all pixels in a 360° rotation can be drawn by rotational movement,
It returns to the starting point on the X-axis again, but at that time the range signal generator 17 has outputted a new range value r5+1.

At the starting point, rfi+1 is again taken as the value of x6 (y s = O), and by calculation of rotational movement, addresses are sequentially calculated from point pIl to point Pa+1 shown in FIG. 4.

Repeat the above operation and change the radius from 0 to R.
By changing the coordinates up to 1, the circle is filled in, and the corresponding orthogonal coordinate address (XY) is sent from the coordinate converter 16 to the address switch 21 as the write address of the video memory 20.

The address switcher 21 switches this write address and sends it to the video memory 20 while synchronizing with the read timing described later, and transfers the digital data sent from the A/D converter 14 to the address specified by this write address. Write. The video memory 20 is a memory arranged in orthogonal coordinates corresponding to the display.

25 is a raster scanning signal generator for raster scanning, such as in a television, which generates horizontal and vertical synchronizing signals HD and VD. As a result, the sweep signal generator 2
4 generates horizontal and vertical deflection signals to cause the CRT 23 to perform raster scanning.

In addition, in parallel with the above operation, the raster scanning signal generator 25 generates a reference pulse (the above-mentioned readout timing) which is a timing signal independent of the transmission/reception timing.
and generates a read address (X, Y) in synchronization with this,
It is output to the address switch 21 and its read address (X.

Y) Control the data to be sent to the video memory 20.

As a result, the received signal, which is a digital signal written on the video memory 20, is read out and sent to the D/A converter 22.

The signal converted into analog again by the D/A converter 22 is C
The information is sent to the RT 23 and displayed as brightness and color information in synchronization with raster scanning, so that the contents of the video memory 20 are displayed as an image.

The ultrasonic signals transmitted and received in this manner are displayed on a CRT as a scanning sonar image.

(Effect of the invention) As explained above, according to the coordinate converter of the present invention, 3
Since all processing is performed by rotational movement calculations without using angular functions, it is possible to eliminate the need for a large memory circuit to store data of trigonometric functions, and further reduces data storage capacity. The previously required high-speed multiplier is no longer necessary, and this has the effect of significantly reducing the circuit scale and lowering the cost.

In addition, since calculations are performed only by fixed additions and subtractions and digit shifts realized by wiring, calculation speed is extremely fast.
It also has the effect of being able to be used for images with high resolution, which is the case these days.

[Brief explanation of drawings]

FIG. 1 is a diagram explaining the principle of coordinate transformation of the present invention, FIG. 2 is a block diagram of the configuration of a coordinate transformer according to an embodiment of the present invention, and FIG.
The figure is a block diagram of the configuration of an application example device (color scanning sonar) of the present invention, and FIG.
An explanatory diagram of the state in which a circle is filled in by giving an initial value on the FIG. 3 is an explanatory diagram of the relationship between orthogonal coordinate pixels. 1.5...Adder, 2.3...X
Register, 4... Timing signal generator, 6
...Y register, 7.8...Switcher, 9...Inverter, 11...Transmitter/receiver, 12...Automatic transmission/reception Switch, 13...
...Receiver, 14...A/D converter 15...Timing generator, 16...
... Coordinate converter of the present invention, 17 ... Range signal generator that generates an initial value, 18 ... Power amplifier, 19 ... Transmission signal generator, 20
...Video memory (orthogonal coordinate memory 1, address switch, D/A converter, 3...Cathode ray tube (CRT) sweep signal generator, 5...Raster scanning signal generator.

Claims (1)

[Claims] A coordinate converter that obtains the values of orthogonal coordinates (X, Y) of a rectangular coordinate memory into which signals expressed in polar coordinates (r, θ) are written, as values for each minute angle Δθ on the circumference of the radius;
This coordinate converter includes a first switch that selects and outputs an initial value of the X-coordinate axis set externally and each subsequent X-coordinate value according to a switching signal; and stores the output of the first switch sequentially according to an X-coordinate axis timing signal. an X register with a predetermined bit length for outputting; a second switch for selectively outputting the initial value of the Y coordinate axis set externally and each subsequent Y coordinate value according to a switching signal; a Y register of a predetermined bit length that is sequentially stored and output according to a timing signal; and a complement of the output consisting of several bits corresponding to the output of the Y register shifted by the minute angle Δθ which is a constant value of a power of 2. a first adder that adds the output of the X register and the output of the X register to generate and output each of the X coordinate values; a second adder that adds the output of the input signal and the output of the Y register to generate and output each of the Y coordinate values; and a timing signal generation circuit that generates the switching signal and the various timing signals. A coordinate converter that takes