SU1472902A1 - Coordinate converter - Google Patents

Abstract

The invention relates to digital computing and can be used as a peripheral processor in which a vector rotation operation is performed, and auxiliary calculations are performed in a central computer. The purpose of the invention is to expand the class of tasks to be solved due to the possibility of arbitrarily setting the resulting axis of rotation of the vector. For this, three registers and six multipliers are entered into the device. In this case, the vector is simultaneously rotated around three axes, and the rotation steps around each of the axes are different. As a result, an effective solution of the problems described by the mathematical apparatus of quaternions is achieved. 2 Il.

Description

This invention relates to digital computing and can be used as a peripheral processor.

The purpose of the invention is to expand the class of tasks to be solved due to the possibility of arbitrarily setting the resulting axis of rotation of the vector.

FIG. 1 shows a functional diagram of the device; in fig. 2 shows an embodiment of the control unit.

The device contains registers 1-6, adders-subtractors 7-12, multiplication blocks 13-18, decoder 19, counter 20, control block 21, inputs 22X1 Xcfc + c (l-cos0) (o (X + Y - Ycosfi + ( i (i -co80) (p / X + Z1 ZcosQ +3 (1-cos0) (ofX +

24 setting the device coordinates, inputs 25-27 setting the rotation steps at the corresponding device angles, input 28 setting the device angle, rotating direction sign input 29, device starting input 30, device coordinate outputs 31-33, conversion conversion output 34. The control unit 21 contains triggers 35-37 of the signs of the direction cosines, the HE element 38, the AND elements 39-47.

The device operates according to the following algorithm.

Quaternion transformation

/ 3 Y + j-Z) + (pZ - Yjsine, pY + yZ) + (} - X-of Z) sin6 (1) / JY + f Z) + (c (Y -p X) sin6

3 - 1472902

performed by rotating the vector

R (X, Y, Z) in accordance with the algorithm

X- + AJ (Y | dj-A /}, i,, (2) Z,, W, Л

Y,

- coordinates of the vector X, Y, Z, expanded

around the axis of rotation by angle b)

L p

2 - single components

the vector defining the axis of rotation so that o (+ + pr + y2 1.

In algorithm (2), the rotation steps around the axes of the rectangular coordinate system are

yo (

2-m

AR

And signt /, Lr sign /}, L, "sign j (4)

The rotation is performed in a rotation block of a vector formed by registers 1-6, subtractors 7-12 and multiplication blocks 13-18. The development of the angle 0 is carried out according to the algorithm

E ;,

0; -2

Mm - v (5)

The device works as follows.

Before the beginning of the calculations, the coordinates 1-3, the coordinates X, Y, Z are added to the registers (which are the initial data for the algorithm (2), the registers are the rotation steps to /, ampf, Du, the counter 20 is the angle of the control unit 21 (at input 29) the signs of the direction cosines of the axis of rotation (4). The information on the inputs 22-29 is accompanied by the corresponding gates.

According to the start signal of the calculations, coming in at input 30, in block 21, control signals are generated for registers 1-3, which are used to record the next approximations Xf, X, - + 1, Z, - +. ,, and control signals operation modes of the 12-12 / V, L, /, subtractors / | "In blocks 13–18 of the multiplication, the partial products of Y, - dj, X t -4,

. X.-d / Ь, Zj d / 3, Zpdo (HY, respectively. On the subtractor 7, the quantity S {+1 X, - + +) is calculated, and on the subtractor 10 - the coordinate X +1 S; + i -ApZj-dp, written in register I, - Similarly, on adders-subtractors 8, And and 9, 12 coordinates Y; -MH + i are recorded in registers 2 and 3, respectively

2 t- / 3

.-t

Du-2-7, (3)

0

five

thirty

five

40

five

0

five

, t

venno. In each iteration in the control unit 21, a pulse is generated corresponding to the angular quantum 2 and fed to the input counter 20, which is used to calculate the next approximation of the angle (5). After working off, the angle (Sftt + i 0) converts the decoder i9, the signal of which stops the generation of counting pulses, the operators D / L, L-ji, the synchronization signals of registers 1–3, and an input signal for the end of transmutation is set at input 34. Calculations end. The coordinates of the unwrapped vector x X f + t Y Yf41 Z are taken from the outputs 31-33.

The control unit 2 can be executed according to the scheme shown in FIG. 2. Before starting the calculations, the triggers 35-37 record (at input 29) the signs of the direction of rotation. An element is supplied to the HE 38 by a signal from the decoder 19, which appears when the contents of counter 20 are zero, i.e. after the end of the vector reversal. In the absence of this signal, the element 38 prepares the element AND 45, the second input of which (input 30) receives the signal to start the calculations. This signal opens the element 45 and the elements 39 and 40 generate signals ± / (, on the elements And 43, 44 - ± AI, on the elements And 45, 46 - + A These signals are produced in accordance with expressions (4) and are the signals for setting the operation modes of the adders-7 7 2 (the third output of the control unit 21 ). Simultaneously on

five

element 46 produces synchronization signals of registers 1-3 (second output of control unit 21) and counting pulses 2 (first output of control unit 21). The second inputs of the elements 46, 47 (input 30) are pulses corresponding to the moments of the recording of the coordinates X; +1, Y $ + 1TU Z | +1 in the registers I-3 and switching t of the counter 20. After the calculation is finished, The signal 34 should be removed, the signal of the beginning of the calculations, coming at the input 30 to the element 45.

Claims (1)

/ Invention Formula A coordinate conversion device containing first to third registers, a decoder, a control unit, a counter, and first to sixth binders, with the outputs of the first, second, and third registers connected to the inputs of the first operands of the first, second, and third addressers, respectively. The outputs of which are connected to the inputs of the first operands, respectively, of the fourth, fifth, and sixth adders-subtractors, the outputs of which are the outputs of the device coordinates and are connected to the first inputs of the corresponding first, second and third registers, Ko tTopbix second inputs are inputs coordinate specifying device, the input specifying the angle of which is connected to the data input of the counter, the first and second inputs of the control unit respectively connected to inputs of the sign naprav9026 rotate and start the device, and the third input is with the output of the decoder, the input of which is connected to the output of the counter, the input of which is connected to the first output of the control unit, the second and third outputs of which are connected to the synchronization inputs of the first, second and third registers and job inputs modes of adders-subtractors, respectively, and the fourth output of the control unit is the output of the termination signal, device conversion, which is so that, in order to expand the class of tasks to These arbitrary assignment of the resulting axis are the rotations of the vector, four to sixth registers and six multiplication blocks are entered into it, the outputs of which are connected to the inputs of the second operands of the same subtractors, the output of the fourth register is connected to the first inputs of the first and second multiplication blocks, the register is connected to the first inputs of the third and fourth multiplication blocks, the output of the sixth register - with the first inputs of the fifth and sixth multiplication blocks, the outputs of the first, second and third registers are connected respectively to the combined in pairs of the second inputs of the second and third, first and sixth, fourth and fifth multiplication blocks, the inputs of the fourth, fifth and sixth registers are connected with the inputs of the steps of rotation for the corresponding corners of the device.