JPS62249285A - Rotation arithmetic unit - Google Patents

Abstract

PURPOSE:To execute processing at a high speed by storing the data of sintheta and costheta into a data memory and providing an arithmetic means to calculate a matrix for a rotation transformation. CONSTITUTION:A rotating arithmetic unit RC to execute the calculating processing of a transformation matrix to rotate and transform a graphic is composed of a data memory DM to store the value of a controller CONT and trigonometric functions sintheta and costheta [=sin(pi/2-theta)] for a prescribed angle from 0 deg. to 45 deg. for the value of theta and an arithmetic circuit OPE operated port code flag signals phisig1 and phisig2 under the control of the controller CONT. When rotation angle data alpha, beta and gamma are supplied to the rotation arithmetic unit RC, the controller CONT successively outputs an address signal Add respectively corresponding to the rotation angle data in accordance with a prescribed timing, the prescribed trigonometric function data are read from the data memory DM and the rotation transformation matrix is calculated by the arithmetic circuit OPE.

Description

DETAILED DESCRIPTION OF THE INVENTION [Field of Industrial Application] The present invention relates to a rotation arithmetic device, and relates to a technique that is effective when applied to, for example, graphic conversion in a computer graphics system.

[Prior art]

In computer graphics, which is a technology that uses computers to generate figures and images.

In order to display a desired image on an image output device such as a CRT display device, in a predetermined coordinate system, figure transformation processing such as scaling, translation, and rotation is performed on the reference figure or symbol to create the desired image. Composite figure data may be obtained.

By the way, 1.Normally, there are many constituent points of a figure.

In order to speed up graphic conversion processing such as scaling, parallel translation, and rotation multiple times, for example, 1 is described in R Microcomputer Handbook J P877, published by Ohmsha on December 25, 1985. As described above, it is possible to combine the respective transformation matrices necessary for all the transformation processes into one in advance, and then transform each data constituting the reference figure using the transformation matrix. Alternatively, the same graphic conversion process can be performed on different pixels in parallel using a plurality of element processors.

[Problem that the invention seeks to solve]

The inventor studied such graphic conversion processing and found that
When performing rotation calculations using a transformation matrix, data on trigonometric functions such as cosine and sine are required, unlike scaling and parallel diameter, and since the transformation matrix differs for each coordinate axis,
If we attempt to execute these rotational calculations using computer software alone, the conversion process will be delayed compared to conversion processes such as scaling and parallel diameter, making it impossible to speed up the shape conversion process as a whole. It has become clear that real-time display of single-image information will also be restricted.

SUMMARY OF THE INVENTION An object of the present invention is to provide a rotation arithmetic device that can quickly perform arithmetic processing on a transformation matrix for rotationally transforming a figure specified by figure data in a predetermined coordinate system.

The above and other objects and novel features of the present invention include:
It will become clear from the description of this specification and the accompanying drawings.

[Means for solving problems]

A brief overview of typical inventions disclosed in this application is as follows.

That is, for angle θ, sin θ and 5in(π/
2-θ) based on one rotation angle data, and a calculation means for calculating a rotation transformation matrix based on the trigonometric function data output from the data storage means. It is configured as follows.

[For production]

According to the above means, the sine and cosine data corresponding to the rotation angle data are simultaneously output and the calculation of the necessary rotation transformation matrix is performed by a dedicated calculation means, thereby reducing the size of the storage means and This is to achieve faster processing.

〔Example〕

FIG. 1 is a functional block diagram showing one embodiment of the rotation calculation device of the present invention, FIG. 2 is a functional block diagram of a graphic conversion processing device including the rotation calculation device, and FIG. 3 is a functional block diagram showing a graphic conversion processing device including the rotation calculation device. It is a system configuration diagram of computer graphics (hereinafter also simply referred to as graphics).

The system shown in FIG. 3 is a system that uses a computer to generate figures and images and displays the desired images on an image output device such as a CRT display device.
Although not particularly limited, it is a three-dimensional graphics system. In this system, the main memory MM coupled to the system bus SB is a central processing bag [stores various data necessary for executing instructions according to a CPU program, but especially graphic conversion for displaying images]. A variety of basic figure data are stored in which basic figures, which are the basis of the image, are defined in a predetermined coordinate system (hereinafter also simply referred to as a mask coordinate system). Such basic figure data is not particularly limited, but
This is data indicating positions corresponding to the edges of figures such as planes, hyperboloids, conical surfaces, spheres, cubes, cylinders, and ellipsoids. The image output device employed in the system is not particularly limited, but is
The image display control system of the RT display device Dis has a dual port that is connected to the system bus SB and can store image display data for each frame and serially supply the stored data to the CRT display device rliDis. frame buffer memory FBM,
and a CRT controller CRTC which performs address control of this frame buffer memory FBM and forms various synchronization signals such as a horizontal synchronization signal H8YNC for the CRT display device Dis.

In FIG. 3, the FC performs a predetermined graphic transformation on the basic graphic data based on an instruction for displaying an image given from an input device (not shown) and the basic graphic data read out from the main memory MM. This is a graphic conversion processing device that performs processing to generate image display data.

Here, although not particularly limited, one figure in this example refers to a three-dimensional pattern consisting of relatively simple elements consisting of lines and planes that are exclusively specified by position data, and also refers to one image. refers to a two-dimensional pattern specified by a data format that also has brightness and color.

The above figure conversion processing device l! As shown in FIG. 2, the FC reads necessary basic graphic data from the main memory MM based on an instruction for displaying an image given from an input device (not shown), and displays data based on the basic graphic data. A general-purpose logic circuit LOG is included that receives instructions for graphic conversion processing necessary to obtain a desired graphic. This general-purpose logic circuit LOG first masks a basic figure based on basic figure data and instructions for figure conversion processing (hereinafter also simply referred to as primitive data) supplied to the general-purpose logic circuit LOG, although there are no particular restrictions. Performs operations on a transformation matrix for scaling in the coordinate system and a transformation matrix for translating the basic figure in the mask coordinate system, and further performs rotation as described below to rotate the basic figure in the mask coordinate system. By combining each transformation matrix, including the transformation matrix, based on it, converting a given basic figure to the desired size and position in the mask coordinate system, and repeating the transformation process according to the hierarchical relationship of the figures. Figures are synthesized Next, the coordinate system of the transformed and synthesized figures is converted from the mask coordinate system to the desired world coordinate system.

In FIG. 2, RC is a rotation calculation device that calculates a transformation matrix for rotating the basic figure in the mask coordinate system, and when rotation of the basic figure is required, rotation angle data is obtained from the general-purpose logic circuit LOG. The arithmetic processing in the one-rotation arithmetic unit RC that supplies the transformation matrix computed based on the transformation matrix to the general-purpose logic circuit LOG is carried out in parallel with the transformation matrices for scaling and parallel movement being computed in the general-purpose logic circuit LOG. This is how it is done.

In FIG. 2, VC is a perspective conversion circuit that obtains a two-dimensional perspective view from three-dimensional graphic data whose coordinates have been transformed into the world coordinate system by the general-purpose logic circuit LOG, and thereby converts the three-dimensional graphic data into two-dimensional into a displayable form. The two-dimensional graphic data output from such perspective conversion circuit VC is as follows.

The image data generation unit PC converts the image data into image data having brightness, color, etc., and the image data is stored in a predetermined memory area of the frame buffer memory FBM under address control of the CRT controller CRTC.

Here, an example of a transformation matrix calculated by the general-purpose logic circuit LOG and rotation calculation device RC will be explained.

For example, the i-dimensional coordinates (xl,...,xi) are i+1
Graphical data is expressed by homogeneous coordinates represented by a dimensional vector [WXl...wxi w].

Graphical transformation in three-dimensional space can be calculated using equation (1).

[xm ym zm wm] = [xn
yn zn wnko×T・・・・・・・・・
...(1) In equation (1), [xn yn zn wnl is the basic figure data before figure conversion, which is X in the master coordinate system.

This is a position vector centered on the origin of the y and z coordinate axes.

In equation (1), [xm ym zrm wml
is the coordinate system X that masks the basic figure data after figure conversion.

'/l This is a position vector centered on the origin of the Z coordinate axis.

In equation (1), T is a transformation matrix with 4 rows and 4 columns, which is changed and set according to the contents of the graphic transformation, such as a translation transformation matrix Td, a scaling transformation matrix Ts, and a rotation transformation matrix Tr.

The translation transformation matrix Td is XwV in the mask coordinate system
When moving by Dx, Dy, and D2 in each direction of the eZ coordinate axis, it is expressed by a general equation such as equation (2).

(Lower margin) The scaling conversion matrix Ts is based on the origin of the master coordinate system and the magnification in the +x, y, and z axis directions is Sx.

Letting S y and S z be expressed by a general formula such as equation (3).

In a mask coordinate system such as a right-handed coordinate system, the rotation transformation matrix Tr is expressed as (4 ) to (6).

(The following is a blank space.) Next, details of the rotation calculation device RC will be explained with reference to FIG. 3.

The rotation calculation device RC serves as a data storage means capable of outputting cosine and sine data based on the rotation angle data α, β, and γ supplied from the general-purpose logic circuit LOG. It has a data memory DM such as a ROM (read-only memory) that can output data of sin (π/2-θ), which is data of QOIIθ, based on one rotation angle data. In particular, the data memory DM has sin θ and 8 in (π
/2-θ) are stored in pairs for each predetermined angle in the range from 0 degrees to 45 degrees.

Addressing to the data memory DM is based on rotation angle data α, β, γ supplied from the general-purpose logic circuit LOG.
This is performed based on the address signal Add output from the controller C0NT which receives the address signal Add. Data memory D
M has dual ports that can output sin θ and sin (π/2−θ) data stored in the same row in parallel according to the addressing.

Here, the controller C0NT sequentially outputs address signals Add corresponding to the rotation angle data α, β, and γ supplied thereto, according to predetermined timing. That is, when the rotation angle data is in the range of 0 degrees to 45 degrees, the data memory DM is addressed so as to select the data of θ which is conceptually equal to the rotation angle data.

As a result, sine data corresponding to θ is output from the first port Portl, and cosine data corresponding to θ is output from the second port Portl. in this case,
In order to indicate whether the output from both ports PORT and PORT is cosine data or sine data, an output port flag is set in a register (not shown) included in the controller C0NT. That is, when sine data is output from the first port Porti and cosine data is output from the second port Port, a flag such as a high level is set, and the level is set according to the state of the output port flag. An output port flag signal φPf is output. Furthermore, a first port code flag and a second port code flag for setting the code of data output from both ports Part and Port are set in a register (not shown) included in the controller C0NT. That is, when the sine and cosine corresponding to one rotation angle data are respectively positive, the first boat code flag and the second boat code flag are set to high level corresponding to the boat to which the sine and cosine data are to be output. is set, and the first and second levels of the flag are set according to the state of the flag.
The port code flag signal φsig, φsig, is output from 0 to 1 when it is included in the first quadrant, for example, when the rotation angle data is in the range of 0 degrees to 45 degrees. Both φsig and φsig are set to high level.

If the rotation angle data is in the range 45 degrees to 90 degrees, the data memory DM is addressed to select the data of O which is conceptually equal to (90 degrees - rotation angle data). 1st boat P according to
Cosine data is output from ort, and P is output from the second port.
Sine data is output from ort. In this case, contrary to the above, the output port flag will not be set, and the output port code flag will be set.

When the rotation angle data is in the range of 90 degrees to 135 degrees, the data memory DM is addressed to select data of θ which is conceptually equal to [rotation angle data of 90 degrees]. Thereby, the first boat P according to that θ
Sine data is output from ortl, cosine data is output from the second port, and an output port flag is set. Since the rotation angle data in this case is in the second quadrant, the first boat code flag is set and the second boat code flag is not set.

If the rotation angle data is in the range of 135 degrees to 180 degrees, θ is conceptually equal to [100 one rotation angle data]
The data memory DM is addressed to select the data of , the output port flag and the first port flag are not set, and the second port flag is set.

When the rotation angle data is in the third and fourth quadrants, the data memory DM is addressed in almost the same way as above, the output port flag is set accordingly, and the sine and cosine data in that angle range are A boat code flag is set according to the code.

Through such address control and flag control by the controller C0NT, θ is set at a predetermined value in the range of 0 degrees to 45 degrees so that data of sin θ and sin (π/2−θ) form a pair in each row of the memory area. A data memory DM with a small storage capacity that stores data for each angle.
Accordingly, arbitrary cosine and sine data in the first to fourth quadrants can be obtained simultaneously.

Cosine and sine data output from data memory DM, output boat flag signal φPf and port sign flag signal φsig output from controller C0NT, φ
sig is supplied to the arithmetic circuit OPE. Arithmetic circuit O
PE contains such cosine and sine data and various flag signals φ
Pft φli1gx * φsig.

The rotation transformation matrix shown in equations (4) to (6) above is calculated based on the rotation angle data α, β.

The calculations are performed in the order in which γ is supplied, and finally the rotation transformation matrices are combined into one, and the result is supplied to the general-purpose logic circuit LOG.

Next, the general-purpose logic circuit LOG and rotation calculation device!
An example of figure conversion operation by RC will be explained with reference to Fig. 4.0 For example, a cylinder 1 as a basic figure is translated, enlarged, and rotated, and synthesized into a cube 2 as a basic figure. To obtain the composite figure 3, first, the general-purpose logic circuit LOG performs calculations based on primitive data to obtain a translation transformation matrix according to equation (2) and an enlargement transformation matrix according to equation (3). In parallel, the one-rotation arithmetic unit RC performs (4) to (6).
An operation for obtaining a rotational transformation matrix according to the formula is performed based on the primitive data.Next, each of these transformation matrices is combined into one by a general-purpose logic circuit LOG, and a graphical transformation is performed on the cylindrical body 1, and further,
If there is no need to perform rotational transformation of a figure in which a composite figure 3 is obtained by a composite operation of the cylindrical body 4 after the conversion and the cube 2 as the basic figure, the rotation arithmetic unit RC is not operated;
Necessary graphical conversion is performed only by the general-purpose logic circuit LOG. Although Fig. 4 is a diagram in which land lines and shadow surfaces have been deleted, land line deletion and one-plane deletion are not performed in the actual basic figure conversion process, and these deletion processes are performed using the above-mentioned perspective. This can be performed during perspective conversion in the conversion circuit VC.

According to the above embodiment, the following effects can be obtained.

(1) A rotation calculation device RC, which is hardware dedicated to rotation conversion operations of basic figures, is provided, and the rotation calculation device RC
is operated via the general-purpose logic circuit LOG, the proportion of the arithmetic processing carried out by the computer software of the central processing unit 1 ICPU is reduced, and the calculation of the rotation transformation matrix can be performed at high speed.

(2) From the above effect, the number of steps required to develop computer software for converting one figure can be reduced.

(3) From the above effect (1), the rotation transformation matrix is calculated at high speed by the rotation calculation device in parallel with the calculation of the translation transformation matrix and the scaling transformation matrix in the general-purpose logic circuit, so such parallel processing This allows graphic conversion to be performed at high speed.

(4) Each row of the memory area has sinθ and 5in(π/
2-θ) data is stored in pairs for each predetermined angle in the range from 0 degrees to 45 degrees, and has a dual port that can output sine and cosine data based on one rotation angle data. Since output boat flag control and boat code flag control are performed by a controller C0NT that is equipped with a memory DM and addresses the data memory DM, arbitrary rotation angle data in the first to fourth quadrants can be controlled by an extremely small data memory DM. Cosine and sine data can be obtained simultaneously based on . Although the invention made by the present inventor has been specifically described above based on examples, the present invention is not limited to the above-mentioned examples, and can be modified in various ways without departing from the gist thereof.

For example, in the above embodiment, the basic figure is converted in a static state, but if the address control by the controller is performed by taking into consideration the rate of change of rotation angle data, it is possible to convert the figure in a dynamic state. Furthermore, it can be easily applied to applications such as expressing the movement locus of a basic figure by continuous surfaces or lines.

In addition, in the above embodiment, one set of data memory DM and arithmetic circuit OPE is provided to sequentially calculate rotation transformation matrices based on rotation angle and degree data α, β, and γ, but one rotation angle data α, β.

It is also possible to provide three sets of data memories DM and arithmetic circuits OPE for each γ to further reduce the total calculation time of the rotation transformation matrix. In this case, it is unavoidable that the rotation calculation device be larger than that of the above embodiment.

The configuration of the data memory is not limited to the configuration for miniaturization as in the above embodiment, but may also be configured to specifically hold cosine and sine data in pairs within the range of the first to fourth quadrants. In that case, output boat flag control and boat code flag control can be made unnecessary depending on the storage scale of the data.

In the above embodiment, a case has been described in which basic figure data, which is the basis of one figure conversion, is supplied from the main memory MM, but it is not limited to this, and it can be supplied from various figure input devices such as a light pen, tracker ball, joystick, etc. The image output device in the above embodiment is a rask scan type CRT display device, but it can also be configured to output various images and figures such as a random scan type display device, an x-y plotter, and a dot printer. It is possible to change the equipment.

In addition, the calculation method for one-figure transformation is not limited to the one using homogeneous coordinates as explained in the above embodiment, and any appropriate coordinate format can be adopted. In particular, if homogeneous coordinates are used, It is convenient for

In the above explanation, the invention made by the present invention was mainly applied to three-dimensional graphics, which is the background technical field, but the present invention is not limited thereto, and the present invention is not limited to two-dimensional graphics, CAD/CAM systems, etc. It can be applied to various graphics and image processing technologies such as , animation systems, remote sensing systems, and computed tomography.

The present invention can be applied at least to conditions where a figure is rotated.

〔Effect of the invention〕

A brief explanation of the effects obtained by typical inventions disclosed in this application is as follows.

In other words, sine and cosine data corresponding to one rotation angle data are simultaneously output from the data storage means, and the necessary rotation transformation matrix calculation is performed by a dedicated calculation means, thereby reducing the size of the data storage means and rotation calculation processing. It is possible to achieve faster speeds.

[Brief explanation of drawings]

FIG. 1 is a functional block diagram showing one embodiment of the rotation calculation device of the present invention, and FIG. 2 is a functional block diagram of a graphic conversion processing device including the rotation calculation device. FIG. 3 is a diagram showing the configuration of a computer graphics system including the graphic conversion processing device, and FIG. 4 is an explanatory diagram of the graphic conversion operation. CPU...Central processing unit, MM...Main memory,
FC...Graphic conversion processing device, LOG...General purpose logic circuit, RC...Rotation calculation device, VC...Perspective conversion circuit. PC...image data generation unit, C0NT...controller, DM...data memory, OPE...arithmetic circuit. Figure 3 Figure 4

Claims (1)

[Claims] 1. A rotation calculation device that calculates a transformation matrix for rotationally transforming a figure specified by figure data in a predetermined coordinate system, which outputs trigonometric function data based on rotation angle data. 1. A rotation arithmetic device comprising: a data storage means capable of performing rotational transformation, and an arithmetic means for calculating a rotation transformation matrix based on trigonometric function data output from the data storage means. 2. The rotation calculation device according to claim 1, wherein the storage means is configured to be able to output sine data and cosine data based on rotation angle data. 3. The storage means stores sin θ and s for the angle θ.
3. The rotation calculation device according to claim 2, having a dual port capable of outputting in(π/2−θ) data based on one rotation angle data.