JP3479184B2 - Image generation method and image generation device - Google Patents

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an image generating apparatus applied to, for example, three-dimensional computer graphics, and more particularly to drawing a curved surface.

[0002]

2. Description of the Related Art In three-dimensional computer graphics, an object is displayed as a set of many polygons (eg, polygons such as triangles and quadrangles). For this reason, in an image generation device applied to three-dimensional computer graphics, in order to more naturally express the curved surface portion of an image including a curved surface, a large number of fine polygons are generated to draw the image. Should be generated.

However, in order to store the vertex coordinate data of a large number of polygons, a large-capacity memory is required, and when the memory capacity is limited as in a game machine, the size of the polygons is large. Is large, and it is difficult to represent a finely curved surface.

Therefore, conventionally, a method of expressing a shape of a curved surface or the like by combining a spline function and the like, and storing only the data of the control points that determine the curved surface instead of the vertex coordinates of the polygon in the memory to save the memory. Is used.

However, this method must generate a spline function, which is a multidimensional function such as three-dimensional, at high speed, and requires a large number of multiply-add calculators. For this reason, the hardware configuration becomes complicated, and when it is made into an LSI, the chip area becomes large and the cost becomes high.

In order to avoid such a problem, a method of using a function such as a Bezier surface which can easily divide a curved surface is generally used as a spline function for expressing the curved surface.

[0007]

However, when drawing is performed using a Beze surface, the usable spline function is limited, so that the shape of the curved surface that can be expressed is limited and can be expressed with a small amount of data. There was a limit to the shape of the curved surface.

In view of the above points, the present invention uses simple hardware, has no limitation on the spline function used for expressing a curved surface, and draws a smooth curved surface at a high speed with a small amount of data. An object of the present invention is to provide an image generation method and an image generation device that can perform the image generation.

[0009]

In order to solve the above problems, the image generating method according to the present invention uses control point data for determining the shape of a curved surface expressed by using an nth-order spline function. In the method of generating an image of the curved surface by using the initial value data obtained by processing the data of the control point, and the information of the dividing step when dividing the curved surface is given to the differential analyzer, Based on the first step of initializing the analyzer, the second step of obtaining the value of the spline function for each division step from the differential analyzer, and the value of the spline function obtained in the second step. And a third step of generating information on each division plane when the curved surface is divided in the dividing step, to generate an image of the curved surface.

The image generating apparatus according to the present invention further comprises a function generator including a differential analyzer, polygon dividing means,
Conversion means for converting the polygon data from the polygon dividing means into data for displaying the polygon data, and the polygon dividing means determines the shape of the curved surface represented by using an n-th order spline function. Initial value data obtained by processing the control point data of
Information on the size of the division step when dividing the curved surface is given to the function generator, the value of the spline function for each division step obtained from the function generator is acquired, and based on the obtained value. Then, polygon data of each division plane when the curved surface is divided in the dividing step is generated.

In the present invention having the above-mentioned structure, the data of the control points for determining the shape of the curved surface is processed in the function generator composed of the differential analyzer which can be formed by using a plurality of adders. Given the initial value data obtained by and the information of the size of the dividing step when dividing the curved surface, the value of the spline function for each dividing step, which is obtained by dividing the curved surface to be drawn from this function generator. Is obtained.

Then, from the value of the spline function for each division step, polygon data of each division plane when the curved surface represented by the spline function is divided is generated. If this polygon data is converted into, for example, polygon vertex coordinate data for display, a curved surface is drawn.

[0013]

BEST MODE FOR CARRYING OUT THE INVENTION A case in which an embodiment of an image generating method and an image generating apparatus according to the present invention is applied to a game machine will be described below with reference to the drawings.

FIG. 3 shows an example of the configuration of an image generating apparatus according to an embodiment of the present invention, which is an example of a game machine having a 3D graphics function and a moving image reproducing function.

FIG. 4 shows the appearance of the game machine of this example. The game machine of this example comprises a game machine body 1 and a control pad 2 which constitutes an operation input section for the user. The control pad 2 is connected to the game machine body 1 by coupling a connector plug 4 attached to the tip of a cable 3 connected to the control pad 2 to a connector jack 5A of the game machine body 1. . In this example, two connector jacks 5A and 5B are provided on the game machine main body 1 so that the two control pads 2 can be connected to the game machine main body 1 for so-called competitive games and the like. ing.

In the game machine of this example, a game can be enjoyed by loading the CD-ROM disk 6 in which the game program and image data are written into the game machine body 1.

Next, the configuration of the image generating apparatus of this example will be described with reference to FIG. The game machine as the image generation apparatus of this example includes a main bus 10 and a sub-bus 2.
It has a configuration including two system buses consisting of 0 and 0. Data exchange between the main bus 1 and the sub bus 2 is controlled by the bus controller 30.

The main CP is connected to the main bus 10.
The U11, the main memory 12, the image decompression unit 13, the preprocessing unit 14, the drawing processing unit 15, and the main DMA controller 16 (hereinafter referred to as the main DMAC) are connected. A processing memory 17 is connected to the drawing processing unit 15, and the drawing processing unit 15 includes a so-called frame memory for display data and a D / A conversion circuit. The signal is output to the video output terminal 18. Although not shown, this video output terminal 18 is connected to, for example, a CRT display as a display device.

On the sub bus 20, a sub CPU 21, a sub memory 22, a boot ROM 23, a sub DMA controller 24, a voice processing processor 25, an input unit 26, a CD-ROM decoder 27, and an expansion unit. The communication interface unit 28 is connected. Boot ROM
23 stores a program for starting up as a game machine. A voice processing memory 25M is connected to the voice processing processor 25. The voice processing processor 25 is a D / A
A conversion circuit is provided, and an analog audio signal is output from the audio output terminal 29.

The CD-ROM decoder 27 has a C
The CD-RO is connected to the D-ROM driver 40.
An application program (for example, a game program) or data recorded on the CD-ROM disc 6 loaded in the M driver 40 is decoded. CD-R
The OM disk 6 has, for example, a discrete cosine transform (DC
Image data of a moving image or a still image compressed by T) and image data of a texture image for modifying polygons are also recorded.

The application program of the CD-ROM disc 6 includes a polygon drawing command,
In the case of a curved surface, data for specifying the spline function to be used and control point data for determining the curved surface are stored in this CD-ROM 31. As will be described later, instead of the control point data, data suitable for the initialization data to be given to the spline function generator composed of the differential analyzer may be stored.

The input section 26 includes the control pad 2 as the operation input means described above, a video signal input terminal, and an audio signal input terminal.

The main CPU 11 manages and controls each unit on the main bus 10 side. Also, this main CP
U11 performs a part of the processing when drawing an object as a collection of many polygons. As will be described later, the main CPU 11 creates an example of drawing commands for creating a drawing image for one screen on the main memory 12.

The main CPU 11 has a cache memory 11M, and a part of the CPU instructions can be executed without fetching from the main bus 10. Further, the main CPU 11 is provided with a coordinate calculation unit 11G as a CPU internal coprocessor for performing coordinate conversion calculation for polygons when creating a drawing command. The coordinate calculation unit 11G performs calculation of three-dimensional coordinate conversion and conversion from three-dimensional to two-dimensional on the display screen.

As described above, since the main CPU 11 has the instruction cache 11M and the coordinate calculation unit 11G inside, the main CPU 11 can perform its processing to some extent without using the main bus 10. Easy to open 10.

The main memory 12 has a memory area for compressed image data and a memory area for expanded image data subjected to expansion decoding processing for moving image and still image image data. Further, the main memory 12 includes a memory area for graphics data such as a drawing command string (this is called a packet buffer). This packet buffer is used to set a drawing command sequence by the main CPU 11,
It is used to transfer the drawing command sequence to the drawing processing unit.

The image decompression unit 13 decompresses the compressed image data reproduced from the CD-ROM disk 6, and includes hardware such as a Huffman code decoder, an inverse quantization circuit, and an inverse discrete cosine transform circuit. Prepare The main CPU 11 may perform the processing of the Huffman code decoder as software.

The drawing processing section 15 executes the drawing command transferred from the main memory 12 and writes the result in the frame memory. The image data read from the frame memory is sent to the video output terminal 1 via the D / A converter.
8 and is displayed on the screen of the image monitor device.

The pre-processing section 14 is constituted by a processor having a CPU, and can share a part of the processing of the main CPU 11. In the case of this example, as described later, the pre-processing unit 14 is configured to perform the image generation processing on the curved surface.
In this case, the preprocessing unit 14 also performs the curved surface dividing process and the process of converting a large number of polygon data obtained by the dividing process into two-dimensional coordinate data for display.

The basic processing of this game machine will be described below.

[Acquisition of Data from CD-ROM Disc 6] When the power of the game machine shown in FIG. 3 is turned on and the game machine body 1 is loaded with the CD-ROM disc 6,
The program of the so-called initialization process for executing the game in the boot ROM 23 is the sub CPU 21.
Executed by. Then, the record data of the CD-ROM disc 6 is taken in as follows.

That is, from the CD-ROM disc 6,
The compressed image data, the drawing command, and the program executed by the main CPU 11 are the CD-ROM driver 40 and the CD-ROM driver.
The sub DMAC is read out via the ROM decoder 27.
It is temporarily loaded into the sub memory 22 by 24.

The data taken into the sub memory 22 is stored in the sub DMAC and the bus controller 3.
0, and further transferred to the main memory 12 by the main DMAC 16. Note that the sub CPU 21 is configured to be able to directly access the frame of the drawing processing unit 15, and this sub CPU 21 can also change the content of the display image apart from the control of the drawing processing unit 15. It is said that.

[Expansion and Transfer of Compressed Image Data] Of the input data of the main memory 12, the compressed image data, in this example, is processed by the main CPU 11 after decoding the Huffman code, and then the main CPU 11 again performs the main memory 12. Written in. And the main DMAC16
Transfers the image data after the decoding processing of this Huffman code from the main memory 12 to the image expansion unit 13. The image decompression unit 13 performs dequantization processing and inverse DCT processing to decompress and decode image data. The main DMAC 16 stores the expanded image data in the main memory 1
Transfer to 2.

The main CPU 11 transfers the decompressed data to the frame memory of the drawing processing unit 15 when a certain amount of unit data called a macroblock of the decompressed image data is accumulated in the main memory 12. At this time, if the decompressed image data is transferred to the image memory area of the frame memory, it is displayed as it is on the image monitor device as a background moving image. It may also be transferred to the texture area of the frame memory. The image data of this texture region is used as a texture image for modifying a polygon.

[Processing and Transfer of Drawing Command Sequence] The polygons forming the surface of the object are drawn in order from the polygon at the deep position in the depth direction according to the Z data which is the three-dimensional depth information. Images can be three-dimensionally displayed on the three-dimensional image display surface. Main CPU1
1 creates a drawing command sequence in the main memory 12 so that the drawing processing unit 15 draws in order from the polygons at the deep positions in the depth direction.

The main CPU 11 calculates the movements of the object and the viewpoint based on the user's operation input from the control pad of the input unit 26, and creates a polygon drawing command sequence on the main memory 12.

When this drawing command sequence is completed, the main DM
The AC 16 transfers the drawing command from the main memory 12 to the drawing processing unit 15 through the preprocessing unit 14. At this time, in the pre-processing unit 14, curved surface data is subjected to curved surface division calculation and polygon generation processing, which will be described later.

The drawing processing unit 15 sequentially executes the received data and stores the result in the drawing area of the frame memory. At the time of this polygon drawing, the data is sent to the gradient calculation unit of the drawing processing unit 15 and the gradient calculation is performed. The gradient calculation is a calculation for obtaining the inclination of the plane of the mapping data when filling the inside of the polygon with the mapping data in drawing the polygon. In the case of texture, polygons are filled with texture image data,
In the case of Gouraud shading, the polygon is filled with the brightness value.

Furthermore, the texture of a moving image is possible.
That is, in the case of a moving image texture, as described above, the compressed moving image data from the CD-ROM disc is once read into the main memory 12. And
This compressed image data is sent to the image decompression unit 13. The image expansion unit 13 expands the image data. At this time,
As described above, part of the decompression processing is performed by the main CPU 11
Will be borne.

The decompressed moving image data is sent to the texture area on the frame memory of the drawing processing section 15. Since the texture area is provided in the frame memory of the drawing processing unit 15, the texture pattern itself can be rewritten for each frame.
In this way, when a moving image is sent to the texture area, the texture is dynamically rewritten and changed every frame. The texture of the moving image is realized by performing the texture mapping on the polygon by the moving image in the texture area.

[Explanation of Curved Surface Drawing Process] FIG. 1 is a diagram showing a configuration of a main part of the preprocessing unit 14 and the drawing processing unit 15 for the curved surface drawing process.

As shown in FIG. 1, the preprocessing unit 14 is
Polygon dividing means 141 and spline function generator 14
2 and coordinate conversion means 143. The polygon dividing means 141 and the coordinate converting means 143 show the functions of the preprocessing unit in the case of the curve drawing processing as blocks. The spline function generator 142 is composed of a differential analyzer composed of a plurality of adders as described later.

The drawing processing section 15 comprises a drawing means 151 as a functional means and a frame memory 152.

In the case of curved surface drawing processing, the controller point data of the curved surface is transferred from the main memory 12 to the preprocessing section 14 in this example. The polygon dividing means 141 processes the data of the controller points to generate initialization data to be supplied to the spline function generator 142. Also, the polygon dividing means 141
In advance, the size of the dividing step when dividing the curved surface to be drawn is determined in advance. Then, the generated initialization data and the information about the size of the division step are given to the spline function generator 142, and the spline function generator 142 is initialized.

The spline function generator 142 performs a function calculation process using the initialization data as a starting point. Then, the spline function value for each division step is generated. The generated spline function value is read by the polygon dividing unit 141.

The polygon dividing means 141 is based on the spline function value read from the spline function generator 142, and divides the curved surface to be drawn in the above dividing step into polygons, for example, quadrangular polygons of a divided plane. Generate data. The polygon data of each divided plane is sent to the coordinate conversion means 143. The coordinate conversion means 143 converts this polygon data into two-dimensional vertex data of a screen coordinate system suitable for a CRT display as a display device, and sends it to the drawing means 151.

The drawing means 151 fills the plane on the basis of the received two-dimensional vertex data, and if necessary, the image data which has been subjected to the processing such as shading based on the brightness value obtained from the texture and the light source calculation. Write to the frame memory 152. The data in the frame memory 152 is appropriately read, D / A converted, and supplied from the video output terminal 18 to a CRT display as an image monitor device to display an image including a curved surface.

Next, the curved surface drawing processing described above will be further described.

FIG. 2 shows an example of one curved surface to be drawn. In FIG. 2, u and v are parameter coordinates relating to the curved surface, and are assumed to increase along the curved surface in the directions of the arrows as shown in FIG. Q
(U, v) are points on this curved surface and are three-dimensional vectors. Now, consider a curved surface using a cubic spline function, and if the control point of this curved surface is a three-dimensional vector Pij, the point Q (u, v) on the u, v curved surface is expressed by the equation (eq1) in FIG. expressed.

In this equation (eq1), Bi (u), Bj
(V) is a third-order spline function, Bi (u) is represented by the equation (eq2) in FIG. 5, and Bj (v) is represented by the equation (eq3) in FIG.

Then, when the equation (eq1) of FIG. 5 is modified, it becomes the equation (eq4) of FIG. However, Sk (v) of the equation (eq4) is a spline function represented by the equation (eq5) of FIG. 5, and is a three-dimensional vector. The coefficient Rkl of the term of each degree of v in the equation (eq5) is the equation (eq6) in FIG. 5, which is also a three-dimensional vector.

From the above, when the three-dimensional vector Rkl represented by the equation (eq6) is obtained, the three-dimensional vector Sk (v) represented by the equation (eq5) is obtained, and the point Q (u, v ) Will be required. In the equation (eq6), akj and alj are values determined if the spline function is determined, and the CD-ROM disc 6 specifies the spline function determining the curved surface in addition to the control point data as the curved surface data. It is stored as information for doing.

Therefore, now, G curved surfaces in the u direction, v
If it is equally divided into H pieces in the direction, the vertices of the division plane obtained by each division can be obtained by the algorithm described below. This algorithm will be described with reference to the flowcharts of FIGS. 6 and 7.

First, in step S1, the expression (eq
From 6), for k, lε {0,1,2,3}, from the three-dimensional vector Pij of the control point,
Obtain the dimension vector Rkl. In this way,
Instead of obtaining the three-dimensional vector Rkl by calculation,
Instead of the control point data, this three-dimensional vector Rkl is used as the curved surface data in advance on the CD-ROM.
It may be stored in the disk 6 and read directly from the CD-ROM disk 6.

When step S1 ends, step S2
In this example, G curved surfaces in the u direction and H curved surfaces in the v direction.
The division step widths Δu and Δv in the u direction and the v direction when equally dividing into
Set as H.

Next, in step S3, kε {0,
Each cubic spline function Sk for 1, 2, 3}
In the function generator of (v), the division step width Δv in the v direction is
Then, the three-dimensional vector Rkl is passed to initialize the spline function generator. That is, at this time,
The spline function generator 112 uses the spline function Sk
It functions as a function generator of (v).

Then, in the next step S4, the value of v is set to 0 and the step number r _v of the v direction is repeatedly set to 0, and then the following processing in the v direction is repeated only r _v = H times. . That is, in step S5,
It is determined whether or not r _v = H times of processing in the v direction is completed, and if not completed, the process proceeds to step S6.

In step S6, the function generator 112
, The current three-dimensional vector Sk (v) is obtained, and the obtained Sk (v) and the division step width Δu in the u direction are used as initialization data for the function generator of the spline function Q (u, v). Pass to initialize this spline function generator. That is, at this time, the spline function generator 112 works as a function generator of the spline function Q (u, v).

[0060] Then, at the next step S7, after the initial setting value of u 0, u direction of repetition of the number of steps r _u 0, the following process in the u direction r _{u =} only G times, repeated . That is, in step 85,
It is determined whether or not the processing of _u = G times in the u direction is completed, and if not completed, the process proceeds to step S9.

In step S9, the current value of the spline function Q (u, v) is obtained, and that value is output to the polygon dividing means 141. Then, in step S10, u
Is increased by the division step width Δu, and the number of times _{u u} of the repeated steps is incremented by 1. Then, the processes of steps S8 to S10 are repeated, and at the next division step in the u direction,
The value of the spline function Q (u, v) is obtained, and the value is output to the polygon dividing means 141.

The processing of steps S8 to S10 is
When the values of the spline function Q (u, v) for all the dividing steps in the u direction at one dividing step in the v direction are obtained by repeating _ru = G times, the process proceeds from step S8 to step S11. Then, the value of v is increased by the division step Δv, and the number of repeated steps r _v in the v direction is incremented by 1. Then, the processing after step S5 is repeated. This allows
Spline function Q (u, v) for all division step points in the u direction for each division step point in the v direction
Value is obtained, and the value is sent to the polygon dividing means 141.

When the iterative process is performed as described above and it is determined in step S5 that the number of repeated steps in the v direction is r _v = H, the process proceeds from step S5 to step S12, and the polygon division is performed. Means 1
The reference numeral 41 creates G × H quadrilateral polygons based on the stored values of the spline function Q (u, v) for each division step point, and sends them to the coordinate conversion means 143.

The coordinate transformation means 143, as described above,
The drawing processing unit 15 converts the data of the quadrilateral polygon into the two-dimensional vertex data to be displayed on the CRT display.
Send to. Based on this, the drawing processing unit 15 executes the above-described drawing processing, and the curved surface image is displayed on the screen of the CRT display.

Although three-dimensional vectors are dealt with in the above algorithm, it is possible to extend to a four-dimensional vector system of simultaneous coordinate system by a similar method. Further, in the above-described algorithm, after obtaining all the values of the spline function Q (u, v) for each of the division step widths Δu and Δv, G × H quadrangular polygons are created, and this is converted into the coordinate conversion means 143.
However, when the spline function Q (u, v) is obtained in step S9, the polygon dividing means 141 creates a corresponding quadrangular polygon and outputs it to the coordinate converting means 143. May be.

As described above, the information for specifying the spline function of the curved surface and the data of the control points of the curved surface are not stored in the CD-ROM disc 6, but instead of the data of the control points. , The information suitable for the initialization data of the spline function generator, for example, the three-dimensional vector Rkl in the above example, CD-
If it is stored in the ROM disk 6, the calculation time of the above-mentioned calculation algorithm can be shortened.

The spline function generator 142 is constructed by using a differential analyzer as described above, but in the case of calculating a three-dimensional vector value as in the case of the above-mentioned algorithm, It can be configured using three types of differential analyzers. FIG. 8 shows the spline function generator 14 for calculating a three-dimensional vector value in this way.
2 shows an example of the configuration of No. 2.

In this example, the spline function generator 142 is composed of three adders A1 and A constituting a differential analyzer.
2, A3 and 4 buses B0, B1, B2, B3 and 4
The register banks BANK0, BANK1, BANK2 and BANK3 are provided.

Then, generalizing the explanation, i (i∈
The {0, 1, 2, 3}) th bus Bi is connected to the ith register bank BANKi. i-th adder A
The two input terminals of i are the (i-1) th bus B (i-
1) and the i-th bus Bi. The output terminal of the i-th adder Ai is connected to the i-th bus Bi.

If there is a register RAi in the register bank BANKi, the adder Ai is
Read data from A (i-1) and register RAi,
The operation of writing the addition result in the register RAi is performed.

Here, the cubic spline function for u for each division step width Δu is as shown in FIG.
It is obtained from the spline function generator 142 having the following configuration.

In this case, the initial value as shown in FIG. 9A is written in the register RAi of each register bank BANKi. As can be seen from FIG. 9A, this initial value is
The division step width Δu is included. It should be noted that, as described above, the size of Δu is determined by the number of divisions in the case of equal division, and the number of divisions is input by the user,
It is set by the setting based on the information stored in the CD-ROM disc 6, and is not fixed. Of course, the curved surface may not be equally divided.

After the initial value is set in the register RAi of each register bank BANKi in this way, the adders A1 and A
When the additions by 2 and A3 are executed at the same time, the content of the register RAi of each register bank BANKi changes as shown in FIG. 9B depending on the number of executions. As can be seen from FIG. 9B, when the additions by the adders A1, A2 and A3 are simultaneously executed three times in this example, the value of the cubic spline function is obtained in the register RA3.

In this way, the adder A is used a predetermined number of times r times.
When the additions by 1, A2 and A3 are executed at the same time, a. (R.Δu) ³ + b · (r · Δu) ² + c · (r ·
Δu) + d is stored. That is, the division step width Δ
For each u, a cubic spline function for u is available in register RA3. Therefore, each division step width Δu
The value of the register RA3 after the simultaneous execution of addition by the adders A1, A2, and A3 for each time is set as the output of the spline function generator 142, so that the spline function of each division step in the above-described algorithm is The value is given to the polygon dividing means 141.

A function generator for generating an nth-order spline function of the third order or higher is obtained by the same method as described above by configuring the function generator with a differential analyzer using n adders. You can

FIG. 10 shows an embodiment of the spline function generator 142 in that case. The spline function generator 142 of this example includes the adders A1 and A1 in addition to the configuration of FIG.
Switch circuits SW1, SW2, SW on the output side of A2, A3
3 is provided. The switch circuit SWi provided on the output side of the i-th adder Ai outputs the output of the i-th adder Ai to the (i-1) -th bus B (i-1) or i.
The second bus Bi is configured to be selectively switched and connected. These switch circuits SW1 to S
W3 is switched and controlled by a control means (not shown) in the spline function generator 142.

For example, in the case of the sixth-order spline function generator, each register bank BANK0, BANK1, BANK2, BANK
3, the following registers are provided. BANK0: RA0, RA6 BANK1: RA1, RA5 BANK2: RA2, RA4 BANK3: RA3.

The switch circuits SW1, SW2, S
W3 is all in the state shown in the figure, that is, the i-th adder Ai
When the output of is connected to the i-th bus Bi, the respective adders A1, A2 and A3 simultaneously perform the following calculations, and the calculation results correspond to each other as indicated by the arrow. Store in register. RA3 ← RA2 + RA3 RA2 ← RA1 + RA2 RA1 ← RA0 + RA1.

The switch circuits SW1, SW2, SW
When all 3 are set in a state opposite to that in the figure, that is, when the output of the i-th adder Ai is connected to the (i-1) -th bus B (i-1), the respective adders A1, A
2, A3 simultaneously perform the following calculations, and store the calculation results in the corresponding registers as indicated by the arrows. RA6 ← RA6 + RA5 RA5 ← RA5 + RA4 RA4 ← RA4 + RA3.

In the spline function generator 142 having the above configuration, appropriate initial values RA0, RA1,
..., by setting RA6 in advance, the switch circuit S
By executing the calculation performed by switching W1 to SW3 alternately r times, a. (R.Δu) ⁶ + b · (r · Δu) ⁵ + c · (r ·
Δu) ⁴ + d · (r · Δu) ³ + e · (r · Δu) ² +
The value of the 6th-order spline function represented by f · (r · Δu) + g can be obtained.

If the above calculation is further expanded, it is possible to realize a function generator which efficiently calculates a high-order spline function of 2 m or higher without increasing the number of adders. Therefore, it is possible to configure a function generator that can efficiently obtain a high-order spline function with a small number of adders.

In the above example, the polygon dividing means 141
Is 3 from the control point data Pij of the curved surface
Obtain the dimension vector Rkl, or use CD-RO in advance.
This three-dimensional vector R stored in the M disk 6
kl and the information about the size of the division step ΔV are supplied to the spline function generator 142, and the spline function generator 14
2 calculates the spline function Sk (v) using the values of Rkl and the division step Δv so as to obtain the initial value given to the register of the spline function generator.

However, if the following is done, the initial value is directly set in each register without calculating the initial value set in the register of the spline function generator 142 from the three-dimensional vector Rkl and the division step Δv. can do.

That is, if the spline function is expressed as a vector, the equations (eq2) and (eq3) shown in FIG.
Are equations (a-1) and (a-2) of FIG. 11, respectively.
Can be expressed as In these equations (a-1) and (a-2), A is a vector represented by equation (a-3) in FIG. 11.

Here, when the control point data P = Pij of the curved surface is expressed as a vector, the equation (a-4) in FIG. 11 is obtained, and the curved surface equation (eq1) in FIG.
It can be expressed as the formula (a-5) in FIG. Then, by substituting the expression (a-1) and the expression (a-2) in FIG. 11 into the expression (a-5), the expression (a-5) becomes the expression (a-6) in FIG. Like

[0086] Incidentally, the circuit of example 8 spline function generator 142, _{r u} times u direction, when invoked by executing _{r v} times v _{direction, u = r u Δu (a} -7) v = because represented as _{r v Δv (a-8)} , the equation of FIG. 11 _{(a-6), r u} , r v
If expressed by, it can be transformed as shown in the equation (a-9) in FIG.

In the configuration of the differential analyzer shown in FIG. 8, in order to output ar ³ + br ² + cr + d in the r-th simultaneous addition, the initial values of the registers RA0, RA1, RA2 and RA3 are 6a, 6a + 2b. , A + b + c, d. When this initial value is represented by a vector, the equation (a-10) in FIG. 12 is obtained. However, in the formula (a-10), M
Is a vector represented by equation (a-11).

That is, when the polynomial calculated by the spline function generator 142 is decomposed into an initial value vector, FIG.
Formula (a-12) of 3 is obtained. Then, by rewriting the formula (a-9) to decompose it using (M ⁻¹ ) ^T , it can be expressed as the formula (a-13) in FIG. 13. Here, D in the equation (a-13) is represented by the equation (a-14) in FIG.

The value D of the vector D in this equation (a-14)
_{If kl} is used instead of the three-dimensional vector Rkl of the equation (eq6) of FIG. 5, in the curved surface division algorithm,
Each initialization data and each register bank of the circuit of FIG.
The initial values given to the registers RA0 to RA3 of BANK0 to BANK3 can be made equal, and the spline function generator 1
In the case of 42, the initialization data obtained from the polygon dividing means 141 can be set in the registers RA0 to RA3 as they are, and the calculation speed can be increased.

The above is a description of the method of calculating the initial value for the case where a plurality of adders are simultaneously operated in the configuration of the differential analyzer shown in FIG. 8. However, it is assumed that a plurality of adders are simultaneously operated. Instead, it can be executed sequentially. The initial value in that case is as follows.

That is, in this case, for example, taking the circuit configuration of FIG. 8 as an example, after the adder A1 writes to the register RA1, the adder A2 reads it and the adder A2 outputs the result to the register RA2. After writing to
The adder A3 performs an operation of reading it. In this case, the initial value required to calculate the polynomial ar ³ + br ² + cr + d is found to be the expression (a-15) shown in FIG. 14 from the table of FIG. 15 showing a table similar to that of FIG. 9B.

Therefore, instead of the equation (a-11) shown in FIG. 12, M expressed by the equation (a-16) shown in FIG. 14 is used to calculate the equation (a-14) shown in FIG. The initial value that can be directly substituted into the register of the spline function generator of this example can be obtained. This method can be applied to the same kind of spline function generator using a plurality of adders.

As described above, appropriate initial values for various differential analyzers are calculated from the control points, the coefficients of the spline polynomial, and the division step size values Δu and Δv, and directly set to set the curved surface. Will be able to split.

In this case, the division operation of various curved surfaces can be performed at high speed without being restricted by the shape of the curved surface. Also, since it is a configuration using a differential analyzer using a plurality of adders, compared to the case of the conventional product-sum calculator,
Since the multiplier is unnecessary, the hardware is simpler,
It can be constructed at low cost.

Further, by transforming the control point data of the curved surface into data suitable for the initial data of the spline function generator and storing it in the storage medium in advance, unnecessary calculation is omitted and the curved surface dividing processing is performed at high speed. It can be performed.

Further, the structure of the data bus and the adder of the instruction type arithmetic unit for dividing the curved surface can be made appropriate, and the high speed spline function generator can be realized without increasing the arithmetic resources so much.

The initial values converted for these differential analyzers may be calculated in advance and stored in the main memory, for example, and the preprocessing unit 14 may read them out.

In the curved surface division algorithm described with reference to FIGS. 6 and 7, the outer loop calculates the v direction and the inner loop calculates the u direction, and the differential analyzer is used in each loop. If the differential analyzer itself or the registers of the differential analyzer are limited, the equation (eq5) in FIG. 5 is directly calculated by the product-sum operation without using the differential analyzer in the outer loop, It is also possible to use the obtained value as the initial value of the operation of the differential analyzer in the inner loop. In that case, the value of v is directly handled only in the outer loop, so that D in Expression (a-14) is changed to Expression (a-1) in FIG.
The same curved surface division can be performed by changing to 7).

[0099]

As described above, according to the present invention, simple hardware can be used, and
There is no limitation on the spline function used to represent a curved surface, and a smooth curved surface can be drawn at high speed with a small amount of data.

[Brief description of drawings]

FIG. 1 is a block diagram showing an embodiment of a configuration of a main part of an image generating apparatus according to the present invention.

FIG. 2 is a diagram for explaining an example of dividing a curved surface.

FIG. 3 is a block diagram showing a configuration example of a game machine as an embodiment of an image generating apparatus according to the present invention.

FIG. 4 is a diagram showing an example of an external appearance of the game machine of the example of FIG.

FIG. 5 is a diagram for explaining a cubic spline function.

FIG. 6 is a part of a flowchart explaining an operation procedure of a main part of the embodiment of the image generating method according to the present invention.

FIG. 7 is a part of a flowchart illustrating an operation procedure of a main part of the embodiment of the image generating method according to the present invention.

FIG. 8 is a block diagram of an example of a function generator in the embodiment of the image generating apparatus of the present invention.

9 is a diagram used for explaining initial value data given to the function generator of FIG. 8 and a function generating operation.

FIG. 10 is a block diagram of an example of a function generator in the embodiment of the image generating apparatus of the present invention.

FIG. 11 is a diagram used for explaining an example of calculation of initialization data given to the spline function generator in the embodiment of the image generating apparatus of the present invention.

FIG. 12 is a diagram used for explaining an example of calculation of initialization data given to the spline function generator in the embodiment of the image generating apparatus of the present invention.

FIG. 13 is a diagram used for explaining an example of calculation of initialization data given to the spline function generator in the embodiment of the image generating apparatus of the present invention.

FIG. 14 is a diagram used for explaining an example of calculation of initialization data given to the spline function generator in the embodiment of the image generation apparatus of the present invention.

FIG. 15 is a diagram showing another example of initialization data given to the spline function generator in the embodiment of the image generating apparatus of the present invention.

[Explanation of symbols]

141 ... Polygon dividing means, 142 ... Spline function generator, 143 ... Coordinate converting means, 15 ... Drawing processing section, 15
1 ... Drawing means, 152 ... Frame memory, A1 to A3 ...
Adder, B0 to B3 ... Bus, BANK0 to BANK3 ... Register bank, SW1 to SW3 ... Switch circuit

Claims (7)

(57) [Claims] 1. A method of generating an image of a curved surface using control point data for determining the shape of a curved surface expressed by using an nth-order spline function, wherein the control point data is processed. A first step of initializing the differential analyzer by giving the initial value data obtained as a result and information of the dividing step when the curved surface is divided to the differential analyzer; and the dividing step from the differential analyzer. A second step of obtaining the value of the spline function for each, and based on the value of the spline function obtained in the second step, information of each division plane when the curved surface is divided in the division step is obtained. An image generating method for generating an image of the curved surface by executing the third step of generating. 2. A function generator comprising a differential analyzer, polygon dividing means, and converting means for converting polygon data from the polygon dividing means into data for displaying the polygon data, wherein the polygon dividing means comprises: Initial value data obtained by processing the control point data for determining the shape of the curved surface expressed by using the nth-order spline function, and the size of the dividing step when the curved surface is divided. And to the function generator, obtain the value of the spline function for each dividing step obtained from the function generator, based on the obtained value, when the curved surface is divided in the dividing step An image generating apparatus characterized by generating polygon data of each division plane. 3. An image generating apparatus according to claim 2, further comprising a reading means for reading data for drawing an image stored in a storage medium, and an apparatus for generating an image using the read data. In the storage medium, instead of the data of the control points, data suitable for initial value data given to the function generator created from the data of the control points is stored. The image generating apparatus is characterized in that the initial value data is created from data suitable for the initial value data and is supplied to the function generator. 4. The image generating apparatus according to claim 3,
The initial value data stored in the storage medium includes size information of the division step, and the function generator is directly initialized by the initialization data. Image generating device. 5. The image generating apparatus according to claim 3, wherein game data is stored in the storage medium together with data for drawing the image to form a game machine. 6. The function generator includes at least m (m is an integer of 2 or more) adders and at least 0 to m.
(M + 1) buses of (m + 1), and two inputs of the i-th ( 1 ≦ i ≦ m) adder of the m adders are (i− 1) connected to the i-th bus and the i-th bus
The image generation apparatus according to claim 2, wherein the output of the th adder is connected to the i th bus. 7. The function generator includes at least m (m is an integer of 2 or more) adders and at least 0 to m.
(M + 1) buses of the (m + 1) buses, and two inputs of the i-th ( 1 ≦ i ≦ m) adder of the m adders are (i− 1) connected to the i-th bus and the i-th bus
The image generation apparatus according to claim 2, wherein the output of the th adder is switched and connected to one of the (i-1) th and i th buses.