JPH0544712B2 - - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION (Field of Industrial Application) The present invention relates to a polygonal scan converter used in conjunction with a three-dimensional image display device.

(Prior technology) Raster scanning type CRT for 3D colored images
As a method for generating and displaying images on the display screen of a display device, there is a display processing method using a Z-buffer method of a polygonal model. First, I will explain the method step by step.

() Shape modeling Define the object shape within the 3D world coordinate system. In a polygonal model, the surface of a three-dimensional object is expressed as a set of polygons. If the object surface includes a curved surface, the curved surface is divided into polygons and approximated.

() Coordinate transformation Specify the projection plane and projection method (parallel projection or central projection) in the 3D world coordinate system, and perform projection transformation to the 2D coordinate system set on the projection plane. For polygonal models, project all vertices of the polygon. At this time, the depth value (depth Z) reaching the projection plane is also determined for each vertex in order to eliminate hidden surfaces, which will be described later. Next, clipping may be performed. This sets a rectangular window frame on the projection plane, and in order to display only the part inside the window frame of the projection, removes the polygons outside the window frame, and removes the polygons that intersect with the window frame. is a process that leaves only the part included inside the window frame.

() Scan conversion Converts a polygon represented by a sequence of vertices into a sequence of pixels on the display screen. To do this, pixels on the edges of the polygon are interpolated from the coordinates of the vertices of the polygon, and then pixels inside the polygon are generated. In order to remove hidden surfaces, the depth Z from the projection plane to the polygon is also calculated for each pixel.

() Image memory update with hidden surface removal When multiple polygons overlap on the display screen, it is necessary to preferentially display the polygon that is closest to the viewer as viewed from the viewpoint. The Z buffer method performs this hidden surface removal process pixel by pixel. According to the Z buffer method, the pixel address (x, y) on the screen
In addition to the image memory that stores the intensities of the three primary colors (R, G, B), a Z buffer memory (also called depth buffer memory) that stores the depth Z is used. ) as the background color,
Fill the Z buffer memory with the maximum depth Z _nax . Scan-convert the polygon to obtain a sequence of pixels (x _i , y _i , z _i , R _i , G _i , B _i ) with depth and three primary colors i=
1, 2, 3, ..., and before writing the three primary color intensities (R _i , G _i , B _i ) to the image memory address (x _i , y _i ), the Z buffer memory address (x _i ,
The depth Z _M at y _i ) is read out, the magnitude of Z _M and Z _i is compared, and only when Z _i < Z _M , the depth Z M at (R _i , G _i ,
B _i ) and Z buffer memory.
Replace the value of Z _M with Z _i . That is, the Z buffer memory stores the depth of the polygon closest to the viewpoint that has been drawn so far, and suppresses writing of pixels with a greater depth than this. By sequentially performing the above processing on all scan-converted pixels of all polygons, pixels whose hidden surfaces have been correctly removed are finally obtained in the image memory (R, G, B).

Since the above processing method has a simple algorithm and can be processed at high speed by hardware, three-dimensional image display devices exist that are equipped with a coordinate converter, a scan converter, and a Z buffer memory in addition to an image memory. Such devices are, for example, IEEE Computer Graphics and Applications
Applications), vol.4, No.6, (1984) P.11-23
There is a device disclosed in , and its configuration diagram is shown in FIG. 11. Further, figures showing the types of polygons whose coordinates have been transformed are shown in FIGS. 12a to 12b. The polygon data stored in the segment memory 101 is projected onto the projection plane of the two-dimensional coordinate system by the coordinate converter 35 as described above, and its coordinates are converted (in the case of central projection, the divider 105 is also used).

Next, the coordinate-converted polygon is sent to a scan converter 11.
It is divided into triangles by a triangulator 103 in 2. For example, a hexagon V ₁ as shown in Figure 12a
V ₂ V ₃ V ₄ V ₅ V ₆ is the three diagonal lines V ₁ V ₃ , V ₁ V ₄ , V ₁
Divided into 4 triangles by V ₅ . The coordinates of one of these divided triangles, V ₁ V ₂ V ₃ , are
V ₁ (x ₁ , y ₁ , z ₁ ), V ₂ (x ₂ , y ₂ , z ₂ ), V ₃ (x ₃ , y ₃ ,
z ₃ ), initializer 1 in scan converter 112
04 and the divider 105 calculate the increment value using the following equation.

∂z/∂x=(z ₂ −z ₁ )(y ₃ −y ₁ )−(z ₃ −
z ₁ )(y ₂ −y ₁ )/(x ₂ −x ₁ )(y ₃ −y ₁ )−(x ₃ −x ₁ )(
y ₂ −y ₁ )... ∂z/∂y=(x ₂ −x ₁ )(z ₃ −z ₁ )−(x ₃ −
x ₁ )(z ₂ −z ₁ )/(x ₂ −x ₁ )(y ₃ −y ₁ )−(x ₃ −x ₁ )(
y ₂ −y ₁ )... These values indicate the slope of the depth Z in the x direction and the y direction inside the triangle. When the incrementer 106 and the memory updater 107 fill consecutive pixels inside the triangle, they add or subtract ∂z/∂x or ∂z/∂y to the depth Z each time the pixel is moved left, right, up, or down. , the pixel depth Z can be calculated correctly.

The interior depth Z of the polygon thus obtained
As mentioned above, the pixel data including the
09, the hidden surface is removed and the image is displayed on the display screen of the CRT 111 via the video refresh 110.

It should be noted that a concave polygon including two or more concave vertices as shown in FIG.

(Problems to be Solved by the Invention) However, the scanning converter of the conventional device has a concave polygon as described above, a polygon with a hole as shown in FIG. 12c, or a plurality of polygons as shown in FIG. There was a problem that polygons divided into islands could not be processed. In addition, since four arithmetic calculations involving highly accurate multiplication and division are required to perform complex incremental value calculations as shown in equation (2) for initialization, there is a problem in that processing time is long.

The present invention solves the above-mentioned problems, enables scan conversion of polygons of arbitrary shapes without being restricted by the shape of the polygon, and provides a highly functional and high-speed scan converter with a relatively simple configuration. The purpose is to provide.

(Means for Solving the Problems) In order to solve the above problems, the present invention provides a polygonal scan converter in a three-dimensional image display device, which includes an input terminal, an output terminal, and at least a first data memory. , a left edge processor consisting of a first vertex pointer, a first edge pointer, a first arithmetic logic unit, and at least a second data memory, a second vertex pointer, a second edge pointer, and a second arithmetic logic unit. a right edge processor consisting of an arithmetic unit, a divider for dividing two integers, a microprogram controller for controlling the entire scan converter, the input terminal, the output terminal, the left edge processor, the right edge processor, the It consists of a divider, an internal data bus that connects the microprogram controller, and performs data transfer.
Consists of coordinates, z coordinates, and a pointer to the next vertex,
Polygonal data expressed as a series of vertex data arranged so that the inner region of the polygon is seen on the right side is inputted from the input terminal, and the first and second
polygon data input processing to be stored in the data memory of , and all the edges surrounding the polygon using the left edge processor and the right edge processor, the left edge line moving in the direction of increasing y-coordinate and the direction of decreasing y-coordinate. A series of left edge data consisting of initial values and increment values of x and z coordinates, height, and a pointer to the next edge is created in the first data memory, and A series of right edge data consisting of the initial value and increment value of the z coordinate, height, and a pointer to the next edge is created in the second data memory, and the x coordinate and the left edge data of the left and right edge data are created using the divider. an edge line data creation process of calculating an increment value of the z coordinate and creating in the first data memory a series of approach vertex data consisting of the y coordinate, approach difference, and a pointer to the approach edge and sorted in ascending order of the y coordinate; , point to the first approach vertex of the series of approach vertex data with the first vertex pointer, and set the y-coordinate of the scan line to a minimum value;
Scan line initialization processing to empty the left active edge list and right active edge list,
A scan line update process in which the y coordinate is increased by 1 for each scan line and the approach difference is decreased by 1, and when the approach difference of the approach vertex data becomes 0, the pointer to the approach edge of the next approach vertex is moved to the left edge entry processing for inserting the first pair of left and right edge data into the active edge list and the right active edge list so as to be sorted in ascending order of x-coordinates; Initialize the edge pointer pointed by the second edge pointer, and update the edge pointer by pointing the next left and right edge data in the left and right active edge list with the first and second edge pointers each time left and right edge data is processed. processing and
Using the left and right edge data, create scanning line segment data belonging to the internal region of the polygon and consisting of at least the x and z coordinates of the left end point, the increment value of the z coordinate, and the length, and output it to the output terminal. , a segment generation process for updating the x-coordinate and z-coordinate of the left and right edge data to the values of the next scan line, the scan line initialization process, the scan line update process,
All scan line segment data belonging to the internal region of the polygon is created using the edge entry process, the edge pointer initialization process, the edge pointer update process, and the segment generation process, and scan conversion process is performed. It is.

Preferably, the divider has a reciprocal table that generates a reciprocal of an input, and a multiplier that multiplies the output of the reciprocal table and the input.

(Operation) According to the present invention, since the scanning converter is configured as described above, the technical means operates as follows.

The edge data creation process creates left and right edge data from polygon vertex data and stores them in the left and right edge processors, respectively. At this time, the increment value (dx/dy, dz/dy) in the ridge direction included in the ridge line data is calculated using a divider. Next, the scan conversion process sequentially sweeps the scan lines that intersect the polygon in the vertical direction of the screen (from bottom to top, or from top to bottom), and each time the scan line is updated, the left and right edge data are processed by the left and right edge processors. While reading and updating the edge line data, scanning line segment data is created and output from the intersection of the scanning line and the polygon. At this time, the increment value (dz/dx) of depth Z in the line segment direction included in the scanning line segment data is calculated using a divider. In this way, polygons are directly decomposed into scanning line segments and processed in parallel by the left and right processors, so that scan conversion of polygons of arbitrary shapes can be performed at high speed. Therefore,
The problems of the prior art described above can be solved.

(Embodiment) FIG. 1 is a block diagram of a scan converter showing an embodiment of the present invention. In the same figure, 1 is an input terminal, 2 is an internal bus, 3-1, 3-2, 3-3, 3
-4, 3-5 are bus drivers, 4 is a bus receiver, 5 is a first-in first-out memory (FIFO), and 6 is an output terminal. The internal bus 2 includes a left edge processor 29, a right edge processor 30, a divider 31, and a microprogram controller 32, which are surrounded by dotted lines.
is connected. The left edge data memory DM1, 12-1 is located in the left edge processor 29, and the approach vertex pointer VP1,
7-1, the edge pointer PEP1, 8-1,
Edge pointers EP1, 9-1 are connected via address multiplexers MXA1, 10-1 and address adder 11-1. DM1,1
2-1 output data is data multiplexer
MXD1, 13-1 and register S1, 14-
1, or arithmetic unit through register R1, 15-1
DM1,12-1 via ALU1,16=1
or bus driver 3-
3 to the internal bus 2. MXD
The other input terminals of 1 and 13-1 include internal buses 2 and 13-1.
The outputs of MAX1 and 10-1 are connected. The right edge processor 30 is the left edge processor 29.
It has the same structure as (the reference number is indicated by a hyphen 2). The divider 31 includes divisor registers R3, 17,
Reciprocal table INV18, reciprocal register R4,1
9, a dividend register R5, 20, a multiplier 21, and a quotient register R6, 22.As is clear from the figure, the value of R5/R3 is determined. The microprogram controller 32 includes a microprogram sequencer SEQ23 and a microprogram memory.
MPM24, micro program register MPR
25 and controls the entire scan converter by executing a microprogram stored in MPM 24. One data line 26 from the output of the MPR 25 supplies constant data to the internal bus 2 via the bus driver 3-4, or
23 with the destination address. The other data line 27 supplies a common address addition amount to address adders 11-1 and 11-2. Control lines 28 provide control signals to various parts of the scan converter.

Next, the operation will be explained. The processing procedure for scan conversion of the scan converter in this embodiment is as follows after input processing:
The process can be broadly divided into left and right edge list creation processing and scan conversion processing.

First, input processing and edge line list creation processing will be explained.

Figures 2a to 2e are explanatory diagrams of polygon data, in which figure a is a specific example of a polygon, and figures b and c are polygon data stored in DM1, 12-1, DM2, and 12-2, respectively. Figure a shows a memory block for storing polygon data, and figures d and e show the internal elements of each memory block shown in figures b and c.

The polygon data in Figure 2a is input from input terminal 1,
Internal bus 2, MXD1, 13-1 and MXD2,
13-2, ALU1, 16-1 and ALU2, 16
-2 to the data memories DM1, 12-1 and DM2, 12-2, as shown in Fig. 2 b, c.
The same polygon data is stored in . The polygon data is a fixed length memory block (here, 8 words x
20 bits), and consists of one common data block C and as many vertex data blocks _V1 to _V9 as the number of vertices, as shown in Fig. 2b and c, and the contents of each block are Assume that it has the format shown in Figures d and e. The storage blocks in the memory and the elements within the blocks are numbered starting from 0 as shown in _FIG . In this example, polygon data is stored so that the vertex number and memory block number match, and element numbers ~ are empty. The memory block numbers in Figures 2b and 2c are MXA1, 10-1 and MXA1 in Figure 1.
The output data of MXA2, 10-2 is specified, and the second
The element numbers in FIGS. d and e are connected as specified by the data line 27. The number of words in one memory block is 2.
Address adders 11-1 and 1
There is no need to use 1-2. 6 vertices V ₁ ~ _{V 6}
defines the outer boundary loop of the polygon with three vertices V ₇ ~
V ₉ forms inner boundary loops, but these vertex loops are oriented to look into the inner region of the polygon (shaded) to the right.
That is, the outer boundary loop is clockwise, and the inner boundary loop is counterclockwise. The vertex pointer vp in the vertex data stores the number of the next vertex (element ◎ in FIG. 2d). The formation of a vertex loop by the vertex pointer vp is shown by the solid arrow in FIG. 2b. In the common data area C, the first to third loop pointers, which are pointers to these loops, are stored (element d to element 2 in Figure 2). Indicated by dashed arrows.
In addition, the color c of the ◎ element in Fig. 2 d is the three primary colors R,
It has G, B values or coded color information.

Next, edge line (also called edge) data is created from the vertex data. FIGS. 3A to 3D are explanatory diagrams of an edge line list and an approach vertex list. Each edge of the polygon is oriented in the direction of increasing y coordinate (from bottom to top) as shown in FIG. 3a, and is given initial values and increments of x and z coordinates. On the edge line from vertex V _i to vertex V _j along the vertex loop, if the y coordinate y _i of vertex V _i is smaller than the y coordinate y _j of vertex V _j (i.e., y _i < y _j ), set V _i as the starting point. Then, the forward direction edge data V _i V _j −−→=E _ij with V _j as the end point is stored in the left edge data memory.
Create on DM1, 12-1. Moreover, if y _i >y _j , the edge line data in the opposite direction V _j V _i −−→=E _ji is created in the right edge line data memory DM2, 12-2. Vertex V ₄ ,
The vertex that is the common starting point of the left and right edges, such as V ₆ and V ₉ , is called the approach vertex, and the approach vertex data is
Create EV ₄ , EV ₆ , and EV ₉ from the 10th memory block of DM1 and 12-1 to the 12th memory block (3rd
Figure b). For example, EV ₄ has a left ridgeline E ₄₅ and a right ridgeline.
A pointer to E ₄₃ is stored. All approach vertices are in ascending order of y coordinate, i.e. EV ₆ , EV ₄ , EV ₇
h′ ₆₄ = y 4 − y 6 is EV 6, h′ 49 = h ₉ − h ₄ is EV 6, and h′ ₆₄ = y ₄ − y ₆ is EV ₆ as the difference in the y coordinate of the approach vertex.
Stored in EV ₄ . Vertices that are the common end points of the left and right edges, such as vertices V ₂ , V ₅ , and V ₇ , are called exit vertices, and E ₁₂ and E ₃₂ have V ₂ as the end point, and E ₄₅ has V ₅ as the end point. E ₈₇ and E ₉₇ , which end at E ₆₅ and V ₇ , are called exit ridges.

The left edge list, right edge list, and approach vertex list created in this way are shown in FIG. 3b, and the contents of the edge line data and approach vertex data are shown in FIG. 3c. It is assumed that the edge line data E _ij is created in the same memory block as the vertex V _i with the smaller y-coordinate among both end points. However, the correspondence within the storage block between edge data and vertex data is not taken into account. The left ridge line E ₄₅ starting from approach apex V ₄ is DM1, 12
-1 V ₄ area, right edge E ₄₃ is DM2,12-
Created in the V ₄ area of 2. Exiting vertices V ₂ , V ₅ , V ₇
The area becomes empty.

FIG. 4 shows a flowchart of processing for creating an edge line list and an approach vertex list. Step 40 sets the vertex number of the first vertex loop to the variable _i0 .
The process in step 42, which is surrounded by a dotted line, follows a loop from vertex i ₀ , finds the first non-horizontal edge E _ij ,
The starting point i of the ridge line E _ij is set to i ₀ again, and if the ridge line E _ij is an ascending vector whose y coordinate increases, then s _p =
If sgn(y _j −y _i )>0 and E _ij is a descending vector, then
Let _sp < 0. Here, sgn is a function symbol that gives a positive, negative, or 0 sign. In step 49, the type of ascending, descending, and horizontal of the next ridge line E _ij is determined in s, and s
>0, in step 51 the left edge data is DM1,
In step 12-1, if x<0, right edge data is created in DM2, 12-2 in step 55. Successive 2
When the signs s _p and s of the two ridgelines are of different signs, assuming that the starting point V _i of E _ij is the entry apex or the exit apex,
Perform the following processing. When s _p <0, s > 0, the direction of the ridge changes from descending (or horizontal) to ascending, so in step 53 approach vertex data EV _i having a pointer to the ridge E _ij is created, and in step 54 s _p Change the sign of from negative to positive and proceed to the next edge. s _p ＞0, s
When <0, the direction of the ridgeline changes from rising (or horizontal) to descending, so in step 56, the descending right ridgeline created this time and the previous rising (or horizontal) left ridgeline are changed in step 57. This is set as the exit edge, and in step 58, the sign of _sp is changed from positive to negative and the process proceeds to the next edge. For horizontal edges, s=0
Therefore, it is processed in step 59, but simply setting hij=0 indicates that Eij is a horizontal edge. However, the horizontal edge that follows the left edge is considered a left edge, and is added to block i of DM1.
Eij, the horizontal edge that follows the right edge is regarded as the right edge, and is added to block j in DM2.
Create as Eji. Step 60 determines whether the starting point i of the edge E _ij has returned to the starting point of the vertex loop. The loop 60a is executed as many times as the number of vertices included in the vertex loop, and the loop 61a is executed as many times as the number of vertices included in the vertex loop. If i ₀ =0 in step 41, this indicates that the processing of all vertex loops has been completed, and therefore, in step 62, the incoming vertex data EV _i is sorted.

Next, the contents of the edge line data E _ij shown in FIG. 3 c and the approach vertex data EV _i shown in FIG. 3 d will be explained. The difference h′ _ij (th element) of the approach vertex data EV _i is a non-negative integer and indicates the number of scanning lines to the next approach vertex, so every time you update the scanning line, reduce h′ _ij by one. If h′ _ij =0, it is known that the next approach vertex has been reached. h′ _ij of the last approach vertex EV ₉ is set to a negative value. The edge line data E _ij is the corrected initial value x _ip and z _ip at the starting point _Vi , and the increment value (dx/dy) _ij and (dz/dy) _ij , y when the y coordinate increases by 1.
It includes the height in the direction h _ij and two pointers sep and aep (from the ◎th element to the th element). Edge line data E _ij
sep at and approach vertex data EV _j at evp
is a pointer indicating the connection of edges from the entry vertex to the exit vertex, and this connection is shown in FIG. 3b.
The exit edge is indicated by setting sep=0. The pointer aep of the edge data E _ij is converted to an active edge list (AEL) by the scan conversion process described later.
used to form

A method of calculating various elements of the edge line data E _ij will be explained using FIG. 5. Starting point V _i (x _i , y _i , z _i ) and ending point V _j (x _j ,
y _j , z _j ) are all integers,
Let y _i y _j . Further, assuming that the scanning line is a horizontal band-shaped area partitioned by horizontal lines whose y coordinates are integers, the ridgeline E _ij crosses y _j −y _i =h _ij (main) scanning lines. These scanning lines are used as ridge lines as shown in Figure 5.
Called the first, second, ..., h _ij scan lines in E _ij ,
The intersection points of the center line of these scanning lines and the edge line E _ij are respectively P ₁ , P ₂ , ..., Ph _ij , and the values of (x, y, z) at these equinox points are linearly calculated from both end points of E _ij . I want to interpolate. For that purpose, the value at P ₁ (X _ip , y _ip , zi _ip ) as the initial value and P ₁ P ₂ --- as the increment.
→=
((dx/dy) _ij , 1, (dz/dy) _ij ) is determined by the following formula.

h _ij =y _i −y _i ... (dx/dy) _ij =x _j −x _i /h _ij ... (dz/dy) _ij =z _j −z _i /h _ij ... y _ip =y _i +0 .5... x _ip = x _i +0.5×(dx/dy) _ij ... z _ip =z _i +0.5×(dz/dy) _ij ... Edge line data E _ij are these other than y _ip in the equation The value of is stored as described above (FIG. 3c). For a horizontal edge line where h _ij =0, there is no equinox P ₁ , P ₂ , . . . , so there is no need to store the above values other than h _ij .

The above has described the procedure for creating left and right edge lists and the results thereof.Next, the procedure for executing this using the scan converter shown in FIG. 1 will be explained. The process at step 43 in FIG. 4 is performed using the value of the loop pointer in FIG.
i _p is read from DM1, 12-1, register R1, 15-1 in FIG. 1, arithmetic unit ALU1, 16-
1. Set in register EP1, 9-1 via bus driver 3-3 and internal bus 2, and set the value of EP1, 9-1 to i. Next, DM1 pointed to by EP1, 9-1,
The pointer vp of the vertex data _V1 of the storage block 12-1 is read out, and the register R1, 15-1,
Arithmetic unit ALU1, 16-1, bus driver 3-3,
Set it in register EP2, 9-2 via internal bus 2, set the value of EP2 to j, and set the vertex data of DM2 as V _j
refers to In the following explanation, the data transfer route will be omitted.

The process of step 44 in FIG. 4 is similar to that in FIG.
The y coordinate y _i of the vertex data V _i of DM1, 12-1 pointed to by EP1, 9-1, and the DM2 pointed to by EP2, 9-2
Read the y coordinate y _j of the vertex data V _j of , and set y _i to register R1, 15-1 and y _j to register S1, 14.
-1, and the calculation unit ALU1, 16-1 calculates y _j −y _i
is calculated and its sign is set as _sp in the status register provided in ALU1. Step 47 in Figure 4
and 48 processing is EP1, 9-1 in Fig. 1
Move the value i of EP1,8-1 to PEP1,8-1, move the value j of EP2,9-2 to PEP2,8-2, then move EP1,9-
The pointer vp _i of the vertex data V _i of DM1, 12-1 pointed to by DM1, 12-1 is transferred to EP1, 9-1, and
By transferring the pointer vp _j of the vertex data V _j of DM 2, 12-2 pointed to by 2 to EP 2, the values of i, j are updated. PEP1,8-1, PEP2,8-
2 holds the values of i and j of the edge line processed last time.
The process at step 46 in FIG. 4 resets the value i of EP1,9-1 to the loop pointer in DM1,12-1. The process at step 49 in _{FIG .}
1, set in the status register in 16-1. y _j−
If y _i > 0, in step 51, the left edge data E _ij is
Create it in the memory block of DM1 pointed to by EP1, 9-1. First, the value of the equation h _ij =y _j −y _i is stored as h _ij of the edge line data E _ij in FIG. 3c. Next, h _ij is set in the register R3, 17 in the divider 31, and 1/h _ij is determined using the inverse number table (INV) 18. Next, in the equation, x _i is read from DM1, 12-1 and set to R1, 15-1, x _j is read from DM2, 12-2 and set to S1, 14-1, and ALU1, 1
In 6-1, calculate x _j −x _i and store the result in register R.
5, 20, the multiplier 21 calculates (dx/dy) _ij = x _j −x _i /h _ij , and this value is expressed as (dx/dy) of E _ij in Figure 3c.
) memorized as _ij . The method for finding (dz/dy) _ij in the equation is the same as (dx/dy) _ij . The formula is (dx/dy) _ij is R1
, 1 5-1, read x _i to S1, 14-1, read R1, 15-1 in ALU 1, 16-1
The value obtained by arithmetic shifting 1 bit to the right and S1,14-
1 is added to obtain x _ip = x _i +0.5×(dx/dy) _ij , and the result is stored as x _ip of the edge data E _ij in Figure 3c. Find z _ip in the formula in the same way as x _ip . y _j −y _i
If <0, in step 55 the right edge data E _ji is
It is created in the memory block of DM2, 12-2 pointed to by EP2, 9-2. In this case, the subscripts i and j are exchanged, and the following values are obtained and stored in the DM 2, 12-2.

h _ji ＝y _i −y _j ……′ (dx／dy) _ji ＝x _i −x _j ／h _ji ……′ (dz／dy) _ji ＝z _i −z _j ／h _ji ……′ x _jp ＝ x _j +0.5×(dx/dy) _ji …′ z _jp =z _j +0.5×(dz/dy) _ji …′ The pointer sep of the left edge data E _ij can be used as is, the pointer vp of the vertex loop. However, the pointer sep of the right edge data E _ji needs to be in the opposite direction of the vertex loop to the pointer vp. For that
DM that EP2,9-2 points to the value i of EP1,9-1
2, the sep of the j-th storage block of 12-2 is transferred. To create the approach vertex data EV _i in step 53 of FIG. 4, the first memory block number of the approach vertex is stored as vp0 in a common data block, etc.
First set vp0 to VP1, then use VP1 as a counter to specify the memory block number, and
1,9-1 value i is pointed to by VP1,7-1 DM1,
Set the pointer evp of the memory block EV _i of 12-1 to the pointer evp of the memory block EV i of DM1, 12-1, and set the y coordinate y _i of the vertex V i of the memory block of DM1, 12-1 pointed to by EP1, _9-1 to VP1, 7-
Set to y _ip of EV _i pointed to by 1. This y _ip does not add 0.5 as in the formula. This is because the y-coordinate value of the scanning line has the form (integer + 0.5), and this 0.5 can be omitted. Steps in Figure 4
The processes 56 and 57 change the edge line attributes of the right edge data E _ji pointed to by EP2, 9-2 and the previous left edge line data E _ij pointed to by PEP1, 8-1 to "exit". This is displayed by setting the value of the pointer sep to 0. The process of step 60 in Fig. 4 is performed in EP1 and 9.
-1 and the loop pointer i _p of the common data area in the DMs 1 and 12-1 are compared in the ALUs 1 and 16-1. To sort the entry vertex list in step 62 in Figure 4, use VP1, 7-1 in Figure 1 and
Using EP1 and 9-1 as two pointers for sorting, rearrange them in ascending order using y _ip as a key, and then calculate h' _ij .

The above is the procedure for creating the left and right edge list and the approach vertex list. Next, the active edge list (also called AEL) and edge pointer (also called EP) for performing scan conversion will be explained.
AEL is all the left and right edges that intersect with one scanning line, arranged in ascending order of x coordinate.
Using the active edge pointer aep of the edge data _Eij , a left active edge list (left AEL) is created in DM1, 12-1, and a right active edge list (right AEL) is created in DM2, 12-2.
Examples of AEL are shown in Figures 6a and b. In FIG. 6a, the left active edge root pointer aep1 in the common data area C1 of DM1, 12-1 points to the first left edge _E61 , and the active edge pointer _{E61 .} aep points to the second left edge E ₉₇ , and the active edge pointer E ₉₇ of this E ₉₇ .
aep points to the third left ridgeline E ₄₅ . This E ₄₅ active edge pointer E ₄₅ . 0 is written in aep to indicate the end. In Figure 6b, DM
Similarly, the right active edge root pointer aep2 in the common data area C2 of 2 and 12-2 is
The second and third right edge lines E ₉₈ , E ₆₅ , and E ₄₃ are sequentially pointed to form a right active edge list. To generate a line segment (also called a scan segment or segment) of a polygon and a scan line, the first left edge E ₆₁ of the active edge list AEL and the first
Find two intersection points with the scanning line by pairing the right edge E ₉₈ of , generate the first scanning segment using these as both end points, and similarly create the second left and right edges E ₉₇ and E _65.
the second scanning segment to the third left and right edges.
The pair E ₄₅ and E ₄₃ generates the third scan segment. The left active edge root pointer aep1 is
In the common data area C1 of DM1, 12-1, the right active edge root pointer aep2 is set to DM2,
12-2 in the common data area C2. Next, there are four pointers that scan the edge pointers EP and AEL, as shown in FIG. 1, each using the register of the same name in the scan converter of FIG.
In Figure 6 a and b, EP1 and EP2 are the second left and right ridgelines.
They are pointing at E ₉₇ and E ₆₅ , and PEP1 and PEP2 are pointing at first left and right ridge lines E ₆₁ and E ₉₈ .

Next, the processing procedure for performing scan conversion of a polygon using the left and right edge list and entry vertex list created as shown in Fig. 3 is shown in the flowcharts of Figs. 7, 8, and 9, and the processing shown in Fig. 10. The content will be explained using an explanatory diagram. In order to simplify the explanation in these processing steps, it is assumed that the polygon does not include horizontal edges. Scan line initialization (step
64) stores the start address vp0 of the entry vertex list in register VP1,7-1 as shown in Figure 10.
, and the approach apex EV pointed to by VP1, 7-1
The y coordinate of 6 is set as ymin, and this ymin is read out and set as the variable y in the common data area C2. Further, AEL is emptied by setting aep1=aep2=0. Next, when the edge entry process (step 65) in FIG. 7 is executed, aep1 points to _E61 and aep2 points to _E65 . Details of the edge entry process will be described later. Next, in step 66 of FIG. 7, since the AEL is no longer empty, the process proceeds to step 67 to initialize the EP. this
EP initialization (step 67) is as shown in Figure 10.
EP1, 9-1 points to the first left ridgeline, EP2,
9-2 points to the first right ridgeline, and PEP
This is an operation to set PEP1, 8-1 and PEP2, 8-2 to 0. Also, EP update (step 70) is performed for EP1, 9-1, EP2, 9-2 as shown in Figure 10.
are moved to PEP1, 8-1, PEP2, 8-2 respectively, and the aep of the edge line data pointed to by EP1, 9-1, EP2, 9-2 are moved to EP1, 9-1, EP2, EP2, respectively.
By resetting to 9-2, the AEL is moved one step to the right. Also, the EP end determination (step 69) is EP1, 9-1 or EP2, 9
This is an operation to determine 0 of the value of aep pointed to by -2.

The segment generation process at step 68 in FIG.
As shown in FIG. 8, the left edge processor 29 and the right edge processor 30 operate in parallel and cooperate to generate segment data. That is, EP1,
Left edge data x ₁ , z ₁ , dx ₁ /dy, dz ₁ /dy indicated by 9-1 and right edge data x _r , z _r , indicated by EP 2, 9-2.
Use dx _r /dy and dz _r /dy to calculate and output segment data, update left and right edge data, and update left and right AEL. Segment data includes the y coordinate of the scanning line, the color c of the polygon, the x coordinate of the left end point x ₁ , the length of the segment x _r −x ₁ , the z coordinate of the left end point z ₁ , and the increment value of the z coordinate on the segment dz/ dx=z _r -z ₁ /x _r -x ₁ is calculated, written in this order to FIF05 in FIG. 1, and output (steps 74 to 80 and 86, 87). Addition and subtraction are performed by the arithmetic unit ALU
1, 16-1, and the division is calculated using the divider 31. In the left and right edge data, x ₁ , x _r ,
z ₁ , z _r , h ₁ , h _r are updated to the next scanning line. h ₁ =
0 or h _r =0, edge updating or edge exit processing is performed (steps 82 to 85). As shown in the upper part of FIG. 10, the left edge update (step 84a) updates the front left edge and the edge pointed to by PEP1, 8-1 to replace the current edge pointed to by EP1, 9-1 with the updated edge pointed to by pointer EP1, sep. Rewrite the update edge pointer aep. The left edge exit (step 85a) is performed by moving the aep of the front left edge to remove the left current edge, as shown in the upper part of FIG.
Rewrite PEP1, 8-1 for EP1, 9-1.
Shift the value of The right edge update (step 84b) and right edge exit (step 85b) are also similar as shown in the lower part of FIG. 10. Steps in Figure 7
71 scan line update changes the common data area y and the approach vertex data h' as shown in FIG. When h'=0 in step 72, edge entry processing (step 65) is executed. In this edge entry process, the entry vertex number is i, and the left entry edge is E _i1 ,
If the right entry edge is E _ir , E _i1 is the left AEL, E _ir
Insert into the right AEL so that the x coordinate is in ascending order.

FIG. 9 shows the edge entry processing procedure for E _i1 and E _ir . In this processing procedure, the left and right edge processor 2
Although processors 9 and 30 are operating in parallel, there is no interference between the two processors. In step 89, the vertex number i is read from the entry vertex data indicated by VP1, 7-1, and the value of i refers to E _i1 and E _ir , and is used by both edge processors 29, 30 in the AEL search process. Therefore, the entry vertex pointer VP1, 7-1
is saved in the common data area, and the value of i is set to VP1, 7.
-1 and VP2, 7-2, and set the entry vertex pointer to VP1, 7-2 immediately before the judgment process in step 96.
-1 shall be returned. The left edge processor 29 scans the left AEL using EP1, 9-1 and PEP1, 8-1, and in step 92a, EP1, 9
When the x-coordinate of the edge indicated by -1 exceeds the x-coordinate of E _i1 for the first time, the process proceeds to step 93a, and E _i1 and PEP
E _i1 is inserted by rewriting aep of 1 and 8-1. In step 96, when there are a plurality of approach vertices on the scanning line, h'=0 is stored, so the approach process for the next approach vertex is repeated through step 97. The same applies to the right edge processor 30 (steps 90b to 95b). Next, step 66 in Figure 7
At step 73, aep1 or aep2 is determined to be zero, and at step 73, VP1, h' (VP1, 7-1
h') in DM1 and DM12-1 is determined to be zero, and when both are zero, the scan conversion process is completed.

(Effects of the Invention) As explained above in detail, the scanning converter according to the present invention can directly decompose a polygon of any shape into scanning line segments, so there is no need for complicated procedures for dividing it into triangles, etc. A high-speed scan converter can be realized. Since polygons of arbitrary shapes can be handled, closed areas such as character patterns drawn on a plane or map areas with holes or islands can be scan-converted by approximating them to polygons. The embodiment of the present invention describes a method of interpolating the depth Z on the vertex of a polygon, but when a curved surface is approximated as a polyhedron, the brightness value I on the vertex is linearly interpolated in the same way as the depth Z. This also enables high-speed processing of smooth shading. In addition, since a large number of mutually independent scanning line segment data are output as output data, it is possible to create a high-performance image display device by dividing the image memory in units of scanning lines and connecting it to a multiprocessor that updates the memory in parallel. realizable.

[Brief explanation of the drawing]

FIG. 1 is a configuration diagram of a scan converter showing an embodiment of the present invention, FIGS. 2 a to e are explanatory diagrams of polygon data,
Figures 3 a to d are explanatory diagrams of the edge list and approach vertex list, Figure 4 is a flowchart of the edge list creation process, Figure 5 is an explanatory diagram of the calculation method of edge line data, and Figures 6 a and b are active diagrams. Illustration of Edgelist,
FIG. 7 is a flowchart of scan conversion processing, FIG. 8 is a flowchart of segment generation processing in FIG. 7, FIG. 9 is a flowchart of edge entry processing in FIG. 7, and FIG. 10 is an explanatory diagram of processing contents. , FIG. 11 is a block diagram of a conventional three-dimensional image display device, and FIGS. 12 a to 12 d are diagrams showing types of polygons. 1...Input terminal, 2...Internal bus, 3-1 to 3
-5...Bus driver, 4...Bus receiver, 5
...First-in first-out memory (FIF0), 6...Output terminal, 7-1, 7-2...Entry vertex pointer (VP
1, VP2), 8-1, 8-2... Previous edge pointer (PEP1, PEP2), 9-1, 9-2... Edge pointer (EP1, EP2), 10-1, 10-
2...Address multiplexer (MXA1,
MXA2), 11-1, 11-2... Address adder, 12-1, 12-2... Data memory (DM1, DM2), 13-1, 13-2... Data multiplexer (MXD1, MXD2), 14-
1, 14-2...Register (S1, S2), 15
-1, 15-2...Register (R1, R2), 1
6-1, 16-2... Arithmetic unit (ALU1, ALU
2), 17, 19, 20, 22...Register (R
3, R4, R5, R6), 18... Reciprocal table (INV), 21... Multiplier, 23... Micro program sequencer (SEQ), 24... Micro program memory (MPM), 25... Micro program register (MPR), 26, 27...data line, 28...control line, 29...left edge processor, 30...right edge processor, 31...
Divider, 32...Microprogram controller.

Claims (1)

[Scope of Claims] 1. A polygonal scan converter in a three-dimensional image display device, comprising: an input terminal, an output terminal, at least a first data memory, a first vertex pointer, a first edge pointer, and a first edge pointer. a left edge processor consisting of an arithmetic and logic operation unit; a right edge processor consisting of at least a second data memory, a second vertex pointer, a second edge pointer, and a second arithmetic and logic operation unit; A divider, a microprogram controller that controls the entire scan converter, and a connection between the input terminal, the output terminal, the left edge processor, the right edge processor, the divider, and the microprogram controller for data transfer. Polygon data consisting of an internal data bus, x coordinates, y coordinates, z coordinates, and a pointer to the next vertex, expressed as a series of vertex data arranged so that the internal area of the polygon is seen on the right side. is inputted from the input terminal and stored in the first and second data memories, and all edges surrounding the polygon are calculated using the y-coordinate using the left edge processor and the right edge processor. A series of left edge data consisting of initial values and increment values of x and z coordinates, height, and a pointer to the next edge, categorized into left edge that increases in the direction of increase and right edge that increases in the direction of decrease in y coordinate. is created in the first data memory, and a series of right edge data consisting of initial values and increment values of x and z coordinates, height, and a pointer to the next edge is created in the second data memory, calculating increment values of the x and z coordinates of the left and right edge data using the divider;
an edge line data creation process of creating in the first data memory a series of approach vertex data consisting of a y-coordinate, an approach difference, and a pointer to an approach edge, sorted in ascending order of the y-coordinate; and scan line initialization processing that points to the approach vertex of by the first vertex pointer, sets the y-coordinate of the scan line to the minimum value, and empties the left active edge list and the right active edge list; a scan line update process in which the y coordinate is increased by 1 and the approach difference is decreased by 1; and when the approach difference of the approach vertex data becomes 0, a pointer to the approach edge of the next approach vertex is added to the left active edge list. and edge entry processing for inserting the first pair of left and right edge data into the right active edge list so as to be sorted in ascending order of x-coordinates;
and an edge pointer initialization process that points by a second edge pointer, and an edge pointer that points to the next left and right edge data in the left and right active edge list by the first and second edge pointers each time left and right edge data is processed. updating processing, using the left and right edge data to create scanning line segment data belonging to the internal region of the polygon and consisting of at least the x and z coordinates of the left end point, the increment value of the z coordinate, and the length; segment generation processing for outputting to a terminal and updating the x and z coordinates of the left and right edge data to the values of the next scanning line; the scan line initialization processing; the scan line update processing; the edge entry processing; A scan converter characterized in that the pointer initialization process, the edge pointer update process, and the segment generation process are used to create all scan line segment data belonging to the internal area of the polygon and perform scan conversion. 2. The divider according to claim 1, wherein the divider has a reciprocal table that generates a reciprocal of a first input, and a multiplier that multiplies the output of the reciprocal table and a second input. Scan converter.