JPS61195469A - Picture displaying method - Google Patents

Abstract

PURPOSE:To simplify the interpolation calculation by determining the pixel on 2-dimensional display scope to which triangular area cut out from 3 dimensional object it belongs using the centroid of the triangular area and 3 side members of the triangle. CONSTITUTION:The surface of object is cut out into triangular unit area, and the data composed of object surface information connecting the 3 apexes of the triangular unit area. Out of these data, the position data of the apexes are perspectively converted into 2 dimensional plane which corresponds to display screen according to the sight position, and the data is obtained to indicate apex position on 2 dimensional plane which correspond with the 3 apexes. The centroid of the triangular area are obtained from these data, position relation between the centroid and pixel is judged, and the pixel is judged whether it is in the triangular area. Then, the object furnace information data is vertically placed at the apex position of the triangular area, and the triangular data plane is placed on the point edge of its, and interpolation calculation is made for the triangular area.

Description

[Detailed description of the invention] The present invention will be explained in the following order.

A: Industrial field of application B: Outline of the invention C: Conventional technology - Problems to be solved by the invention Effll! Means for solving one point F action G Example (G1) Shading processing (Figure 2) (G2) Hidden surface processing (Figures 3 and 4) (G3) Conversion processing procedure (Figure 1) Various tables Generation procedure (Figures 5 to 10) Linear interpolation, shading, hidden surface processing (Figures 11 to 16) (G4) Effects of the embodiment (G5) Variations H Effects of the invention A Field of industrial application The present invention relates to an image display method, and in particular to a method in which three-dimensional image information written in advance in a memory is converted into an image by computer processing and displayed three-dimensionally on a rask display screen of a display.

B. Summary of the Invention The present invention provides an image display method for converting and displaying the surface of an object in a three-dimensional space on a two-dimensional display screen of a display.
AI, UA2 are cut out, first data consisting of object surface information at the first vertex PX representing the three vertices of this unit area is obtained, and position data representing the position of the vertex PX among this first data is displayed. Obtain second data representing the positions of second vertices PI, P2, and P3 on the two-dimensional plane by performing perspective transformation to a two-dimensional plane corresponding to the rask display screen of Based on the object surface information of P t sP, the object surface information of pixels within the triangular area surrounded by the vertices PISPg,P is linearly interpolated.

At that time, it is determined whether or not the triangular area includes a pixel that becomes the processing point P by using the three straight lines DLI, DL2, and DL3 that form the three sides of the triangular area and the center of gravity P0. All pixels of the PC are straight lines DLI, DL2,
When the determination result that the processing point PC is on the centroid side of DL3 is obtained, by determining that the processing point PC is a pixel included in the triangular area, the interpolation calculation is performed only for the pixel for which the determination has been obtained. This is a good thing, so the calculation time can be further reduced.

C. Conventional technology Computer graphics (cG) is a technology for displaying three-dimensional image information on a display screen.
known as. In other words, in computer graphics, graphic image data regarding an object located in a three-dimensional space is written in advance as three-dimensional coordinate information in a memory, and this information is successively output and image transformed based on a predetermined calculation formula. By doing so, a graphic image that is three-dimensionally expressed on the display is obtained.

Here, in order to express an image three-dimensionally on a two-dimensional display screen, three methods are used when performing calculations for image conversion: perspective conversion processing, shadow processing, and hidden surface processing. There is.

Perspective transformation processing focuses on the fact that when the human eye looks at an object, things in the foreground appear large and things in the distance appear small, and by changing the size of the object according to the distance from the viewpoint. It represents a sense of distance.

In addition, shading processing focuses on the fact that the brightness of each surface appears to change to the human eye because the slope of each surface of an object differs with respect to a light source located at one point in three-dimensional space. , the undulations of the surface of an object are expressed by changing the brightness of each surface of the graphic image displayed on the display.

Furthermore, hidden surface processing focuses on the fact that when viewed from a viewpoint located at one point in three-dimensional space, the back side of a single object and the overlapping surfaces of objects in the back of multiple objects that appear to overlap each other cannot be seen. Perspective is expressed by not displaying the graphic image of the invisible part.

All of these processes are based on the idea that if we use physical calculations to apply the empirical rules for humans when it comes to objects located in three-dimensional space, we can express the object three-dimensionally when displayed. A number of algorithms have been proposed.

These processes can achieve some effect even when used alone, but by combining them as necessary, a more natural three-dimensional effect can be obtained. Two methods were used.

D Problems to be Solved by the Invention The first method is to predetermine the spatial positional relationships among the viewpoint, light source, and object, and then use the results obtained by perspective transformation processing, shading processing, and hidden surface processing as a data string. A graphic image is displayed by writing it into a memory and reading the memory as needed.

According to this first method, although it takes a lot of time to generate a data string to be written into the memory, there is an advantage that converting the image information itself does not require much time.

However, there are problems such as the need to determine the spatial position information of the viewpoints in advance, and when the number of viewpoints increases (the viewpoints move), it is necessary to form a data string for each viewpoint. Therefore, it has the disadvantage that the position of the viewpoint cannot be changed in detail and that it requires a large amount of memory capacity to store data strings, so it is practically used only when representing objects with relatively simple shapes. could not.

In addition, the second method makes it possible to initialize the spatial positional relationship between the light source and the object, and also allows perspective transformation processing, shadow processing, and hidden surface processing to be executed as subroutines. When position information is given, the above-described three-dimensional representation processing is sequentially executed.

According to the conventional graphic image display device using this second method, although the spatial position of the viewpoint can be set freely, the configuration is such that perspective transformation processing, shading processing, and hidden surface processing must be performed for each pixel. As a result, the amount of calculation required by the computer was enormous, making it impractical. For example, if the image is composed of 1000 x 1000 pixels, perspective conversion processing, shading processing, and hidden surface processing are performed for each pixel 1000 times.
The calculation has to be repeated 000 times, which has the drawback that the calculation processing time takes several hours, for example.

The present invention has been made in consideration of the above points, and among the above-mentioned second calculation processing methods, shadow processing and hidden surface processing, which particularly require a huge amount of calculation time, are significantly improved compared to conventional methods. The purpose of this paper is to propose an image display method that is simple and can be executed in a short period of time.

E Means for Solving the Problem In order to solve this problem, in the present invention, data regarding the surface of an object in a three-dimensional space when viewed from a predetermined viewpoint position is displayed on a two-dimensional display on a display. In an image display method for displaying and converting objects on a screen, an object 1.
Surfaces LA and 4A of 4 are triangular unit areas UAI and UA2
The first data consisting of the object surface information at the three vertices PX of the unit areas UAI and UA2 of the triangle is obtained, and the position data representing the position of the vertex PX of this first data is set to the viewpoint position. Based on this, perspective transformation is performed to a two-dimensional plane corresponding to the display screen of the display to obtain second data representing the positions of vertices P1, Pz, P, on the two-dimensional plane corresponding to the three vertices PX, and this Two of the three vertices P+, Pz, Pz represented by the second data
vertices P1 and Pt, Pz and PI, PI and PI
The first, second and third straight lines DLI, DL passing through respectively
The center of gravity P0 of the triangular area UAX surrounded by the first . Second and third straight lines DLI, DL2, DL
3, it is determined whether or not they are on the same side as the position of the center of gravity P, and as a result, the first, second, and third direct waDL
When a determination result is obtained that 1, DI, 2, and DL3 are all on the same side as the center of gravity, the processing point Pc is determined to be a pixel included in the triangular area UAX, and the determined triangular area The object surface information data included in the first data is vertically erected at the apex P+ -Pt of UAX and the position Ps, and a triangular data plane is attached to the tip of the object surface information data, and a processing point P included in the triangular area UAX of the display screen is obtained.

The intersection point between a straight line erected perpendicular to the data plane and the data plane is determined by interpolation calculation, and the data on the data plane at this intersection point is determined as the image data for the processing point Pc on the display screen of the display.

2 Actions To perform an interpolation operation for J A
It is necessary to confirm that the pixel serving as the processing point PC is included in the triangle UAX. If not, interpolation operations for other triangles must be performed. As a means for determining which triangular area UAX includes the processing point P for the pixel currently serving as the processing point Pc, in the present invention,
Focusing on the fact that the center of gravity of a triangle is always within the area surrounded by three sides, the straight line DLL that forms the three sides of the triangle area UAX,
Using DL2, DL3 and center of gravity P0, each straight line DLI,
Arithmetic processing can be easily performed by simply determining whether or not the processing point PC is on the center of gravity P0 side for DL2 and DL3. Therefore, the calculation time can be further reduced by this amount.

Embodiment G An embodiment of the present invention will be described in detail with reference to the drawings, in which image data of an object having a curved surface is converted.

In the graphic image conversion method described below, 2
The shadow processing and hidden surface processing necessary to express a three-dimensional graphic image on a dimensional rask screen are performed using the method described below.

(Gl) Shading processing Shading processing is a process of shading the surface of a graphic image displayed on a display.
When light is irradiated from the light source 2 to the curved surface IA, which has a surface of If the angle θ between the two changes, it will change accordingly. Therefore, for shading processing, the following formula % formula % (
1) Express the shadow caused by the light source 2 on the surface of the object l by expressing the brightness 1 at the position PL. In equation (1), D is a variable represented by a constant A. This variable A is 0 to the light source vector.
The inner product of the normal unit vector N0 at the position P1 is divided by the product of the light source vector '' and the absolute value of the normal unit vector N1, and this equation is The cosine c of the angle θ that 1′ makes with the light source vector
becomes osθ. .

In FIG. 2, the position of the light source 2 is represented by the position vector S81 of the light source 2 in absolute coordinates xy2, and the position P1 on the curved surface IA is represented by the position vector S1 of the curved surface. The slope of the curved surface IA at this position P1 is the slope of the curved surface IA
is represented by the normal unit vector N0 of , and the position pt
, the direction of the light incident from the light source 2 is expressed by 9, which is a vector drawn from the position fP1 to the light source 2, and the angle of incidence of the incident light is expressed by the normal unit vector N'' to the light source vector. 1 is expressed by the angle θ.

In this way, the brightness ■ at the position PI on the curved surface IA is determined by the variable A. Therefore, if the incident angle θ of the light incident on the position apt from the light source 2 changes, the variable A changes from -1 to +1 accordingly. By changing the range, the incident angle θ becomes the brightest (when the light source 2 is in the direction of the normal unit vector N1 set at the curved surface IA and WtP1), and from this state the incident angle θ becomes ±90 ”, the brightness at the position PI will become darker (the brightness I will become 0).

(G2) Hidden surface processing Hidden surface processing is the processing of graphic image data so that parts of the surface of an object that cannot be seen from the viewpoint are not displayed on the display. As shown in , a curved surface 4A formed by the surface of the object 4
Based on the fact that when viewed from viewpoint 3, there are visible parts (this is called the visible part) and invisible parts (this is called the invisible part), only the parts that correspond to the visible parts are displayed on the display. let

Here, the determination as to whether each part of the curved surface 4A is a visible part is made based on the following two conditions.

In other words, the first condition is that, as shown in FIG. 3, when viewing the curve W4A of the object 4 from the viewpoint 3 along the visual line 1tJIEL1, the line of sight ELL intersects the curved surface 4A at the point P11SP12.
, PI3, the surface portions at positions P12 and PI3 are the line of sight EL 117) Position fFfP11 on the viewpoint 3 side #aE
Due to the existence of a surface portion that intersects with L1, the surface portions at positions P12 and PI3 are determined to be invisible, and are therefore hidden by the surface portions located between object 4 and viewpoint 3. Image data conversion processing is performed such that the surface portion of the position pH that is visible on the virtual screen 5 is viewed through.

The second condition is that the surface portion of interest is not hidden by other curved surfaces. That is, in Figure 3,
When another object 6 exists between the curved surface 4A of the object 4 and the viewpoint 3, and the object 4 is viewed along the line of sight EL2, the line of sight EL2
intersects with the curved surface 6A of the object 6 and then intersects with the curved surface 4A of the object 4, the surface portion of the position P14 on the curved surface 4A of the object 4 is the curved surface 6 of the object 6 on the viewpoint 3 side.
It is hidden by the surface part of position jfEP15 on A,
Therefore, the invisible surface portion (the surface portion at position P14) is not displayed on the virtual screen 5, but the visible surface portion (the surface portion at position P1) is displayed.
The graphic image data is converted so as to display the surface area of 5).

The first condition (ie, visible-invisible) is determined by the method shown in FIG. That is, draw the line-of-sight unit vector E1 pointing in the direction of the viewpoint 3 on the surface of the point of interest P21 on the object 7 (for example, a circular sphere) having a closed curvature @7A, and draw this line-of-sight unit vector E0 and the normal line unit vector N1. When calculating the inner product, the necessary and sufficient condition for the surface portion of the point of interest P21 to be visible can be expressed as N*・Ell>O (3). Here, if the angle between the line-of-sight unit vector E0 and the normal unit vector N''' is φ, the value of the inner product of the line-of-sight unit vector E0 and the normal unit vector N''' is N''・E''-l N''l・IE“1・CoS
φ” cosφ −−−−−−(
4). Therefore, it can be seen that the condition for satisfying equation (3) is satisfied when φ is an acute angle, that is, π 0 × φ × □ . . . (5).

For example, if the angle φ is an acute angle, as shown by the intersection of the line of sight EL3 and the surface position P21 in FIG. ) satisfies the condition of the expression, therefore, the point of interest P21
It can be determined that the surface part of is visible. On the other hand, the fourth
As shown by the intersection of the line of sight EL3 and the surface portion of the point of interest P22 on the back side in the figure, when the angle φ becomes π/2 or more, the inner product of the line of sight level t (the vector E0 and the normal unit vector N0 becomes negative). Therefore, it can be determined that the condition of equation (3) is not satisfied and the surface portion of the target point P22 is invisible.

This determination is made by determining whether the slope of the surface portion of each point of interest existing on the curved surface 7A is oriented toward the viewpoint 3, and the points of interest that are determined to be visible by this determination are the same as those described above. If the second condition is satisfied, the point finally becomes visible (such a point is called a visible candidate point).

The determination of the second condition described above is then performed for the visible candidate point. In other words, as described above with reference to FIG.
The visible candidate point having the closest distance to viewpoint 3 is selected,
The visible candidate point is determined to be the final visible point.

(G3) Conversion processing procedure Kusunoki table's image display device using computer graphics is
A central processing unit (cPU) executes graphic image conversion processing according to the processing procedure shown in FIG.

First, in step SPI, the conversion processing program is started, and in step SP2, the position of viewpoint 3 (Fig. 3), the position of light source 2 (Fig. 2), and patches required when converting the graphic image are determined. The number is input by the operator.

At this time, the CPU, based on the three-dimensional graphic image data stored in advance, displays the three-dimensional graphic image represented by the graphic image data on the virtual screen 5 (the third point) determined by the viewpoint 3 specified in step SP2. 3) A perspective transformation matrix is generated that is used to transform points on the curved surface of the three-dimensional graphic image to corresponding points on the virtual screen 5 when viewing upward.

Next, as shown in FIG. 5, the CPU reads data DATA for l patches from the graphic image data to be converted, and cuts it into triangles in the next step SP5.

In the case of this embodiment, the triangles are cut out by sequentially arranging one batch of data DATA based on predetermined parameters at intervals such that the parameters are at equal intervals (not necessarily at equal intervals on the curved surface). 2nd group cutting line group Ll
and L2 are sequentially calculated. Here, the number of cutting lines included in the cutting line groups L1 and L2 is selected to be 5 vertically and horizontally, and the cutting line group Ll and the cutting line group L2 are They are set to intersect with each other in a grid pattern. In this way, the curved surface made up of data DATA for l patches is formed by cutting line groups Ll and L2.
is divided into a small area UA surrounded by two adjacent cutting lines, and the small head area UA is cut out so as to be surrounded by four intersection points PX.

The size of this small area UA is determined in relation to the number of pouches input in step SP2, so that when the small area UA is converted onto the rask screen of the display, the pixels included in the converted small area are The number is determined.

The small head area UA is divided into two triangular unit areas UAI and U by a diagonal line L3 connecting two mutually opposing intersection points.
A2, and thus the curved surface represented by the data DATA is divided into a large number of unit areas UAI and UA2. The number of pixels included in each unit area UAI and UA2 is set to, for example, about 20 to 30.

After cutting out the unit areas UAI and UA2 from the curved surface in this way, the CPU cuts out each unit area UAI and UA2.
The normal unit vector N″′ is calculated for the three intersection points at the vertices of 2.

In this way, dividing the data DATA of the curved surface to be processed into the triangular unit areas UAI and UA2 and obtaining data about the three vertices means that the triangular unit area UAI
And when UA2 is converted onto the rask display screen of the display, 20 to 3 included in the converted unit area
This means that the data for 0 pixels is represented by the data of three vertices, so by performing the subsequent processing based on the data of three vertices,
This means that data processing speed can be dramatically increased.

The CPU generates a table consisting of visible and invisible data to be used in hidden surface processing in the next step SP6. In this step, as shown in FIG. 6, the line-of-sight unit vector E'' is calculated for the three vertices of the unit areas UA1 and UA2, and the line-of-sight unit vector E'' and the normal unit vector N''' are The inner product is calculated, and the calculation result is stored in the visible-invisible table T of the table 10 provided inside the computer, as shown in FIG.
The data will be sequentially stored in ABLE4.

In this case, table 10 is the curved surface data DA for one batch.
TA (Fig. 5) in the direction in which the cutting line group L2 is arranged (this is called the U direction) and in the direction in which the cutting line group Ll is arranged (this is called the V direction). The data of each of the five intersection points Px is stored as data for one batch of 25 words.

In this way, the visible-invisible table TABLE4 stores the visible-invisible data for the 25 intersection points PX for each patch, and based on the codes, as described above with reference to FIG. 1 condition data will be generated.

Following this, the CPU generates a distance table in step SP7. This distance table is the curved surface data DA
As shown in FIG. 8 for each vertex of TA in correspondence with FIG.
ABLE3&:l: Store.

The distance data D of this distance table TABLE3 is used when determining the second condition (Fig. 3) in hidden surface processing, and the distance vector from the vertex PX to the viewpoint 3 is D"-E"-S ” ...river (6
), the absolute value of the distance vector D1' is obtained as the distance data D.

In this way, when distance data for a plurality of curved surface portions are obtained for the same pixel on the rask display screen of the display, the data for the curved surface portion closest to the viewpoint 3 can be determined.

Next, the CPU moves to step SP8 and performs a brightness table generation process. This step is to calculate the brightness at each vertex PX as shown in FIG. 9 corresponding to FIG. Calculate. Then, using the calculation result, calculate the cosine cos θ of the incident angle θ based on the inner product with the normal unit vector N1 of the vertex Px using the following formula, and set this as the variable A (.

Furthermore, using this variable A, the brightness I can be calculated using the following formula 1 formula % (9) Calculate by

Here, the value of the constant R is, for example, about 0.22, whereas the variable A fluctuates in the range of 0 to l (θ is ±π/2
), thus the brightness 1 changes according to the change in the direction of incidence from the light source 2 with respect to the vertex Px, and this provides the data used for the shading process described above with respect to FIG. The data is stored in brightness table TABLE2 of table 10 (FIG. 7).

Next, the CPU moves to step SP9 and executes perspective transformation processing. This perspective transformation process is performed as shown in FIG. 10 corresponding to FIG.
When the position of . Such conversion processing is performed in step S described above.
The position data of the vertex PX obtained in P5 is transferred to step S
Using the perspective transformation matrix generated in P3,
This is executed by performing a conversion operation on the Y plane, and the result of this operation is stored in the XY table TABLEI of table 10.

By executing this conversion process, data about vertices on a curved surface in three-dimensional space can be treated as data on the XY plane, and as a result,
The following processing can be executed based on the XY plane, that is, the rask display screen of the display.

(Thus, the CPU can generate data representing various types of object surface information at each vertex position of the triangle cut out based on the data for one patch in table 10, which is set as an initial value in the next step 5 PIO. It is determined whether or not the processing has been completed for all the patches, and if it has not been completed, the process returns to step SP4 and executes the data generation process for the next batch to table 10.As a result, in step 5 PIO , when a positive result is obtained, the CPU stores all the information representing the state of the curved surface to be displayed on the display screen in the table IO as data of the three vertex positions of the unit areas UAI and UA2 (Fig. 5). can be taken into account.

The curved surface information captured in the table 10 in this way is such that the unit areas UAI and UA2 are 20 to 20 on the display screen.
Since it corresponds to 30 pixels, the CPU selects the unit area U in the following steps 5P11 to 5P18.
For each pixel corresponding to AI and UA2, linear interpolation is performed using the data in Table 10 to obtain image data that has been subjected to shading processing and hidden surface processing, so that it appears three-dimensionally on the display screen of the display. Reproduces the processed planar image.

That is, the CPU executes display area determination processing in step 5PII. This process is a step of determining the display area for displaying the image to be displayed at approximately the center of the display screen with appropriate dimensions.As shown in FIG.
I (Fig. 7), the maximum value X saw and minimum value X m 5m in the X-axis direction of the perspective-transformed vertices constituting the two-dimensional display image DES, and the maximum value X m 5m in the Y-axis direction. Maximum value Y. and the minimum value Y17, respectively, and the maximum value X□8 and the minimum value X @ in the X-axis direction.
The center position XC of ia is determined by the following equation, and the maximum value Y in the Y-axis direction. , the center position Yc of the minimum value Y a i * is determined by the following equation. The center position (Xc, Yc) thus obtained is set as the center position of the rask display screen 11 of the display, and
A display area ARE is determined such that the display image DBS fits within the size of a frame buffer containing memory cells corresponding to pixels forming the display screen 11 of the display.

As is clear from FIG. 11, the displayed Kaesong ARE has a region from the maximum value X wamx to the minimum value X1 in the X-axis direction, and has the maximum value Y, 1. ~Minimum value Y,!
, has an area of .

After determining this display area ARE, the CPU executes subsequent processing steps only for pixels within the display area ARE. This means that the amount of conversion calculations for images to be displayed on the rask display screen can be further reduced. In other words, in general, when attempting to display an image that has undergone image conversion processing on the rask display screen, the frame buffer memory is calculated while calculating the presence or absence of image data to be displayed and its contents for all pixels that make up the rask display screen. A method is adopted in which the calculation results are stored in the corresponding memory area. This point 11
In the case of the figure, calculation processing is not performed for pixels on the rask display screen 11 that do not have data to be displayed.
In the end, the amount of image conversion calculations can be significantly reduced as a whole.

In the next step 5P12, the CPU selects unit areas UAI and UA2 (FIG. 5) in this display area ARE.
Position data DAT for one patch corresponding to two vertices Px
AX (Fig. 12) as xy table TA of table IO
Data is sequentially extracted from BLEI and interpolation calculation processing is performed on the data. Thus, the CPU displays the display screen 11 (Figure 11).
The triangular area UAIX inside the display area ARE
and supplies data for interpolation calculations to determine the brightness of pixels included in UA2X.

Next, in step 5P13, the CPU displays the display area A.
It is determined to which triangular area UAIX or UA2X the pixel (referred to as a processing point) Pc whose brightness is to be calculated and determined at the present moment among the pixels for one patch included in the RE belongs. This determination is made by perspectively transforming the three vertices of each triangular area UAIX and UA2X on the XY plane, as shown in FIG.
YI), point Pt (Xg, Yt), point Ps
(Xs, Ys) as vertices, these vertices PI, P
g, the straight line that connects 21 to each other! IIDLI,,DL2
, DL3, using its center of gravity P@(Xll, Yo), a processing point PC(
It is determined whether or not Xc, Yc) exists.

First, the equation of the straight line DLI between the vertex P and Pt'ciIl is expressed as (12), which is rewritten as (Y YI) (Xt - XI) - (yz - Y,) ( x-xt)-0--・-(13
) However, this formula (13) means that if the values of the X and Y coordinates of the point on the straight line DLI are substituted as the values of X and Y, the left side becomes O.

Therefore, let the left side of equation (13) be F (X, Y), and F
(XI Y)-(Y-Yl)(xt XI)(Yt
Y +) (X -
While the value of Y) becomes 0, if the coordinate values of points inside or outside of the straight line DL1 are substituted, F(XSY) becomes a number that becomes a positive or negative value.

Focusing on this point, the center of gravity P0 (Xs
, Yo ) coordinate value a! F'(XO,'y'a)-(yo-Yl)
CXt-XI)-(Yl-Yl)
(X, -XI) (17) and the value of F (xc, Yc) when substituting the coordinate values of the processing point Pc (Xc, Yc) F (Xe, Yc)'' (Yc YI) (Xz −X
t)-(Yt-Yt)(Xc
, YI) - F (XC, YC) > 0, processing point P
C (XcSYc) is the center of gravity of the direct WDLI P@ (Xll
, YI ) side.

Of course, in general, the center of gravity P @ (XI, Yl) is inside the triangular area UAX, so the position of the processing point PC (Xc, Yc) that satisfies the condition of equation (19) is the straight line DL.
It can be said that it is inside of 1.

Similar calculations are performed on the straight lines DL2 and DL3 forming the other sides of the triangular area UAX as shown in the following formula, F (Xc%Yc)-(Yc-Yl)(xa-xt)
(Y 3- Y g) (X c X g)...
...(20) F (Xc, Yc)-(Yc-Y3)(XI
-X3)(Y+-Ys)(Xc )
If a determination result is obtained that the product is positive, the processing point P
C (XcSYc) is located on the same side as the center of gravity Po (Xs, Ya) for all the straight lines vADL1, DL2, and DL3 (7) that constitute the three sides of the triangular area UAX. Of course, it is clear that the center of gravity of a triangle is generally on the inside of all three sides, so the processing point P, (Xc, Y
c) can be determined to exist within the triangular area UAX.

On the other hand, if a negative judgment result is obtained for one of the values of equations (18), (20), and (21), as shown in the following equation (%), processing point PC (Xc
, Yc) exists on the opposite side of the center of gravity P6 (XI, Y,) for one or more of the straight lines DLI, DL2, and DL3, and in this case, the processing point PC is inside the triangular area UAX. It turns out that there is no.

In this way, the position of the processing point PC is changed to the triangular area UAX
When it is determined that the processing point is outside of
The determination for new triangular areas UAX is repeated until a triangular area UAX that includes the inside thereof can be found.

As a result, when the triangular fifl area UAX in which the processing point Pc is located is found in step 5P13, the CPU moves to the next step 5P14 and executes visible or invisible determination processing by linear interpolation. This process is performed by the CPU in the visible-invisible table TABLE4 (7th
The visible-invisible data stored for the vertices Pt, Pg, Ps of the triangle are sequentially read out from FIG. Vl
,,vt,,vt, are set vertically. And visible-invisible data vII, vI! A visible-invisible plane vPX is stretched at the tip of , vI. This visible-invisible plane vpx is the visible-invisible data VI+ of the vertices P+ -Pt SPs.
, Vlt, Vls (7) When all of the values Nyotte and visible-invisible data V l+ -V Is have a value of "+1", a triangular area UA is created as shown in FIG. 14(A).
Visible-invisible plane vP extending upward and parallel to X
X is obtained, for which visible-invisible data V1. ~
(2) When I is all "-1", as shown in FIG. 14(B), a visible-invisible plane VPX extending in parallel below the triangular area UAX is obtained.

On the other hand, visible-invisible data V1. ~ ■ When a part of I (e.g., Vl and Vt) is "+1" and the other part (i.e., Vl3) is "-1", as shown in FIG. 14(c). Visible-invisible plane vP
X intersects the triangular area UAX, the visible-invisible plane vPX on the vertex Pl and P2 side is positive across the intersection line LIN, and the boundary i%1LIN is sandwiched between
The sign of the visible-invisible plane vPX on the vertex P side becomes negative.

Therefore, the intersection of the straight line LCI passing through the processing point Pc and perpendicular to the triangular area UAX (therefore, the rask display screen of the display) and the visible-invisible plane vPX is determined, and its value V1.
c is interpolated as visible-invisible data of the processing point PC.

In this way, the visible-invisible data vII, vI! about the three vertices P+, Pg, Ps are obtained from the three-dimensional curved surface to be displayed. , Via is obtained, visible-invisible data at all processing points PC (this represents pixels on the display screen) included in the triangular area UAX on the display screen can be converted to a straight line LCI passing through the processing point PC. This can be easily obtained by calculating the intersection of the visible-invisible plane vPX formed by a triangular plane (this becomes a linear interpolation calculation).

Incidentally, the linear interpolation operation is an operation for finding a solution between a plane and a straight line, and the solution can be easily and uniquely found.

Next, the CPU moves to step 5P15 and executes brightness determination processing by linear interpolation. This process, as shown in FIG. 15, includes luminance data 1 . , T
! , I is used to interpolate the luminance 6 at the processing point PC consisting of pixels included in the triangular mark area UAX, and the calculation process is performed according to the following procedure.

That is, the brightness data I+-1t, Is of the vertices P, , pg, P, of the triangular area UAX are read from the brightness table TABLE2 of the table 10, and the positions of the corresponding vertices PI%P, , P, on the display screen of the display are read out. stand vertically. Then, a brightness plane BPX connecting the tips of the brightness data 11s Izs13 is drawn. Then, a straight line LC2 is drawn perpendicularly to the display screen of the display from the processing point Pc for each pixel included in the triangular area UAX, and the straight line L
The intersection between C2 and the brightness plane BPX is determined, and the value of the brightness plane BPX at the intersection is determined to be 1°C at the processing point PC.

In this way, if all pixels included in the triangular area UAX are sequentially selected as processing points PC, a three-dimensional curved Luminance data for all pixels can be easily obtained from the three pieces of luminance data obtained from .

Incidentally, in this case as well, the solution between the straight line LC2 and the plane BPX is determined, so the calculation is simple and the solution is uniquely determined.

Next, in step 5P16, the CPU executes distance determination processing by interpolation calculation. As shown in FIG. 16, this process interpolates the distance from the viewpoint for pixels included in the triangular area UAX on the display screen of the display, and the CPU performs the interpolation calculation according to the following processing steps. .

That is, first, the vertex P on the display screen of the display,
Let the distance data DI%D, ,D, for P and P2 be,
Read from the distance table TABLE3 of table 10 and stand vertically at the positions of vertices P*, Pg, and Ps. Then, a distance plane DPX is stretched so as to connect the ends of the distance data Dt, Dt, D, leaving a processing point Pc, and the intersection point of the distance plane DPX and a straight line LC3 that is perpendicular to the display screen of the display is calculated. . Then, the value Ds>c of the distance plane DPX at this intersection is determined as distance data from the viewpoint of the processing point PC.

Thus, in this case as well, by sequentially specifying all the pixels included in the triangular area UAX as the processing point Pc, the distance data Dtsc of the processing point PC can be obtained by linear interpolation calculation. In this case as well, since the interpolation calculation involves finding a solution between the straight line LC3 and the distance plane DPX, a unique solution can be found by a simple calculation.

Thereafter, the CPU moves to step 5PI7 and executes pixel data generation processing based on distance comparison. This process calculates the brightness data corresponding to the curved surface with the smallest distance data Dec for all pixels included in the display area ARE (FIG. 11) on the west display surface of the display. , C (Figure 15) and visible-invisible data VI,
c (FIG. 14), luminance data for the curved surface for which visible data is obtained and for which the distance data Dme is the smallest is generated as pixel data to be displayed on the display.

In practice, the CPU has a frame buffer memory having a memory cell corresponding to each pixel of the display, and a depth buffer memory corresponding to each pixel of the frame buffer memory, and in step 5P16, distance data D□ is determined, and when the smallest distance data D, c is obtained for the same pixel, the distance data is stored in the memory area corresponding to the pixel in the depth buffer memory, and the brightness determined in step 5P15 is The data ■□ are written to the frame buffer memory, and thus the luminance data llIC obtained from the curved surface with the smallest distance data D□ is written to the frame buffer memory.

The series of arithmetic processing in steps 5P12 to 5P17 is executed for each pixel included in one patch, and the CP
Every time the processing in step 5PL7 is completed, U judges in step 5P18 whether or not the arithmetic processing for all patches has been completed, and when a negative result is obtained, it returns to step 5PI2 again and calculates data for a new pixel. Repeat the calculation process. For this step 5P1B
If a positive result is obtained in step 5P, the CPU
The program moves to step 19 and ends the program.

(G4) Effects of the Embodiment According to the data processing method shown in FIG. 1, a perspective-converted image of an object curved surface in a three-dimensional space viewed from a predetermined viewpoint position is converted and displayed on a two-dimensional display screen of a display. In this way, the curved surface of an object in a three-dimensional space is cut out into triangular unit areas UAI and UA2, and the object surface information at the three vertices px is obtained as data in the three-dimensional space. After perspectively converting the two vertices PX to a two-dimensional plane forming the rask display screen of the display, the vertices P converted to the two-dimensional plane,
By constructing a triangular data plane consisting of the object surface information obtained from the curved surface using the positions , p, , ps, we can calculate linearly from the data plane for each and every pixel included in the triangular area on the display screen. Image data can be obtained by interpolation calculations.

In this way, only three pieces of data are required for each unit area when performing perspective transformation from the surface of an object in three-dimensional space to a two-dimensional plane, which further reduces the transformation calculation time. In order to obtain image data for each pixel, it is only necessary to perform an operation to find a solution between a plane and a straight line, so this interpolation operation is linear, and a simple operation in which the solution is uniquely determined is sufficient.

Furthermore, according to the image display method shown in FIG. 1, the data plane is formed based on the triangular area UAX on the two-dimensional plane, so that the position of the light source is shown on the screen displayed on the display. It is possible to easily apply appropriate shading, and thus the undulations on the curved surface can be reliably expressed.

Furthermore, according to the image display method shown in FIG. 1, by creating a visible-invisible data plane based on a two-dimensional plane, when a visible area and an invisible area exist within the triangular area UAX on the two-dimensional plane, Also, the boundary between the visible region and the invisible region can be clearly determined based on the linear interpolation result for each pixel, and thus hidden surface processing can be easily realized.

In addition, when performing such hidden surface processing, when multiple pieces of visible data are obtained for the same pixel, the distance data representing the distance from the unit area UAI and UA2 on the curved surface to the viewpoint is used to select the curved surface with the shortest distance. By determining that only the image data of 1 is valid and displaying it, hidden surface processing can be performed reliably without confusion, and thus an image with a clear sense of perspective can be obtained on the display screen of the display. I can do it.

Furthermore, according to the image display method shown in FIG. 1, when performing interpolation calculations on the triangular area UAX obtained by perspective transformation into a two-dimensional plane, the processing point Pc corresponding to the currently processed pixel is located in which triangular area UAX. In order to detect whether it belongs to the triangular area UAX0, the straight lines DL1, DL2, and DL3 that constitute the three sides of the triangular area UAX0 and the triangular area U
Using the center of gravity P0 of AX, it is easy to calculate (
Since i1 can be recognized, the overall calculation processing time can be further shortened.

In executing such image conversion processing, data regarding objects in a three-dimensional space viewed from a specified viewpoint are
As a result of perspective transformation to a dimensional plane, a display area ARE (Fig. 11) in which the converted data is located is determined, and a series of subsequent image display processing operations (i.e.,
Determining the triangular area where the processing point is located, determining whether it is visible or invisible,
(determination of the distance from the viewpoint, determination of the visible surface, etc.), the overall calculation time can be further reduced.

(G5) Modification In the above embodiment, data representing the surface of an object surrounded by a curved surface is used as data regarding an object in a three-dimensional space. However, the present invention is not limited to this. The present invention can be similarly applied to the case of using data representing the surface of an object.

H Effects of the Invention As described above, according to the present invention, the curved surface of an object in a three-dimensional space is cut out into triangular unit areas UAI and UA2, and the unit areas UAI and UA2 are divided by the three vertices PX of the unit areas UAI and UA2. In an image display method that represents the image information of UA2 and obtains a perspective transformation image on a two-dimensional display screen using the unit areas UAI and UA2 as units, each pixel on the two-dimensional display screen By using the center of gravity and three sides of each triangular region to determine which triangular region is included in the triangular region, the interpolation calculation process can be further simplified.

[Brief explanation of the drawing]

FIG. 1 is a flowchart showing an embodiment of the image display method according to the present invention, FIG. 2 is a route map showing the principle of the shadow processing method, and FIGS. 3 and 4 are route maps showing the principle of the hidden surface processing method. , Fig. 5 is a route map showing the procedure for cutting out a triangular unit area, Fig. 6 is a route map showing the procedure for generating visible-invisible data, and Fig. 7 is a route map showing the procedure for generating visible-invisible data. FIG. 8 is a route map showing the distance data generation procedure; FIG. 9 is the route map showing the brightness data generation procedure; FIG. 1θ is the route map showing the appropriate viewing conversion procedure; Figure 11 is a route map showing the procedure for determining the display area;
Figure 12 is a route map showing the procedure for extracting vertex data within the display area, Figure 13 is a route map showing the procedure for determining whether a processing point is in a triangular area, and Figure 14 is visible-invisible data. FIG. 15 is a route map showing the interpolation procedure for luminance data, and FIG. 16 is a route map showing the interpolation procedure for distance data. 14.6...Object, IA, 4A, 6A...
...Curved surface, 2-...Light source, 3...Viewpoint,
11...Display screen.

Claims (1)

[Scope of Claims] An image display method for converting and displaying data regarding the surface of an object in a three-dimensional space when viewed from a predetermined viewpoint position on a two-dimensional display screen of a display, comprising: (a) the above-mentioned method; Cutting out the surface of the object into a triangular unit area, obtaining first data consisting of object surface information at a first vertex consisting of three vertices of the triangular unit area, (b) among the above first data; The position data representing the position of the first vertex is perspectively transformed into a two-dimensional plane corresponding to the display screen of the display based on the viewpoint position, and the position data on the two-dimensional plane corresponding to the first vertex is Obtaining second data representing the position of the second vertex, (c) forming first, second, and third straight lines passing through two of the three vertices represented by the second data, respectively; (d) The position of the processing point made up of pixels on the display screen is
With respect to the first, second, and third straight lines, it is determined whether or not they are on the same side as the center of gravity, and as a result, all of the first, second, and third straight lines are When a determination result indicating that the processing point is on the same side as the center of gravity is obtained, the processing point is determined to be a pixel included in the triangular area, and (e) the processing point is placed at the second vertex position of the determined triangular area. The object surface information data included in the first data is erected vertically, and a triangular data plane is attached to the tip thereof; (f) a straight line is erected perpendicularly to the processing point included in the triangular area of the display screen; (g) determining the data of the data plane at the intersection point as image data for the processing point on the display screen of the display;