JPS61195468A - Picture displaying method - Google Patents

Abstract

PURPOSE:To make shadow processing of a picture by simple calculation, by cutting out the surface of object placed in a dimensional space into triangular unit area, and by calculating the inner product of sight direction vector at each apex and the normal line unit vector of the surface. CONSTITUTION:The surface of object is cut out into triangular unit area, and the inner product of sight direction vectors at 3 apexes of the unit area and normal line unit vector. According to the sign of the calculation result, the visible-invisible data to show whether the apex is in visible area or invisible area is obtained. On the other hand, the position data of these 3 apexes is prospectively converted into 2-dimensional plane which corresponds with a display scope according to the sight position, and forms triangular area which corresponds with the area on 2-dimensional plane. And, by making interpolation calculation about visible-invisible data with respect to a pixel within the triangular area, the border line is established between visible area and invisible area on the 2-dimensional plane.

Description

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

A. Industrial field of application B. Overview of the invention C. Conventional technology Problems to be solved by the invention E. Means for solving the problems 1. Effect G. Example (G1) Shading processing (Figure 2) (G2) Hidden surface processing (Figures 3 and 4) (G3) Conversion processing procedure (Figure 1) Various table generation procedures (Figures 5 to 10) Linear interpolation, shading, hidden surface processing (Figures 11 to 16) (G4) Effect of the embodiment (G5) Modification H Effect of the invention A Field of industrial application The present invention relates to an image display method, and in particular, the present invention relates to an image display method, and in particular, three-dimensional image information written in advance in a memory is displayed by computer processing. This converts the image and displays it three-dimensionally on the rask display screen of the display.

B Summary of the Invention In the first invention, in 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, the surface of the object is cut out into a triangular unit area, and the unit area is It is obtained by calculating the inner product of the vector in the line of sight direction and the normal unit vector of the surface at the three vertices of Obtain visible-invisible data representing - Perspectively transform the position data for the three vertices of the 10,000 unit area into a two-dimensional plane corresponding to the display screen of the display based on the viewpoint position to form a corresponding triangular area on the two-dimensional plane, and By performing a linear interpolation operation on visible-invisible data for the included pixels, boundaries between visible and invisible areas can be clearly formed on a two-dimensional plane, and thus negative image processing can be easily performed.

Further, in the second invention, in addition to this configuration, when visibility determination results are obtained for a plurality of surfaces for the same pixel, the distance from the viewpoint is expressed for each vertex of a unit area on the surface of the object. Distance data is obtained, and any data other than the image data for the surface with the smallest distance data is determined to be the surface of the unit mackerel area in the negative image, and is not displayed on the display. Ensure that the process can be carried out reliably.

C. Conventional technology Computer graphics (cG) is a technology for displaying three-dimensional image information three-dimensionally on a display screen.
known as. In other words, computer graphics involves writing graphic image data regarding an object located in a three-dimensional space into a memory in advance as three-dimensional coordinate information, reading out this information, and converting the image based on a predetermined calculation formula. This provides a three-dimensional graphic image on the display.

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 the object is different relative to the light source located at one point in three-dimensional space. However, the undulations of the surface of the 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 behind are invisible among multiple objects that appear to overlap each other. Perspective is expressed by not displaying the graphic image of the invisible part.

All of these processes are based on the idea that if the empirical rules used when humans view an object located in a three-dimensional space are realized through physical calculations, the object can be expressed three-dimensionally when displayed. Several 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. For this reason, 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 in practice it is only useful when representing objects with relatively simple shapes. Couldn't use it.

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. For example, if the image is composed of 1000 x 1000 pixels, perspective transformation processing, shading processing, and hidden surface processing are performed for each pixel for one viewpoint. 1000 to
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.

EMeans for solving the problem In order to solve the problem, in the first invention, 3.
In an image display method for converting and displaying data regarding the surface of an object in a dimensional space when viewed from a predetermined viewpoint position on a two-dimensional display screen of a display, an object 1.4 viewed from a viewpoint position 3 The surfaces IA and 4A are cut out into triangular unit areas UA1 and UA2, and the first vertex PX is formed by the three vertices of the triangular unit areas UA1 and UA2.
The first position data representing the position of Obtain visible-invisible data indicating that it is an invisible area, and based on the viewpoint position, perspectively transform the first position data into a two-dimensional plane forming the rask display screen of the display to correspond to the three vertices px. Obtain second position data representing the positions of the second vertices P+, Pg, and P3, and set visible-invisible data vertically at the positions of the second vertices P+, Pg, and Ps on the two-dimensional plane. The visible-invisible data plane ■PX of the triangle is stretched, and the second vertices P+, P on the two-dimensional plane
g, The intersection point between the straight line perpendicular to the processing point pc, which is made up of pixels included in the triangular area UAX surrounded by Ps, and the visible-invisible data plane ■PX is determined by interpolation, and the visible-invisible data at this intersection point is calculated. When the data contents of the plane VBX are invisible, the unit areas UAI and UA
It is determined that the surface of No. 2 is a hidden surface, and the processing point P is determined.

Prevent image data from being displayed.

Further, in a second invention, in 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, .4 surface IA, 4A
is cut out into triangular unit areas UAI and UA2, and first position data representing the position of the first vertex PX consisting of the three vertices of the triangular unit areas UAI and UA2, and the line of sight at the position of this first vertex PX. Inner product E1 of direction vector E0 and surface normal unit vector N0 Visible-invisible data obtained by calculating N1 and indicating that it is a visible or invisible area depending on the sign of the calculation result, and the first vertex Distance data representing the distance from the PX position to the viewpoint 3 is obtained, and the first position data is calculated based on the viewpoint position on a two-dimensional plane 5 corresponding to the display screen of the display.
The second vertices Pt and Pg −Ps on the two-dimensional plane corresponding to the first vertex px are
Obtain the position data of the second vertex pt on the two-dimensional plane,
The visible-invisible data is set vertically at the pm and ps positions, and a triangular visible-invisible data plane vPX is attached to the tip of the visible-invisible data plane vPX, and the triangle surrounded by the second vertices P,, Po, and Pg on the two-dimensional plane The first line between a straight line perpendicular to the processing point PC included in the area UAX and the visible-invisible data plane vPX.
When the data content of the visible-invisible data plane vPX at this first intersection point is invisible, it is determined that the curved surfaces of the unit areas UAI and UA2 are hidden surfaces, and the image is transferred to the processing point PC. In addition to not displaying the data, if there are multiple surfaces for which the content of the visible-invisible data at the first intersection point is determined to be visible for the same processing point Pc, the two-dimensional plane Place the distance data vertically at the second vertices P, , P, , P3 above, and attach a triangular distance data plane DPX to the tip of the distance data, and set the distance data at the second vertices P of the two-dimensional plane.
The second intersection point between the distance data plane DPX and a straight line perpendicular to the processing point PC included in the triangular area UAX surrounded by I', Pg, and Pz is found by interpolation, and the second intersection of the surfaces IA and 4A is Distance data plane D at the intersection of 2
For data other than the data for the surface with the smallest data content of PX, it is determined that the surfaces of the unit areas υA1 and UA2 are hidden surfaces, and the image data is not displayed at the processing point Pc.

2 Effects In the first invention, for the surface IA of the object 14 in the three-dimensional space, the unit area UAI of 4A, and the three vertices PX of tJA2, the vector E1 in the viewing direction and the normal unit vector N'' Calculate the inner product N1 ・Eo.The result of this inner product calculation is the normal unit vector N* and the line-of-sight vector E
It is expressed as the cosine cos φ of the angle φ formed with 1, and therefore, when the surfaces IA and 4A have a surface portion facing the viewpoint 3, it becomes a positive value. On the other hand, when φ becomes ±π/2, it becomes 0, and when it becomes a value of ±π/2 or more, the value of the inner product becomes negative.

Therefore, if the sign of the inner product calculation result is 0 or negative, it can be determined that the unit areas UAI and UA2 are on the hidden surface.

In this way, it is possible to easily determine whether or not the data corresponds to a surface portion that is a hidden surface based on the sign of the inner product calculation result, so that the calculation time can be shortened accordingly.

In addition to this, in the second invention, the same processing point PC
, distance data representing distance is obtained from visible-invisible data obtained from multiple surfaces IA and 4A on the same line of sight, and for surfaces other than the surface for which the content of the distance data is the smallest, this is calculated as a hidden surface. By determining that there is a hidden surface, the determination of a hidden surface can be made more reliable.

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.

(G1) Shading processing Shading processing is a process of shading the surface of a graphic image displayed on a display.As shown in Fig. 2, an object 1 arranged in a three-dimensional space expressed by absolute coordinates xyz
When light is irradiated from the light source 2 to the curved surface IA, which has a surface of If the angle θ made between
) expresses the shadow caused by the light source 2 on the surface of the object 1 by expressing the brightness ■ at the position P1. In equation (1), D is a variable represented by a constant A. This variable A is the light source vector K”
The inner product of the normal unit vector N” at the position P1 is
It is expressed by the formula divided by the product of the absolute values of the light source vector K" and the normal unit vector N", and this formula is the normal unit vector N*
The cosine cosθ of the angle θ that * makes to the light source vector
become.

In FIG. 2, the position of the light source 2 is represented by the position vector S88 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 curved surface I
is represented by the normal unit vector N1 of A, and the position P
1, the direction of the light incident from the light source 2 is represented by 0 on the vector drawn from the position P1 to the light source 2, and the angle of incidence of the incident light is 1 on the light source vector with respect to the normal unit vector N1. It is expressed by the angle θ formed by

In this way, the brightness ■ at the position P1 on the curved surface IA is determined by the variable. Therefore, if the incident angle θ of the light incident on the position P1 from the light source 2 changes, the variable A changes from -1 to +1 accordingly. By changing the range, the incident angle θ becomes 0° (that is, the normal unit vector N* set at the position Pl of the curved surface IA)
(when the light source 2 is in the direction of
The brightness of becomes darker (the brightness becomes O)
It turns out.

(G2) Hidden surface processing Hidden surface processing refers to processing graphic image data so that parts of the surface of an object that are not visible from the viewpoint are displayed on the display. This processing is shown in Figure 3. 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.

That is, the first condition is that, as shown in FIG. 3, when viewing the curved surface 4A of the object 4 from the viewpoint 3 along the line of sight ELI, the points P11, PI3, PI where the line of sight ELI intersects the curved surface 4A are
3, the surface portions at positions P12 and PI3 are in the line of sight EL.
The presence of a surface portion that intersects the line of sight EL1 at the position pH on the viewpoint 3 side of I results in being hidden by the surface portion, and therefore the surface portions at positions P12 and PI3 are determined to be invisible, Image data conversion processing is performed to see through the surface portion of the position pH that is visible on the virtual screen 5 provided between the object 4 and the viewpoint 3.

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.
The position P of Ah is hidden by the surface portion of 15, and therefore the invisible surface portion (position P
The visible surface portion (position P15) is not displayed.
The graphic image data is converted so as to display the surface area).

The first condition (ie, visible-invisible) is determined by the method shown in FIG. That is, draw a line-of-sight unit vector E0 pointing in the direction of the viewpoint 3 at the point of interest P210 on the object 7 (for example, a circular sphere) having the closed curved surface 7A,
When calculating the inner product of this line-of-sight unit vector E* and normal unit vector N0, the necessary and sufficient condition for the point of interest P210 to be visible is N1・E">0 - (3) Here, if the angle of the line-of-sight unit vector E* and the modulus wAm order 6 vectors N' is φ, then line-of-sight unit vector E
The value of the inner product of the position vector E1 and the normal unit vector N” is N1・E”−lN”l・IE* 1・cos φ”
cosφ ・・・・・・(4) Therefore, the condition for satisfying equation (3) is satisfied when φ is an acute angle, that is, 0〈φ×□ ・・・・・・(5) I understand that.

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. The condition of equation (3) is satisfied, so it can be determined that the surface of the point of interest P21 is visible.On the other hand, as shown by the intersection of the line of sight EL3 and the surface of the point of interest P22 on the back side in FIG. When the angle φ becomes π/2 or more, the inner product of the line-of-sight unit vector E* and the normal unit vector N* becomes negative, so the condition of equation (3) is not satisfied and the surface portion of the target point P22 can be considered invisible.

This judgment is made by determining whether the slope of the surface portion of each point of interest existing on the curved surface A is oriented toward the viewpoint 3, and the points of interest that are determined to be visible by this judgment are A point finally becomes a visible point if it satisfies the second condition described above (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. 3, among the plurality of visible candidate points (Pll, PI3), (PI3, PI3) on the same line of sight ELL, EL2, the visible candidate point having the closest distance to viewpoint 3 is The selected visible candidate point is determined to be the final visible point.

(G3) Conversion processing procedure ■ Satonoji 1st soil! An 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 out one batch of data DATA from among 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 the data DATA for one patch at intervals such that the parameters are at equal intervals (not necessarily at equal intervals on the curved surface) based on predetermined parameters. 2nd group cutting line group L1
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. (Then, with data DATA for one patch, the Naro curved surface is divided into cutting line groups L1 and L2.
is divided into a small area UA surrounded by two adjacent cutting lines, and the small area tJA 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 patches 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 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 υA.
The normal unit vector N1 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 inner product of this line-of-sight unit vector E1 and the normal unit vector N1 is calculated. , this calculation result is stored in the visible-invisible table TAB of the table 10 provided inside the computer, as shown in FIG.
Store them in LE4 sequentially.

In this case, the table 10 contains the surface data DA for l patches.
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 L i is arranged (this is called the V direction). The data of each of the five intersection points PX is stored as data for one patch 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.
Store in ABLE3.

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 expressed as D" = E" -3 ” ・・・・・・
After calculating according to (6), the absolute value of the distance vector D0 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, the cosine CO3θ of the incident angle θ is calculated based on the inner product with the normal unit vector N'' of the vertex PX, and this is set as a variable A.

Furthermore, using this variable A, calculate the brightness! 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 θ to l (θ is ±π/2
). In this way, the brightness I changes in response to changes in the light incident on the vertex PX from the light source 2, and this provides data used for the shading process described above with respect to FIG. ) is stored in the brightness table TABLE2.

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 IO.

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.

In this way, 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 l patches in the table 10, and in the next step 5PIO, all the data set as initial values It is determined whether or not the processing for the patch has been completed, and if it has not been completed, the process returns to step SP4 to execute data generation processing for the next patch in the table IO. As a result, if a positive result is obtained in step 5PlO,
The CPU stores all information representing the state of the curved surface to be displayed on the display screen in the unit areas UAI and U.
A2 (FIG. 5) can be imported into the table IO as data of the three vertex positions.

1. The curved surface information thus methodically imported into the table 10 is such that the unit areas UAI and UA2 are 20 to 20 on the display screen of the display.
Since it corresponds to 30 pixels, the CPU selects the unit area U in the following steps 5PII to 5P1B.
For each pixel corresponding to AI and UA2, linear interpolation calculations are performed using the data in Table 10 to obtain image data that has undergone shading processing and positive image 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 a display area for displaying an image to be displayed at approximately the center of the display screen with appropriate dimensions.As shown in FIG.
(FIG. 7), the maximum value X11 in the X-axis direction of the perspective-transformed vertices constituting the two-dimensional display image DES. and the minimum value X + sim, the maximum value Y in the Y-axis direction, □, and the minimum value Y1. ．． and the maximum value X, 18 and the minimum value X*ia in the X-axis direction.
The center position Xc of the maximum value Y, . The center position thus obtained (Xc.

Yc) is set at 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 having memory cells corresponding to pixels forming the display screen 11 of the display. .

Here, as is clear from FIG. 11, the display area ARE has an area from maximum value ,1
．． It 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. In this respect, in the case of FIG. 11, since arithmetic processing is not performed on pixels on the rask display screen 11 for which there is no data to be displayed, the overall amount of image conversion calculation can be significantly reduced.

In the next step 5P12, the CPU selects unit areas UAI and UA2 (FIG. 5) in this display area ARE.
One batch of position data DAT corresponding to one vertex PX
AX (Fig. 12) as XY table TA of table 10
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 PC (referred to as a processing point) whose brightness is to be calculated and determined at the present time belongs to among the pixels for one patch included in the RE. As shown in FIG. 13, this determination is made at a point PI (X
I, YI), point Pz (Xt SYt), point Ps
CXs, ys) as vertices, these vertices P, , P
, 23 are connected to each other by straight lines DLI , DL2 , DL
Using the center of gravity Pa (Xo, Yo) of the triangular area UAX surrounded by 3, a processing point PC (XcSY
Determine whether c) exists.

First, the equation of direct*DL1 passing through vertices P and P2 is expressed as (12), and rewriting this, (Y-Yl)(xz -XI) -(Yt -Yl) ( X-XI)-0...(
13) However, this equation (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 0.

Therefore, the left side of equation (13) is set as F (XSY), and F
(Xt Y)-(Y-yo(Xs Xt)(Yg-Y
t) (X
, Y) becomes 0, but if the coordinate values of points inside or outside 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
, YI ) coordinate value Xt + X 2 +
z Xt) - (YI - YI) (XI - F (Xc, Yc) - (Yc - Yl) (Xt - xt)
-(Yg YI)(Xc
, yo)-F (Xc, Me) >'0...
...(19), it can be determined that the processing point PC (Xc, Yc) is on the center of gravity P (1 (Xll, Yo) side of the straight line DLI.

Of course, the center of gravity Pa (Xo, Yo) is generally 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 D.
It can be said that it is inside the LI.

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 - Yt) (XI - xt)
(Ys Yz) (Xc −Xs) ・・・・・・(20) F (XcSYc)= (Y−−Ys)(Xt−Xs
)-(Yt-Ys) (Xc-Xs)...
(21) Based on the calculation results, as described above for equation (19), F (Xs, Yo) and F (Xc, Yc)
If a determination result is obtained that the product is positive, the processing point P
c (Xc, Yc) is the center of gravity P for all straight lines DLI, DL2, and DL3 that constitute the three sides of the triangular area UAX.
It will be on the same side as a (Xo, Yo). Heat Theory Generally speaking, it is clear that the center of gravity of a triangle is on the inside of all three sides, so the processing point P, (Xc, Yc
) 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') is any one of the straight lines DLI, DL2, and DL3.
It can be seen that one or more of the points exist on the opposite side from the center of gravity P(1(XOlY,), and that the processing point PC is not inside the triangular area UAX.

In this way, the position of the processing point P9 is changed to the triangular area UAX
When it is determined that the triangle M
processing point PC without performing subsequent interpolation operations on the area.
The determination for a new triangular area UAX is repeated until a triangular area υAX that includes the inside thereof can be found.

As a result, when the triangular area UAX in which the processing point Pe 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
From the visible-invisible table TABLE 4 (FIG. 7) of 0, the vertices of the triangle are sequentially changed to P+ 1P! , Ps is read out, and as shown in FIG.
+, Pt, and Ps, the corresponding visible-invisible data V1+, Vlt, and VIs are set vertically. Then, a visible-invisible plane vPx is set at the tips of the visible-invisible data VIl, Vl, , Vls. This visible-invisible plane vpx is the visible-invisible data VI t , VI z , VI s of the vertices P1, P2, P (depending on the D value, the visible-invisible data V 1 *'=VI
When all s have the value of "+l", Figure 14 (A)
As shown in FIG. 14 (B ), the triangular area UA
A visible-invisible plane vPX is obtained that extends parallel to and below X.

On the other hand, if some of the visible-invisible data Vt, -Vl (e.g., Vl and Vt) are "+1" and the other part (i.e., Vl,) is r-IJ, is the visible-invisible plane vP as shown in FIG. 14(c).
X intersects the triangular area UAX, and the vertices P and P! The visible-invisible plane vpX on the side is positive, and across the boundary vALTN,
The sign of the visible-invisible plane vPX on the vertex P side becomes negative.

Therefore, a straight line LC'l passing through the processing point PC and perpendicular to the triangular area UAX (therefore, the rask display surface of the display)
and the visible-invisible plane vPx, and its value vI
,. is interpolated as visible-invisible data of the processing point PC.

In this way, visible-invisible data vt, v1 . , Vl, the triangular area UA on the display screen
The visible-invisible data at all processing points P, (which represent pixels on the display screen) included in
Visible line consisting of straight line LCI passing through processing point PC and triangular plane -
This can be easily obtained by calculating the intersection with the invisible plane vpx (this is 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, involves the luminance data I*,
Based on It, 4m, the brightness IC at the processing point PC consisting of pixels included in the triangular area UAX is calculated by interpolation, and the calculation process is performed according to the following procedure.

That is, the brightness data I1, It, Is of the vertices P+, Pg, P8 of the triangular area UAX are read from the brightness table TABLE2 of the table 10, and the corresponding vertices PI%P! on the display screen of the display are read out. , stand vertically at P8 position. Then, a brightness plane BPX connecting the tips of the brightness data It, It, and Is is drawn. Then, draw a straight line LC2 perpendicularly to the display screen of the display from the processing point PC for each pixel included in the triangular area UAX, find the intersection of the straight line LC2 and the brightness plane BPX, and process the value of the brightness plane BPX at the intersection. The brightness of point PC is determined to be 1, c.

In this way, by sequentially selecting all pixels included in the triangular area UAX as processing points P, a linear interpolation calculation is performed to find the intersection of the straight line LC2 and the triangular brightness plane BPX.

Therefore, the brightness data for all pixels can be easily obtained from the three brightness data obtained from the three-dimensional curved surface.

Incidentally, in this case as well, since the solution between the direct &11LC2 and the plane BPX is found, 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 triangle M area UAX on the west side of the display, and the CPU performs the interpolation calculation according to the following processing steps. Execute.

That is, first, the vertex P on the display screen of the display,
, P, SP, distance data DI %Dt,D
s is read from the distance table TABLE3 of the table 10 and is set perpendicular to the vertex P, , P, , P, position.

Then, a distance plane DPX is drawn to connect the ends of the distance data D, , D, , D3, and a straight line LC3 that passes through the processing point Pc and is perpendicular to the display screen and the distance plane D
Calculate the intersection with PX. Then, the value of the distance plane DPX at this intersection is determined as ct - distance data from the viewpoint of the processing point Pc.

Thus, in this case as well, by sequentially specifying all pixels included in the triangular area UAX as the processing point PC, the distance data DIIC 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.

After that, the CPU moves to step 5P17 and compares the distances. Executes pixel data generation processing. This process is carried out in the display area ARE (
For all pixels included in Figure 11), the brightness data Ipc (Figure 15) and visible-invisible data MLc correspond to the curved surface with the smallest distance data D and c, respectively.
(FIG. 14), the luminance data of the curved surface for which visible data is obtained and the distance data D□ is the smallest is generated as pixel data to be displayed on the display.

In practice, the CPU has a frame buffer memory having memory cells 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, the distance data D for each pixel is stored. When pc is determined, the smallest distance data D for the same pixel,
When c is obtained, the distance data is stored in the memory area corresponding to the pixel in the depth buffer memory, and the luminance data □ determined in step 5P15 is written in the frame buffer memory and Thus, the brightness data IPC obtained from the curved surface with the smallest distance data DDc is written into 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 5P17 is completed, U judges in step 5P1B whether or not the arithmetic processing for all patches has been completed, and if a negative result is obtained, it returns to step 5PI2 again and calculates the data for the new pixel. The calculation process of step 5pia is repeated.
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 second-view transformed image of an object curved surface in a three-dimensional space viewed from a predetermined viewpoint position is converted onto a two-dimensional display screen of a display. However, (to do so, the curved surface of the object in the 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 three vertices PX to a two-dimensional plane forming the rask display screen of the display, the vertex P* converted to the two-dimensional plane
, Pz, and Pa positions to form a triangular data plane consisting of object surface information obtained from the curved surface, linear interpolation is performed from the data plane for each and every pixel included in the triangular area on the display screen. Image data can be obtained by calculation.

In this way, since only three pieces of data are required for each unit area when perspectively converting the surface of an object in a three-dimensional space to a two-dimensional plane, the conversion calculation time can be further shortened. In order to obtain image data for each pixel from the data plane, it is only necessary to perform an operation to find the solution between the plane and the straight line, so this interpolation operation is linear and a simple operation that uniquely determines the solution 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 screen displayed on the display screen is displayed according to the position of the light source. It is possible to easily add shading, and thus the undulations on a 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,
Even if a visible area and an invisible area exist within the triangular area UAX on the two-dimensional plane, the boundary between the visible M area and the invisible area can be clearly determined based on the linear interpolation calculation result for each pixel. , whereby 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 pixel currently being processed is located in which triangular area UAX. In order to detect whether it belongs to the triangular area UAX, the straight lines DLL DL2 and DL3 that constitute the three sides of the triangular area UAX and the triangular area U
Using the center of gravity P0 of AX, it can be easily confirmed by arithmetic processing that simply determines whether the processing point P is on the side of the center of gravity P, which further reduces the overall calculation processing time. be able to.

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 surface of an object in a three-dimensional space is cut out into triangular unit areas UAI and υA2, and at each vertex px, a vector in the viewing direction and a unit vector normal to the surface are By calculating the inner product of , it is possible to simply express whether the unit areas UAI and UA2 are visible areas or invisible areas from the viewpoint by the sign of the inner product calculation result. Hidden surface processing of the above perspective-transformed image can be performed by extremely simple calculations. Therefore, when multiple visibility determination results are obtained for the same pixel, the one with the larger distance data representing the distance from each surface to the viewpoint is determined to be a hidden surface, making hidden surface processing more reliable. obtain.

[Brief explanation of drawings]

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. 10 is the route map showing the perspective conversion procedure; The figure shows 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. 1.4.6...Object, IA, 4A, 6A...
... Curved surface, 2 ... Light source, 3 ... Viewpoint, 11 ... Display screen.

Claims (2)

[Claims] (1) In 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, (a) the surface of the object; Cut out into a triangular unit area, and (
b) Calculate the inner product of the first position data representing the position of the first vertex consisting of the three vertices of the unit area of the triangle, the vector in the line of sight direction at the position of the first vertex, and the normal unit vector of the surface. (c) Display the first position data on the display screen of the display based on the viewpoint position. (d) obtaining second position data representing the position of a second vertex on the two-dimensional plane corresponding to the first vertex by performing perspective transformation to a corresponding two-dimensional plane; The visible-invisible data is vertically erected at the second vertex position, and a triangular visible-invisible data plane is stretched at the tip of the visible-invisible data plane, and (e) a triangular area surrounded by the second apex of the two-dimensional plane is formed. (f) Find the intersection point of the visible-invisible data plane with a straight line perpendicular to the processing point made up of pixels included in the data plane by interpolation, and (f) determine the content of the data in the visible-invisible data plane at the intersection point. An image display method characterized in that when the unit area is invisible, the surface of the unit area is determined to be a hidden surface and image data is not displayed at the processing point. (2) An image display method for converting and displaying data regarding the surface of an object in three-dimensional space when viewed from a predetermined viewpoint on a two-dimensional display screen of a display, comprising: (a) the surface of the object; Cut out into a triangular unit area, and (
b) Calculate the inner product of the first position data representing the position of the first vertex consisting of the three vertices of the unit area of the triangle, the vector in the line of sight direction at the position of the first vertex, and the normal unit vector of the surface. (c ) The first position data is perspectively transformed into a two-dimensional plane corresponding to the display screen of the display based on the viewpoint position, and a second vertex on the two-dimensional plane corresponding to the first vertex is obtained. (d) Stand the visible-invisible data vertically at the second vertex position on the two-dimensional plane, and place a triangular visible-invisible data plane at the tip of the visible-invisible data. The first intersection of the visible-invisible data plane and a straight line perpendicular to the processing point made up of pixels included in the triangular area surrounded by the second vertices of the two-dimensional plane is used for interpolation calculation. When the content of the data on the visible-invisible data plane at the first intersection point is invisible, the surface of the unit area is determined to be a hidden surface and image data is not displayed at the processing point. and (e) when there are multiple surfaces for which the content of the visible-invisible data at the first intersection point is determined to be visible for the same processing point, the two-dimensional data for each of the plurality of surfaces is determined to be visible. The distance data is vertically erected at the second vertex position on the plane, a triangular distance data plane is stretched at the tip of the distance data plane, and the above processing is included in a triangular area surrounded by the second vertices of the two-dimensional plane. A second intersection between a straight line perpendicular to the point and the distance data plane is determined by interpolation, and the surface has the smallest data content on the distance data plane at the second intersection among the surfaces. An image display method characterized in that for data other than the data, the surface of the unit area is determined to be a hidden surface, and the image data is not displayed at the processing point.