JP2002236935A - Image display device, image display method, information storage medium and image display program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide an image display device, an image display method, an information storage medium and an image display program capable of reducing distortions of each polygon shape when displaying an image of a three dimensional object composed of polygons on a curved screen. SOLUTION: An intermediate point calculating part 41 calculates coordinates of an intermediate point between two vertexes of a polygon arranged in three dimensional space. A coordinate transformation process part 42 calculates a storing position of a circular frame buffer 50 corresponding to each vertex coordinates and the intermediate point coordinates. A borderline calculating part 43 specifies an arc shape passing three points on the circular frame buffer 50 respectively corresponding to the two adjacent vertexes and the intermediate point in between. After a borderline corresponding to the polygon is approximated by an arc, a texture mapping process part 44 generates image information regarding a polygon interior surrounded by the arc as a drawing area.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

The present invention relates to an image display device, an image display method, an information storage medium, and an image display program for projecting an image on a curved screen through a wide-angle lens.

[0002]

2. Description of the Related Art Conventionally, an image display device for projecting an image on a non-planar screen has been known. For example, JP-A-9-81785 and JP-A-3-82493 disclose various image display devices that project an image on a non-planar screen and correct distortion of the projected image. When an image created for projection on a flat screen is projected on a non-flat screen as it is, a distorted image is displayed. For this reason, in the image display device described above, in consideration of the distortion at the time of display, by generating an image that is distorted in the opposite direction in advance so as to obtain a normal display content as a result of the distortion, a non-planar screen is displayed. Display distortion is corrected.

[0003]

In the above-described conventional image display device, when the image is distorted into a convex shape by projecting it on a non-planar screen, an image distorted into a concave shape is generated in advance. As a result, the distortion on the non-planar screen is corrected. However, with this method, when a three-dimensional object arranged in a three-dimensional space is displayed on a non-planar screen, distortion cannot be sufficiently corrected. For example, when the projection position of the image and the viewpoint position are different, the degree of distortion given to the generated image varies depending on the degree of perspective of the three-dimensional object. The distortion of can not be removed.

In particular, although it is considered that the two-dimensional image distortion correction is essentially different from the three-dimensional image distortion correction, the image display apparatus disclosed in the above-mentioned publication discloses a method of simply correcting the two-dimensional image distortion. However, the use of only these methods cannot sufficiently remove distortion of each polygonal shape caused when a three-dimensional object composed of a plurality of objects is projected on a screen. was there.

SUMMARY OF THE INVENTION The present invention has been made in view of the above circumstances, and has as its object to reduce distortion of each polygon shape when displaying an image of a three-dimensional object constituted by polygons on a curved screen. It is an object of the present invention to provide an image display device, an image display method, an information storage medium, and an image display program, which are capable of displaying an image.

[0006]

In order to solve the above-mentioned problems, an image display apparatus of the present invention projects an image of a three-dimensional object arranged in a virtual three-dimensional space onto a curved screen through a wide-angle lens. For this purpose, a frame buffer, a projection device, a contour calculation unit, and an image information storage unit are provided. In the frame buffer, the position to be projected on the curved screen corresponds to the storage position of the image information. The projection device irradiates an image corresponding to the image information stored in the frame buffer toward the wide-angle lens.
The outline calculating means approximates the shape of the outline of the polygon on the frame buffer corresponding to the outline of the polygon constituting the three-dimensional object by a curve. The image information storage means stores the image information of the corresponding three-dimensional object at the storage position of the frame buffer surrounded by the contour approximated by the contour calculation means. If the three-dimensional object is composed of polygons and the outline of each polygon is drawn as a straight line on the frame buffer, the image on the curved screen will be distorted. Is distorted into a non-linear shape. According to the present invention, the outline of each polygon constituting the three-dimensional object projected on the curved screen is formed into a substantially linear shape with little distortion by approximating the outline of the polygon on the frame buffer with a curved shape instead of a linear shape. Can be

It is desirable that the image display device of the present invention further includes an intermediate point calculating means and a coordinate calculating means. The intermediate point calculating means calculates coordinates of an intermediate point in a virtual three-dimensional space located on or near a straight line connecting two adjacent vertices included in the polygon. The coordinate calculation means calculates a storage position of the frame buffer corresponding to each of the two vertices and the intermediate point in the virtual three-dimensional space. Then, the above-described contour calculating means determines the shape of the curve passing through each point on the frame buffer corresponding to each of the two vertices and the intermediate point. By performing the curve approximation in this manner, the contour of each polygon constituting the actually projected three-dimensional object is approximated to a shape passing through a plurality of points arranged on a straight line, that is, a straight line with little distortion. be able to.

When it is necessary to designate N points in order to determine the shape of the above-mentioned curve, the intermediate point calculating means calculates coordinates of at least (N-2) intermediate points. Is desirable. Thus, two vertices and (N
-2) Since the number of intermediate points is specified, it is possible to obtain an accurate curve shape for the outline of the polygon.

In particular, the above-mentioned curve is a circular arc, and it is desirable that the coordinates of one intermediate point be calculated by the intermediate point calculating means. When performing curve approximation using an arc, 1
Since it is only necessary to add the number of intermediate points, it is possible to reduce the amount of computation required for performing the curve approximation and the amount of computation required for calculating the intermediate points.

The above-mentioned intermediate point calculating means calculates an angle formed by two line segments connecting the projection position corresponding to the position of the wide-angle lens and each of the two vertices, to a line segment connecting the projection position and the intermediate point. It is desirable to set the intermediate point so as to divide the middle point into two. By using such an intermediate point,
Since the position of the intermediate point on the frame buffer corresponding to the intermediate point used for curve approximation is located at substantially the same distance as each vertex on the frame buffer corresponding to each vertex, the accuracy of curve approximation can be improved.

Further, it is desirable that the above-mentioned wide-angle lens is a fisheye lens. By using a fisheye lens,
Since a projection angle of almost 180 ° can be realized,
By displaying the image projected on the curved screen in this way, it is possible to project a realistic image without distortion.

It is preferable that the above-described coordinate calculation means calculates the storage position of the frame buffer in correspondence with the position on the curved screen when the three-dimensional object is viewed from a predetermined viewpoint position. When the 3D object is viewed from the viewpoint position, it is calculated which position on the curved screen actually corresponds, and the storage position of the frame buffer required to project the image at this position is calculated. It is possible to project an accurate image without distortion.

The coordinate calculation means stores the frame buffer based on at least one of the position information of the three-dimensional object in the virtual three-dimensional space and the projection position corresponding to the viewpoint position or the position of the wide-angle lens. It is desirable to calculate the position. The state of the distortion of the three-dimensional shape and the display position of the three-dimensional object is determined by the relative relationship with the position information, the viewpoint position, and the projection position of the three-dimensional object in the virtual three-dimensional space. Therefore, by calculating the storage position of the frame buffer based on the position information, it is possible to project an image with almost no distortion.

It is desirable that the viewpoint position and the projection position are different from each other. In fact, it is not possible to see the image on the curved screen from the projection position. Therefore, by performing distortion correction on the assumption that the viewpoint position and the projection position are different, it is possible to project an image without distortion under conditions that are realistic.

Further, when the projection position is set to be shifted from the center position of the curved screen, the above-mentioned image information storage means takes into account the distance between the projection position and the position to be projected on the curved screen. It is desirable to perform brightness correction on the image information stored in the frame buffer.
If the projection position is shifted from the center position, the brightness of the projected image will be biased even when an image with uniform brightness is projected. Therefore, by performing the brightness correction in consideration of the distance, it is possible to eliminate the bias of the brightness and obtain an image with substantially uniform brightness.

The image information storage means performs a texture mapping process of specifying image information included in texture data corresponding to a polygon and storing the image information in a frame buffer. In order to determine the texture coordinates, it is desirable to determine the coordinates in the polygon in the virtual three-dimensional space corresponding to the storage position, and determine the texture coordinates corresponding to the coordinates. If the outline of the polygon on the frame buffer becomes curved, the correspondence between the arbitrary position in the polygon and the texture coordinates cannot be established, but the corresponding position in the polygon having the polygon shape in the virtual three-dimensional space is determined. By calculating, it is easy to take this correspondence, and necessary image information can be read.

Further, the apparatus further comprises an object calculating means for calculating the coordinates of the vertices of the polygon in the virtual three-dimensional space at predetermined intervals, and repeating the process of storing the image information in the frame buffer at the predetermined intervals. Is desirable. When a three-dimensional object moves in a virtual three-dimensional space or a viewpoint serving as a reference for perspective projection transformation moves, coordinates of the three-dimensional object are calculated at predetermined intervals, and an image without distortion is generated each time. Therefore, a moving image without distortion can be projected on a curved screen in a game or a presentation using a three-dimensional object.

Further, in the image display method according to the present invention, a first step of acquiring position information in a virtual three-dimensional space of each vertex included in a polygon constituting a three-dimensional object; A second step of approximating the shape of the outline of the polygon on the frame buffer corresponding to the outline of the polygon with a curve based on the image information, and storing the image information in the storage position of the frame buffer surrounded by the approximated outline. The method includes a third step of storing the image information, and a fourth step of reading out the image information stored in the frame buffer and projecting the image information on a curved screen through a wide-angle lens.

The information storage medium of the present invention includes a program for executing the first to fourth steps. Further, the image display program of the present invention executes the first to fourth steps on a computer to project an image of a three-dimensional object arranged in a virtual three-dimensional space onto a curved screen through a wide-angle lens. It is intended to be executed.

By executing the image display method of the present invention, or executing the program stored in the information storage medium of the present invention or the image display program of the present invention, the outline of the polygon on the frame buffer is changed. Since it is approximated not by a straight line but by a curved line, the outline of each polygon constituting the three-dimensional object projected on the curved screen can be made into a substantially straight line with little distortion.

Also, two adjacent polygons included in a polygon
A fifth step of calculating coordinates of an intermediate point in the virtual three-dimensional space located on or near a straight line connecting the two vertices, and each of the two vertices and the intermediate point in the virtual three-dimensional space And a sixth step of calculating the storage position of the frame buffer corresponding to the above are inserted before the above-described second step. It is desirable to determine the shape of the curve passing through each point of. By performing the curve approximation in this manner, the contour of each polygon constituting the actually projected three-dimensional object is approximated to a shape passing through a plurality of points arranged on a straight line, that is, a straight line with little distortion. be able to.

The curve used for the approximation processing in the above-mentioned second step is a circular arc, and this approximation processing is desirably performed using the coordinates of one intermediate point.
When the curve approximation is performed using an arc, only one intermediate point needs to be added. Therefore, the amount of computation required to perform the curve approximation and the amount of computation required to calculate the intermediate point are reduced. be able to.

In the above-mentioned sixth step,
It is desirable to calculate the storage position of the frame buffer in correspondence with the position on the curved screen when the three-dimensional object is viewed from a predetermined viewpoint position. When the 3D object is viewed from the viewpoint position, it is calculated which position on the curved screen actually corresponds, and the storage position of the frame buffer required to project the image at this position is calculated. It is possible to project an accurate image without distortion.

Further, in the sixth step described above,
It is desirable to calculate the storage position of the frame buffer based on at least one of the position information of the three-dimensional object in the virtual three-dimensional space and the projection position corresponding to the viewpoint position or the position of the wide-angle lens. The state of the distortion of the three-dimensional shape and the display position of the three-dimensional object is determined by the relative relationship with the position information, the viewpoint position, and the projection position of the three-dimensional object in the virtual three-dimensional space. Therefore, by calculating the storage position of the frame buffer based on the position information, it is possible to project an image with almost no distortion.

Further, when the projection position is set to be shifted from the center position of the curved screen, the image information stored in the frame buffer is considered in consideration of the distance between the projection position and the position to be projected on the curved screen. It is desirable to insert a seventh step of performing brightness correction before the fourth step. By performing the brightness correction in consideration of the distance, it is possible to obtain an image with substantially uniform brightness without unevenness in brightness.

In the above-mentioned fourth step,
A texture mapping process of specifying image information included in texture data corresponding to a polygon and storing the image information in a frame buffer is performed. In order to obtain texture coordinates corresponding to a storage position on the frame buffer, the texture mapping process is performed. It is desirable to obtain coordinates in a polygon in a virtual three-dimensional space and determine texture coordinates corresponding to the coordinates. If the outline of the polygon on the frame buffer becomes curved, the correspondence between the arbitrary position in the polygon and the texture coordinates cannot be established, but the corresponding position in the polygon having the polygon shape in the virtual three-dimensional space is determined. By calculating, it is easy to take this correspondence, and necessary image information can be read.

[0027]

DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, a game system according to an embodiment of the present invention will be described with reference to the drawings. FIG. 1 is a diagram showing a configuration of the game system of the present embodiment. The game system shown in FIG. 1 includes a game device 1, a projector 2, a lens 3, and a spherical screen 4.

The game apparatus 1 performs various game calculations in response to operations performed by the player, and generates image information for displaying a game image according to the progress of the game. The projector 2 irradiates a game image to the spherical screen 4 based on image information generated by the game device 1. The lens 3 projects the game image emitted from the projector 2 on the spherical screen 4. In the present embodiment, a wide-angle lens, more specifically, a fish-eye lens having a projection angle of about 180 ° is used as the lens 3. The spherical screen 4 is a kind of a curved screen and has a hemispherical projection surface. A game image emitted from the projector 2 and passed through the lens 3 is projected inside.

Next, a detailed configuration of the game apparatus 1 will be described. The game device 1 shown in FIG. 1 includes an input device 10, a game calculation unit 20, an information storage medium 30, an image processing unit 40,
It is configured to include a circular frame buffer 50. The input device 10 is used by a player to input various instructions to the game device 1, and includes various operation keys, operation levers, and the like corresponding to the type of a game performed on the game device 1. I have. For example, the input device 10 provided for playing a drive game includes a steering wheel, an accelerator, a brake, a shift lever, and the like.

The game calculation section 20 performs a predetermined game calculation necessary for the progress of the game. The game calculation unit 20 includes an input determination unit 22, an event processing unit 24, and a game space calculation unit 26. The game calculation unit 20 is realized by executing a predetermined game program using a CPU, a semiconductor memory such as a ROM or a RAM.

The input determining section 22 determines the operating state of the steering wheel, accelerator, brake and the like provided in the input device 10 and outputs a signal corresponding to the operating state to the event processing section 24. The event processing unit 24 generates various events,
Processing necessary for game progress, such as branch determination corresponding to the progress of the game, is performed. The game space calculation unit 26 calculates position information of various three-dimensional objects existing in the game space, which is a virtual three-dimensional space. Each of the three-dimensional objects in the present embodiment is configured by a plurality of polygons, and the game space calculation unit 26 calculates the vertex coordinates of each polygon that forms the three-dimensional object.

The information storage medium 30 stores a program and data for operating the game apparatus 1 having a function as a computer. Specifically, the information storage medium 30 stores a game program executed by the game calculation unit 20, data (texture data for texture mapping, etc.) necessary for displaying a game image, and an image display program. The information storage medium 30 is realized by a CD-ROM, a DVD-ROM, a hard disk device, a semiconductor memory, or the like.

The image processing section 40 receives the coordinates of the vertices of each polygon calculated by the game space calculation section 26 in the game calculation section 20, and has a circular frame buffer for displaying an image on the spherical screen 4. A process for storing the image information in 50 is performed. The image processing unit 40 includes an intermediate point calculation unit 41, a coordinate conversion processing unit 42, and a contour line calculation unit 4.
3. It includes a texture mapping unit 44 and a shading unit 45. Normally, the image processing unit 40 includes a dedicated graphic LSI or D
Although it is realized by using the SP or the like, if the performance of the CPU realizing the game calculation unit 20 is high and the processing capacity has a margin, even if the CPU performs the processing of the image processing unit 40, Good.

The midpoint calculation section 41 is provided by the game space calculation section 2.
The coordinates of the vertices of each polygon calculated in step 6 are input, and the coordinates of an intermediate point on a straight line connecting two adjacent vertices are calculated. When the three-dimensional object is viewed from the viewpoint position, the coordinate conversion processing unit 42
The position on the circular frame buffer 50 necessary for projecting an image on the spherical screen 4 is calculated by calculating which position on the spherical screen 4 the three-dimensional object corresponds to. Specifically, the coordinate conversion processing unit 42 receives the coordinates of the vertices of the polygon calculated by the game space calculation unit 26 and the coordinates of the intermediate point calculated by the intermediate point calculation unit 41. The coordinate conversion processing unit 42 calculates the coordinates on the spherical screen 4 corresponding to each of these vertices and intermediate points, and further calculates the storage position of the circular frame buffer 50 using the calculation results.

The contour calculation unit 43 includes a coordinate conversion processing unit 42
Based on the calculation result, the shape of the outline of the polygon on the circular frame buffer 50 corresponding to the outline of each polygon (each side of a polygon having a polygonal shape) is calculated. Generally, each polygon existing in the game space has a polygonal shape (for example, a triangular shape) in which each side is a straight line. However, since the shape of each side is distorted when projected on the curved screen 4, the shape of each side on the circular frame buffer 50 is not a straight line but a curve. Therefore,
As in general three-dimensional image processing, after simply calculating the storage position in the frame buffer for each vertex of a polygon, simply performing texture mapping processing will result in the shape of each side of the polygon being the actual shape Will be deviated. For this reason, in the present embodiment, by approximating the shape of the outline of each polygon on the circular frame buffer 50 with a curve, each side of each polygon displayed on the spherical screen 4 from a predetermined viewpoint position The device has been devised so as to be substantially straight when the shape is viewed. Specifically, the contour calculation unit 43 calculates the three coordinates based on the coordinates of two adjacent vertices in each polygon and an intermediate point on a straight line having both ends in the game space. Calculate the arc shape passing through the point. In the following, each polygon shape in the game space will be described as a triangle.

After the contour shape of each polygon on the circular frame buffer 50 is calculated by the contour calculation unit 43, the texture mapping processing unit 44 pastes the texture data inside the polygon defined by these contour lines. A processing (texture mapping processing) is performed. Further, the shading processing unit 45 performs shading correction processing on the result of the texture mapping processing. In this way, image information of each pixel included in an area (corresponding area on the circular frame buffer 50) surrounded by a plurality (for example, three) of vertex coordinates constituting each polygon is obtained. For example, color information represented by RGB data is used as image information.

The circular frame buffer 50 stores the image information obtained by the image processing section 40. Each storage position of the circular frame buffer 50 corresponds to each position to be projected on the spherical screen 4, and is specified by the image information by storing the image information at a predetermined position of the circular frame buffer 50. A color image is projected on a corresponding position on the spherical screen 4.

The above-mentioned projector 2 serves as a projection device, and the intermediate point calculating section 41 serves as an intermediate point calculating means.
2 corresponds to the coordinate calculating means, the contour calculating section 43 corresponds to the contour calculating means, the texture mapping processing section 44 and the shading processing section 45 correspond to the image information storing means, and the game space calculating section 26 corresponds to the object calculating means. I have.

The game system of the present embodiment has such a configuration, and its operation will be described next. FIG. 2 is a flowchart showing an outline of an operation procedure of the game system of the present embodiment, and shows a flow of the entire game.
Note that a series of processes illustrated in FIG. 2 is repeatedly performed at a cycle (for example, 1/60 second) corresponding to a predetermined display interval.

When the input device 10 is operated and a game start instruction is given by the player, the game calculation unit 20
Starts a predetermined game calculation based on the game program read from the information storage medium 30. In particular,
The input determination unit 22 in the game calculation unit 20 includes the input device 10
A predetermined input determination process of outputting a signal corresponding to the content of the operation performed by the player is performed based on the signal output from (step 100).

Next, the event processing section 24 generates various events necessary for the progress of the game in response to the signal output from the input determination section 22 (event generation processing).
Is performed (step 101). In addition, the game space calculation unit 2
6 calculates the coordinates of various three-dimensional objects existing in the game space in response to the event generation processing performed by the event processing unit 24 (step 102).
By this coordinate calculation, the coordinates of each vertex of a plurality of polygons forming the three-dimensional object are calculated.

When the coordinates of each three-dimensional object are calculated by the game space calculation unit 26 and the position information of the three-dimensional object is obtained, the image processing unit 4
The intermediate point calculation unit 41 within 0 determines that the adjacent 2
The coordinates of an intermediate point corresponding to one vertex are calculated (step 103). Further, the coordinate conversion processing unit 42 performs a predetermined coordinate conversion process of converting the coordinates of the vertex of the polygon and the coordinates of the intermediate point into the coordinates on the circular frame buffer 50 (step 104). In addition, the contour calculation unit 43 calculates the circular frame buffer 50 based on the calculation result of the coordinate conversion processing unit 42.
The contour shape of each polygon above is calculated (step 105).

Next, the texture mapping processing section 44 and the shading processing section 45 obtain image information (color information) to be stored in the circular frame buffer 50, and write the image information to a corresponding position of the circular frame buffer 50 (step 106). ). Specifically, predetermined texture mapping processing is performed by the texture mapping processing unit 44, and then predetermined shading processing is performed by the shading processing unit 45, so that the area on the circular frame buffer 50 corresponding to each polygon is Image information is written.

The image information written in the circular frame buffer 50 is read out in a predetermined scanning order and sent to the projector 2. The projector 2 forms an image based on the image information, and projects the image on the spherical screen 4 through the lens 3 (Step 107).

In this way, a game image having a new content is generated at a predetermined repetition cycle and projected on the spherical screen 4. In the above description of the operation, the drawing process is performed by performing the series of processes illustrated in FIG. 2 at a cycle corresponding to the display interval. However, the display interval and the repetition interval of the drawing process do not necessarily have to match. Good. In addition, if the drawing process is performed in time for the display timing, the drawing process is performed in synchronization with each display timing, and if the screen processing is not performed in time, the same content is displayed on the screen. May not match.

Next, the intermediate point calculation processing in step 103, the coordinate conversion processing in step 104,
Contour calculation processing in step 105, step 10
6 will be described in detail. (1) Intermediate Point Calculation Process FIGS. 3 and 4 are diagrams illustrating an outline of the intermediate point calculation process performed in the intermediate point calculation unit 41. FIG. In these figures, points P ₀ and P ₁ indicate two vertices included in one polygon arranged in the game space.

When performing the simplest calculation, as shown in FIG. 3, the intermediate point calculating section 41 calculates the coordinates of the intermediate point P 'in the game space of the two vertices P ₀ and P _1. . The coordinates of the midpoint P 'of the case, it is simply obtained by determining the two arithmetic mean of the coordinate values of the vertex P _0, P _1.

The position on the circular frame buffer 50 corresponding to the above-mentioned intermediate point P 'is not equidistant from the vertices on the circular frame buffer 50 corresponding to the vertices P ₀ and P ₁ . Accordingly, as shown in FIG. 4, the coordinates of the projection position P _r (eg, one that matches the sphere center) and two vertices P _0, the midpoint of the formed projection angle between P ₁ bisecting P " By using such an intermediate point P ″, a circle corresponding to the intermediate point P ″ is obtained from each of the vertices on the circular frame buffer 50 corresponding to the two vertices P ₀ and P _1. Since the distance to the intermediate point on the frame buffer 50 can be set substantially equal,
In step 105, an error in obtaining a contour by interpolation can be reduced.

More specifically, from the vertices P ₀ and P ₁ to the intermediate point P ″
L1 and L2 are the distances from the ball center to the vertex P
_0, if the respective L3, L4 and distance to P _1, the nature of the bisector of the triangle, L1: L2 = L3: L4 satisfy the relationship. Since the coordinates of the spherical center and the two vertices P ₀ and P ₁ are known, the coordinates of the intermediate point P ″ can be obtained by performing a simple calculation.

(2) Coordinate Conversion Processing FIG. 5 is a diagram showing a drawing range of the circular frame buffer 50. The projector 2 according to the present embodiment has a rectangular projection whose image projection range is horizontally long (for example, the aspect ratio is 3: 4), and a part of the region has a drawing corresponding to the image projected on the spherical screen 4. Used as an area. This drawing corresponds to a case where a projection surface S in FIG. 6 described later is viewed from the positive direction of the z-axis (the upper side in FIG. 6) toward the origin.
In FIG. 5, a rectangular area 200 corresponds to the projection range of the projector 2. Further, the circular region 210 is the lens 3
Corresponding to the area actually projected on the spherical screen 4 through the Therefore, in the present embodiment, writing of image information is performed only in a range included in the circular area 210 among the coordinates of the circular frame buffer 50.

As shown in FIG. 5, the X axis is taken in the horizontal direction and the Y axis is taken in the vertical direction. The center (circle center) of the circular region 210 is defined as the origin O, and the radius of the circular region 210 is defined as R. Image information stored in the arbitrary point F (X, Y) of the circular frame buffer 50 is projected to a point P _d on the spherical screen 4.

(2-1) Both the viewpoint position and the projection position are spherical.
FIG. 6 is a diagram showing an outline of the coordinate conversion process when setting to the spherical center position of the surface screen 4 . As shown in the figure, the hemispherical projection surface corresponding to the spherical screen 4 is designated as S, and the spherical center of the projection surface S is set as the origin o. Further, the z axis is defined from the origin o toward the plane center of the projection plane S, and the x axis and the y axis are defined perpendicular to the z axis. Furthermore, in this example, the viewpoint position P _e and the projection position of the player (the lens 3 position) P _r is coincide with the origin o.

It is assumed that an arbitrary point P _p (x _p , y _p , z _p ) in the game space which is a three-dimensional space is mapped to a point F (X, Y) on the circular frame buffer 50. In FIG. 6, when a point P _p (x _p , y _p , z _p ) in the game space is viewed from the origin o, the intersection of the straight line connecting the point P _p and the origin o with the projection plane S is represented by P _{d (x d, y d,} z d) and. Projection surface S
If the radius of the hemisphere corresponding to is r, x _d , y _d , z
_d is represented by the following equation.

[0054]

(Equation 1)

[0055] Further, in FIG. 6, when the angle between the straight line and the z axis connecting the origin o and the point P _d and theta, the angle theta
Is represented by the following equation.

[0056]

(Equation 2)

When the point F (X, Y) shown in FIG. 5 is projected onto the projection surface S, the distance L from the origin O to the point F is set to the angle shown in FIG. It has a characteristic proportional to θ. Therefore, when θ = 0, L =
When 0 and θ = π / 2, L = R, and the distance L corresponding to an arbitrary angle θ therebetween can be expressed by the following equation.

L = θ / (π / 2) × R In FIG. 5, the angle between the straight line connecting the origin O on the circular frame buffer 50 and the point F (X, Y) and the X axis is Φ. I do. In FIG. 6, a point P _d (x _d , y _d , z _d )
Is mapped to the xy plane P _d ′ (x _d , y _d , 0) and the origin o
Is the angle between the straight line connecting the x and the x axis. This angle Φ
And the angle φ are equal. Here, cos φ and sin φ can be represented by the following equations.

[0059]

(Equation 3)

The point F (X, Y) is the point P on the projection surface S
Using the coordinate values of each axis of _d (x _d , y _d , z _d ), it can be expressed as the following equation.

[0061]

(Equation 4)

Therefore, the vertices P of each polygon constituting the three-dimensional object placed in the game space
_{When p} (x _p , y _p , z _p ) is known, to calculate the storage position of the corresponding circular frame buffer 50,
First, the coordinate conversion processing unit 42 first vertex P _p (x _p , y _p ,
The coordinates of the point P _d (x _d , y _d , z _d ) on the projection plane S are calculated by substituting the coordinate values of z _p ) into the above-described equations (1) to (3). After that, the coordinate conversion processing unit 42 substitutes the coordinate values of the point P _d (x _d , y _d , z _d ) obtained by this calculation into the above-described equations (4) and (5), and obtains the circular frame. The point F (X, Y) on the buffer 50 is calculated. The intermediate point P ′ or P ″ shown in FIG. 3 and FIG.
Is calculated.

In this way, the storage positions of the circular frame buffer 50 corresponding to the vertices and intermediate points of each polygon of the three-dimensional object are calculated. In particular, since the coordinate transformation process performed in this manner is accurately performed using the position of the three-dimensional object in the game space, the viewpoint position, and the projection position, theoretically, distortion is observed when viewed from the viewpoint position. Circular frame buffer 5 needed to project accurate game images onto spherical screen 4
A storage position of 0 can be obtained.

FIG. 7 shows a case where the data is stored in the circular frame buffer 50.
Showing the correspondence between the vertices of the polygon and the intermediate points
is there. For example, triangular polygons are used
Circular frames corresponding to each of the three vertices
Vertex on the buffer 50 _a, F_b, F_cAnd Ma
That of three intermediate points between two adjacent vertices
The intermediate point on the circular frame buffer 50 corresponding to each
F₁, F_Two, F_ThreeAnd As shown in FIG.
Focusing on two vertices and the intermediate point between them,
These three points are not arranged on a straight line.

(2-2) Only a projection position is a spherical screen
When shifted from the fourth spherical center Incidentally, in the above description, but consider the case where the viewpoint position P _e and the projection position P _r to match the sphere center of the spherical screen 4, in fact, such a positional relationship It is difficult to realize. Considering a practical geometrical arrangement, if a player wants to show a highly realistic game image by using the spherical screen 4 to the player, the viewpoint of the player should be set near the spherical center of the spherical screen 4. Is desirable. Therefore, in this case, it is necessary to set by shifting the projection position P _r from the sphere center of the spherical screen 4.

FIG. 8 is a diagram showing an outline of the coordinate conversion processing when the projection position is shifted from the spherical center position of the spherical screen 4. The coordinate axes shown in the figure are the same as those shown in FIG. The projection position P _r (x _r , y _r , z _r ) is set at a predetermined position other than the center of the spherical screen 4 (for example, above the player). As for the circular frame buffer 50, since the origin is associated with the projection position P _r, in order to distinguish it from the display of the coordinate axes in the case of the above-described (2-1) (see FIG. 5), the origin O '
The axis along the horizontal direction is referred to as the X 'axis, and the axis along the vertical direction is referred to as the Y' axis.

[0067] As described in the above-described (2-1), when to match the viewpoint position P _e to the position of the origin o which corresponds to the spherical center of the spherical screen 4, a point in the game space P _p ( x
_p , y _p , z _p ) is a point P _d (x _d ,
y _d , z _d ). That is, a point on the spherical screen 4 from any projection position P _r P _d (x _d,
y _d , z _d ), the point becomes the viewpoint position P _e
Will be recognized as a point P _p (x _p , y _p , z _p ) in the game space.

[0068] Thus, in response to an arbitrary projection position P _r, by performing the steps similar to the coordinate transformation process shown in the above (2-1) with respect to the point P _d, the point from the projection position P _r P The point F ′ (X ′, Y ′) on the circular frame buffer 50 required for projecting on _d can be obtained. However, the x 'axis and y' when the projection position _Pr is shifted from the origin o
The axes and z 'axes are obtained by translating the original x, y, and z axes, and assume that there is no rotation around the axes. Also, x _r ^{2
_{+ Y r 2 + z r 2}} < range satisfying r ² (hereinafter radius r from the origin o) in the projection position P _r is assumed to be set.

[0069] In FIG. 8, when 'the angle between the axis theta' straight line z connecting the projection position P _r and a point P _d and the angle theta '
Is represented by the following equation.

[0070]

(Equation 5)

The angle between a straight line connecting the origin O 'on the circular frame buffer 50 and the point F' (X ', Y') and the X 'axis is Φ'. In FIG. 8, the point P _d (x _d , y _d ,
z _d ) is a mapping point P _d ″ (x _d −x _r , y _d
When -y _r, 0) and 'an angle between the axis phi' straight line x which connects the point P _r and, these angles [Phi 'and phi' are equal. Here, cos φ ′ and sin φ ′ can be represented by the following equations.

[0072]

(Equation 6)

A point P _d (x _d , y _d ,
The coordinate value of z _d ) is obtained based on the above equations (1) to (3). The point F ′ (X ′, Y ′) is a point P _d (x _d , y _d , z _d ) and a projection position P _r (x _r ,
y _r , z _r ) can be expressed by the following equation using the respective coordinate values.

[0074]

(Equation 7)

Therefore, the vertices P of each polygon constituting the three-dimensional object placed in the game space
_{When p} (x _p , y _p , z _p ) is known, the coordinate transformation processing unit 42 first calculates the vertex P _p (x _p , z _p ) in order to calculate the corresponding storage position on the circular frame buffer 50.
By substituting the coordinate values of y _p , z _p ) into the above equations (1) to (3), a point P _d (x _d , y _d , z _d ) on the projection plane S is obtained.
Calculate the coordinates of. Thereafter, the coordinate conversion processing unit 42 substitutes the coordinate values of the point P _d (x _d , y _d , z _d ) obtained by this calculation into the above-described equations (7) and (8), and The coordinates of the point F ′ (X ′, Y ′) on the buffer 50 are calculated. Further, the intermediate point P 'shown in FIGS.
Alternatively, the storage position of the circular frame buffer 50 is calculated by the same procedure for P ″.

In this way, the storage positions on the circular frame buffer 50 corresponding to the vertices and intermediate points of each polygon of the three-dimensional object are calculated. In particular, since the coordinate transformation process performed in this way is accurately performed using the position, viewpoint position, and projection position of the three-dimensional object in the game space, when the projection position is moved to an arbitrary position. The circular frame buffer 50 necessary for projecting an accurate game image theoretically free from distortion when viewed from the viewpoint position on the spherical screen 4.
Can be obtained.

In FIG. 8 described above, for convenience of explanation,
While the projection position P _r was drawn to the region of z _r ≧ 0, in fact, since the projection angle of the lens 3 is 180 degrees, in order to display the game image on the entire spherical screen 4, the projection position P _r is preferably set in a range of z _r ≦ 0.

The fish-eye lens used as the lens 3 of the present embodiment generally has a deep depth of focus.
The feature is that the range in focus is wide.
For this reason, even when the projection position is shifted, the game image displayed on the spherical screen 4 is substantially in focus as a whole.

(2-3) Both the viewpoint position and the projection position are spherical
When shifted from the spherical center of the surface screen 4 Incidentally, in the description of the above-described (2-2), although the projection position P _r had described the case that is set at a position shifted from the spherical center position of the spherical screen 4, actually,
Player's viewpoint position P _e also may wish shifted from the spherical center position of the spherical screen 4. Hereinafter, a case where both the viewpoint position and the projection position are set so as to be shifted from the spherical center position of the spherical screen 4 will be described.

FIG. 9 is a diagram showing an outline of a coordinate conversion process when the viewpoint position and the projection position are shifted from the spherical center position of the spherical screen 4. The coordinate axes shown in the figure are the same as those shown in FIG. Viewpoint position P _e, both projection position P _r is set at a predetermined position other than the spherical center of the spherical screen 4. The circular frame buffer 50
For, since the origin is associated with the projection position P _r, in order to distinguish it from the display of the coordinate axes in the case of the above-described (2-1) (see FIG. 5), in the case of the above-described (2-2) Similarly, the origin is O ', the axis along the horizontal direction is X' axis, and the axis along the vertical direction is Y 'axis.

In FIG. 9, a point P in the game space
A straight line connecting _p (x _p , y _p , z _p ) and the viewpoint position _Pe (x _e , y _e , z _e ) is represented by the following equation.

[0082]

(Equation 8)

The hemisphere corresponding to the projection plane S is represented by the following spherical equation (where z ≧ 0). x ² + y ² + z ² = r ² (10) From the viewpoint position _Pe to a point P _p (x _p , y _p ,
When looking at z _p ), the coordinates of the point P _d (x _d , y _d , z _d ) on the projection plane S corresponding to this point P _p are represented by the straight line shown in the above-described equation (9) and ) Can be obtained by calculating the coordinates of the intersection with the hemisphere shown in the equation.

Specifically, the following equations are derived by modifying equation (9).

[0085]

(Equation 9)

By substituting equations (11) and (12) into equation (10), the following equation is obtained. ^{_{((x p -x e) 2}} + (y p -y e) 2 + (z p -z e) 2) × x 2 -2 × ((y p -y e) × (x e × y p - _{y e × x p) + (} z p -z e) × (x e × z p -z e × x p)) × x + ((x e × y p -y e × x p) 2 + (x _{e × z p -z e × x} p) 2 -r 2 × (x p -x e) 2) = 0 ... (13) _{where, a = (x p -x e} ) 2 + (y p -y _{^{e) 2 + (z p -z}} e) 2 b = (y p -y e) × (x e × y p -y e × x p) + (z p -z e) × (x e × z p _{-z e × x p) c =} (x e × y p -y e × x p) 2 + (x e × z p -z e × x p) 2 -r 2 × (x p -x e) 2 In other words, the solution of the above equation (13) is expressed as the following equation.

[0087]

(Equation 10)

Therefore, the point P in the game space_p(X_p,
y_p, Z_p) And viewpoint position P_e(X_e, Y _e, Z_e)
By calculating equation (14) using
Point P _dX coordinate value (x_d) Is required. Also, equation (14)
By substituting into the above equations (11) and (12)
Point P_dY coordinate value (y_d), Z coordinate value (z_d) Asked
Can be

The x coordinate value is actually calculated using equation (14).
Then, two solutions x₁, X_TwoIs obtained. These two solutions
One of the solutions x₁Into equations (11) and (12)
By substituting each value, the corresponding y coordinate value (y₁)
And z coordinate value (z₁) Is obtained. As a result, the point P_dSeat
The standard value is (x₁, Y₁, Z₁). Also, the other solution x_TwoTo
By substituting into equations (11) and (12),
And the corresponding y coordinate value (y_Two) And z coordinate values (z_Two)But
can get. As a result, the point P_dIs (x_Two, Y _Two,
z_Two). Of these two coordinate values, the required solution
As a point P_eFrom each coordinate value (x₁, Y₁, Z₁)and
(X_Two, Y_Two, Z_Two) Of the two vectors going to the point
And the viewpoint position P_eFrom point P_p The same direction as the vector going to
The coordinate value corresponding to the vector having the shift is selected.

Thus, the point P _d (x _d , y _d , z _d )
Can be obtained. Then, by substituting this coordinate value mentioned above (7) and (8), on a circular frame buffer 50 necessary for projecting the image at a point P _d on the projection plane S from the projection position P _r The point F '
The coordinates of (X ', Y') can be obtained.

Therefore, the vertices P of each polygon constituting the three-dimensional object arranged in the game space are
_{When p} (x _p , y _p , z _p ) is known, the coordinate transformation processing unit 42 first calculates the vertex P _p (x _p , z _p ) in order to calculate the corresponding storage position on the circular frame buffer 50.
y _p, coordinate values and the viewpoint position P _e (x _e of z _p), y _e, by calculating the z described above with reference to coordinate values of _e) (14) type or the like, a point on the projection plane S P _{d (x d, y d,} z d) calculating the coordinates of. Thereafter, the coordinate conversion processing unit 42 substitutes the coordinate values of the point P _d (x _d , y _d , z _d ) obtained by this calculation into the above-described equations (7) and (8), and The coordinates of the point F ′ (X ′, Y ′) on the buffer 50 are calculated.
Further, the intermediate point P 'or P "shown in FIGS.
The same procedure is applied to the circular frame buffer 5
The storage location of 0 is calculated.

In this way, the storage positions on the circular frame buffer 50 corresponding to the vertices and intermediate points of each polygon of the three-dimensional object are calculated. In particular, since the coordinate transformation process performed in this manner is accurately performed using the position, the viewpoint position, and the projection position of the three-dimensional object in the game space, the viewpoint position and the projection position are moved to arbitrary positions. Even in this case, the storage position of the circular frame buffer 50 necessary for projecting an accurate game image theoretically free of distortion when viewed from the viewpoint position on the spherical screen 4 can be obtained.

In FIG. 9 described above, for convenience of explanation, the projection position _Pr is drawn in an area where z _r ≧ 0.
For the same reason as in the case of (2-2) described above, it is desirable that the actual projection position _Pr be set in a range of _zr ≦ 0. (3) Contour Line Calculation Processing FIG.
FIG. 9 is a diagram showing an outline of a polygon outline calculation process. In FIG. 10, the mapping of the two vertices included in the polygon on the circular frame buffer 50 is represented by F _a (X _a ,
Y _a ) and F _b (X _b , Y _b ), and the intermediate point sandwiched between them is F ₁ (X ₁ , Y ₁ ). In addition, these three points F _a ,
The center of a circle passing through F ₁ and F _b is E (X ₀ , Y ₀ ), and the radius of the circle is R 1.

The equation of the circle with the center of the circle as E (X ₀ , Y ₀ ) is as follows: (X−X ₀ ) ² + (Y−Y ₀ ) ² = R1 ² (15) By substituting the coordinate values of the three points F _a , F ₁ , and F _b into the equation of this circle, the following simultaneous equations are obtained.

[0095] ^{_{(X a -X 0) 2 +}} (Y a -Y 0) 2 = R 1 2 (X b -X 0) 2 + (Y b -Y 0) 2 = R 1 2 (X 1 -X _{^{0) 2 + (Y 1 -Y}} 0) by solving ² = R ₁ ² this simultaneous _{equation, Y 0 = (i × j} -g × h) / (2 × (Y a × g-Y 1 × g
−Y ₁ × i + Y _b × i)) X ₀ = (h + 2 × Y _a × Y ₀ −2 × Y ₁ × Y ₀ ) / i R ₁ = √ ((X _a −X ₀ ) ² + (Y _a − Y ₀ ) ² ) is obtained. _{Here, g = -2 × X 1 +} 2 × X b h = -X a 2 + X 1 2 -Y a 2 + Y 1 2 i = -2 × X a + 2 × X 1 j = -X 1 2 + X b 2 −Y ₁ ² + Y _b ²

In this way, the contour calculation unit 43 determines the shape of the contour (arc shape) passing through the three points F _a , F ₁ , and F _b by determining the equation of the circle. (4) Texture Mapping Process FIG. 11 is a diagram showing an outline of the texture mapping process. As shown in FIG. 11, in the present embodiment, vertices F _a , F _b , and F _c corresponding to the three vertices of the polygon, respectively.
Are connected to each other by arcs, and the inside of these lines is a drawing area for writing image information corresponding to one polygon.

The texture mapping processing section 44 sequentially scans the drawing area in the X direction from the upper end (Y _max ) to the lower end (Y _min ), and includes the area between the contour lines approximated by an arc. Image information of each pixel to be generated. The generation of the image information is performed using a general texture mapping technique. That is, the processing is performed by acquiring data corresponding to the drawing position in the polygon from texture data (image information of the texture corresponding to the polygon) prepared separately.

By the way, in the conventional texture mapping processing, since the polygon shape on the frame buffer also has a polygonal shape, a simple linear interpolation calculation is performed when obtaining the texture coordinates corresponding to an arbitrary drawing position in the polygon. I just had to do. However, in the present embodiment, since the outline of the polygon shape on the circular frame buffer 50 is approximated by an arc shape, texture coordinates corresponding to an arbitrary drawing position cannot be obtained by a simple linear interpolation operation.

FIG. 12 shows the texture mapping processing section 4
FIG. 4 is a diagram showing an outline of a processing procedure for obtaining texture coordinates corresponding to an arbitrary drawing position on the circular frame buffer 50 according to FIG. First, the texture mapping processing unit 44
Calculates the corresponding position P _p 'in the polygon arranged in the game space after determining the coordinates of the drawing point F' on the circular frame buffer 50 for which image information is to be generated.
Next, the texture mapping processing unit 44 calculates the texture coordinates T based on the corresponding position P _p 'in the polygon. Since the polygon in the game space has a triangular shape in which three vertices are surrounded by straight lines, the texture coordinates T corresponding to the specific position P _p ′ in the polygon can be obtained by a simple linear interpolation operation. it can.

As described above, in the game system of the present embodiment, when the image information of the three-dimensional object constituted by the plurality of polygons is written into the circular frame buffer 50, the outline shape of the polygon represented by the polygon is changed. It is approximated by an arc. Therefore, the shape of the three-dimensional object in the game space can be accurately reproduced, and the distortion of the image projected on the spherical screen 4 can be reduced.

Note that the present invention is not limited to the above-described embodiment, and various modifications can be made within the scope of the present invention. For example, in the embodiment described above,
(2-1) When both the viewpoint position and the projection position match the spherical center position of the spherical screen 4, (2-2) When only the projection position is shifted, (2-3) The viewpoint position and the projection position The method of the coordinate conversion processing has been described for each of the cases where both are shifted from each other. By applying these methods, even when only the viewpoint position is shifted from the spherical center of the spherical screen 4, the distortion is small. Image information for displaying a game image can be generated.

More specifically, as described in (2-3) where both the viewpoint position and the projection position are set to be shifted, each of the three-dimensional objects arranged in the game space is constituted. The vertex coordinates of each polygon
_The above-mentioned (1) is used by using these coordinate values and the coordinate values of the viewpoint position P _e (x _e , y _e , z _e ) as _p (x _p , y _p , z _p ).
4) By calculating the equation and the like, the point P _d (x
_d , y _d , z _d ) are obtained. Thereafter, the storage position on the circular frame buffer 50 may be obtained by calculating the above-described equations (4) and (5) based on these coordinate values.

[0103] Further, the case (described above to set by shifting the projection position P _r from the sphere center position of the spherical screen 4 (2-
2) and (2-3)), the projection position _Pr
Taking into account the distance to the position P _d on the spherical screen 4 from may perform brightness correction on the image information to be stored in the circular frame buffer 50.

FIG. 13 is a diagram for explaining a modification for performing brightness correction, and shows a state in which the cross section of the spherical screen 4 is simplified. If the projection position P _r is deviated from the spherical center position Q of the spherical screen 4, the projection position P
The distance from _r to an arbitrary position on the spherical screen 4 is not equal. For example, as shown in FIG. 13, a distance D1 from the projection position _Pr to a point _Pd1 on the spherical screen 4 is significantly different from a distance D2 to another point _Pd2 . The intensity of the light emitted from the projection position P _r (light corresponding to each pixel constituting the game image), i.e., the brightness is inversely proportional to the square of the distance, the spherical screen 4
The brightness of the game image displayed above will be biased.

Therefore, for example, a predetermined coefficient which is inversely proportional to the square of the distance from the projection position _Pr to the position on the spherical screen 4 is set, and this is set to the circular frame buffer 50.
, The brightness of the image information can be corrected. Thereby, the unevenness in brightness of the game image can be reduced, and a higher quality game image can be projected.

As a simpler method, for example,
A predetermined coefficient that is inversely proportional to the distance from the projection position _Pr to the position on the spherical screen 4 may be set, and this may be multiplied by the image information stored in the circular frame buffer 50. In this case, the unevenness in brightness of the game image can be reduced to some extent, and the amount of calculation required for brightness correction can be reduced. Further, since the projection angle has a predetermined correlation with the distance from the projection position to the position projected on the spherical screen 4, the brightness correction may be performed using the projection angle instead of the distance. The brightness correction processing as described above can be performed by the shading processing unit 45 in the image processing unit 40.

Further, in the above-described embodiment, the case where the image is projected on the spherical screen which is a kind of the curved screen has been described. However, when the three-dimensional object arranged in the game space is viewed from the viewpoint position, the curved surface is projected. When the position projected on the screen is obtained by calculation, the present invention can be applied to a case where an image is displayed on a curved screen other than a spherical surface. For example, an image may be projected on a curved screen having a projection surface obtained by cutting a rotating body obtained by rotating an ellipse in half. Even when such a curved screen is used, the position projected on the curved screen is calculated based on the position information of the three-dimensional object arranged in the game space, and further, an image is displayed at the calculated position. By calculating the storage position on the circular frame buffer 50 necessary for projecting the image, it is possible to display an image with almost no distortion.

In the above-described embodiment, the outline of the polygon is approximated by using the equation of a circle. However, the outline may be approximated by using another curve. For example, there is a case where approximation is performed using a spline curve or another function. In these cases, for example, if it is assumed that each coefficient of the approximation function can be determined by specifying N points, (N-2) intermediate points excluding two vertices are set in the game space. It can be calculated by By obtaining the storage positions of the circular frame buffer 50 corresponding to these intermediate points, an approximate function can be obtained in the same procedure as in the above-described embodiment.

Further, in the above-described embodiment, an example in which the present invention is applied to a game system has been described. However, the present invention is applied to various devices for projecting a three-dimensional image using a three-dimensional object on a curved screen. Can be applied. For example, the present invention can be applied to a device that makes a presentation using a three-dimensional object, various simulator devices such as a flight simulator, and the like.

[0110]

As described above, according to the present invention, the outline of a polygon on a frame buffer is approximated not by a straight line but by a curved line, thereby forming a three-dimensional object projected on a curved screen. The outline of the polygon can be formed into a substantially linear shape with little distortion.

[Brief description of the drawings]

FIG. 1 is a diagram illustrating a configuration of a game system according to an embodiment.

FIG. 2 is a flowchart showing an outline of an operation procedure of the game system.

FIG. 3 is a diagram illustrating an outline of an intermediate point calculation process.

FIG. 4 is a diagram showing an outline of an intermediate point calculation process.

FIG. 5 is a diagram illustrating a drawing range of a circular frame buffer.

FIG. 6 is a diagram illustrating an outline of a coordinate conversion process.

FIG. 7 is a diagram showing the correspondence between vertices of polygons on a circular frame buffer and intermediate points;

FIG. 8 is a diagram showing an outline of a coordinate conversion process when only the projection position is shifted from the spherical center of the spherical screen.

FIG. 9 is a diagram illustrating an outline of a coordinate conversion process when the viewpoint position and the projection position are shifted from the spherical center of the spherical screen.

FIG. 10 is a diagram showing an outline of a polygon outline calculation process.

FIG. 11 is a diagram illustrating an outline of a texture mapping process.

FIG. 12 is a diagram showing an outline of a processing procedure for obtaining texture coordinates corresponding to an arbitrary drawing position on a circular frame buffer.

FIG. 13 is a diagram illustrating a modified example for performing brightness correction.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 Game device 2 Projector 3 Lens 4 Spherical screen 10 Input device 20 Game operation part 22 Input judgment part 24 Event processing part 26 Game space operation part 30 Information storage medium 40 Image processing part 41 Intermediate point calculation part 42 Coordinate transformation processing part 43 Outline Line calculation unit 44 Texture mapping processing unit 45 Shading processing unit 50 Circular frame buffer

Claims (33)

[Claims] 1. An image display device for projecting an image of a three-dimensional object arranged in a virtual three-dimensional space onto a curved screen through a wide-angle lens, and storing a position to be projected on the curved screen and image information. A frame buffer corresponding to a position, a projection device for irradiating an image corresponding to the image information stored in the frame buffer toward the wide-angle lens, and a contour line of a polygon constituting the three-dimensional object. Contour calculating means for approximating the shape of the contour of the polygon on the frame buffer with a curve; and the tertiary corresponding to the storage position of the frame buffer surrounded by the contour approximated by the contour calculating means. An image display device, comprising: image information storage means for storing image information of an original object. 2. The intermediate point according to claim 1, wherein coordinates of an intermediate point in the virtual three-dimensional space located on or near a straight line connecting two adjacent vertices included in the polygon are calculated. Calculating means; and coordinate calculating means for calculating a storage position of the frame buffer corresponding to each of the two vertices and the intermediate point in the virtual three-dimensional space. And determining a shape of a curve passing through each point on the frame buffer corresponding to each of the two vertices and the intermediate point. 3. The intermediate point calculation unit according to claim 2, wherein when it is necessary to specify N points to determine the shape of the curve, the intermediate point calculating means includes at least (N−2) intermediate points. An image display device, which calculates coordinates of 4. The image display device according to claim 2, wherein the curve is an arc, and the intermediate point calculating means calculates coordinates of one intermediate point. 5. The intermediate point calculation unit according to claim 2, wherein the intermediate point calculation unit determines an angle formed by two line segments connecting the projection position corresponding to the position of the wide-angle lens and each of the two vertexes. An image display device, wherein the intermediate point is set so as to be bisected by a line connecting the projection position and the intermediate point. 6. The image display device according to claim 2, wherein the wide-angle lens is a fisheye lens. 7. The frame buffer according to claim 2, wherein the coordinate calculation unit corresponds to a position on the curved screen when the three-dimensional object is viewed from a predetermined viewpoint position. An image display device for calculating a storage position. 8. The coordinate calculation unit according to claim 7, wherein the coordinate calculation unit determines at least one of position information of the three-dimensional object in the virtual three-dimensional space and a projection position corresponding to the viewpoint position or the position of the wide-angle lens. An image display device, wherein a storage position of the frame buffer is calculated based on one of them. 9. The image display device according to claim 8, wherein the viewpoint position is different from the projection position. 10. The image information storage unit according to claim 9, wherein, when the projection position is set so as to be shifted from a center position of the curved screen, the image information storage unit determines the projection position and a position to be projected on the curved screen. An image display device that performs brightness correction on the image information stored in the frame buffer in consideration of a distance from the image buffer. 11. The image information storage unit according to claim 1, wherein the image information storage unit performs a texture mapping process of specifying image information included in texture data corresponding to the polygon and storing the image information in the frame buffer. And determining coordinates in the polygon in the virtual three-dimensional space corresponding to the storage position to obtain texture coordinates corresponding to the storage position on the frame buffer, and calculating the texture coordinates corresponding to the coordinates. An image display device characterized by determining. 12. The apparatus according to claim 1, further comprising: an object calculation unit configured to calculate coordinates of vertices of the polygon in the virtual three-dimensional space at predetermined intervals. An image display device, wherein storage processing of image information is repeated at the interval. 13. A first step of acquiring position information in a virtual three-dimensional space of each vertex included in a polygon constituting a three-dimensional object, and based on the position information acquired in the first step. The shape of the outline of the polygon on the frame buffer corresponding to the outline of the polygon is approximated by a curve.
And a third step of storing image information of the corresponding three-dimensional object at a storage position of the frame buffer surrounded by the outline approximated in the second step; Reading out the stored image information and projecting the image information onto a curved screen through a wide-angle lens. 14. The method according to claim 13, further comprising calculating coordinates of an intermediate point in the virtual three-dimensional space located on or near a straight line connecting two adjacent vertices included in the polygon. And calculating a storage position of the frame buffer corresponding to each of the two vertices and the intermediate point in the virtual three-dimensional space, before the second step An image display method, comprising: inserting, in the second step, determining a shape of a curve passing through each point on the frame buffer corresponding to each of the two vertices and the intermediate point. 15. The method according to claim 14, wherein the curve used for the approximation process in the second step is a circular arc, and the approximation process is performed using the coordinates of one intermediate point. Image display method. 16. The storage position in the frame buffer according to claim 14 or 15, wherein in the sixth step, the three-dimensional object corresponds to a position on the curved screen when viewed from a predetermined viewpoint position. An image display method characterized by calculating 17. The method according to claim 16, wherein, in the sixth step, positional information of the three-dimensional object in the virtual three-dimensional space and a projection position corresponding to the viewpoint position or the position of the wide-angle lens. An image display method, wherein a storage position of the frame buffer is calculated based on at least one. 18. The method according to claim 17, wherein, when the projection position is set to be shifted from a center position of the curved screen, a distance between the projection position and a position to be projected on the curved screen is considered. An image display method, wherein a seventh step of performing brightness correction on the image information stored in the frame buffer is inserted before the fourth step. 19. The texture mapping process according to claim 13, wherein in the fourth step, the image information included in the texture data corresponding to the polygon is specified and stored in the frame buffer. Determining coordinates in the polygon in the virtual three-dimensional space corresponding to the storage position to determine texture coordinates corresponding to the storage position on the frame buffer; and determining the texture coordinates corresponding to the coordinates. And an image display method. 20. A first step of obtaining position information in a virtual three-dimensional space of each vertex included in a polygon constituting a three-dimensional object, and based on the position information obtained in the first step. The shape of the outline of the polygon on the frame buffer corresponding to the outline of the polygon is approximated by a curve.
And a third step of storing image information of the corresponding three-dimensional object at a storage position of the frame buffer surrounded by the outline approximated in the second step; A fourth step of reading the stored image information and projecting the image information on a curved screen through a wide-angle lens. 21. The method according to claim 20, wherein a coordinate of an intermediate point in the virtual three-dimensional space located on or near a straight line connecting two adjacent vertices included in the polygon is calculated. And calculating a storage position of the frame buffer corresponding to each of the two vertices and the intermediate point in the virtual three-dimensional space, before the second step A program to be inserted and executed, wherein in the second step, the shape of the curve passing through each point on the frame buffer corresponding to each of the two vertices and the intermediate point is determined. Information storage medium. 22. The method according to claim 21, wherein the curve used in the approximation process in the second step is a circular arc, and the approximation process is performed using the coordinates of one intermediate point. Information storage medium. 23. The storage position of the frame buffer according to claim 21, wherein in the sixth step, the three-dimensional object is stored in the frame buffer in a manner corresponding to a position on the curved screen when viewed from a predetermined viewpoint position. An information storage medium characterized by calculating 24. The method according to claim 23, wherein, in the sixth step, position information of the three-dimensional object in the virtual three-dimensional space and a projection position corresponding to the viewpoint position or the position of the wide-angle lens. An information storage medium, wherein a storage position of the frame buffer is calculated based on at least one. 25. The apparatus according to claim 24, wherein when the projection position is set to be shifted from a center position of the curved screen, a distance between the projection position and a position to be projected on the curved screen is considered. An information storage medium including a program for inserting and executing a seventh step of performing brightness correction on the image information stored in the frame buffer before the fourth step. 26. The method according to claim 20, wherein in the fourth step, a texture mapping process of specifying image information included in texture data corresponding to the polygon and storing the image information in the frame buffer is performed. And determining coordinates in the polygon in the virtual three-dimensional space corresponding to the storage position to obtain texture coordinates corresponding to the storage position on the frame buffer, and calculating the texture coordinates corresponding to the coordinates. An information storage medium characterized by being determined. 27. A computer for projecting an image of a three-dimensional object placed in a virtual three-dimensional space onto a curved screen through a wide-angle lens, the computer comprising: A first step of acquiring position information in a general three-dimensional space, and, based on the position information acquired in the first step, a contour of a polygon on a frame buffer corresponding to the contour of the polygon. The second approximating the shape with a curve
And a third step of storing image information of the corresponding three-dimensional object at a storage position of the frame buffer surrounded by the outline approximated in the second step; A fourth step of reading out the stored image information and projecting the image information on a curved screen through the wide-angle lens. 28. The method according to claim 27, further comprising calculating coordinates of an intermediate point in the virtual three-dimensional space located on or near a straight line connecting two adjacent vertices included in the polygon. And calculating a storage position of the frame buffer corresponding to each of the two vertices and the intermediate point in the virtual three-dimensional space, before the second step And an image display program for executing, in the second step, determining a shape of a curve passing through each point on the frame buffer corresponding to each of the two vertices and the intermediate point. 29. The image display program according to claim 28, wherein the curve used for the approximation process in the second step is a circular arc, and the approximation process is performed using the coordinates of one intermediate point. . 30. The storage position of the frame buffer according to claim 28 or 29, wherein in the sixth step, the three-dimensional object is stored on the curved screen in a manner corresponding to a position on the curved screen when viewed from a predetermined viewpoint position. Image display program for calculating 31. The method according to claim 30, wherein, in the sixth step, position information of the three-dimensional object in the virtual three-dimensional space and a projection position corresponding to the viewpoint position or the position of the wide-angle lens. An image display program for causing a storage position of the frame buffer to be calculated based on at least one. 32. The method according to claim 31, wherein when the projection position is set so as to be shifted from a center position of the curved screen, a distance between the projection position and a position to be projected on the curved screen is considered. An image display program for causing a seventh step of performing brightness correction on the image information stored in the frame buffer to be executed before the fourth step. 33. A texture mapping process according to claim 27, wherein in the fourth step, image information included in texture data corresponding to the polygon is specified and stored in the frame buffer. And determining coordinates in the polygon in the virtual three-dimensional space corresponding to the storage position to obtain texture coordinates corresponding to the storage position on the frame buffer, and calculating the texture coordinates corresponding to the coordinates. An image display program for making a decision.