JP2006243458A - Three dimensional map display device and three dimensional map display program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a three-dimensional map display device and a three-dimensional map display program which, even when a wide viewing angle especially in a horizontal direction is set in displaying a three-dimensional map, prevent deterioration of visibility caused by three-dimensional display by making a display as a driver sees an actual scene by relatively greatly deforming the vicinity of the center of the screen while suppressing distortion. <P>SOLUTION: The three-dimensional map display device comprises: a storage means 4 for storing road map information; a position detecting means 2 for detecting the present position P; an image transformation processing means 72 for obtaining, from the storage means 4, the road map information within a display area based on the present position P as reference; and an image display means 5 for displaying a three-dimensional road image. The image transformation processing means 72 transforms the road image into a three-dimensional image by projecting the three-dimensional coordinate obtained from the road map information on a virtual solid centered on the present position P, then further projecting it in parallel on a drawing surface. <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  The present invention relates to a technology for displaying a three-dimensional map on a screen of a display device, and in particular, a tertiary that prevents a decrease in visibility near the center of the screen even when a large horizontal viewing angle is ensured and displayed. The present invention relates to an original map display device and a three-dimensional map display program.

  2. Description of the Related Art Conventionally, a car navigation device is known as a device that facilitates driving of a car. This car navigation device detects the current position of the vehicle by a GPS (Global Positioning System) sensor or the like, reads a route from the map data recorded on a storage medium such as a CD-ROM, and the road on the screen. A map in which buildings and buildings are drawn is displayed.

  By the way, in recent car navigation devices, it is possible to display not only a 2D map but also a 3D map. By switching the screen as necessary, the 3D map can be displayed and the surroundings of the current location can be easily grasped. It has become like this. For example, the viewpoint to be drawn is set to the viewpoint of the driver or the viewpoint from the sky, and the three-dimensional display close to the scenery that the driver actually sees or the bird's-eye view display that can be seen far away is adopted.

  As such a three-dimensional map display technique, for example, a map display device described in JP-A-2003-263102 has been proposed (Patent Document 1). When displaying a three-dimensional map, this map display device is a landscape in which the line of sight is viewed from an oblique direction, so map components such as buildings, roads, and terrain are shaded by other map components, and their related information The object is to solve the problem that the visibility of (name, guidance, etc.) decreases. And in order to solve such a purpose, a perspective transformation process and a hidden surface removal process are performed, or based on the display area of the map composition, the display area of the related information of the map composition is set, and the related information is It has been proposed to follow a change in the map composition and display it at a position that is always easy to see to prevent a reduction in visibility.

JP 2003-263102 A

  However, since there is a limit to the size of the screen allowed for the car navigation device, the conventional method of converting to three-dimensional drawing produces a portion that is different from the driver's appearance, which reduces visibility. May end up. For example, in the conventional 3D map display including the invention described in Patent Document 1, the viewing angle in the horizontal direction is generally set to about 90 °. For this reason, there is a problem that the display range is narrower than a human viewing angle of about 180 °, and buildings and facilities still visible to the driver disappear from the display screen one after another.

  Therefore, in order to eliminate such a sense of incongruity, it is conceivable to set a large viewing angle. However, since the normal three-dimensional display is drawn by the perspective projection method, the larger the horizontal viewing angle is set, the more the viewing angle is set. The vicinity of the center of the screen is compressed to a small size and the drawing is crushed. For example, as shown in FIG. 5A, in a three-dimensional map by the perspective projection method, buildings in the vicinity of the left and right are displayed abnormally long in the back direction, and the buildings in the back are too small. Also, the intersections that exist between the buildings are almost crushed and become linear, and even if a driver who is traveling is looking at them, the existence of the intersections cannot be grasped.

  The present invention has been made to solve such problems, and when displaying a three-dimensional map, even when a large horizontal viewing angle is set, the distortion is suppressed and the vicinity of the center of the screen is suppressed. It is an object to provide a 3D map display device and a 3D map display program that can be brought close to the actual appearance of the driver by relatively large deformation and prevent deterioration in visibility caused by 3D display. It is said.

  The three-dimensional map display device according to the present invention is characterized by storage means for storing road map information, position detection means for detecting a current position, and the road map information within a display range based on the current position. An image conversion processing unit that obtains from the storage unit and converts the image into a three-dimensional image; and an image display unit that displays a three-dimensional road image. The image conversion processing unit includes the road map information. 3D coordinates are obtained by projecting onto a virtual solid centered on the current position and then projecting them in parallel on a drawing plane to transform the road image into a three-dimensional image.

Also, in the present invention, when the virtual solid is a sphere, the image conversion processing means uses the coordinates projected in parallel on the drawing plane as (X, Y), and the three-dimensional coordinates with the current position as the origin. Is (x, y, z), the following formula X = x / √ (x ² + y ² + z ² )
Y = y / √ (x ² + y ² + z ² )
Therefore, it is preferable to perform conversion processing into a three-dimensional image.

  The three-dimensional map display program according to the present invention is characterized by storage means for storing road map information, position detection means for detecting a current position, and the road map information within a display range based on the current position. Is acquired from the storage means and converted into a three-dimensional image, and the computer is executed as an image display means for displaying a three-dimensional road image. The image conversion processing means After projecting the three-dimensional coordinates obtained from the map information onto a virtual solid centered on the current position, the computer further transforms the road image into a three-dimensional shape by parallel projecting on the drawing plane. It is in the point to be executed.

Also, in the present invention, when the virtual solid is a sphere, the image conversion processing means uses the coordinates projected in parallel on the drawing plane as (X, Y), and the three-dimensional coordinates with the current position as the origin. Is (x, y, z), the following formula X = x / √ (x ² + y ² + z ² )
Y = y / √ (x ² + y ² + z ² )
Therefore, it is preferable to execute the computer so as to perform conversion processing into a three-dimensional image.

  According to the present invention, when displaying a three-dimensional map, even if the horizontal viewing angle is set to be large, it is possible to make the driver's real landscape by relatively deforming the vicinity of the screen center while suppressing distortion. It is possible to prevent a reduction in visibility caused by three-dimensional display.

  Hereinafter, an embodiment of a 3D map display device 1 and a 3D map display program according to the present invention will be described with reference to the drawings. FIG. 1 is a block diagram showing a three-dimensional map display device 1 in the present embodiment. In the present embodiment, a car navigation device is described as an example, but the present invention can be applied to various navigation devices such as a portable navigation device carried by a user.

  As shown in FIG. 1, the three-dimensional map display device 1 of the present embodiment mainly includes a position detection means 2 for detecting the current position P of the own vehicle, and an input means 3 for inputting a destination S and the like. Storage means 4 for storing road map information and various programs, image display means 5 such as a monitor for displaying a road map, and image data to be displayed on the image display means 5 It comprises an image memory 6 and arithmetic processing means 7 for controlling each of these components and performing various arithmetic processes.

  In more detail about each component means, the position detection means 2 detects the present position P of the vehicle, and detects a vehicle speed sensor, a direction sensor that detects the traveling direction of the vehicle, or GPS. (Global Positioning System) It is configured by a GPS sensor or the like that identifies the current position P based on latitude / longitude information received from a satellite. The input unit 3 includes a push button, a touch sensor on the display screen, and the like, and is used for inputting the destination S and the like, changing display settings, and the like.

  The storage means 4 comprises a DVD (Digital Versatile Disc), a hard disk or the like, and stores road map information including road information, target information such as buildings, and traffic information such as right and left turn instructions. Yes. In addition, a three-dimensional map display program for executing the display process of the present embodiment is stored. The image memory 6 is constituted by a RAM (Random Access Memory) or the like, and stores image data appropriately processed by the arithmetic processing means 7.

  The image display means 5 is composed of an LCD (Liquid Crystal Display) or the like, and displays a road map, a target, and the like based on image data stored in the image memory 6. As shown in FIG. 2, the image display means 5 of the present embodiment is composed of a three-dimensional display area 51, a two-dimensional fixed scale display area 52, and a two-dimensional variable scale display area 53 in order from the bottom. . Then, the entire route from the current position P to the destination S is divided according to an appropriate distance from the current position P and displayed in each display area. In the boundary portion of each display area, the ends of the roads are continuously connected, and the guide route U from the current position P to the destination S is continuously displayed along the left and right center line O.

  Here, each display area will be described in detail. The three-dimensional display area 51 is an area for displaying route information from the current position P to a first passing point Q within a drawing range described later on a three-dimensional map. . The two-dimensional fixed scale display area 52 is an area for displaying the route information from the first passage point Q to the second passage point R a few kilometers ahead on a two-dimensional map drawn at a fixed scale. The two-dimensional variable scale display area 53 is an area for displaying a route information from the second passing point R to the destination S on a two-dimensional map drawn at a variable scale. In the present embodiment, a 3D map that has been subjected to a drawing process by a predetermined conversion method is displayed in the 3D display area 51.

  The arithmetic processing means 7 is constituted by a CPU (Central Processing Unit) or the like, and controls each constituent unit based on a three-dimensional map display program stored in the storage means 4 and stores various data and setting information. The image data is acquired and processed appropriately. As shown in FIG. 1, the arithmetic processing means 7 of this embodiment mainly includes a route search unit 71, an image conversion processing unit 72, and a two-dimensional map drawing unit 73.

  Each component will be described in more detail. The route search unit 71 acquires the current position P of the host vehicle from the position detection unit 2, acquires the destination S set by the input unit 3, and acquires the current position P. The guide route U from the destination to the destination S is calculated. In addition, when the destination S is not set, the destination S may be predicted and automatically set by a destination prediction unit (not shown). This destination prediction unit automatically stores, for example, a route with a high driving frequency of a driver, or stores a route with a high driving frequency from general statistics and compares it with the current driving route. The destination S is set to be predicted.

  The image conversion processing unit 72 obtains road map information existing within a predetermined drawing range from the current position P from the storage unit 4 and draws a three-dimensional map. Further, the two-dimensional map drawing unit 73 creates a road map from the first passing point Q to the destination S along the guidance route U. Specifically, as shown in FIG. 2, the storage unit 4 stores road map information from the first passing point Q to the second passing point R that is a predetermined distance out of the guidance route U calculated by the route searching unit 71. And draw a 2D map at a fixed scale. For the guidance route U from the second passing point R to the destination S, road map information is acquired from the storage means 4 and a two-dimensional map is drawn at a variable scale.

  Hereinafter, a specific drawing method of the three-dimensional map by the image conversion processing unit 72 will be described. First, the image conversion processing unit 72 acquires the current position P and the traveling direction of the vehicle from the position detection unit 2 and also acquires drawing range data for setting the drawing range. In the present embodiment, as shown in FIG. 3, a drawing range in which the viewing angle in the horizontal direction is about 150 ° is set. In addition, by setting the depth to 50 to 100 m, a three-dimensional map close to the landscape seen from the driver is drawn. The drawing range data is stored in a memory means (not shown) and can be set and changed as appropriate by a driver.

  Next, the image conversion processing unit 72 determines a drawing range based on the current position P, the traveling direction, and the drawing range data, and acquires road map information existing in the drawing range from the storage unit 4. In the present embodiment, it is assumed that the destination S is input by the user and the guide route U is calculated. However, even if the destination S is not set, the drawing range can be determined as long as the current position P, the traveling direction, and the drawing range data are available.

Then, the image conversion processing unit 72 projects each point on the three-dimensional space obtained from the acquired road map information on a virtual solid centering on the current position P, in this embodiment, on a virtual sphere. Specifically, a three-dimensional vector V (x, y, z) based on the current position P is calculated from the three-dimensional coordinates of each point, and this three-dimensional vector is calculated by the following equations (1) and (2). Polar coordinates are converted into a two-dimensional vector v (θ, Φ).
θ = arctan (x / z) (1)
Φ = arctan (y / z) (2)

Here, as shown in FIG. 4, the points P ₀ , Q ₀ , R ₀ on the three-dimensional space will be described as an example. The points P ₀ , Q ₀ , R ₀ are converted by polar coordinates. , Projected onto a virtual sphere of radius r centered on the current position P, and converted to points P ₁ , Q ₁ , R ₁ . Among the two-dimensional vectors v (θ, Φ) of these points P ₁ , Q ₁ , R ₁ , the θ component represents the horizontal position, and the Φ component represents the vertical position.

Then, the image conversion processing unit 72 further parallel-projects each point P ₁ , Q ₁ , R ₁ after polar coordinate conversion onto a drawing plane for displaying a three-dimensional map. Specifically, by applying a sine filter to the two-dimensional vector v (θ, Φ) of each point obtained by polar coordinate transformation, the coordinates of the points P ₂ , Q ₂ , R ₂ on the drawing plane ( X, Y) is calculated. In the present embodiment, since the drawing plane is a plane perpendicular to the line of sight extending in the drawing direction from the drawing viewpoint, each point P ₁ , Q ₁ , R ₁ is orthogonally projected on the drawing plane. Accordingly, the coordinates (X, Y) of each point orthogonally projected on the drawing plane are finally calculated by the following mathematical formulas (3) and (4).
X = x / √ (x ² + y ² + z ² ) (3)
Y = y / √ (x ² + y ² + z ² ) (4)

  By the above image conversion processing, a three-dimensional map in which the center portion of the screen is deformed relatively large is drawn. Here, the effect of deformation in the three-dimensional map of the present embodiment will be described in comparison with a conventional three-dimensional map or the like. FIG. 5A is a three-dimensional map drawn in the drawing range shown in FIG. 3 by a conventional perspective projection method, and FIG. 5B is a three-dimensional drawing drawn on a two-dimensional plane after polar coordinate conversion. FIG. 5C is a three-dimensional map drawn by performing image conversion processing according to the present embodiment.

  As shown in FIG. 5 (a), in the drawing by the conventional perspective projection method, the drawing plane is enlarged in proportion to the tangent of the viewing angle, so that the center portion of the drawn three-dimensional map is compressed very small. I understand that. For this reason, the buildings on both sides are expressed with an unusually long depth, and the buildings on the far side are extremely small. Furthermore, it is almost impossible to grasp despite the presence of an intersection.

  Further, as shown in FIG. 5B, in the three-dimensional map subjected to only the polar coordinate transformation, although the compression of the central portion is somewhat eliminated, the distortion becomes large and the straight portion is bent. Moreover, the discomfort due to the difference from the scenery that the driver will actually see, such as the display of the intersection and the scenery of the building on the back side, has not been eliminated. Furthermore, since the inverse trigonometric function is used in the drawing process, the amount of calculation increases and the drawing process speed may be reduced.

  On the other hand, in the three-dimensional map according to the present embodiment, as shown in FIG. 5C, image distortion is effectively suppressed. The drawing at the center of the image is greatly deformed and easy to see, and is modified so that unnecessary information at the left and right ends of the image is thinned out. For this reason, compared with FIG. 5 (a) and FIG. 5 (b), the situation of the intersection existing in the center of the screen is much easier to grasp, and almost matches the actual scenery seen by the driver. It is. Also, by applying the sine filter, the calculation formula is simplified as in the above formulas (3) and (4), so that the drawing processing speed is improved as compared with the case where only polar coordinate conversion is performed.

  In the above-described embodiment, each point on the three-dimensional space is projected on the virtual sphere, but the present invention is not limited to this. For example, the solid to be projected may be an appropriate virtual solid such as a polyhedron or an ellipsoid close to a sphere. For example, in the case of a polyhedron, as shown in FIG. 6, the angle of view is divided into five partial viewing cones V1 to V5. Then, by rendering each partial view cone V, each point on the three-dimensional space is projected onto the corresponding partial view cone V. Then, the projection is performed in parallel on the partial areas A1 to A5 on the drawing plane corresponding to each partial view cone V. With the above drawing process, a natural three-dimensional map can be drawn even with a wide angle of view. However, in this case, since the boundary of each partial area A cannot be differentiated, there is a possibility that the connected part may become unnatural, and only the number of partial visual cones V is required to draw one 3D map. Since it is necessary to perform rendering processing, the drawing processing speed may be delayed. In order to solve such a problem, it is necessary to perform a virtual sphere orthogonal projection conversion process.

  In this embodiment, the image conversion process is performed for each of the horizontal direction and the vertical direction. However, the present invention is not limited to this, and the image conversion process may be performed for at least the horizontal direction component. As a result, the horizontal direction component is deformed even if the height direction component remains as it is, so that the center portion can be easily seen. In other words, it is also a projection onto a cylindrical virtual solid. Then, the coordinates in the vertical direction may be projected onto the drawing plane by only polar coordinate conversion without applying the sin filter. This is because the viewing angle in the vertical direction, that is, the height direction is not so large, so that the influence on the center portion of the image is small, and the influence on the driver's visibility is not so great.

  Next, the operation of the 3D map display device 1 executed by the 3D map display program of the present embodiment will be described with reference to the flowchart of FIG.

  First, when the driver uses the 3D map display device 1 of the present embodiment, the arithmetic processing means 7 starts the 3D map display program stored in the storage means 4 (step S1). As a result, a menu screen (not shown) is displayed on the image display means 5, and the driver inputs a desired destination S using the input means 3 (step S2). At this time, various settings such as the drawing range data described above may be performed. Subsequently, the arithmetic processing means 7 acquires the current position P of the vehicle detected by the position detecting means 2 based on the GPS signal (step S3). In the present embodiment, since the position detection means 2 detects the position of the vehicle every predetermined time, it is determined whether or not the vehicle has moved by the arithmetic processing means 7 in accordance with the cycle (step S4).

  If the arithmetic processing means 7 determines that the vehicle is not moving in step S4 (step S4: NO), the process proceeds to step S12 described later, and the same road map is displayed as image display means until the movement of the vehicle is detected. 5 is displayed. On the other hand, if the arithmetic processing means 7 recognizes the movement of the vehicle (step S4: YES), the process proceeds to step S5, where the route search unit 71 detects the destination S input in step S2 and the current detected in step S3. The position P is acquired, and a guidance route U from the current position P to the destination S is searched (step S5).

  Subsequently, the image conversion processing unit 72 obtains the current position P of the vehicle detected by the position detection unit 2 and the traveling direction of the vehicle detected by the azimuth sensor, and sets a drawing range in order to determine a three-dimensional drawing range. Data is acquired (step S6). Then, the drawing range of the three-dimensional image is determined based on the current position P, the traveling direction, and the drawing range data, and road map information in the drawing range is acquired (step S7).

  Subsequently, the image conversion processing unit 72 reads out the three-dimensional coordinates of each drawing target point from the acquired road map information, and applies polar coordinate conversion to each of these points, thereby forming a virtual sphere centered on the current position P. Projection is performed (step S8). A three-dimensional map is drawn by applying a sine filter to each of the projected points in the horizontal direction and the vertical direction and orthogonally projecting on the drawing plane (step S9). The two-dimensional map drawing unit 73 draws the guidance route U from the first passage point Q to the second passage point R on a fixed-scale two-dimensional map and guides from the second passage point R to the destination S. The route U is drawn with a variable-scale two-dimensional map (step S10).

  The arithmetic processing unit 7 acquires the 3D map drawn by the image conversion processing unit 72, acquires the fixed scale 2D map and the variable scale 2D map drawn by the 2D map drawing unit 73, and A road map connected so that the route ends of these road maps are continuously connected is stored as image data in the image memory 6 (step S11).

  Note that step S10 is performed when the image display means 5 includes a three-dimensional display area 51, a two-dimensional fixed scale display area 52, and a two-dimensional variable scale display area 53 as in the present embodiment. It is a process that is performed only. Therefore, when displaying only a three-dimensional map, the process of step S10 is not performed, and in step S11, only the three-dimensional map drawn by the image conversion processing unit 72 is stored in the image memory 6 as image data.

  Next, the image display means 5 displays a road map based on the image data stored in the image memory 6 (step S12). Thus, the 3D display area 51 displays a 3D map within the drawing range subjected to the processing according to the present embodiment, and the 2D fixed scale display area 52 includes the first passage point Q to the first pass. A two-dimensional map up to two passing points R is displayed, and a two-dimensional map from the second passing point R to the destination S is displayed in the two-dimensional variable scale display area 53.

  And the arithmetic processing means 7 has a time measuring means (not shown), and always determines whether or not a predetermined time has passed while the 3D map display program is being executed (step S13). And when predetermined time has not passed (step S13: NO), it waits until predetermined time passes. On the other hand, if it is determined that the predetermined time has elapsed (step S13: YES), the process returns to step S3, and the current position P of the vehicle is acquired from the position detection means 2 again. The road map displayed on the image display means 5 is updated more smoothly as the vehicle is moved as the predetermined time is set shorter.

  Thereafter, the arithmetic processing means 7 compares the newly acquired current position P with the previous current position P to determine whether or not the vehicle has moved (step S4). As a result, when it is determined that the vehicle is not moving (step S4: NO), the process proceeds to step S12, and the same road map is displayed until the movement of the vehicle is detected. On the other hand, when the movement of the vehicle is detected (step S4: YES), the above-described processing of step S5 to step S12 is repeatedly executed, and the three-dimensional map and the first passing point Q within the drawing range from the new current position P. To a destination S is displayed. Thereby, in the image display means 5, a road map is updated in real time according to the movement of a vehicle.

According to the 3D map display device 1 of the present embodiment as described above,
1. Even when a 3D map with a large horizontal viewing angle is drawn to eliminate the poor visibility near the center of the 3D map, which has been a problem in the past, the center of the image is relatively controlled while suppressing distortion. Therefore, the user's visibility can be improved.
2. Since the conversion process can be performed with a simple calculation formula, the drawing processing speed can be improved as compared with the case where only the polar coordinate conversion is performed.

  In addition, the three-dimensional map display apparatus 1 which concerns on this invention is not limited to embodiment mentioned above, It can change suitably.

  For example, in the above-described embodiment, the example in which the three-dimensional map display device 1 according to the present invention is applied to a car navigation device has been described. However, the present invention is not limited to this, and walking implemented in a mobile terminal such as a mobile phone. It may be applied to a navigation device for a person.

It is a block diagram which shows one Embodiment of the three-dimensional map display apparatus which concerns on this invention. It is a schematic diagram which shows the image display means of this embodiment. It is a schematic diagram which shows the drawing range in this embodiment. It is a figure for demonstrating the image conversion process of this embodiment. 3 is a three-dimensional map within the drawing range of FIG. 3, (a) a three-dimensional map drawn by a perspective projection method, (b) a three-dimensional map subjected to polar coordinate transformation, and (c) a three-dimensional map according to the present embodiment. It is a schematic diagram which shows. In this embodiment, it is a schematic diagram explaining the drawing method at the time of projecting on a polyhedron. It is a flowchart figure explaining operation | movement of the three-dimensional map display apparatus and program of this embodiment.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 3D map display apparatus 2 Position detection means 3 Input means 4 Memory | storage means 5 Image display means 6 Image memory 7 Arithmetic processing means 51 3D display area 52 2D fixed scale display area 53 2D variable scale display area 71 Path | route search part 72 Image conversion processing unit 73 Two-dimensional map drawing unit O Left and right center line P Current position Q First passage point R Second passage point S Destination U Guide route A Partial region V Partial visual cone

Claims (4)

Storage means for storing road map information;
Position detection means for detecting the current position;
Image conversion processing means for acquiring the road map information within a display range based on the current position from the storage means and converting the information into a three-dimensional image;
Image display means for displaying a three-dimensional road image,
The image conversion processing unit deforms the road image by projecting the three-dimensional coordinates obtained from the road map information onto a virtual solid centered on the current position, and further projecting the three-dimensional coordinates onto the drawing plane. A three-dimensional map display device characterized by three-dimensionalization. 2. The image conversion processing unit according to claim 1, wherein when the virtual solid is a sphere, the coordinates projected in parallel on the drawing plane are (X, Y), and the three-dimensional coordinates with the current position as an origin are used. Assuming (x, y, z), the following formula X = x / √ (x ² + y ² + z ² )
Y = y / √ (x ² + y ² + z ² )
A three-dimensional map display device characterized by converting into a three-dimensional image. Storage means for storing road map information;
Position detection means for detecting the current position;
Image conversion processing means for acquiring the road map information within a display range based on the current position from the storage means and converting the information into a three-dimensional image;
The computer is executed as an image display means for displaying a three-dimensional road image,
The image conversion processing unit deforms the road image by projecting the three-dimensional coordinates obtained from the road map information onto a virtual solid centered on the current position, and further projecting the three-dimensional coordinates onto the drawing plane. 3D map display program characterized in that a computer is executed so as to be three-dimensional. 4. The image conversion processing unit according to claim 3, wherein when the virtual solid is a sphere, the coordinates projected in parallel on the drawing plane are (X, Y), and the three-dimensional coordinates with the current position as the origin are used. Assuming (x, y, z), the following formula X = x / √ (x ² + y ² + z ² )
Y = y / √ (x ² + y ² + z ² )
A 3D map display program that causes a computer to execute a conversion process into a 3D image.

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