KR20060069232A - Device and method for representation of multi-level lod 3-demension image - Google Patents

Abstract

The present invention relates to an apparatus and method for representing a model having a large scale of data, such as a large-scale terrain model, on a computer system in real time in three dimensions.

In the three-dimensional image display apparatus having a multi-level resolution according to the present invention, a triangular patch of a lower layer (m + 1 level) includes k * k (k is the number of horizontal and vertical grids of an upper layer) of upper layers (m levels). Each layer constitutes a multi-level hierarchical mesh having different resolutions, and each vertex of the triangular patches included in the hierarchical mesh by regularly sampling height information of a target image. Patch configuration unit for assigning; A resolution determiner configured to determine a resolution of each triangular patch according to a viewpoint of the virtual camera; And a patch connection unit connecting the adjacent triangular patches without a gap to each other when resolution is different between adjacent triangular patches among the triangular patches included in the hierarchical mesh.

DEM, PM, ROAM, MESH, GIS, Virtual Reality, Terrain Models, Computer Graphics

Description

DEVICE AND METHOD FOR REPRESENTATION OF MULTI-LEVEL LOD 3-DEMENSION IMAGE}

1 is a block diagram of a three-dimensional image representation device having a multi-level resolution according to an embodiment of the present invention.

FIG. 2 is a diagram illustrating a hierarchical mesh for expressing terrain of multi-level resolution using a triangular patch according to an embodiment of the present invention. FIG.

3 illustrates a hierarchical mesh having n levels of hierarchies according to an embodiment of the present invention.

4 illustrates an example of disposing vertices of a hierarchical mesh with respect to height information of a regularly sampled target image.

Fig. 5 is a diagram showing an example of the resolution distribution of each triangular patch when the resolution is determined based on the error of the screen.

Fig. 6 is a diagram showing an example of the resolution distribution of each triangular patch in the case where the resolution is determined based on the distance from the virtual camera.

7 (a) to 7 (g) are views showing a connection method for removing a gap between adjacent patches having different resolutions according to an embodiment of the present invention.

8 (a) to 8 (d) are diagrams illustrating a method for connecting patches between two lower level triangle patches adjacent to one lower level triangle patch.

FIG. 9 is a diagram illustrating a terrain of multi-layer resolution expressed based on screen error-based resolution according to an embodiment of the present invention. FIG.

FIG. 10 is a diagram illustrating a process of constructing a hierarchical mesh of multi-level resolution having different resolutions by using a triangular patch according to an embodiment of the present invention. FIG.

11 is a view showing a process of connecting without gaps between adjacent patches having different resolutions according to an embodiment of the present invention.

TECHNICAL FIELD The present invention relates to a computer graphics system, and more particularly, to an apparatus and method for representing a model having a large scale data such as a large-scale terrain model in a real-time three-dimensional computer system.

Due to the rapid development of virtual reality systems, computer game technologies, and the like, many technologies for expressing various objects and terrain of the real world in three dimensions are being developed using computer systems. As such, a mesh model is mainly used to represent a three-dimensional image of the real world on a computer. The mesh model is composed of a set of interconnected triangles, squares, or polygons to represent a three-dimensional surface such as an object or a terrain.

In order to express massive amounts of data such as large-scale terrain in real time on a computer system in three dimensions using such a mesh model, proper terrain generation, management, and representation techniques are required to effectively use the limited graphic resources of the computer system. . Conventional technologies for representing large-scale terrain data in real time include PM (Progressive Mesh) -based technology, DEM (Digital Elevation Model), and ROAM (Real-time Optimally Adaptive Meshes) technology. Computer graphics, virtual reality, GIS (Geographical Information System) technology is used.

U.S. Patent No. 6,611,267, "SYSTEM AND METHOD FOR COMPUTER MODELING OF 3D OBJECTS OR SURFACES BY MESH CONSTRUCTION HAVING OPTIMAL QUALITY CHARACTERISTICS AND DYNAMIC RESOLUTION CAPABILITIES. Modeling methods and systems are disclosed. The PM-based technique determines the insertion order of the vertices of polygons constructed in the mesh, and dynamically inserts the vertices to dynamically construct the mesh model to maintain optimal meshes at all times, as well as to insert and remove vertices. You can quickly remove vertices from a mesh by maintaining a list. However, the PM-based technology takes up a lot of memory of a computer system and has a problem of slowing data representation because the mesh model needs to be changed dynamically to represent a 3D image.

See also previous paper, Duchaineau et al., 'ROAMing Terrain: Real-time Optimally Adapting Meshes', IEEE Visualization on '97 Proceedings, pp. 81-88, 1997 disclose the Real-time Optimally Adaptive Meshes (ROAM) technique. The ROAM technique constructs a binary tree with triangles to minimize the reconstruction of meshes processed in real time and optimizes progressive triangle division and computational priority by combining the smoke list. However, the ROAM technology also has a problem that it is not suitable for a large-scale terrain system that needs to express the terrain faster because meshes having various resolutions are dynamically reconfigured to represent a 3D image.

An object of the present invention for solving the above problems is to provide an apparatus and method for efficiently reconstructing a large-scale terrain data in a computer system through a small memory and a small calculation and to represent it in real time.

In order to achieve the above object, a three-dimensional image display apparatus having a multi-level resolution includes a triangle patch of a lower layer (m + 1 level) of k * k (k is the number of horizontal and vertical grids of a higher layer). It includes triangular patches of layer (m level), and each layer forms a multi-level hierarchical mesh having different resolutions, and regularly samples the height information of the target image to the hierarchical mesh. A patch component for assigning each vertex of the included triangle patches; A resolution determiner configured to determine a resolution of each triangular patch according to a viewpoint of the virtual camera; And a patch connection unit connecting the adjacent triangular patches without a gap to each other when resolution is different between adjacent triangular patches among the triangular patches included in the hierarchical mesh.

In addition, the three-dimensional image representation method having a multi-level resolution according to the present invention for achieving the above object, the triangular patch of the lower layer (m + 1 level) is k * k (k is the number of horizontal and vertical grid of the upper layer) A first step of forming a hierarchical mesh of higher layer (m level), each layer forming a multi-level resolution hierarchical mesh having different resolutions; A second step of regularly sampling the height information of the target image and assigning to each vertex of the triangular patches included in the hierarchical mesh; Determining a resolution for each triangle patch according to the viewpoint of the virtual camera; And a fourth step of connecting the adjacent triangular patches without a gap to each other when resolution is different between adjacent triangular patches among the triangular patches included in the hierarchical mesh.

In addition, the recording medium in which the computer program according to the present invention is recorded to achieve the above object, the triangular patch of the lower layer (m + 1 level) is k * k (k is the number of horizontal and vertical grid of the upper layer) upper layers (m level) triangular patches, each layer comprising a first step of forming a multi-level hierarchical mesh having different resolutions; A second step of regularly sampling the height information of the target image and assigning to each vertex of the triangular patches included in the hierarchical mesh; Determining a resolution for each triangle patch according to the viewpoint of the virtual camera; And a program for causing a computer to execute a fourth step of connecting the adjacent triangular patches without gaps when the resolutions are different between adjacent triangular patches among the triangular patches included in the hierarchical mesh.

DETAILED DESCRIPTION A detailed description of preferred embodiments of the present invention will now be described with reference to the accompanying drawings. It should be noted that reference numerals and like elements among the drawings are denoted by the same reference numerals and symbols as much as possible even though they are shown in different drawings. In the following description of the present invention, if it is determined that a detailed description of a related known function or configuration may unnecessarily obscure the subject matter of the present invention, the detailed description thereof will be omitted.

1 is a block diagram of a three-dimensional image representation device having a multi-level resolution according to an embodiment of the present invention.

Referring to FIG. 1, the 3D image display apparatus 10 according to an exemplary embodiment of the present invention includes a patch component 11, a resolution determiner 12, and a patch connector 13, and an input apparatus 20. And a display device 30.

The input device 20 provides the 3D image expression apparatus 10 according to the present invention with a target image that the user intends to express on the display device 30. The target image is mainly applied to large-scale data, such as a terrain model, but is not limited thereto, and may include any image that can be expressed in three dimensions, such as an object and a surface. For example, in the case of a topographic model, the target image may use an image scanned by a satellite or an aircraft, or may use a topographic model that is arbitrarily produced by a user.

As illustrated in FIG. 2, the triangular patch component 11 configures a hierarchical mesh of multi-resolution resolution having different resolutions using triangular patches according to an embodiment of the present invention. 2 is a diagram illustrating a hierarchical mesh for expressing terrain of multi-level resolution using a triangular patch according to an embodiment of the present invention. Referring to FIG. 2, the hierarchical mesh according to the present invention is configured to have multi-level resolution by using a triangular patch. The hierarchical mesh is composed of a two-dimensional square mesh having a grid of regular intervals, and then divided from the upper right corner of each grid toward the lower left corner of the grid to form a triangular patch consisting of an isosceles right triangle. It is formed by. The k * k number of isosceles right triangles represented by points in FIG. 2 constitute one patch of the highest resolution (where k is the number of horizontal and vertical grids of level m). The configured level m patches are collected by k * k pieces to form a triangular patch having a resolution of level m + 1. 2 shows a hierarchical mesh of two levels, where k is 4 and consists of an upper layer of level m and a lower layer of level m + 1. In the present invention, such a hierarchical mesh is repeatedly repeated n times according to the needs of the system, so that the hierarchical mesh having a hierarchical structure of n levels as a whole can be configured to be composed of level 1, level 2, ..., level n. Can be.

3 is a diagram illustrating a hierarchical mesh having n levels of hierarchies according to an embodiment of the present invention. 3 shows an example of a hierarchical mesh of n layers having a grid number k of 3 with the highest resolution and having levels 1 to n. The number of grids (k) and level (n) can be arbitrarily determined according to the needs of the system, such as the determined resolution, memory resources and system speed. Referring to FIG. 3, the patch having the highest resolution is composed of nine (3 × 3) unit triangular patches (areas indicated by dots) in the highest layer (level 1). Using nine of the level 1 triangular patches, a triangular patch of a lower layer corresponding to level 2 is configured. Then, by using nine triangular patches of level n-1, a hierarchical mesh of level n is formed. Accordingly, when the hierarchical mesh is k, the number of horizontal and vertical grids of the upper layer (m level) is k * k higher layers in the triangular patch of the lower layer (m + 1 level) one level lower than the upper layer. Contains triangular patches (unit triangular patches).

4 is a diagram illustrating an example of disposing vertices of a hierarchical mesh with respect to height information of a regularly sampled target image. In the present invention, the patch configuration unit 11 regularly samples the height information of the target image input from the input device 20, and then assigns each vertex of the hierarchical mesh according to the present invention. . As shown in FIG. 4, unique vertex information is assigned to each vertex of each unit triangle and the triangle patch. Therefore, the index information includes height information regularly sampled from the target image. The index information of the triangle patch vertex is configured so that the resolution determiner 12 and the patch connector 13 know in advance. Therefore, even if the triangular patch configuration unit 11 transmits only the index information of each vertex to the resolution determination unit 12 and the patch connection unit 13 for the hierarchical mesh according to the present invention, the resolution determination unit 12 And the patch connection unit 13 may determine the height information of the target image allocated to the vertex of the triangular patch corresponding to each index information by using the received index information. As described above, the triangular patch component 11 transmits index information for each vertex separately in order to minimize polygonal information transmitted to the resolution determiner 12 and the patch connection unit 13. Can be prevented from being duplicated. Therefore, when using the index-based hierarchical mesh according to the present invention, not only can the transmitted data be minimized, but also a graphics pipeline supporting index-based polygons (indexed trangles, etc.) can be expected to achieve up to three times speedup. have.

As described above, the resolution determiner 12 uses a triangular patch component 11 to present a multi-stage target image configured in a preprocessing process on the display device 30 in real time. ) To determine the appropriate resolution. Here, the viewpoint of the current virtual camera refers to a viewpoint in which the virtual character looks at the virtual space, assuming that the virtual character is in a three-dimensional virtual space implemented on a computer system. As a method of determining the resolution of the target image according to the viewpoint of the current virtual camera, a method is determined according to the error of each triangle patch on the screen, and a method is determined according to the vertex of each triangle patch and the distance between the virtual camera. This is used.

5 is a diagram illustrating an example of a distribution of resolutions of each triangular patch when the resolution is determined based on an error of a screen. 5 illustrates a screen error that occurs when a target image (for example, terrain, etc.) is expressed in a small or large size on a screen based on a viewpoint of a current virtual camera C. FIG. The case where the resolution of a triangular patch is determined is shown. In FIG. 5, the triangular patch corresponding to the area indicated by the dot is configured to have a higher resolution than the triangular patch corresponding to the area not indicated by the dot.

FIG. 6 is a diagram showing an example of the distribution of resolution of each triangular patch in the case where the resolution is determined based on the distance from the virtual camera. FIG. 6 illustrates a case where a resolution is determined according to a distance from the current virtual camera C in the virtual space. In FIG. 6, when the target image is a terrain model, a terrain, for example, a mount, which is a short distance from the virtual camera C, is represented as a high resolution (area indicated by a dot) and is displayed at a distance. Backgrounds are rendered with low resolution (areas not represented by dots).

The patch connection unit 13 functions to connect triangular patches having different resolutions hierarchically configured without a gap. 3 to 6, the hierarchical mesh according to the present invention includes a triangular patch of an upper layer (eg, n-1 level) composed of a plurality of unit triangular patches of a portion having a high resolution in a target image. The lower resolution part is expressed in a form that does not include a unit triangular patch. Therefore, a gap between adjacent triangular patches may occur due to the difference in size of the triangular patches between layers. Therefore, the patch connection unit 13 may complete the hierarchical mesh according to the present invention by removing gaps by connecting each vertex included between the adjacent triangular patches.

7 (a) to 7 (g) are diagrams illustrating a connection method for removing a gap between adjacent patches having different resolutions according to an embodiment of the present invention. 7 (a) to 7 (g) below show a case where the region indicated by a dot has a level one level higher than the region not indicated by the dots.

FIG. 7 (a) shows a method for connecting patches between three lower level triangle patches adjacent to one lower level triangle patch. In this case, the upper layer located on the boundary lines of the upper layer triangle patches and the lower layer triangle patch so that the triangle patch of the lower layer has a unit triangle patch structure having the same shape as the upper layer triangle patch therein. By connecting the respective vertices of the unit triangular patches within the triangular patches together, it is possible to eliminate the gap between the triangular patches having different adjacent resolutions.

7 (b), 7 (c) and 7 (d) illustrate a patch-to-patch connection method when two lower level triangle patches are arranged adjacent to one lower level triangle patch. In this case, by adjoining each vertex of the unit triangle patches in the upper layer triangle patches located on the boundaries of the upper layer triangle patches and the lower layer triangle patch in a zigzag form, This can eliminate gaps between triangle patches with different resolutions. Referring to FIG. 7 (d) as an example, a method of connecting patches between two high level triangle patches adjacent to one lower level triangle patch will be described in detail as follows. First, as shown in (a) of FIG. 8, a vertex of the unit triangle of the unit triangle of the upper level patch located on the opposite side from one vertex of the upper level triangular patch is connected to the vertex at the closest distance. Subsequently, as shown in FIG. 8 (b), the first vertex of the unit triangles of the unit triangles of the other upper layer patches facing back from the vertices of the unit triangles connected in the previous step are connected. Also, as shown in Fig. 8 (c) (d), triangle patches having different resolutions adjacent to each other are connected by connecting vertices located on opposite sides of the vertices of the unit triangles of other upper layer patches from the vertices of the recently connected unit triangles. The gap can be removed from the liver.

7 (e), (f), (g) illustrate a patch-to-patch connection method when triangular patches of one upper layer are arranged adjacent to one side of a triangular patch of one lower layer. In this case, all other vertices of the unit triangle patches in the upper layer triangle patch located on the boundary line between the upper layer triangle patch and the lower layer triangle patch are connected with the opposite vertices of the lower layer triangle patch, so that another adjacent resolution is obtained. Clearance can be eliminated between triangular patches.

FIG. 9 is a diagram illustrating a terrain of multi-layer resolution expressed based on a screen error-based resolution according to an embodiment of the present invention.

9 is used to determine the resolution based on the error of the screen using the resolution determiner 12, and then using the patch connection unit 13, with reference to FIGS. 7 (a) to 7 (g). As described, it represents the terrain of the multi-layer resolution having a structure connected so that there is no gap between adjacent patches of different resolution. As described above, the final hierarchical mesh configured to have no gap according to the present invention is rendered with low resolution patches. That is, they are rendered in the order of level n, level n-1, ..., level 1. In this case, the patch of the level m to be rendered should not include the patch below the level m + 1 in the final mesh in the region of the patch.

FIG. 10 is a diagram illustrating a process of forming a hierarchical mesh having a multi-resolution resolution having different resolutions by using a triangular patch according to an embodiment of the present invention.

Referring to FIG. 10, first, by using the patch configuration unit 11 in the 3D image rendering apparatus 10 according to the present invention, a triangular patch of a lower layer (m + 1 level) is k * k (k is the highest resolution). Each layer comprises triangular patches of the upper layer (m level), each layer forming a multi-level resolution hierarchical mesh having different resolutions. In addition, the patch configuration unit 11 regularly samples the height information of the target image, such as the terrain model input from the input device 20, and assigns each vertex of the triangular patches included in the hierarchical mesh (step 101). ).

The resolution of each triangular patch included in the hierarchical mesh is determined according to the viewpoint of the virtual camera (step 102). In this case, the resolution of each triangle patch formed in each layer may be determined according to an error of the triangle patch on the screen, as described with reference to FIG. 5. In addition, the resolution of each layer may be determined according to the distance between the vertex of the triangular patch and the virtual camera, as described with reference to FIG. 6.

Thereafter, it is determined whether the expression is completed for all the triangle patches in the hierarchical mesh. If the expression is completed, the procedure is terminated. If the patch is still present, the next procedure is performed (step 103).

Subsequently, one of the plurality of triangular patches constituting the hierarchical mesh is selected to determine whether the patch has the same resolution as the adjacent patch (step 104).

As a result of the determination in step 104, the patch having the same resolution as the adjacent patch is represented by the current resolution (step 105), otherwise the process goes to step 'A'. The steps 103 to 105 are repeated for all other patches to determine whether the resolution matches the adjacent patches and to complete the hierarchical mesh representation.

11 is a view showing a process of connecting without gaps between adjacent patches having different resolutions according to an embodiment of the present invention.

Step 106 of FIG. 11 is performed when the selected patch has a different resolution from the adjacent patch as determined in step 104 of FIG. 10.

In step 106, it is determined whether the resolution of the selected patch is higher than that of an adjacent patch.

If it is determined in step 106 that the resolution of the selected patch is higher than the resolution of the adjacent patch, the selected patch is represented by the current resolution (step 107).

However, if the resolution of the selected patch is the same or lower than the resolution of the adjacent patch (in this case, the selected patch corresponds to a lower layer patch), the higher resolution among the patches adjacent to the selected triangle patch is determined. The number of patches having, that is, the number of patches of the upper layer is determined and determined (step 108).

If the number of patches of the upper layer adjacent to the selected lower triangle patch is three (step 109), as described with reference to FIG. 7 (a), the triangle patch of the selected lower layer may correspond to the triangle patch of the upper layer. The vertices of the unit triangle patches existing in the upper layer triangle patches are connected to each other so as to have a unit triangle patch structure of the same type (step 110).

If the number of patches of the upper layer adjacent to the selected lower triangle patch is two (step 111), as described above with reference to FIGS. 7B, 7C, and 3D, The vertices of the unit triangle patches in the upper layer triangle patches positioned on the boundaries of the selected lower layer triangle patch are sequentially connected to each other in a zigzag form (step 112).

If the number of patches of the upper layer adjacent to the selected lower triangle patch is one, as described above with reference to FIGS. 7E, 7F, and 7G, the upper layer triangle patch and the lower layer triangle are described. The hierarchical mesh according to the present invention can be finally completed by connecting all the vertices of the unit triangular patches in the upper layer triangular patch located on the boundary of the patch with the vertices opposite to the boundary of the lower layer triangular patch.

According to the present invention, a method of representing a 3D image having a multi-level resolution using a hierarchical mesh having a multi-level resolution may be implemented as computer-readable code on a computer-readable recording medium. The computer-readable recording medium includes all kinds of recording devices in which data that can be read by a computer system is stored. Examples of computer-readable recording media include ROM, RAM, CD-ROM, magnetic tape, floppy disk, optical data storage, and the like, and also include those implemented in the form of carrier waves such as transmission over the Internet. The computer readable recording medium can also be distributed over network coupled computer systems so that the computer readable code is stored and executed in a distributed fashion.

Meanwhile, in the detailed description of the present invention, specific embodiments have been described, but various modifications are possible without departing from the scope of the present invention. Therefore, the scope of the present invention should not be limited to the described embodiments, but should be defined not only by the claims below, but also by those equivalent to the claims.

According to the present invention as described above, by constructing a hierarchical mesh having a multi-level resolution using a triangular patch, and using only the height information assigned to the vertex of each triangular patch included in the hierarchical mesh of the target image such as terrain By constructing a mesh, it is possible to reduce the use of computer system memory resources by up to three times.

Further, according to the present invention, unlike the conventional PM-based method of dynamically generating the vertices of the mesh, after pre-configuring the hierarchical mesh having a multi-level resolution, the vertices of the triangular patches constituting the hierarchical mesh By arranging index information differently, there is an advantage that a patch of various resolutions can be generated and expressed in real time more efficiently.

Further, according to the present invention, third, after pre-configuring the hierarchical mesh having a multi-level resolution in the pre-processing process, as well as determining the resolution of each patch by using the index information for the vertices of the triangle patches constituting the hierarchical mesh, By seamlessly connecting patches with different resolutions, the computational resources used for merging or separating patches can be saved.

Claims (15)

The triangular patches of the lower layer (m + 1 level) contain k * k (k is the number of horizontal and vertical grids of the upper layer) of the triangular patches of the upper layer (m level), each layer being multi-level with different resolution A patch constructing unit configured to construct a hierarchical mesh having a resolution and regularly sampling height information of a target image and assigning to each vertex of triangular patches included in the hierarchical mesh; A resolution determiner configured to determine a resolution of each triangular patch according to a viewpoint of the virtual camera; And And a patch connection unit connecting the adjacent triangular patches without gaps to each other when the resolution is different between adjacent triangular patches among the triangular patches included in the hierarchical mesh. The apparatus of claim 1, wherein the resolution of the upper layer is higher than that of the lower layer. The apparatus of claim 1, wherein the triangular patch is formed by dividing the grid from a right upper vertex to a left lower vertex. The apparatus of claim 1, wherein the triangular patch is a right triangle. The unit triangular patch structure of claim 1, wherein the triangular patches of the upper layer are arranged adjacent to the triangular patches of the lower layer. 3D image representation apparatus having a multi-level resolution, characterized in that the vertices of the unit triangular patches present in the upper layer triangular patches are connected to each other. The upper layer triangle of claim 1, wherein when the upper layer triangle patches are arranged adjacent to the lower layer triangle patch, the upper layer triangle positioned on boundaries between the upper layer triangle patches and the lower layer triangle patch. A three-dimensional image display device having a multi-level resolution, characterized in that each vertex of the unit triangular patches in the patches are connected in a zigzag form. The unit of the upper layer triangle patch located on a boundary between the upper layer triangle patch and the lower layer triangle patch when the triangle patch of one upper layer is arranged adjacent to the triangle patch of the lower layer. And all vertices of the triangular patches are connected with vertices opposite the boundary line of the lower layer triangular patch. The apparatus of claim 1, wherein the patch component transmits index information of each vertex of the triangular patches to the resolution determiner or patch connector, and the resolution determiner or patch connector uses the index information to determine the target image. 3D image representation apparatus having a multi-level resolution, characterized in that for determining the height information. The triangular patches of the lower layer (m + 1 level) contain k * k (k is the number of horizontal and vertical grids of the upper layer) of the triangular patches of the upper layer (m level), each layer being multi-level with different resolution A first step of constructing a hierarchical mesh of resolution; A second step of regularly sampling the height information of the target image and assigning to each vertex of the triangular patches included in the hierarchical mesh; Determining a resolution for each triangle patch according to the viewpoint of the virtual camera; And And a fourth step of connecting the adjacent triangular patches without gaps to each other when the resolution is different between adjacent triangular patches among the triangular patches included in the hierarchical mesh. 10. The method of claim 9, wherein in the first step, the resolution of the upper layer is higher than the resolution of the lower layer. 10. The method of claim 9, wherein the triangular patch is formed by dividing the grid from the upper right vertex to the lower left vertex. 10. The method of claim 9, wherein the triangular patch is a right triangle. The method of claim 9, wherein the fourth step, When the triangular patches of the upper layer are arranged adjacent to the triangular patches of the lower layer, the upper layer such that the triangular patches of the lower layer have a unit triangular patch structure of the same form as the triangular patches of the upper layer therein. 3D image representation method having a multi-level resolution, characterized in that connecting the vertices of the unit triangle patch present in the triangle patches. The method of claim 9, wherein the fourth step, In the case where two upper layer triangle patches are arranged adjacent to the lower layer triangle patch, the unit triangle patch in the upper layer triangle patches positioned on the boundaries of the upper layer triangle patches and the lower layer triangle patch. Three-dimensional image representation method having a multi-level resolution, characterized in that each of the vertices of the zigzag form connected to each other in series. The method of claim 9, wherein the fourth step, When one triangular patch of a higher layer is arranged adjacent to the triangular patch of the lower layer, all vertices of unit triangle patches in the upper layer triangular patch located on a boundary between the upper layer triangle patch and the lower layer triangle patch are removed. And a vertex opposite to the boundary line of the lower layer triangular patch.

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