KR101068324B1 - Rendering method on spherical coordinate system and system thereof - Google Patents

Abstract

A spherical coordinate system rendering method and system are disclosed. The disclosed spherical coordinate rendering method includes generating a data structure for a vertex of an object model represented by a spherical coordinate system, forming a boundary surrounding the object model, setting a frustum of an object photographing apparatus, and the frustum And if the entirety of the boundary is included, constructing a convex hull, and if a portion of the boundary is included, extracting and rendering a visible region by obtaining a plane equation of the frustum.

Rendering, spherical coordinates, frustums, boundaries

Description

RENDERING METHOD ON SPHERICAL COORDINATE SYSTEM AND SYSTEM THEREOF}

The present invention relates to a rendering method and system, and more particularly to a rendering method and system using a spherical coordinate system.

The technology of rendering scenes with a lot of data in real time is a very important research topic in the field of computer graphics. Graphics hardware processing power is steadily evolving, but as the number of scene data to be rendered increases, there is a limit to the performance improvement of real-time rendering.

In order to solve this problem, a spatial data structure method for efficiently constructing geometric data of a scene, a method of reducing the number of data of a model considered in the rendering process while maintaining the accuracy of the final image, and a distance from a camera Accordingly, a progressive mesh method for controlling a geometric representation has been proposed.

In addition, a priority-based layered projection (PLP) method has been proposed that approximates a set of visible geometric elements of an object at a given point in time to improve rendering performance for real-time processing. Since the PLP method determines the view-based visibility in the divided object space, it is accurate for most of the resulting images, but it is difficult to guarantee the quality of the image because it is approximated for the view. CPLP (Conservative PLP) has been developed to solve this problem, but there are disadvantages such as poor rendering performance.

One embodiment of the present invention has been made to improve the prior art as described above, to provide a spherical coordinate system rendering system and method that can improve the speed of rendering in consideration of only the visible region.

In one embodiment of the present invention, to provide a spherical coordinate system rendering system and method that can effectively remove the hidden surface to improve the rendering performance and reliability.

In addition, according to an embodiment of the present invention to provide a spherical coordinate system rendering system and method capable of rendering in real time.

In order to achieve the above object and solve the problems of the prior art, the present invention comprises the steps of generating a data structure for the vertex of the object model represented by the spherical coordinate system; Forming a boundary surrounding the object model; Setting a frustum of the object photographing device; And constructing a convex hull when the entirety of the boundary is included in the frustum, and extracting and rendering a visible region by obtaining a plane equation of the frustum when a portion of the boundary is included. .

According to another aspect of the invention, the data structure for generating a data structure for the vertices of the object model represented by the spherical coordinate system, and forming a boundary surrounding the object model; And setting a frustum of an object photographing apparatus and constructing a convex hull when the entirety of the boundary is included in the frustum, and extracting and rendering a visible region by forming a plane equation of the frustum when a portion of the boundary is included. Provided is a spherical coordinate system rendering system comprising a rendering unit.

According to an embodiment of the present invention, the spherical coordinate range of the object existing in the visible space can be accurately distinguished, thereby improving the speed of rendering.

In addition, according to an embodiment of the present invention, when the objects are all included in the visible region, the plane may be accurately determined and removed, thereby improving performance and reliability of the entire system.

In addition, according to an embodiment of the present invention, rendering can be performed in real time.

Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings.

1 is a flowchart illustrating a method of rendering a spherical coordinate system according to an embodiment of the present invention.

When the object model is input, a rendering pipeline for forming a three-dimensional object into a two-dimensional image is executed. The rendering pipeline generally consists of three phases: the application phase, the geometry phase, and the rasterization phase. In the present invention, a geometrical step is considered, and only the number of vertices of the visible region is processed among the number of vertices considered in the rendering pipeline, thereby rendering speed up.

In the spherical coordinate system rendering method according to an embodiment of the present invention, first, a data structure for a vertex of an object model represented by the spherical coordinate system is generated (S1).

In general, the object model is composed of vertices in the Cartesian coordinate system (x, y, z), the surface of each vertex, the information of the normal vector, and the like. To convert the object model to the spherical coordinate system (R, θ, Φ), the altitude angle (zenith: θ = 0 to 360 °), the azimuth (Φ = 0 to 180 °), and the distance from the center of the sphere to that point ( R) A variable is introduced as in Equation 1.

FIG. 2A is a diagram showing an object model (kettle), and FIG. 2B is a diagram showing a representation of a spherical coordinate system for the object model of FIG. 2A.

In general, the basic geometric element of rendering is triangles. In the step (S1) of generating a data structure in a method of rendering a spherical coordinate system according to an embodiment of the present invention, the distance of the distance R and the angle θ, Φ) and store it in the center of gravity map, and arrange the faces that exist at the same angle according to the distance information. The triangles at the corresponding angles θ and Φ of the center of gravity map thus formed are stored in the memory access map.

That is, the altitude and azimuth of the spherical coordinate system of the triangles corresponding to the visible region to which the ray of the photographing apparatus (camera, etc.) is irradiated are determined, and the triangles in the range are passed to the rendering pipeline using the OpenGL vertex array. Render using the Graphics Processing Unit.

In the spherical coordinate system rendering method according to an embodiment of the present invention, since only the center of gravity map and the memory access map are used in step S1, memory space may be saved, and preprocessing speed and performance may be improved.

When the data structure is generated as described above, a bounding sphere surrounding the object model is formed (S2).

3 is a conceptual view showing a boundary surrounding an object model. The object model is rabbit-shaped and wraps around the object model so that the outline of the object model does not intersect or protrude out of the boundary.

In the spherical coordinate rendering method according to an embodiment of the present invention, it is important to include the boundary sphere and the frustum of the object photographing apparatus. Therefore, the frustum is formed after the boundary is formed (S3). In step S3 of setting the frustum, the X and Y axis view angles for perspective projection, the distance of the near plane, the distance of the far plane, the projection center (center of projection), window center or up vector.

4 is a view showing a frustum of the photographing apparatus. A frustum is formed where the light rays from the photographing device intersect the object. As shown, when the frustum comprises part of the boundary, it consists of eight vertices and six planes. The part to which the imaging device light beam is irradiated becomes a visually visible area.

In the spherical coordinate rendering method according to an embodiment of the present invention, only the visible region at the intersection of the frustum and the object is considered. Therefore, it is determined whether the entirety of the boundary sphere is included in the frustum (S4).

When a part of the boundary is included as shown in FIG. 4, the normal vector of the plane is calculated and the plane equation of the frustum is obtained using the normal vector and the vertices on the plane (S6). If the distance between the plane forming the frustum and the center of the boundary of the object is smaller than the radius of the boundary, it means that they intersect. Therefore, the geometric relationship can be used to determine whether the object and the frustum intersect. The range of the coordinates of the sphere in the plane is obtained from the distance between each plane and the center of the sphere and the radius of the sphere. In addition, the surface corresponding to the visible range is determined by obtaining an angle between the base axis of the object and the visual direction for generating the frustum.

FIG. 5 is a view showing a set of visible areas PVS and an actual visible area RVS when the boundary is partially included in the camera frustum.

In the spherical coordinate rendering method according to an embodiment of the present invention, the visible area is set to PVS (Possible Visible Set), and the actual visible surface is considered in consideration of all surfaces of the object, and RVS (Real Visible Set) is set to the entire surface of the object. If each is defined as TOS (Total Object Set), the following equation is satisfied.

In other words, the visible area is smaller than the total set of objects and should not be less than what is actually visible, but at least equal to or greater than. In the field of visualization such as medicine and science, it is necessary to increase the processing speed of rendering. However, considering too few geometric elements, the resulting image quality may be degraded. Therefore, it should be possible to properly select the actual visible area for the target scene while maintaining rendering performance.

When the boundary of the object is included in the frustum less than half as shown in Figures 4 and 5 satisfy the condition of equation (2). When the plane equation of the frustum is obtained, the visible region is extracted using this (S7), and only the triangles corresponding to the visible region are rendered (S8).

On the other hand, when more than half of the boundary of the object is included in the frustum, the set of extracted visible regions is smaller than the set of visible regions.

When the entirety of the boundary sphere is included in the frustum, a convex hull is configured to determine an area that is covered in the object (S5). In a mathematical sense, convex hull is defined as the convex envelope of a set of points in real vector space. Convex Hull is widely used in the rendering modeling phase of computer graphics. The number of vertices and polygons that make up a convex hull is much smaller than real objects, making it efficient for real-time visibility checking.

6 shows the generation pseudo code constituting the three-dimensional convex hull. The algorithm constituting the 3D convex hull may use an incremental algorithm. Convex hulls for three-dimensional objects have at least four vertices that do not exist on at least the same plane. Convex Hull's basic model is a tetrahedron consisting of four vertices.

FIG. 7 is a view showing a set of visible areas PVS and an actual visible area RVS when the boundary sphere is included in both camera frustums.

In this case, a consistency check on the constituent surface of the convex hull is performed, and then the left and right longest side components are extracted around a vertical axis orthogonal to the eye vector. Based on the azimuth angle of the spherical coordinate system with respect to the two points obtained, the area that exists later in each direction is treated as a silver plane covered by the preceding triangle.

The following equation is for extracting the longest component in both directions with respect to the viewpoint of the photographing apparatus. Using the extracted longest component, the visible area of the spherical coordinate system is extracted (S7), and the triangular surfaces of the model existing in the visible area of the spherical coordinate are transferred to the rendering pipeline (S8).

8 is a conceptual diagram illustrating a spherical coordinate system rendering system using a spherical coordinate system rendering method according to an embodiment of the present invention.

Referring to FIG. 8, the spherical coordinate system rendering system 10 according to an embodiment of the present invention generates a data structure for a vertex of an object model represented by a spherical coordinate system, and forms a boundary surrounding the object model. A data structure 11 and a frustum of an object imaging apparatus are set, and if the entirety of the boundary is included in the frustum, a convex hull is formed, and if a portion of the boundary is included, a plane equation of the frustum is formed to form a visible region. It includes a rendering unit 12 for extracting and rendering.

Each function executed by the data structure unit 11 and the rendering unit 12 is the same as the method of rendering a spherical coordinate system according to an embodiment of the present invention described above with reference to FIGS. 1 to 7.

The data structure unit 11 stores a center of gravity map storing the position of the center of gravity of the triangle forming the surface of the object model according to distance and angle, and a memory storing an address where triangles existing at the corresponding angle of the center of gravity map are stored. Create a data structure with an access map.

The rendering unit 12 sets the frustum using a view angle for perspective projection, a distance of a near end face, a distance of a distal plane, a projection center, a window center, and an up vector.

Then, the rendering unit 12 constitutes the convex hull composed of four or more vertices that do not exist on at least the same plane when the entirety of the boundary is included in the frustum. Then, the left and right longest side intersection components are extracted around the vertical axis orthogonal to the line of sight vector among the intersection points between the vertices and the boundary spheres constituting the convex hull, and are later in each direction based on the azimuth angle of the spherical coordinate system for the two intersection components. Existing areas are removed by the silver surface obscured by the preceding triangle.

When a part of the boundary is included, the rendering unit 12 obtains the plane equation using a normal vector and a vertex of a plane in a frustum having eight vertices and six planes, the distance between the center of each plane and the sphere, and the radius of the sphere. The range of spherical coordinates included in the plane is obtained to extract the visible area.

A spherical coordinate system rendering method and system according to an embodiment of the present invention proposes a real-time rendering algorithm using the spherical coordinate system.

In addition, the spherical coordinate system rendering method according to an embodiment of the present invention is implemented in the form of program instructions that can be executed by various computer means may be recorded on a computer readable medium. The computer readable medium may include program instructions, data files, data structures, etc. alone or in combination. Program instructions recorded on the media may be those specially designed and constructed for the purposes of the present invention, or they may be of the kind well-known and available to those having skill in the computer software arts. Examples of computer-readable recording media include magnetic media such as hard disks, floppy disks, and magnetic tape, optical media such as CD-ROMs, DVDs, and magnetic disks, such as floppy disks. Magneto-optical media, and hardware devices specifically configured to store and execute program instructions, such as ROM, RAM, flash memory, and the like. Examples of program instructions include not only machine code generated by a compiler, but also high-level language code that can be executed by a computer using an interpreter or the like. The hardware device described above may be configured to operate as one or more software modules to perform the operations of the present invention, and vice versa.

As described above, the present invention has been described by way of limited embodiments and drawings, but the present invention is not limited to the above-described embodiments, which can be variously modified and modified by those skilled in the art to which the present invention pertains. Modifications are possible. Accordingly, the spirit of the present invention should be understood only by the claims set forth below, and all equivalent or equivalent modifications thereof will belong to the scope of the present invention.

1 is a flowchart showing a method of rendering a spherical coordinate system in an embodiment of the present invention;

2a shows an object model,

FIG. 2B shows a representation in the spherical coordinate system for the object model of FIG. 2A;

3 is a conceptual diagram showing a boundary surrounding an object model,

4 is a view showing a frustum of a photographing apparatus;

5 is a view showing a set of visible areas (PVS) and an actual visible area (RVS) when a boundary is partially included in a camera frustum;

6 is a generating pseudo code constituting a three-dimensional convex hull,

7 is a view showing a set of visible areas (PVS) and an actual viewable area (RVS) when the boundary is included in the camera frustum.

8 is a conceptual diagram showing a spherical coordinate system rendering system using a spherical coordinate system rendering method according to an embodiment of the present invention.

Claims (13)

Generating a data structure for a vertex of an object model represented by a spherical coordinate system; Forming a boundary surrounding the object model; Setting a frustum of the object photographing device; And Extracting and rendering a visible region by constructing a convex hull when the entirety of the boundary is included in the frustum, and obtaining a plane equation of the frustum when a portion of the boundary is included; Spherical coordinate system rendering method comprising a. The method of claim 1, In generating the data structure, The data as a center of gravity map which stores the position of the center of gravity of the triangle forming the surface of the object model according to distance and angle, and a memory access map which stores an address where triangles existing at the corresponding angle of the center of gravity map are stored; How to render a spherical coordinate system that creates a structure. The method of claim 1, In setting the frustum, A method of rendering a spherical coordinate system for setting the frustum using a view angle for perspective projection, a distance between a near end face, a distance between a far-end face, a projection center, a window center, or an up vector. The method of claim 1, In the rendering step, A method of spherical coordinates rendering the convex hull with at least four vertices that do not exist on at least the same plane. 5. The method of claim 4, The rendering step, When the entirety of the boundary is included in the frustum, the left and right longest side intersection components are extracted from the intersections between the vertices constituting the convex hull and the boundary sphere with respect to the vertical axis orthogonal to the eye vector, and the spherical coordinate system for the two intersection components is extracted. Spherical coordinate system rendering method in which the region existing behind each direction based on the azimuth of is removed by the hidden surface obscured by the preceding triangle. The method of claim 1, In the rendering step, When a part of the boundary is included, the plane equation is obtained using a normal vector and a vertex of a plane in a frustum having eight vertices and six planes, and is included in the plane by the distance of the center of each plane and the sphere and the radius of the sphere. A sphere coordinate system rendering method of extracting the visible region by obtaining a sphere coordinate range. A data structure unit for generating a data structure for a vertex of an object model represented by a spherical coordinate system, and forming a boundary surrounding the object model; And A rendering unit for setting a frustum of an object photographing apparatus, and constructing a convex hull when the entirety of the boundary is included in the frustum, and forming a plane equation of the frustum to extract and render a visible area. ; Spherical coordinate system rendering system comprising a. The method of claim 7, wherein The data structure unit stores the center of gravity of the triangle forming the surface of the object model according to distance and angle, and a memory access map storing an address storing triangles existing at corresponding angles of the center of gravity map. A spherical coordinate rendering system for generating data structures. The method of claim 7, wherein And the rendering unit sets the frustum using a view angle for perspective projection, a distance of a near end face, a distance of a distal plane, a projection center, a window center, and an up vector. The method of claim 7, wherein And the rendering portion constitutes the convex hull of at least four vertices that do not exist on at least the same plane. The method of claim 10, When the entirety of the boundary is included in the frustum, the renderer extracts the left and right longest side intersection components around the vertical axis orthogonal to the eye vector among the intersection points between the vertices and the boundary constituting the convex hull, Spherical coordinate system rendering system that removes the region existing behind each direction with respect to the azimuth angle of the spherical coordinate system. The method of claim 7, wherein The rendering unit obtains the plane equation from a frustum having eight vertices and six planes by using a normal vector and a vertex of a plane, and the distance between the center of each plane and the sphere and the radius of the sphere. A spherical coordinate rendering system for extracting the visible region by obtaining an included spherical coordinate range. A computer-readable recording medium containing instructions for performing the spherical coordinate rendering method of any one of claims 1 to 6.

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