KR20110114010A - Method for generating randomly bumpy surface for korean traditional stone wall without boundary and recording medium for the same - Google Patents

Abstract

According to an embodiment of the present invention, a three-dimensional surface generation method for modeling a boundaryless Korean traditional stone wall may include: calculating a unit law vector of each vertex for a boundaryless mesh; Generating random vertices at each displacement of the mesh, and calculating law vectors of the generated random vertices, respectively; Moving all vertices of the mesh in their respective law vector directions; Generating a random unit vector for each of the vertices, respectively; Receiving a mixing ratio vector; And moving all the vertices by using the mixing ratio vector and the random unit vector.

Description

Method for generating randomly bumpy surface for Korean traditional stone wall without boundary and recording medium for the same}

The present invention relates to a method for generating a three-dimensional surface without boundaries and a recording medium therefor. More particularly, the present invention relates to a method for generating a three-dimensional surface having an unevenly partial deflection by using a borderless mesh, and a recording medium therefor.

In general, in order to draw a real-world object on a digitized display device such as a computer monitor, it is necessary to make the surface of the object similar only with points and lines that can be expressed on a computer. Usually, a patch is made by joining polygons such as triangles or rectangles, which requires a lot of manual work by the modeling designer. For this reason, the creation of objects for 3D computer graphics is traditionally used by many modeling designers. It has been produced by labor. This is because they tried to describe in detail many vertices and polygons in order to have a realistic feeling when the objects were observed at close range.

In recent years, however, surface generation algorithms have been developed that attempt to describe the original object using only a small number of control points on the surface, which saves a lot of effort from modeling designers.

One of the most representative is Bezier surfaces, the details of which are well described in many 3D graphics theory books. For example, J. Foley et al., "Computer Graphics: Principles and Practice", Second Edition (Addison-Wesley Publishing Company, Inc., 1996).

 Similar algorithms include the Terrain Generation algorithm and the Displaced subdivision Surface algorithm. The terrain generation algorithm divides a given rectangular area into grid points of regular intervals and generates height information for each grid area. This is described in detail in Chapter 11 of David H. Eberly's "3D Game Engine Design" (Morgan Kaufmann Publishers, 2001). The displacement dividing surface algorithm relates to a method for generating a surface when there are irregularities in detail.

A more widely used method is bump mapping, which is a kind of trick that changes only the shading effect by changing the normal vector at the pixel. The next step in bump mapping is displacement mapping, which moves parts of the surface. The schematic process is described in detail in Section 12.6.6 of “Real-time Rendering 2nd ed.” (AK Peters, Ltd. 2002) by Tomas Akenine-Moller et al.

However, all the existing methods described above are suitable for producing smooth mesh approximation meshes, and are not suitable for producing partially sharp or partially irregular bumpy surfaces such as stone or rock surfaces.

The present invention has been proposed to solve the above problems,

It is an object of the present invention to provide a three-dimensional surface generation method that can generate a partly pointed or partially irregular stone or rock surface and a rugged curved surface by using a non-boundary individual mesh such as a polyhedron.

According to an embodiment of the present invention, a three-dimensional surface generation method for modeling a boundaryless Korean traditional stone wall may include: calculating a unit law vector of each vertex for a boundaryless mesh; Generating random vertices at each displacement of the mesh, and calculating law vectors of the generated random vertices, respectively; Moving all vertices of the mesh in their respective law vector directions; Generating a random unit vector for each of the vertices, respectively; Receiving a mixing ratio vector; And moving all the vertices by using the mixing ratio vector and the random unit vector.

In particular, the mesh is characterized in that the triangulated (triangulation) mesh.

In addition, the step of calculating the unit law vector of each vertex for the boundary-free mesh, characterized in that using a simple average of the law vector of the triangles that share the vertex in the mesh.

In addition, the mesh is characterized in that all edges are polyhedral meshes that share two faces.

In addition, the step of moving all the vertices of the mesh in the direction of their law vector, respectively, characterized in that it comprises the step of adding their law vector to all the vertices by a predetermined ratio.

In addition, generating a random vertex at each displacement of the mesh, characterized in that to generate a random vertex to be biased to the center of the displacement of the mesh.

In addition, the step of generating a random vertex in each displacement of the mesh, it characterized in that using the equation (1) to generate a random vertex to be biased to the center of the displacement of the mesh.

[Equation 1]

)(random (0,1) is a function for finding random numbers between 0 and 1;

)

According to the present invention, the following effects can be expected.

Without much labor of modeling designers, it is possible to realistically generate objects with randomly different shapes such as stones and rocks in a short time, and to provide more realistic images by applying them to areas such as terrain generation in 3D games. Become.

BRIEF DESCRIPTION OF THE DRAWINGS In order to better understand the drawings cited in the detailed description of the invention, a brief description of each drawing is provided.
1 is a flow chart illustrating a three-dimensional surface generation method for modeling a traditional Korean stone wall without boundaries in accordance with the present invention.
2 is an exemplary view for explaining a detailed algorithm of the three-dimensional surface generation method.
3 to 6 are exemplary views showing the shape change of the mesh according to the segmentation.
7 is a schematic structural diagram of a computer device for performing a three-dimensional surface generating method according to the present invention.

Hereinafter, the present invention will be described in detail with reference to the accompanying drawings. Here, the repeated description, well-known functions and configurations that may unnecessarily obscure the subject matter of the present invention, and detailed description of the configuration will be omitted. Embodiments of the present invention are provided to more completely describe the present invention to those skilled in the art. Accordingly, the shape and size of elements in the drawings may be exaggerated for clarity.

In the present invention, a method of generating a collection of individual objects having the same type but slightly different form using a random function will be described.

These set objects naturally produce sharp or irregularly curved surfaces, which can be deflected by changing a few elements.

Hereinafter, all boundaryless meshes (for example, tetrahedron, pentahedron, hexahedron, etc.) applied in the present invention will be described on the assumption that they are made of only triangles.

Making a mesh of a polyhedron (eg, a cube) consisting of polygons other than triangles as a mesh consisting only of triangles is called triangulation, and the left figures of FIGS. 3 and 5 show an example of a triangulated cube mesh.

Triangulation algorithms are already developed in many varieties, and are a publicly known technique. More information on this can be found in articles such as "FIST: Fast Industial-Strength Triangulation" (1998) by Held, Martin.

1 is a flowchart illustrating a three-dimensional surface generation method for modeling a Korean traditional stone wall without boundaries according to an embodiment of the present invention.

Referring to FIG. 1, a three-dimensional surface generation method according to the present invention includes: a) calculating a unit law vector of each vertex for a mesh having no boundary; b) generating random vertices at each displacement of the mesh, and calculating law vectors of the generated random vertices, respectively; c) moving all vertices of the mesh in their respective law vector directions; d) generating a random unit vector of all the vertices, respectively; e) receiving a mixing ratio vector; And f) moving all the vertices using the blend ratio vector and the random unit vector. At this time, when you want to obtain a more refined mesh, the steps a) to f) may be repeated recursively. Recursive subdivision steps [a) to f)] n times (V ⁿ , E ⁿ , F ⁿ ), (n≥0) (V ⁿ : vertex set E ⁿ : side set, F ⁿ : face Set), and the initial mesh can be represented by (V ⁰ , E ⁰ , F ⁰ ).

Unbounded meshes can be polyhedrons such as tetrahedrons, pentagonal cubes, etc., and the final curved surface depends on the shape of a given mesh. In the present invention, the term 'no boundary' means that all edges always share two sides.

First, an initial mesh having no boundary is input and read (S100), and a unit vector of each vertex v of the initial mesh is calculated (S110).

Various methods are known as a method of obtaining the law vector of each vertex of the input initial mesh. A simple and representative method can be obtained by using a simple average of the law vectors of triangles that share the vertices in a given initial mesh. At this time. The vertex law vector that forms part of the boundary is slightly different. Since this always forms a connection point between two boundary lines, it is natural to obtain the average of two unit vectors that are perpendicular to each boundary line and belong to the boundary plane including the boundary line.

Next, random vertices are generated at each displacement of the mesh (S120), and law vectors of the generated random vertices are respectively calculated (S130).

In this case, a method of generating random vertices at each displacement uses linear interpolation, and selects a positive number less than 1 displaced close to 0.5 from a random value less than 1. In addition, the law vector of each random vertex is given by linear interpolation of the law vectors of two vertices sharing a line segment including the random vertex, and the random positive number selected in the above process is used.

Assuming that two given vertices v _i and v _j form an edge, a random vertex is generated by randomly picking the centered points at the sides (i, j). The generated random vertices are represented by Equation 1 below.

In this case, the normal vector of this random vertex is shown in Equation 2.

When the law vectors of the random vertices are calculated through the step S130, all vertices including the existing vertices in the mesh and the random vertices generated through the step S120 are respectively moved in the direction of their law vector (S140).

Next, the mixing ratio vector is input. Then, after generating a random unit vector of all the vertices of the mesh, respectively, multiply the input mixed ratio vector by component and move them (S150 to S170).

At this time, the mixing ratio vector has a function of making the deflection differently in each direction in the three-dimensional space so that the generated mesh has a slightly different shape. If the vertices belong to the boundary line, the components of the law vector direction of the boundary plane are subtracted and united from the random vector generated so that they are still included in the boundary plane.

방향으로 이동시킨 후, 약간의 무작위적인 성질을 주기 위하여 무작위 단위 벡터

을 정해진 비율만큼 더한다.More specifically, the vertex v _ij generated through the step S120 is used as its normal vector.

After moving in the direction, a random unit vector to give some random properties

Add by the set ratio.

만큼 이동할 비율을 r₁ 이라 하고, 더해 질

의 비율을 r₂라 하면 최종적으로 얻어지는 정점은 수학식 3과 같으며, 여기서 움직이는 비율 r₁, r₂를 변수 요소로 생각한다.

Move by r ₁ To be added

Assuming that the ratio of r ₂ is the final vertex as shown in Equation 3, the moving ratios r ₁ and r ₂ are considered to be variable elements.

Since a face has three edges, the number of vertices that can be obtained from one face is six, and the list is as follows.

When the vertex collection is obtained through the above process, a new face is generated from the obtained vertex collection as follows, and the process is applied to each face from the given set of vertices V ⁿ and the face set F ⁿ .

At this time, each time the process is repeated once, the surrounding surfaces pop up, so that the existing vertices are buried. In the present invention, in order to correct this, the existing vertices are also moved in the normal vector direction, which can be expressed as Equation 4.

Next, according to the input of the recursive command, the aforementioned processes are recursively applied to obtain the next set of vertices V ^{n + 1} and the set of faces F ^{n +1} (S180). 2 is an exemplary view for explaining the above detailed algorithm.

On the other hand, in connection with the description of the above process it is necessary to mention a few more points.

First, the s = random (0,1) function used to find the point on the edge from above is a function that finds a random number between 0 and 1. This results in evenly equal probabilities in each interval, with values very close to zero or one, and points very close to both ends. In this case, the segmentation process may not be performed efficiently.

Therefore, the present invention introduces the following function that transforms the function into a function having a probability biased at the center point 0.5.

This function converts random (0,1) to random numbers between 0 and 1 with the same probability, and converts them to numbers closer to 0.5 between r and 1-r.

(수학식 3)에서 나오는 두 개의 비율 r₁, r₂에 관한 것이다.Secondly, the process of displacing arbitrary points on the sides

It is related to the two ratios r ₁ and r ₂ from (Equation 3).

The shape can vary according to this ratio, and r ₁ becomes a vector value if the reduction ratio is changed according to the direction.

The third is to randomly move the vertices of the initial mesh to maintain their initial shape in order to increase the diversity even if the given geometric models are initially placed at regular intervals.

To this end, the present invention measures the distance from the vertex closest to each vertex, obtains a random vector having a size of 1/2 or less thereof, and adds the random vector to move the initial vertex. This process makes it possible to expect more random elements in the final shape.

In the present invention, the above algorithm is implemented by using C ++ and DirectX, and r = 0.1, r ₁ = 0.5 r ₂ = 0.3 (where r is a constant used in the random 'function) and show an example of segmentation. 3 through 6 are shown.

3 to 6, the figures on the left show the mesh in the wire frame, and the figures on the right show the texture in the wire frame.

3 and 5 show triangular initial input meshes, and FIG. 4 (a) shows a case where one subdivision step (steps a) to f) described above is performed for the mesh of FIG. 3. 4 (b) shows a case where two refinement steps are performed on the mesh of FIG. 3.

6A illustrates a case where one subdivision step is performed on the mesh of FIG. 5, and FIG. 6B illustrates a case where two subdivision steps are performed on the mesh of FIG. 5, and FIG. 6. (C) shows a case where three refinement steps are performed for the mesh of FIG. 5.

7 is a schematic structural diagram of a computer device for performing a three-dimensional surface generating method according to the present invention.

Referring to FIG. 7, the computer device 100 may include an input unit 110, a storage unit 120, an operation unit 130, and a display unit 140.

The input unit 110 receives a command signal for modeling the stone wall from a user (eg, a 3D surface generator), and receives a triangular initial mesh.

The storage unit 120 may store various variables for the 3D surface generation method, and an algorithm for generating the 3D surface.

Meanwhile, the 3D surface generating method according to the present invention may be implemented in the form of program instructions that can be executed through the computer device 100 and recorded on a recording medium, for example, a computer readable medium.

In this case, the storage unit 120 may read the recording medium inserted into the computer device 100, that is, the recording medium on which the 3D surface generating method is recorded, and store necessary variables.

Here, 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. Hardware devices such as magneto-optical media and the like.

In addition, examples of program instructions may include high-level language code that can be executed by a computer using an interpreter as well as machine code such as produced by a compiler.

The calculation unit 130 receives the initial mesh through the input unit 110 according to the three-dimensional surface generation algorithm stored in the storage unit 120 to generate a three-dimensional surface for modeling the Korean traditional stone wall. More specifically, the calculation unit 110 calculates the unit law vector of each vertex for the boundaryless mesh input through the input unit 110, generates a random vertex at each displacement of the initial mesh, and generates the random Compute the law vectors of the vertices respectively. Then, the operation unit 130 moves all the vertices of the mesh in the direction of its law vector, respectively, and generates a random unit vector for every vertex. In addition, the operation unit 130 generates a three-dimensional surface by moving all the vertices respectively using the mixed ratio vector and the generated random unit vectors received through the input unit 110. In addition, the operation unit 130 displays the generated three-dimensional surface to the user through the display unit 140.

Films with a lot of capital often require different types of photorealistic or non-realistic 3D meshes. For example, descriptions of similar but randomly different shapes of objects in the natural world are required, which requires many labor-intensive tasks of the modeling designer.

However, according to the present invention, it is possible to realistically generate objects having randomly different shapes such as stones and rocks in a short time without much labor of the modeling designer, and apply them to fields such as terrain generation of 3D games. It becomes possible to provide an image.

As described above, the best embodiment has been disclosed in the drawings and the specification. Although specific terms have been used herein, they are used only for the purpose of describing the present invention and are not used to limit the scope of the present invention as defined in the meaning or claims. Therefore, those skilled in the art will understand that various modifications and equivalent other embodiments are possible from this. Therefore, the true technical protection scope of the present invention will be defined by the technical spirit of the appended claims.

100: computer device 110: input unit
120: storage unit 130: operation unit
140: display unit

Claims (8)

Calculating a unit law vector of each vertex for a boundaryless mesh;
Generating random vertices at each displacement of the mesh, and calculating law vectors of the generated random vertices, respectively;
Moving all vertices of the mesh in their respective law vector directions;
Generating a random unit vector for each of the vertices, respectively;
Receiving a mixing ratio vector; And
Moving all of the vertices using the blend ratio vector and the random unit vector. The method according to claim 1,
The mesh is triangulated (triangulation), characterized in that the three-dimensional surface generation method for the traditional Korean stone wall modeling without boundaries. The method according to claim 2,
Computing the unit law vector of each vertex for the boundaryless mesh,
A method of generating a three-dimensional surface for modeling a boundaryless Korean traditional stone wall using a simple average of law vectors of triangles sharing corresponding vertices in the mesh. The method according to claim 1,
The mesh is a three-dimensional surface generation method for modeling a borderless Korean traditional stone wall, characterized in that all edges are a polyhedron mesh sharing two faces. The method according to claim 1,
Moving all the vertices of the mesh in the direction of their legal vectors, respectively,
And adding a legal vector to all the vertices by a predetermined ratio. The method according to claim 1,
Generating random vertices at each displacement of the mesh,
And generating random vertices to be centered in the center of the corresponding displacement of the mesh. The method of claim 6,
Generating random vertices at each displacement of the mesh,
A method of generating a three-dimensional surface for modeling a boundary-free Korean traditional stone wall, characterized by using Equation 1 below to generate a random vertex to be centered at a center of a corresponding displacement of the mesh.
[Equation 1]

(random (0,1) is a function for finding random numbers between 0 and 1;

) A computer-readable recording medium in which a program for executing the method of any one of claims 1 to 7 is recorded.

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