KR101137924B1 - Method for generating randomly bumpy surface for Korean traditional stone wall with boundary and recording medium for the same - Google Patents

Abstract

The three-dimensional surface generation method for modeling a Korean traditional stone wall with a boundary of the present invention calculates a unit law vector of each vertex by dividing a vertex of a boundary mesh into a mesh boundary and a case where it is not. Making; 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 of each random vertex by dividing all vertices into and from the mesh boundary; Receiving a mixing ratio vector; And moving all vertices using the blending ratio vector and the random unit vector.

Description

Method for generating randomly bumpy surface for Korean traditional stone wall with boundary and recording medium for the same}

The present invention relates to a three-dimensional surface generation method having a boundary and a recording medium therefor. More particularly, the present invention relates to a method of generating a three-dimensional surface having an unevenly partial deflection by using a boundary 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 partly irregular stone or rock surface and an uneven surface by using a given deflection component by using a boundary individual mesh.

According to an embodiment of the present invention, a three-dimensional surface generation method for modeling a Korean traditional stone wall with a boundary includes dividing a vertex of a boundary mesh into a case belonging to a boundary line of the mesh and a case where it is not. Calculating a unit law vector; 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 of each random vertex by dividing all the vertices into and out of the boundary of the mesh; Receiving a mixing ratio vector; And moving all the vertices by using the mixing ratio vector and the random unit vector.

In particular, the step of calculating the unit law vector of each vertex by dividing the vertices of the mesh with the boundary belonging to the boundary of the mesh and if not, if the vertex belongs to the boundary of the mesh, Obtaining two sides included in two boundary lines serving as endpoints; And calculating a unit law vector of a corresponding vertex by using a simple average of two vectors included in the boundary plane of the mesh and perpendicular to the two sides.

In addition, the step of calculating the unit law vector of each vertex by dividing the vertices of the mesh having the boundary belonging to the boundary line of the mesh and if not, if the vertex does not belong to the boundary line of the mesh, The unit law vector of the vertex is calculated using a simple average of the law vectors of the triangles that share.

In addition, the step of generating a random unit vector of each random vertex by dividing all the vertices into the boundary of the mesh and if not, if the vertex belongs to the boundary of the mesh, the corresponding boundary plane of the mesh It is characterized by generating a random unit vector of the vertex by removing the vector direction component.

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

The mesh may be a mesh in which at least one edge that does not share two faces is present.

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 the labor of modeling designers, you can use bounded meshes (polygonal meshes) to create realistically randomly shaped objects, such as rocks or rocks, in a short time. It is possible to provide a more realistic picture by applying to.

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 flowchart illustrating a three-dimensional surface generation method for modeling a boundary Korean traditional stone wall 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 7 are exemplary views showing the shape change of the mesh according to the segmentation.
8 is a schematic structural diagram of a computer device for performing a three-dimensional surface generation 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, it will be described on the assumption that the boundary mesh to be applied in the present invention consists of only triangles. In addition, the boundary mesh in the present invention may be a polygon such as a rectangle, a pentagon, and the final curved surface varies according to the shape of a given mesh. Here, 'there is a boundary' means that there is at least one edge that does not share two sides.

Making a non-triangular polygonal mesh into a triangle-only mesh is called triangulation, and the left figure of FIG. 3 shows an example of a triangulated rectangular 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.

On the other hand, when a three-dimensional surface having a partially deflected component is created using an individual mesh without a boundary (polyhedron mesh), segmentation is performed up to polygons of invisible faces. That is, since one plane is changed into four planes, the increase rate of the number of planes requires a very large amount of calculation in proportion to 4 ⁿ . Here, polygon refers to a polygon, which is the smallest unit used to express a three-dimensional shape in three-dimensional computer graphics.

In order to compensate for this, the present invention allows the segmentation process to be performed on only one surface (that is, the individual meshes having boundaries). A single object is usually thought of as connected, and connecting sides that share only one face results in a closed curve.

In the present invention, the segmentation process using individual meshes with boundaries is similar to the segmentation process using individual meshes without boundaries, but the plane (hereinafter, boundary) that still includes the boundary curve after displacement of the selected vertex in the boundary line is moved. The difference is that it is included in (plane).

1 is a flowchart illustrating a 3D surface generation method for modeling a Korean traditional stone wall with a boundary according to an embodiment of the present invention.

Referring to FIG. 1, a three-dimensional surface generating method according to the present invention is largely divided into a) a unit of each vertex by dividing a vertex of a mesh having a boundary into a case where the vertex belongs to a boundary of the mesh and a case where it is not. Calculating a law vector; 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 each random vertex by dividing all the vertices into and out of the boundary of the mesh; e) receiving a mixing ratio vector; And f) moving all of 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 ).

First, an initial mesh having a boundary is input and read (S100), and a unit vector of each vertex v of the initial mesh is calculated. At this time, in step S110, the vertex of the mesh is divided into a case where the vertex of the mesh is different from the case where the vertex of the mesh is not, and the unit law vector of the vertex is calculated (S110).

If a particular vertex does not belong to the boundary of the mesh, the unit law vector of the vertex may be defined as a simple average value of the law vector of faces (ie, triangles) that share the vertex in the mesh.

However, if a particular vertex belongs to a mesh boundary, that vertex is always the junction of two boundary edges. From this property, it is possible to obtain edges included in two boundary lines having the vertex as the end point, and to obtain two vectors included in the boundary plane and perpendicular to the two sides.

)의 단순 평균값(

)으로 정의될 수 있다(도 2 참조).Therefore, the unit law vector of the vertices included in the boundary line is defined as two vectors perpendicular to the two sides (

Simple mean value of

) (See FIG. 2).

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 random midpoint is represented by the equation (1).

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

On the other hand, since the law vector of the random vertices belonging to the boundary is already included in the boundary plane, v _ij obtained from Equation 1 is also included in the boundary plane. You can see that it belongs to the boundary plane.

When the law vectors of the random vertices are calculated through the step S130, all vertices on the mesh 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 for every vertex, the input mixed ratio vector is multiplied by the component to add and move (S150 to S170). At this time, the blending ratio acts to have a different deflection in each direction in the three-dimensional space so that the resulting mesh has a slightly different shape. If a particular vertex belongs to a boundary line, when generating a random unit vector, the vertex is subtracted from the component of the legal vector direction and then united so that the vertex is still included in the boundary plane.

을 정해진 비율만큼 더한다.More specifically, after moving all vertices in the direction of their normal vector, a random unit vector to give some random properties.

Add by the set ratio.

로부터 해당 경계평면의 법벡터 방향의 성분을 제거한다.In this case, it should be noted that the vertices belonging to the boundary line still have to belong to the boundary plane even after the movement. Therefore, when generating a random unit vector of the vertex, the components of the normal direction of the boundary plane are subtracted and generated. In other words,

Removes components in the legal vector direction of the boundary plane from.

이 경계평면의 법벡터라고 하면, 수학식 3과 같이 경계평면에 포함되도록 무작위 단위 벡터를 생성한다.In other words,

Suppose the law vector of the boundary plane generates a random unit vector to be included in the boundary plane as shown in equation (3).

만큼 이동할 비율을 r₁ 이라 하고, 더해 질

의 비율을 r₂라 하면 최종적으로 얻어지는 정점은 수학식 4와 같으며, 여기서 움직이는 비율 r₁, r₂를 변수 요소로 생각한다.And,

Move by r ₁ To be added

Assuming that the ratio of r ₂ is the final vertex obtained by Equation 4, the moving ratios r ₁ and r ₂ are considered to be variable elements.

On the other hand, since one face has three edges in the mesh, the number of vertices obtained in one face is six.

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 similarly moved in the normal vector direction, which can be expressed as Equation (5).

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).

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 4)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 4).

The shape can vary according to this ratio, and r ₁ can be a vector value if the reduction ratio is changed according to the direction. This will be described in more detail in the following description.

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 to the nearest vertex from each vertex, obtains a random vector having a size of 1/2 or less thereof, adds to it, and moves the initial vertex. This process makes it possible to expect more random elements in the final shape.

On the other hand, it is important to create a shape similar to the visible surface of a stone wall in the case of a bordered mesh. Typically, the stone used in the stone wall is a flat, angular stone, or a flat, angular stone that is processed to stack well. To subdivide this shape, the displacement in the direction perpendicular to the boundary plane needs to be relatively small. To this end, the present invention proposes a method that can change the displacement element according to the individual direction by slightly modifying the above-described displacement process.

와 같이 하고, 두 개의

, 에 대해 각 성분별로 곱해주는 연산을 수학식 7과 같이 정의한다.R ₁ in Equation 4 Is a single real value, but we use it as a vector to give different elements in different directions. In other words,

And two

, And multiply each component by, as shown in Equation 7.

The equation of the vertex that is finally displaced using Equation 7 is shown in Equation 8.

In the present invention, the above algorithm is implemented by using C ++ and DirectX, and it is uniformly given as r = 0.1, = (0.3,0.1,0.3), r ₂ = 0.3 (usually the height direction becomes y-direction in computer graphics). An example of the subdivision is shown through FIGS. 3 to 7.

In Figures 3 to 6, the figures on the left show the boundary mesh in a wire frame, and the figures on the right show the texture of the wire frame.

3 and 5 illustrate triangular initial input meshes, and FIG. 4 (a) shows a case where one subdivision step (described above) is performed for the mesh of FIG. 4B illustrates a case where two subdivision steps are performed on the mesh of FIG. 3, and FIG. 4C illustrates a case where three subdivision 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.

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

Referring to FIG. 8, 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. In more detail, the calculation unit 130 calculates the unit law vector of each vertex by dividing it into a case where the boundary does not belong to the boundary of the mesh of the vertices for the mesh having no boundary input through the input unit 110, Random vertices are generated at each displacement of the initial mesh, and the generated random vertices are calculated for each law vector. Then, the operation unit 130 moves all the vertices of the mesh in the direction of its legal vector, and generates a random unit vector of each random vertex by dividing all the vertices of the mesh into the mesh boundary and the other case. do. The operation unit 130 generates a three-dimensional surface by moving all vertices of the mesh by using the mixing ratio vector received through the input unit 110 and the generated random unit vector. 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 (9)

Calculating a unit law vector of each vertex by dividing the vertices of the mesh with a boundary between and when the vertices of the mesh belong to the boundary line of the 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 of each random vertex by dividing all the vertices into and out of the boundary of the mesh;
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,
Computing the unit law vector of each vertex by dividing the vertices of the mesh with the boundary and the case that is not the boundary of the mesh,
If a vertex belongs to a boundary of the mesh, obtaining two sides included in two boundary lines having the vertex as an end point; And
Calculating a unit law vector of a corresponding vertex using a simple average of two vectors included in the boundary plane of the mesh and perpendicular to the two sides; How to produce. The method according to claim 1,
Computing the unit law vector of each vertex by dividing the vertices of the mesh with the boundary and the case that is not the boundary of the mesh,
When a vertex does not belong to the boundary of the mesh, a unit law vector of the vertex is calculated using a simple average of law vectors of triangles sharing the vertex. 3D surface creation method. The method according to claim 1,
Generating a random unit vector of each random vertex by dividing all the vertices into and out of the boundary of the mesh,
When a vertex belongs to the boundary line of the mesh, a three-dimensional model for boundary Korean traditional stone wall is generated by removing a law vector direction component of a corresponding boundary plane of the mesh to generate a random unit vector of the vertex. Surface creation method. The method according to claim 1,
The mesh is triangulated (triangulation), characterized in that the three-dimensional surface generation method for modeling the boundary Korean traditional stone wall. The method according to claim 1,
The mesh is a three-dimensional surface generation method for modeling a boundary Korean traditional stone wall, characterized in that the mesh that has at least one edge (edge) that does not share two faces. The method according to claim 1,
Generating random vertices at each displacement of the mesh,
And generating random vertices to be oriented to the center of the corresponding displacement of the mesh. delete 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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