KR20180074845A - Method and apparatus for providing chess game - Google Patents

Abstract

The present invention relates to a method and an apparatus for providing a chess game to apply real-time polygonal-light shading algorithm with linearly transformed cosigns to a chess game. The method for providing a chess game comprises the steps of: creating at least one chessman image with respect to at least one chessman applied to a chess game; arranging the chessman image on a chess board previously formed in a lattice type by a chessman arranging unit; shading the at least one chessman image arranged on the chess board by applying a real-time polygonal-light shading algorithm with linearly transformed cosigns, which is a shading algorithm similar to the flat surface of a spherical body, to the at least one chessman image.

Description

[0001] METHOD AND APPARATUS FOR PROVIDING CHESS GAME [0002]

The present invention relates to a method for providing a chess game and an apparatus for providing a chess game.

As the hardware performance of various general purpose game providing devices such as computers, smart devices, various kinds of console game machines including Microsoft's Xbox and Sony's PlayStation, and the like have been developed, the graphics quality of electronic games has dramatically improved.

As a method for improving the graphic quality of the electronic game, there is a rendering. Rendering is a process of creating a three-dimensional image by blowing a sense of reality into a two-dimensional image in consideration of external information such as a light source, And a wire frame rendering method, a ray racing rendering method, and the like are known.

Shading, which is an algorithm for rendering, is a processing technology for calculating a distance from a light source on each surface, brightness of an angular color, etc. to give a three-dimensional surface to a three-dimensional surface in order to give a three- By adding black to a part or all of a specific image, it is a technique of relatively darkening the light-blocked part.

Especially, in real-time rendering where temporal factors of rendering work as important variables, it is costly and time-consuming to directly apply polygonal light sources to graphic images, There is a problem that is difficult to apply.

Korean Patent Registration No. 10-1550934 (2015.09.01.)

It is an object of the present invention to apply a conventional real-time polygonal-light shading with linearly transformed cosines algorithm to a chess game.

According to an aspect of the present invention, there is provided a method of providing a chess game, the method comprising: generating at least one chess horse image, which is an image for each of at least one chess horse applied to the chess game; A step of arranging at least one chess horse image on a chessboard generated in advance in a lattice form and a shading section, a real-polygon type linear transformation which is a shading algorithm approximating a plane of a spherical body to at least one chess horse image, Applying a light source shading algorithm to apply shading to at least one chess horse image disposed on the chess board.

The details of other embodiments are included in the detailed description and the accompanying drawings.

According to the present invention, when real-time rendering is applied by applying a conventional real-time polygonal-light shading with linearly transformed cosines algorithm to a chess game, the time and cost .

FIGS. 1 to 14 are views for explaining a conventional real-time polygon linear conversion light source shading applied to a shading unit in a chess game providing method and apparatus according to an embodiment of the present invention.
FIG. 15 is a diagram illustrating a chess game providing method and apparatus according to an embodiment of the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings in order to facilitate a person skilled in the art to easily carry out the technical idea of the present invention. . In the drawings, the same reference numerals are used to designate the same or similar components throughout the drawings. In the following description of the present invention, a detailed description of known functions and configurations incorporated herein will be omitted when it may make the subject matter of the present invention rather unclear.

Hereinafter, a method and an apparatus for providing a chess game according to an embodiment of the present invention will be described in detail with reference to the accompanying drawings.

First, with reference to FIG. 15, a method and apparatus for providing a chess game according to an embodiment of the present invention will be described.

FIG. 15 is a diagram illustrating a chess game providing method and apparatus according to an embodiment of the present invention.

15, the chess game providing apparatus 100 according to the embodiment of the present invention includes a chess horse generating unit 110, a chess horse arrangement unit 120, and a shading unit 130. [

The chess horse generating unit 110 generates at least one chess horse image, which is an image for each of at least one chess horse applied to a chess game.

The chess horse arrangement section 120 arranges at least one chess horse image in a chessboard previously generated in a lattice form.

The shading unit 130 applies a shading to at least one chess horse image disposed on the chess plate by applying a real-time polygon-type linear transformation light source shading algorithm, which is a shading algorithm that approximates a plane of a spherical body to at least one chess horse image do.

For example, the shading unit 130 may apply a BRDF (Bidirectional Reflectance Distribution Function) to a spherical model of a polygonal light source.

For example, unlike the conventional BRDF, the shading unit 130 approximates the surface of the spherical surface in a plane, expresses the surface of the spherical surface as a plane, applies polygonal light source shading, and then shakes the spherical surface back to the spherical surface, You can apply light shading more effectively to chess horse images.

As a result, texture and light effects applied to the spherical map can be expressed more lightly, and a large number of chess horse images reflected on the chessboard can be realistically represented.

1 to 14, a shading unit 130 of a chess game providing apparatus 100 according to an embodiment of the present invention realizes a real-polygon linear conversion light source shading (Real -Time Polygonal-Light Shading with Linearly Transformed Cosines algorithm.

FIGS. 1 to 14 are views for explaining a conventional real-time polygon linear conversion light source shading applied to a shading unit in a chess game providing method and apparatus according to an embodiment of the present invention.

A real-polygon linear conversion light source shading, which is a conventional algorithm for explaining the operation of the shading unit 130 of the chess game providing apparatus 100 according to the embodiment of the present invention, is a linear transformation represented by a 3x3 matrix Applying it to the direction vector of a spherical distribution takes advantage of the fact that another spherical distribution is calculated and leads to a closed form equation.

Real-time polygon-type linear conversion light source shading generates a new set of spherical distributions with parametric roughness, elliptic anisotropy, and distortion using a spherical distribution as a basic shape. The original distribution is divided into analytic expression, normalization, With integration and importance sampling, these attributes are inherited by a linearly transformed distribution.

Selecting a fixed cosine for the original distribution yields a distributed series called linearly-based modified cosine (LTC), which provides a good approximation to the physically based BRDF, Can be analyzed analytically, and real-polygon linear conversion light source shading algorithms can be applied to show how to use these properties.

1. Introduction

Physical based shading involves integrating the product of the Bidirectional Reflectance Distribution Function (BRDF), which is a calculation of the lighting equation, with the illumination of the spherical domain, and then describes how to apply shading from polygonal lights .

This means calculating the integration of BRDF onto a spherical polygon, and although it is theoretically one of the simplest lighting models, polygon illumination, there are difficulties in real-time rendering for the following two main reasons.

First, integrating parametric spherical distributions into spherical polygons is generally difficult even in the simplest distributions. For example, phong-polygon integrals are expensive, but they are not spherical Gaussian, There is a problem that can not provide an analysis solution for.

Second, the state-of-the-art physical-based material model is not a simple distribution, but has an elaborate shape with anisotropic stretching and distortion, which requires realistic material presentation.

Section 3 describes a new type of linear distribution LTSD (Linearly Transformed Spherical Distributions) that solves the above two problems.

Starting with the original spherical distribution, a linear transformation, represented by a 3x3 matrix, is applied to the direction vector and the result is a parametrization that can modify the shape of the original distribution, such as roughness, elliptic anisotropy and distortion, Can be calculated.

As shown in Figure 3, parametrization allows creation of new families of parametric spherical distributions with different basic shapes using all of the spherical distributions, the main features of which are normalization, for arbitrary spherical polygons And inherit several properties of the original distribution, such as integration and importance sampling.

In Section 4 below, using a fixed cosine for the original distribution produces a distribution series called Linearly Transformed Cosines (LTC) that provides a good approximation to the physically based BRDF thanks to the various spherical shapes, and a fixed cosine distribution Can be analyzed analytically for any rectangular polygon, so LTC is possible.

Hereinafter, in section 5, a method of using the above-described property in the application of real-time polygonal light source shading will be described.

2. BACKGROUND ART

With respect to polygon light source shading, the analysis solution for polygon illumination is limited to the same distribution as the current cosine, and integrating the clamped cosines on the polygon domain has been resolved centuries ago, It has been introduced.

으로 나타난다는 점이며, 여기서 n은 폴리곤 정점의 수이고 e는 Phong 지수를 나타낸다.These analytical solutions have been extended to cosines with exponents that control the Phong distribution, ie, the sharpness of the distribution. Detailed implementations of this technique are well known in the art, and the main limitation of this approach is that the phong- The complexity of Phong-polygon integration

Where n is the number of polygon vertices and e is the Phong index.

That is, there is a problem that the integration cost increases according to the sophistication of the distribution when the above-described method is utilized. This is why video games use an approximate cost that is less expensive than the above-mentioned Pon distribution.

These technologies are cheap enough to be used in real time, but are not accurate and do not guarantee robust integration.

A recent technique for applying polygonal light sources in real time provides an approximate solution to the integration of pong polygons in O (n), but regardless of the sharpness of the distribution, such integrations are fast enough to be computed in real time , There is a problem that is limited to the rotational symmetry shape of Phong Lobe to provide an approximate solution.

In the prior art, it is proposed to use the Phong distribution as a microfacet distribution which needs to be integrated into a non-polygonal halfspace. In the prior art, And calculates the approximate Phong integration on it.

Although the anisotropy of the microphase model can be restored by using the above-described method, there is a problem in that a conspicuous approximation causes a visible heterogeneity in some configurations, and the integrated complexity of real-time polygon linear conversion light source shading is O (n) The result is that accurate and real - time polygon - type linear transformation light source shading can be applied to include complex spherical shapes with elliptic anisotropy and distortion.

In addition, the real-time polygon linear conversion light source shading method is much simpler to implement. Also, the real-time polygon linear conversion light source shading method multiplies the vertices of n polygons by the matrix before calculating the radiation dose using the conventional equation.

With respect to the spherical distribution, there are few spherical distributions that present a sophisticated shape, while at the same time providing useful integration properties, and spherical harmonics are limited to low frequency forms.

All of the most common frequency distributions used in computer graphics are rotationally symmetric protruding distributions, which may be spherical Gaussian, also known as Phong distributions or von Mises-Fisher distributions.

It is difficult to integrate them in spite of simplicity, and as mentioned above, approximation is necessary to efficiently integrate Phong distribution in spherical polygons, and similarly, incorporating spherical Gaussian into spherical regions is only approximate There is a problem that a pre-calculated look-up table is required.

Furthermore, designing more complex distributions often means abandoning simple attributes, for example, there is no useful analytical operator for distribution with elliptic anisotropy in statistics, and Anisotropic Spherical Gaussian (ASG) Is designed to provide an approximate operator for this distribution, but computing the standardization factor has the problem of evaluating complex formulas, and obtaining a practical solution for integrating spherical polygons can be a difficult problem.

3. Linear transformed spherical distribution

This section describes the linear transformed spherical distributions (LTSDs) and shows a method of reconstructing the original distribution by applying a linear transformation to the direction vector, as shown in Fig. 2, and a method of reconstructing the obtained new distribution And describe its characteristics.

3.1 Definitions

With respect to the initial distribution to be transformed, D _o represents an initial distribution to be parameterized again by a linear transformation, and selection of D _o as shown in FIG. 3 controls the basic shape of the transformed distribution.

In relation to the linear transform, to produce a new distribution D, to apply a linear transformation to be defined by the 3 × 3 matrix, and can be applied to a 3 × 3 matrix M to the direction vector w of the initial distribution D _o.

그리고 역으로,

이 성립하며, 역변환과 함께 원래의 방향을 회복할 수 있다.Figure 2 shows how the choice of the matrix M affects the nature of the distribution, assuming that the normalized direction vector is an exact transformation,

And conversely,

And the original direction can be restored with the reverse conversion.

With respect to the closed-form representation, the size of the LTSD may be equal to the magnitude for the initial direction w ₀ of the initial distribution D ₀ and may be the product of the change in the solid angle measurement due to the distortion of the spherical transform, The expression is shown in Equation 1 below.

[Equation 1]

는 정규화 된 방향 벡터의 변형 된 자코비안이고,

는 정규화 된 방향 벡터를 의미하며, 상술한 수학식 1의 결과에 대한 증명은 도 13 및 도 14에 도시된 바와 같은 종래의 자코비안 유도 방법을 통해 확인할 수 있으며, 구체적인 설명은 생략한다.At this time,

Is the modified Jacobian of the normalized direction vector,

And the proof of the result of Equation (1) can be confirmed through the conventional Jacobian derivation method as shown in FIG. 13 and FIG. 14, and a detailed description thereof will be omitted.

에서 불변하며, 또한 회전은 분포의 방향을 변경하는 것이지 모양은 변경하지 않고, 이는 M이 스케일링 또는 회전 행렬

인 경우 구형 변환의 자코비안이 일정하기 때문이다.With respect to shape invariance, since the scaling vector does not change direction, the distribution is transformed into a scaling transformation

And rotation also changes the direction of the distribution and does not change its shape, since M is a scaling or rotation matrix

, The Jacobian of the spherical transformation is constant.

With respect to the median vector, using some classical initial distributions D ₀ , the z-vector (0 0 1) ^T becomes the intermediate vector, that is, every plane containing this vector has an equal weight 1 / can cut the D _o in two parts corresponding to two, of these features can be preserved by the conversion, the converted Midian vector may be a central vector of the transformed distribution D, in Figure 2, the right column of M (0 0 1) ^T , but the center vector is aligned with the z-axis.

For example, in FIG. 2 (d), the distortion exaggerates one of the distributions and distorts the other, while the z-axis maintains the median distribution.

3.2 Properties

The transformed distribution D can inherit some properties of the original distribution D _o .

Regarding normalization, the norm of the distribution D transformed in the LTSD is the norm of the initial distribution D _o , and the following equation (2) can be derived from the above equation (1).

&Quot; (2) "

With respect to the integration using the polygon, the integration of the LTSD-transformed distribution D for the polygon P is performed by integrating the initial distribution D _o for the polygon P ₀ = M ^-1 P obtained by applying the inverse transformation M ^-1 to each vertex of the polygon to be.

&Quot; (3) "

This can be obtained by a variation of the variable as in Equation (2).

The result is shown in FIG. 4, intuitively, Equation 3 is the probability that the direction sampled in D intersects the polygon P. The linear transformation applied to the direction vector of D and polygon P does not change this intersection point, so it maintains the value of integration.

Here again converting the distribution D D _o to the initial distribution, and to apply the M ^-1, and again applied to the polygon Po = P M ^-1, and this property is available and, as a result of the integration of the D P is D _o Is the integral of P _o .

와 같이 변환될 수 있다.With regard to importance sampling, the significance of D can also be sampled if the significance of D _o can be sampled due to the definition of LTSDs. That is, a random sample w ₀ may be generated randomly in the D _o and conversion,

. ≪ / RTI >

This is because the LTSD defined by Equation 1 appears as the product of D ₀ and the Jacobian of the transformation, and the probability density function PDF of the sample w can be expressed exactly as D (w).

4. Physical Based BRDF Approximation Using Linear Transform Cosine

In this section, we show that choosing a clamped cosine distribution for the original distribution yields a good approximation to the physically based BRDF by creating a linearly transformed distribution set.

Regarding the linear transform cosine, the normalized clamp cosine distribution in the hemisphere given in the z-direction for the initial distribution D ₀ can be selected as shown in Equation 4 below, and the linearly linear transformed cosine (LTC) Can be defined by replacing D _o as well.

&Quot; (4) "

With respect to the fitting, the spherical function given by the cosine weight BRDF with respect to the light source direction w _l can be approximated as shown in Equation (5) below.

&Quot; (5) "

For an isotropic material, BRDF depends on the incidence direction W _v = (sin _θv , 0, cos _θv ) and the illumination parameter α, and for any combination θ _v , α, the cosine weight BRDF is matched to the linear transformation cosine The most suitable matrix M can be found, and since the linearly transformed cosine is scale invariant due to the plane symmetry of the isotropic BRDF, M can be expressed as: " (6) "

&Quot; (6) "

Therefore, only four parameters need to be matched. Experimentally, it can be seen that minimizing the error of L ³ gives the best visual result in terms of shading, and FIG. 5 shows the fitting result.

With respect to representation and storage, Equation 3 requires only the inverse matrix M- ¹ and, after the fitting procedure, stores the inverse matrix in a precomputed table, where M- ¹ is the four parameters for the isotropic BRDF Variable.

에 대한 추가 매개 변수를 사용할 수 있으며, 해상도 64×64의 2D 플로트 텍스쳐에 총 5 개의

및

로 파라미터화 된 매개 변수를 저장하고, 선형 보간법으로 가져올 수 있으며, 여기서, 미리 계산 된 데이터의 크기는 80KB일 수 있다.In addition, the norm of the fitted BRDF

, And a total of 5 in 2D 64 × 64 float textures

And

, And can be imported as linear interpolation, where the size of the precomputed data can be 80 KB.

5. Real-time polygon shading using linear cosine

Shading with diffuse polygonal illumination means computing the illumination integral for the polygonal domain.

&Quot; (7) "

는 BRDF, P는 폴리곤, L은 폴리곤에 의해 방사되고 방향 W_l에서 수신 된 광도를 의미한다.Where W _v is the view direction,

Is the BRDF, P is the polygon, and L is the light intensity radiated by the polygon and received in the direction W _l .

를 활용하여 수학식 5를 수학식 7로 근사하면, 아래 수학식 8과 같이 나타난다.In order to use the properties of the linearly transformed cosine, a matrix M ^-1 of a linearly transformed cosine D at the runtime, an incident angle θ _v , a roughness

The equation (5) can be approximated by the equation (7) as shown in the following equation (8).

&Quot; (8) "

5.1 Constant Polygon Shading

If the radiation intensity emitted by the polygon light is a spatial constant, i.e., L (W _l ) = L, then this is represented by Equation 9, which is the separable multiplication factor of the integral.

&Quot; (9) "

Using the polygonal integration characteristic of Equation (3), the following Equation (9) is derived, and the following Equation (10) is derived.

&Quot; (10) "

Where E is the radiation dose of the polygon Po = M ^-1 P, and since D _o is actually a clamped cosine distribution, the integral for the polygon is the radiation dose of this polygon, and using the closed form of expression, have.

&Quot; (11) "

Assuming that j = (i + 1) mode (mod) n and Equation (11) assumes a spherical polygon located at the upper half, each edge of the polygon can be clipped before the summation operation of Equation (11).

5.2 Shading by Polygon Light Source with Texture

In this section, assuming that the luminance L (W _l ) emitted by the polygon is applied as a 2D color texture, it can not be separated from the integral, and the following equations (12), (13) and appear.

&Quot; (12) "

&Quot; (13) "

&Quot; (14) "

The advantage of Equations (12) through (14) is that the problem can be divided into two sub-problems and can be further divided into computing I _D and I _L with different properties.

The value of I _D in relation to the shape of the highlight is the integral of the distribution for the polygonal domain, i. E. The fraction of the ray of light intersecting P, which drives the order of magnitude of I and forms a highlight, 3 < / RTI >

In relation to the color of the highlight, in contrast, I _L can be seen as the average color gathered by the rays of D intersecting at P, responsible for the color of the highlight, can be formulated as a texture space filter, . Hereinafter, a method of prefiltering a texture with LODs (Levels of Detail) and a method of parameterizing a texture import will be described.

5.3 Prefiltering textures

을 통과 한 텍스처 L의 값으로 정의하며,

은 텍스처 공간에 투영될 수 있으며, 사전 필터링 단계에서 F를 텍스처 공간 가우스 필터로 근사화할 수 있다.Equation (14) is a filter I _L

Is defined as the value of the texture L passed through,

Can be projected into the texture space, and in the pre-filtering step F can be approximated with a texture space Gaussian filter.

로 정규화된다는 점이다.Here, there are two properties of F that will be preserved by the approximate filter: F is fixed to the polygon (ie F = 0 outside the texture) and F is the texture

.

That is, it means that the approximate texture space filter can not leak out of the texture. To accomplish this, the texture space Gaussian inside the texture is clamped and re-normalized, and furthermore, the value of the pre- It should be defined everywhere. As shown in Fig. 6, margins can be included around the texture, which can cross the texture by increasing the radius of the filter, which is necessary to define the filter well.

Finally, we fix the texture coordinates to the margins beyond the margins, which defines smooth and low frequency functions in the texture space outside the texture, and is an expected characteristic of the exact filter F.

5.4 Importing Textures

There may be difficulty in getting a light texture in the prefiltered area.

To parameterize a texture fetch requires two quantities, texture coordinates and LOD. A naive approach can consist of calculating the mean (or median) direction intersection coordinates of the distribution in texture space, but this approach is unstable and sometimes Definitions can be wrong.

For example, as shown in Fig. 7 (a), the average direction of the distribution does not intersect the texture plane. Another difficulty is that the appropriate LOD depends on several parameters (sharpness of the distribution, slope and distance of the texture plane).

The cosine composition simplifies the problem described above and can be expressed in a cosine configuration associated with D to simplify the problem. This conversion is as shown in FIG.

With respect to the polygonal integral, in Equation (3), the result of applying the inverse matrix M ^-1 is expressed by Equation (15) below.

&Quot; (15) "

P _o = M ^-1 P is a polygon of cosine composition and L _o (W _l ) is the associated deformed texture.

The advantage of this configuration is to parameterize the texture space filter that approximates a cosine distribution D _o is much simpler and more robust D random distribution.

To obtain the prefiltered texture in the cosine configuration, an orthogonal projection of the shading point on the texture plane in the cosine configuration can be used, as shown in FIG.

As shown in Fig. 7 (b), this point is always well defined, easy to compute, and can produce an accurate texture fetch regardless of the sharpness of the distribution D.

Also, since it is a normal orthogonal projection, the slope of the texture plane at this point is exactly 90 degrees, and there is no problem of anisotropy in the texture space filter shape. That is, low-frequency fluctuations of the cosine distribution and anisotropic distortion of texture parameterization after polygon conversion can be ignored.

의 가우시안으로 사전 필터링 된 LOD를 선택할 수 있다.The choice of LOD can be reduced by a 1D function of the ratio between the square distance r ² to the texture plane and the area A of the polygon,

Gt; LOD < / RTI > that has been prefiltered with Gaussian of < RTI ID =

The result of applying the real-time polygon type linear conversion light source shading to the game engine can be shown in FIG. 8, and the comparison result with the ground truth can be confirmed in FIG. 9 to FIG.

In other words, the light source in a game engine is an important issue in terms of realizing reality, and the conventional real-time polygon linear conversion light source shading can be applied to a BRDF (Bidirectional Reflectance Distribution Function) .

Conventional real-time polygon linear conversion light source shading has a problem in that it is not so long in non-real-time rendering that a polygonal light source is actually applied to a spherical model, but considering the computation time assuming that a general method is used, Applying it as it is, it requires high cost.

That is, the chess game providing method and apparatus according to the embodiment of the present invention can provide a chess game by applying the real time polygon linear conversion light source shading which is a conventional technique.

While the present invention has been described in connection with what is presently considered to be practical exemplary embodiments, it is to be understood that the invention is not limited to the disclosed embodiments, but many variations and modifications may be made without departing from the scope of the present invention. It will be understood that the invention may be practiced.

100: Chess game providing device
110: chess horse generating unit
120: chess piece arrangement part
130: Shading portion

Claims (1)

Generating a chess horse image, the at least one chess horse image being an image for each of at least one chess horse applied to a chess game;
Placing a chess horse arrangement in the chessboard previously generated in a lattice form of the at least one chess horse image; And
Wherein the shading unit applies a shading to the at least one chess horse image disposed on the chess plate by applying a real time polygon type linear transformation light source shading algorithm which is a shading algorithm that approximates the plane of the spheres to the at least one chess horse image ≪ / RTI >

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