JP2019101966A - Image generation device and image formation method - Google Patents

Abstract

To provide a method for artificially and efficiently generate a three-dimensional shape of a structure with a substantially curved surface.SOLUTION: The method includes the steps of: performing mapping so that a curved surface of surface on a three-dimensional object for which an image is generated becomes a flat surface; partitioning the flat surface into regions of a Voronoi diagram; defining respective line segments, which form the Voronoi diagram, as a rectangle by providing finite thickness; analyzing a formula (3), with z=0 inside the rectangle in a formula (1) :z=f(x,y,t),t=0, using (2): z=f(x,y,t),t=0 as an initial condition; and performing inverse mapping with respect to a solution z(x,y,T) obtained in the case of t=T, thereby performing mapping on the curved surface. x and y are orthogonal coordinates, z is a coordinate orthogonal to the flat surface with 0 on the flat surface, and d is a diffusion coefficient having a positive value.SELECTED DRAWING: Figure 4

Description

  The present invention relates to an image generating device and an image generating method, and more particularly to computer graphics.

  In recent years, in the field of three-dimensional computer graphics, three-dimensional shape models are used to generate natural landscapes. In landscape generation with three-dimensional computer graphics, there is a task of modeling objects such as various creatures and buildings that compose the landscape. It is important to conduct modeling efficiently because it requires a lot of effort and time for modeling work.

Japanese Patent Application Laid-Open No. 10-91799

  When creating images in the sea using computer graphics, it may represent coral on the seabed. As a technique for generating an image of coral having branched branches, there is, for example, Patent Document 1 and the like. However, in the case of a kind of coral having a large number of polygonal holes and ridge-like depressions on its surface in the form of a globular shape such as chrysanthemum coral (see FIG. 1) or noocal coral (see FIG. 2) An approximate generation method has not been established, and an image can not be obtained efficiently in a short time. Therefore, it is an object of the present invention to provide a method for artificially and efficiently generating the shape of a three-dimensional structure whose surface is a substantially curved surface.

[Mode 1] According to mode 1, a method of generating an image by a computer is provided, and the step of mapping so that the curved surface of the solid surface to be generated an image becomes a plane; Defining each of the line segments as a rectangle by giving a finite thickness to each of the line segments constituting the Voronoi figure;
Formula (1): z = f ₀ (x, y, t), t = 0
Let z = 0 inside the rectangle at
Formula (2): z = f ₁ (x, y, t), t = 0
With the initial condition,
, And mapping on the surface by inverse mapping to the solution z (x, y, T) obtained when t = T, where x and y are the above The coordinates are orthogonal coordinates on a plane, z is a coordinate orthogonal to the plane where 0 is on the plane, and d is a diffusion coefficient having a positive value.

  [Mode 2] According to mode 2, in the method according to mode 1, each line segment constituting the Voronoi figure is extended in the length direction of each line segment and then given a finite thickness to make each line segment rectangular. It has the step to define. "

[Mode 3] According to mode 3, there is provided a non-volatile computer-readable recording medium storing an instruction to execute steps including the following by being executed by a processor, the step being an object to generate an image The steps of mapping so that the curved surface of the solid surface becomes a plane, dividing the plane into Voronoi figures, and giving finite thickness to each of the line segments constituting the Voronoi figure, each of the line segments is rectangular. Defining as
Formula (1): z = f ₀ (x, y, t), t = 0
Let z = 0 inside the rectangle at
Formula (2): z = f ₁ (x, y, t), t = 0
With the initial condition,
, And mapping on the surface by inverse mapping to the solution z (x, y, T) obtained when t = T, where x and y are the above The coordinates are orthogonal coordinates on a plane, z is a coordinate orthogonal to the plane where 0 is on the plane, and d is a diffusion coefficient having a positive value.

  According to the fourth aspect, in the non-volatile computer readable recording medium according to the third aspect, each line segment constituting the Voronoi figure is extended in the length direction of each line segment and then given a finite thickness. , Defining each line segment as a rectangle.

[Mode 5] According to mode 5, a system for generating an image by a computer is provided, and a mapping processing unit maps the curved surface of a solid surface to be an image to be a plane, and the plane is Voronoi A Voronoi processing unit for dividing into figures, and a rectangle generation unit for defining each of the line segments as a rectangle by giving a finite thickness to each of the line segments constituting the Voronoi figure.
Formula (1): z = f ₀ (x, y, t), t = 0
Let z = 0 inside the rectangle at
Formula (2): z = f ₁ (x, y, t), t = 0
With the initial condition,
And an inverse mapping processor that maps the solution z (x, y, T) obtained when t = T by inverse mapping to the surface z, and x , Y are orthogonal coordinates on the plane, z is a coordinate orthogonal to the plane where 0 on the plane, and d is a diffusion coefficient having a positive value.

  According to the sixth aspect, in the system according to the fifth aspect, each line segment constituting the Voronoi figure is extended in the length direction of each line segment and then given a finite thickness to make each line segment rectangular. Define.

It is a figure which shows the whole shape of a chrysanthemum coral. It is a figure which shows the surface shape of a chrysanthemum coral. It is a figure which shows the surface shape of a no coral. FIG. 1 is a block diagram schematically illustrating a system for generating an image, according to one embodiment. 5 is a flow chart illustrating a method of generating an image according to one embodiment. It is a figure which shows the state which divided | segmented the plane into Voronoi. FIG. 6 is a view showing a state in which extension processing and thickness giving processing are performed on each side of the polygon shown in FIG. 5. It is a figure which shows the state which given fixed height to the rectangular internal area with respect to the figure shown by FIG. 6, and given the depth to the other area | region. It is a figure which shows the state which applied the diffusion equation with respect to the image shown by FIG. FIG. 6 is a diagram illustrating a planar pattern of a generated image, according to one embodiment. FIG. 6 is a diagram illustrating a planar pattern of a generated image, according to one embodiment. It is a sketch figure of the metallic material surface in which corrosion occurred.

  In the following, embodiments of a method for generating an image by a computer and a system for generating an image according to the present invention will be described with reference to the attached drawings. In the accompanying drawings, the same or similar elements are denoted by the same or similar reference symbols, and redundant description of the same or similar elements may be omitted in the description of each embodiment. Also, the features shown in each embodiment can be applied to other embodiments as long as they do not contradict each other.

  FIG. 3 is a block diagram that schematically illustrates a system for generating an image, according to one embodiment. The illustrated image generation system 100 can be configured from a general computer, a dedicated computer, or the like. The illustrated image generation system 100 includes an input unit 102, a storage unit 104, a processing unit 150, and an output unit 106. The input unit 102 includes a mechanism for receiving an input from a user. The input unit 102 includes, for example, a keyboard, a mouse, a touch panel, a display device, and the like that receive an input from a user. The storage unit 104 stores information received by the input unit 102, parameters in the image generation system 100, a program for generating an image, and the like. The storage unit 104 can be configured of a general storage device such as volatile memory, non-volatile memory, hard disk, and the like. The processing unit 150 is configured by a general CPU or the like, and performs processing such as various calculations required for image generation. The output unit 106 displays the generated image, input information, internal parameters, and the like. The output unit 106 can be configured of a general display or the like. The processing unit 150 includes a mapping processing unit 152, a Voronoi processing unit 154, a rectangle generating unit 156, an analysis unit 158, and an inverse mapping processing unit 160. Various operations and functions in the processing unit 150 will be described later.

  FIG. 4 is a flow chart illustrating a method of generating an image according to one embodiment. As an example, a method of generating an image of chrysanthemum coral will be described. Chrysanthemum coral is generally spherical in shape as shown in FIG. 1A, and there are many polygonal holes on the surface as shown in FIG. 1B.

  First, as shown in the flowchart of FIG. 4, the user's input is accepted (S102). Here, the overall shape (for example, a spherical shape) of the generated image and various conditions are input. The user input is, for example, the number of polygons per unit area, the thickness of boundary lines, the number of angles of representative polygons (five strokes, hexagons, etc.). The input step is performed by the input unit 102 of the image generation system 100.

  Next, the curved surface of the surface in the entire three-dimensional shape of the input image is mapped so as to be a plane (S104). Such mapping can be performed mathematically by a method such as conformal mapping. Such mapping processing is performed by the mapping processing unit 152 of the image generation system 100.

Next, the plane after mapping is divided into Voronoi figures (S106). The polygons generated by Voronoi division may have equal areas, or may have different areas so as to have a predetermined distribution. The distribution of mother points when dividing into Voronoi figures is determined, for example, as follows. The distribution of the birth points of the Voronoi diagram can be determined from the number of polygons per unit area input by the user. Since the shape of the Voronoi figure depends on the distribution pattern of the birth points, the birth points distributed approximately in a square grid form a square Voronoi figure, and in the approximately regular triangle grid a hexagonal Voronoi figure is produced Ru. It is desirable that the distribution of mother points be determined by interactively adjusting some basic patterns, their combination, addition of random disturbance, and the like. FIG. 5 is a view showing an example of a plane Voronoi divided. The conditions for division into Voronoi figures can be made in accordance with the user's input in step S102.

  Next, an xyz coordinate system is defined on the Voronoi divided plane. As an example, as shown in FIG. 5, the x direction and the y direction are directions orthogonal to each other in a plane, and the z direction is a direction normal to the plane. Numbers 1 to N are assigned to N line segments that constitute a polygon formed by Voronoi division. A line segment in a plane can be defined by two vertices. The two vertices that make up this line segment are used to define a vector on the plane. Then, if necessary, this vector may be extended in the positive direction and the negative direction, respectively. For example, it extends equally in both positive and negative directions. Such an extension is to prevent the occurrence of a blank area not included in the rectangle described later at the intersection of the Voronoi-divided polygons, and the extension is not necessary if necessary. For example, extension processing can be enabled by user input as needed. Furthermore, when a finite thickness is given to the line segment represented by the extended vector, a rectangle including two vertices defining the vector before the extension is defined (S108). The thickness of the line segment may, for example, be made to follow user input. This rectangle is determined for all N line segments. These rectangles correspond to thickened line segments that are sides of polygons generated by Voronoi division, and the vicinity of each vertex overlaps with another rectangle. FIG. 6 shows a diagram in which these processes are performed on Voronoi divided planes. Such processing is performed by the rectangle generation unit 156 of the image generation system 100.

Next, define the following function.
Formula (1): z = f ₀ (x, y, t), t = 0
f ₀ is a function that defines the depth from the plane that is the surface. f ₀ may be a constant or may be a distribution. t is a parameter for performing calculation described later, and is a variable that is defined as time equivalent for convenience. z = 0 is zero depth, ie on the plane of the surface.

Next, the numerical value in the above-mentioned rectangle is made _{zero with} respect to f0. This results in a shape with vertical rectangular cliffs at the rectangular boundaries, with only rectangular interior regions with tops of constant height (surface height) in the mapped space. FIG. 7 is a diagram showing this state. The distribution of z in this state is again defined as f ₁ .
Formula (2): z = f ₁ (x, y, t), t = 0
The following partial differential equations are analyzed with this as an initial condition (S110).
The equation (3) is an equation generally called a diffusion equation, and d is called a diffusion coefficient and has a positive value. Although d (x, y, t) in the equation (3) is a function of x, y and t, it may be simply a constant. The spreading factor d may follow user input. The solution z (x, y, T) at time t = T has a shape like a natural thing because each side of the above-mentioned rectangular group is spatially chamfered or dissolved due to diffusion. Since it is difficult to derive an exact solution (analytic solution) of the function z (x, y, T) in analyzing the equation (3), it is obtained by numerical analysis. For example, a grid for numerical analysis can be formed on a plane, and the z-values of the points on the grid can be calculated by discretizing equation (3) using the finite difference method or the finite element method. The analysis of Equation (3) can be performed by the analysis unit 158 of the image generation system 100. FIG. 8 shows a figure z (x, y, T) obtained by processing the equation (3) with respect to the figure f ₁ shown in FIG. FIG. 9 shows the surface pattern of the figure created in this way. Such surface pattern is similar to the surface pattern of chrysanthemum coral shown in FIG. 1B.

  Next, for the calculated z (x, y, T), the plane diagram created is initially mapped by reverse mapping using the inverse function of the mapping function in which the initial surface is mapped to a plane in step S104. It can map on the shape provided with a curved surface (S112). Such processing can be performed by the inverse mapping processing unit 160 of the image generation system 100. According to the above method, three-dimensional shape data artificially provided with a complex surface such as coral can be obtained. A realistic coral image can be obtained by subjecting such three-dimensional shape data to a rendering process, which is a standard process of computer graphics technology.

  In the image generation method according to the above-described embodiment, processing is performed by oblongizing all sides of the polygon in the image Voronoi divided in step S106. As another embodiment, the above-described processing may be performed by randomly thinning the sides of the polygon without using all the sides of the polygon in the Voronoi-divided image. In such an embodiment, as shown in FIG. 10, a maze-like pattern is formed on the surface. The surface pattern of FIG. 10 generated by the method of such an embodiment is similar to the surface pattern of blue coral as shown in FIG.

  Although the above-described image generation method has been described by way of example of generating a coral shape, it is also used to generate an image representing corrosion or erosion occurring on the surface of a mechanical device or an artificial object of a building. Can. For example, surfaces such as fluid machines such as pumps for transporting liquids such as water and pipes connected thereto are damaged by various phenomena such as cavitation erosion, corrosion, and collision of solid particles. FIG. 11 is a sketch of the surface of the metal material on which corrosion has occurred. The state of corrosion shown in FIG. 11 is similar to the image generated according to the embodiment described above, and the image can be generated by computer graphics according to the embodiment disclosed in the present document.

100 ... image generation system 102 ... input unit 104 ... storage unit 106 ... output unit 150 ... processing unit 152 ... mapping processing unit 154 ... Voronoi processing unit 156 ... rectangle generation unit 158 ... analysis unit 160 ... reverse mapping processing unit

Claims (6)

A method of generating an image by a computer, comprising:
Mapping so that the curved surface of the surface of the solid to be generated is a flat surface;
Dividing the plane into Voronoi figures;
Defining each of the line segments as a rectangle by giving a finite thickness to each of the line segments constituting the Voronoi figure;
Formula (1): z = f ₀ (x, y, t), t = 0
Let z = 0 inside the rectangle at
Formula (2): z = f ₁ (x, y, t), t = 0
With the initial condition,
Analyzing the
mapping on the surface by inverse mapping the solution z (x, y, T) obtained at the time of t = T;
x and y are orthogonal coordinates on the plane, z is a coordinate orthogonal to the plane with 0 on the plane, and d is a diffusion coefficient having a positive value,
Method. The method according to claim 1, wherein
Each line segment constituting the Voronoi figure is extended in the length direction of each line segment and then given a finite thickness to define each line segment as a rectangle;
Method. What is claimed is: 1. A non-volatile computer readable storage medium storing instructions for performing steps including the following by being executed by a processor, said steps comprising:
Mapping so that the curved surface of the surface of the solid to be generated is a flat surface;
Dividing the plane into Voronoi figures;
Defining each of the line segments as a rectangle by giving a finite thickness to each of the line segments constituting the Voronoi figure;
Formula (1): z = f ₀ (x, y, t), t = 0
Let z = 0 inside the rectangle at
Formula (2): z = f ₁ (x, y, t), t = 0
With the initial condition,
Analyzing the
mapping on the surface by inverse mapping the solution z (x, y, T) obtained at the time of t = T;
x and y are orthogonal coordinates on the plane, z is a coordinate orthogonal to the plane with 0 on the plane, and d is a diffusion coefficient having a positive value,
Nonvolatile computer readable recording medium. The non-volatile computer readable recording medium according to claim 3,
Each line segment constituting the Voronoi figure is extended in the length direction of each line segment and then given a finite thickness to define each line segment as a rectangle;
Nonvolatile computer readable recording medium. A system for generating an image by a computer,
A mapping processing unit that maps so that a curved surface of a solid surface to be generated an image becomes a plane;
A Voronoi processing unit that divides the plane into Voronoi figures;
A rectangle generation unit which defines each of the line segments as a rectangle by giving a finite thickness to each of the line segments constituting the Voronoi figure;
Formula (1): z = f ₀ (x, y, t), t = 0
Let z = 0 inside the rectangle at
Formula (2): z = f ₁ (x, y, t), t = 0
With the initial condition,
An analysis unit that analyzes
an inverse mapping processing unit that maps the solution z (x, y, T) obtained at the time of t = T by inverse mapping on the surface,
x and y are orthogonal coordinates on the plane, z is a coordinate orthogonal to the plane with 0 on the plane, and d is a diffusion coefficient having a positive value,
system. The system according to claim 5, wherein
Each segment constituting the Voronoi figure is extended in the length direction of each segment and then given a finite thickness to define each segment as a rectangle.
system.