JPH09265542A - Method and device for generating unspecified-shape cell pattern and printed matter having the pattern - Google Patents

Abstract

PROBLEM TO BE SOLVED: To represent elements of 'flow' characteristics of animals and plants and generate a cell pattern in an unspecified shape with a feeling of living by displaying many base points which are regularly arranged by using a fractal field, generating Voronoi diagram for the base points after the displacement, and generating the pattern. SOLUTION: A base point Mi (xi, yi) defined on an XY plane is displaced on the XY plane by a displacement quantity Δx in the X-axial direction and moved by a displacement quantity Δy in the Y-axial direction. The displacement quantity Δx is determined on the basis of the scalar value S1 that a grating point Q1i arranged at a position corresponding to the position coordinates (xi, yi) of a two-dimensional fractal grating L1 has, and the displacement quantity Δy is determined on the basis of the scalar value S2 that a grating point Q2i arranged at the position corresponding to the position coordinates (xi, yi) of a two dimensional fractal grating L2 has. Then the Voronoi diagram for the base point after the displacement is generated and on the basis of the generated Voronoi diagram, the pattern is generated.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a generation method and a generation device for generating a pattern composed of a large number of amorphous cells by using a computer, and a printed matter having such a pattern.

[0002]

2. Description of the Related Art In recent years, with the technical progress of computer graphics, a method of generating various patterns and patterns by using a computer has been established. It has become possible to generate relatively easily using.
In addition, the technique of generating an image with a completely new image by applying various effects to the original digital image has become widespread, and various application software for graphic design is commercially available. Has reached the end. Such patterns and patterns
Widely used in various fields such as printing on paper products such as leaflets and catalogs, printing on the surface of building materials such as wall boards and doors, embossing, printing on decorative boards constituting the furniture surface and embossing Has been done. Further, recently, due to the popularization of so-called multimedia, it is not rare that various patterns and patterns are used only for the purpose of displaying on a display screen.

As described above, a pattern composed of a large number of amorphous cells is used as one mode of the pattern generated by using the computer. This amorphous cell pattern is suitable for expressing the skin of animals, cells and fine tissues of plants, and is used as a texture pattern to be mapped on the surface when modeling animals and plants in the field of computer graphics. Often.

This irregular cell pattern is a pattern in which a large number of small irregular polygons are arranged in a cell shape. As a method for generating such a pattern using a computer, a Voronoi diagram (Voronoi diagram) is used. The method using diagram) is generally used. The Voronoi diagram is obtained by defining a large number of generating points on a plane, mathematically defining the influence zone of each generating point, and constructing a plane by polygons composed of the individual influence zones thus defined. It can be said that the plane is divided into a large number of cells. If the distribution of mother points is set in advance and the sphere of influence is mathematically defined, a Voronoi diagram can be obtained relatively easily by a mathematical operation by a computer.

[0005]

As described above, in the current field of computer graphics, it is general to generate an amorphous cell pattern using a Voronoi diagram. Usually, a method is used in which generating points are defined at random using uniform random numbers on a plane and a Voronoi diagram is created based on these generating points to generate an amorphous cell pattern. However, the irregular cell pattern generated in this way is certainly a pattern composed of a large number of cells having irregular sizes and irregular shapes, but it does not correspond to animal skin, plant cells or fine cells. As a pattern for expressing tissues of animals and plants, such as tissues, unnaturalness remains, and in reality, it is not a sufficient pattern. Especially, in the conventional method, "flow" peculiar to plants and animals
It is not possible to express the elements of, and only patterns that have a poor sense of life as plants and animals can be obtained.

Therefore, the present invention is a "flow" peculiar to plants and animals.
It is an object of the present invention to provide a novel method for generating an indeterminate cell pattern with life by expressing the element of.

[0007]

[Means for Solving the Problems]

(1) A first aspect of the present invention is, in a method for generating a pattern composed of a large number of irregular shaped cells, a first step of regularly arranging a large number of generating points to be cores of individual cells,
The second stage of preparing a fractal field that can express spatially self-similar vectors, the third stage of displacing a large number of arranged generating points using the prepared fractal field, and the displacement The fourth step of creating a Voronoi diagram for the later generating points and the pattern are generated based on the created Voronoi diagram.

(2) A second aspect of the present invention is the above-mentioned first aspect.
In the method according to the aspect 1, the generating points are arranged on the two-dimensional plane in the first step, and predetermined scalar values are self-similarly defined at the respective lattice points on the two-dimensional plane in the second step. Prepare a two-dimensional fractal grid, and in the third step, overlay the two-dimensional fractal grid on the plane where the generatrix is arranged, and based on the mutual positional relationship between each generatrix and each grid point, Specific grid points are associated with each other, and each mother point is displaced in a predetermined direction based on the scalar value defined at the corresponding grid point.

(3) A third aspect of the present invention is the above-mentioned second aspect.
In the method according to the above aspect, in the first step, the mother points are XY
They are arranged on a plane, and in the second stage, two independent two-dimensional fractal grids are prepared. In the third stage, each generating point is defined as a grid point of the first two-dimensional fractal grid. It is moved in the X-axis direction based on the scalar value, and is moved in the Y-axis direction based on the scalar value defined at the grid point of the second two-dimensional fractal grid.

(4) A fourth aspect of the present invention relates to the above-mentioned first aspect.
In the method according to the third aspect, in the first step, generating points are regularly arranged on a predetermined plane so that a Voronoi polygon consisting of a triangle, a quadrangle, or a hexagon is formed. is there.

(5) A fifth aspect of the present invention is the above-mentioned first aspect.
In the method according to the fourth to fourth aspects, in the fourth step, a Voronoi diagram is created by making an arbitrary point belong to the sphere of influence of the mother point having the smallest Euclidean distance.

(6) A sixth aspect of the present invention is, in an apparatus for generating a pattern composed of a large number of irregular cells, a parameter input means for inputting a predetermined parameter, a random number generating means for generating a random number, We input a generatrix placement means that regularly arranges a large number of generatrix points that should be the cores of the cell based on the input parameters, and a fractal field that can represent spatially self-similar vectors. Fractal field generating means for generating based on parameters, generating point displacing means for displacing a large number of generating points using the fractal field, Voronoi diagram generating means for generating Voronoi diagram for the displaced generating points, and Voronoi diagram Pattern output means for generating a pattern based on the above and outputting the pattern.

(7) A seventh aspect of the present invention relates to the above-mentioned first aspect.
The printed matter having an irregular cell pattern is produced by the method according to any one of the aspects to.

(8) In the eighth aspect of the present invention, a nucleus distributed with fluctuation based on a fractal field is defined, an amorphous cell is represented by a Voronoi diagram generated for this nucleus, and a large number of amorphous A printed matter having a pattern of cells is produced.

[0015]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS The present invention will be described below based on an embodiment shown in the drawings. First, for convenience of description, a brief description of the Voronoi diagram will be given. Now, as shown in FIG. 1, six mother points M1 to M6 are defined on a plane. Then, the matter of which of the mother points the arbitrary point P on this plane belongs to is defined mathematically. Usually, the most commonly used definition is "belong to the sphere of influence of the mother point with the smallest Euclidean distance (so-called geometric distance between two points)." In the example shown in FIG. 1, since the mother point whose Euclidean distance is closest to the point P is the mother point M2, the point P belongs to the sphere of influence of the mother point M2. As described above, when all the points on the plane belong to any of the generating points M1 to M6, a polygon showing the influence zone of each generating point is obtained as shown in FIG. In FIG. 2, the hatched polygon is the mother point M.
Equivalent to the sphere of influence of 2. That is, the generating point M2 is a generating point having the smallest Euclidean distance with respect to all the points in the hatched area. The polygons thus obtained are called Voronoi polygons, and the set of these Voronoi polygons becomes a Voronoi diagram. In short, the Voronoi diagram is the n mother points M1, M2, ..., M on the plane.
It can be said that the figure shows a state in which the plane is divided by a set of polygons showing the influence zones of each generating point when i, ... Mn are defined.

When generating the Voronoi diagram, if generating points are regularly arranged in advance, the plane division pattern shown by the generated Voronoi diagram is also regular. For example, as shown in FIG. 3, the same equilateral triangle is used to fill the plane, and each generating point Mi is defined at the vertex position of each equilateral triangle. When a Voronoi diagram is created based on a large number of generating points Mi arranged regularly in this way, a large number of regular hexagons Hi as shown in FIG. 4 are obtained as Voronoi polygons, and the plane is the regular hexagon. It is regularly divided by groups.

Thus, the completely regular cell pattern is unsuitable as a pattern expressing the tissues of animals and plants. Therefore, in order to express the tissue of animals and plants, a method has been conventionally adopted in which random displacement is given in advance to the regular mother point arrangement shown in FIG. For example, let the plane shown in FIG. 3 be the XY plane, and the individual generating points Mi regularly arranged as the vertices of the equilateral triangle shown.
With respect to (xi, yi), the displacement amount Δx in the X-axis direction and the displacement amount Δy in the Y-axis direction are generated as random numbers for each generating point, and based on these displacement amounts Δx, Δy, Displacement (movement) is performed so that the new position becomes Mi (xi + Δx, yi + Δy). If such displacement is performed for each individual generating point, a generating point group that is randomly arranged on the whole can be obtained. When a Voronoi diagram is obtained for this randomly arranged mother point group, the obtained cell pattern becomes an irregular cell pattern, which is more preferable as a pattern expressing the tissues of animals and plants. FIG. 5 is a diagram showing an example of an amorphous cell pattern obtained by such a conventional method. That is, the pattern of FIG. 5 is obtained by performing random displacement using uniform random numbers on the mother points arranged regularly as shown in FIG. 3 and obtaining the Voronoi diagram for the mother points after displacement. It is the obtained pattern.

The pattern shown in FIG. 5 can be used as a pattern that expresses the tissue of an animal or plant in the sense that it is a pattern composed of irregularly shaped cells, but the "flow" element peculiar to the animal or plant is expressed. Since it is not present, it must be said that the pattern lacks a sense of life as an animal or plant.
The present inventor believes that it is indispensable to express the elements of this "flow" in a pattern in order to express expressions rich in life as plants and animals. The reason why the element of "flow" is not expressed in the fixed cell pattern is that the displacement amount of each generatrix is set independently in the process of displacing the generatrix arranged regularly. thinking. In other words, even if a random displacement is set using uniform random numbers for each generating point, if there is no correlation in this amount of displacement between adjacent generating points, each generating point is completely independent. Only the displaced state can be obtained, and there is no room for the "flow" element peculiar to plants and animals to enter.

The inventor has found that a fractal field is used to incorporate this "flow" element into the pattern. In general, "fractal field" means a field with spatial self-similarity, and in particular, fractal figures with spatial self-similarity are suitable for expressing many things in nature. It is widely known that A feature of fractal figures is that their complexity is always the same, whether it is microscopic or macroscopic.
The shapes of coastlines, the shapes of trees and veins, the shapes of snowflakes, etc. found in the natural world are all typical of this fractal figure, and they are intricate even when viewed microscopically or macroscopically. It has a unique shape. Such a property is generally called self-similarity, and the essence of fractal theory lies in this self-similarity.

A more general extension of this fractal theory makes it possible to consider a fractal grid in which predetermined scalar values are self-similarly defined at individual grid points. For example, the two-dimensional fractal lattice defines a predetermined scalar value for each lattice point arranged on a two-dimensional plane and gives a two-dimensional scalar field.
In this two-dimensional scalar field, each scalar value changes spatially with natural fluctuations. In other words, this change pattern, whether microscopically or macroscopically, always has the same complexity, that is, self-similarity. It is also possible to define a two-dimensional vector field by giving directionality to each scalar value defined in this two-dimensional scalar field. The basic idea of the present invention resides in that the element of "flow" is incorporated into the amorphous cell pattern by displacing the regular generating points based on the fractal field whose directionality is defined in this way.

FIG. 6 is a flow chart showing the basic procedure of the method for generating an irregular cell pattern according to the present invention. First, in step S1, a large number of generatrix points to be cores of individual cells are regularly arranged. For example, as shown in FIG.
A large number of regularly arranged mother points Mi will be defined. In the following step S2, a fractal field capable of expressing a spatially self-similar vector is prepared. Specifically, by preparing a two-dimensional fractal scalar field and defining the directionality in this scalar field,
It can be used as a fractal vector field. And
In step S3, the large number of generating points arranged in step S1 are moved in the directions indicated by the fractal vector field prepared in step S2. As a result, each generating point is displaced, but the displacement direction and the amount of displacement of each generating point are determined based on the fractal field. This means that the element of "flow" is included. In other words, the displacement mode with respect to the regular arrangement of each generating point has self-similarity. Finally, in step S4, a Voronoi diagram for the displaced mother points is created. That is, the two-dimensional plane is divided by the Voronoi polygon, and an irregular cell pattern is obtained.

FIG. 7 is a diagram showing an example of an amorphous cell pattern obtained by the method according to the present invention shown in FIG. That is, in the pattern of FIG. 7, self-similar displacement using a fractal field is performed on the mother points arranged regularly as shown in FIG. 3, and a Voronoi diagram is obtained for the mother points after the displacement. It is the pattern obtained by. Compared with the conventional cell pattern shown in FIG. 5, all are the same in that they are composed of irregularly shaped cells, but the pattern shown in FIG. 7 clearly expresses the “flow” element peculiar to plants and animals. You can see that For example, in the field of computer graphics, comparing the cell pattern shown in FIG. 5 with the cell pattern shown in FIG. 7 as a texture pattern to be mapped on the skin of reptiles such as crocodile and lizard, the latter is the latter. It can be recognized that a feeling of life as animal skin can be felt.

[0023]

EXAMPLES Next, the present invention will be described based on more specific examples.

§1. One-dimensional fractal lattice The basic idea of the present invention is to reflect the natural fluctuation expressed by the fractal field in the irregular cell pattern. Therefore, first, I will give a brief explanation of this fractal field. Here, a one-dimensional fractal lattice in which a scalar amount is defined for each lattice point arranged in one dimension will be described with reference to the drawings.

Now, as shown in FIG. 8, two grid points A and B (indicated by double circles in the figure) are defined on one line at a predetermined distance, and these grid points A and B are defined. Scalar values a and b are defined in B, respectively. The two grid points A and B defined in this way are in the initial stage (hereinafter referred to as the 0th stage).
, And the scalar values a and b are, so to speak, initial conditions set to these two grid points A and B.

Then, as shown in FIG. 9, the grid point C of the first stage is defined at the midpoint between the two grid points A and B. At this time, a scalar value c is also defined for this lattice point C, but this scalar value c is a scalar value a, b.
, And is defined by a predetermined calculation.
FIG. 9 shows a state in which the scalar value c of the grid point C has not yet been determined. Note that, here, a grid point in a state where a scalar value is undefined is indicated by a single circle, and a grid point in a state where a scalar value is defined is indicated by a double circle. The scalar value c is calculated by the following arithmetic expression c = (a + b) / 2 + T · RND (1). Here, a and b are grid points A
And B are scalar values defined, T is the maximum half-amplitude value of fluctuation, and RND is an arbitrary random number satisfying -1 ≦ RND ≦ + 1. As described above, a random number is used for the definition of the scalar value c, which depends on an accidental element. However, the scalar value c is not defined as a completely slammed value.
Are limited by the scalar values a and b and the maximum half-amplitude value T. That is, as shown in the above equation (1), the average value of the scalar values a and b is −T to
A value obtained by adding an arbitrary value (determined by a random number) within the range of + T is the value of the scalar value c. Therefore, the maximum half-amplitude value T is a parameter that limits the degree of fluctuation that deviates from the average value.

In this way, if the scalar value c for the grid point C in the first stage can be defined, then, as shown in FIG. 10, the midpoints of the grid points A and C and the midpoints of the grid points C and B are set. , And define second-stage grid points D and E, respectively. Then, for these lattice points D and E, scalar values d and e are respectively expressed as d = (a + c) / 2 + (1/2) .T.RND (2) e = (c + b) / 2 + (1 / 2) · T · RND (3) Calculated by the formula: Here, as described above, T
Is the maximum half amplitude value of fluctuation, RND is -1 ≦ RND ≦ +
An arbitrary random number of 1. Equations (2) and (3) are very similar to equation (1), but it should be noted that the maximum half-amplitude value T is multiplied by a factor of (1/2).

Then, a grid point of the third stage is defined at each midpoint of the five grid points A, D, C, E, B defined up to the second stage, and a scalar is also defined at these grid points. Calculate and define the value. For example, a scalar value f for a grid point F (not shown) defined as a midpoint between grid points A and D is given by: f = (a + d) / 2 + (1/4) .T.RND (4) It is calculated by the following formula. In this equation (4), a coefficient of (1/4) is applied to the maximum half amplitude value T.

To facilitate understanding, the above steps will be described using actual numerical values. For example, FIG.
As shown in, consider a case where scalar values “50” and “80” are set as initial conditions for the grid points A and B of the 0th stage, respectively. As a midpoint between the two grid points A and B, as shown in FIG.
In this case, the scalar value c defined for this lattice point C is given by the above equation (1) as follows: c = (50 + 80) /2+T.RND (1) . Here, the maximum half-amplitude value of the fluctuation is set to T = 5.
Let's assume that ND = + 0.6. In this case, the scalar value c = 68 calculated.

Subsequently, grid points A and C and grid points C and B
As shown in FIG. 13, grid points D and grid points E in the second stage are defined as the middle points of the grid points. In this case, the scalar values d, E defined for these grid points D, E are defined. e is d = (50 + 68) / 2 + (1/2) .T.RND (2) e = (68 + 80) / 2 + (1/2) .T.RND from the above equations (2) and (3). (3) is given by Here, when it is assumed that the random numbers RND = -0.4 and RND = + 0.8 happen to occur during the calculation of the above equations, the scalar value d = 5 obtained by the calculation.
8, e = 76. After all, at the stage where the scalar value of the grid point of the second stage is obtained, as shown in FIG. 14, the scalar value is defined for each of the five grid points A, D, C, E, and B. .

Similarly, these five grid points A,
A grid point of the third stage is defined at each of the middle points of D, C, E, and B, and a scalar value is calculated and defined for these grid points, and further, a fourth stage, a fifth stage,. Repeat the same operation as above. Such an operation is performed a predetermined finite number of times n
If this is repeated, a large number of grid points are defined between the grid points A and B of the 0th stage, and a predetermined scalar value is defined at each of these grid points. In addition, if the calculation method of the scalar value s about the lattice point of the nth step is shown by a general formula, it will become s = ((alpha) + (beta)) / 2+ (1/2 ^(n-1) ) * T * RND (5). Here, α and β are the scalar values of the grid points on both sides of the grid point (calculated in the (n−1) th step), and T is the maximum half-amplitude value of the fluctuation, as described above. RND is an arbitrary random number satisfying -1 ≦ RND ≦ + 1.

When a large number of grid points having a predetermined scalar value are defined by such a method, these grid points form a one-dimensional fractal grid. Such a fractal grid generation method is generally called a random midpoint displacement method. In the above-mentioned specific example, the scalar value of "50" is defined at the left end point of this one-dimensional fractal grid and "80" at the right end point thereof, and a large number of grid points defined between these end points are also respectively defined. A unique scalar value is defined. Now, when the horizontal axis represents the array direction of the one-dimensional fractal lattice obtained in this way and the vertical axis represents each scalar value, a graph as shown in FIG. 15 is drawn. Such a graph has, for example, properties similar to the shape of a coastline in nature. That is, the individual scalar values have various distributions such as partially increasing or decreasing, but the complexity of this distribution pattern is microscopically or macroscopically viewed. It is known to be the same. More specifically explaining this property, in FIG. 15, the complexity of the graph between the grid points AB is the same as the complexity of the graph between the grid points AD, and the minuteness between the grid points AD is very small. Even if you magnify the section with a magnifying glass, it still has the same complexity. In other words, the individual scalar values are self-similarly defined at the individual grid points, and are spatially increased or decreased with natural fluctuations.

§2. Two-dimensional fractal grid or more, a method of generating a simple one-dimensional fractal grid by the random midpoint displacement method has been described with a specific example, but the fractal grid actually used in the examples described later is a grid. It is a two-dimensional fractal grid in which points are arranged in a plane. Therefore, here, an example of a method in which the random midpoint displacement method described in the above-described one-dimensional fractal grid is applied to two-dimensional will be described. In order to generate a two-dimensional fractal lattice,
As shown in FIG. 16, grid points A, B, and
C and D are arranged to define scalar values a, b, c and d, respectively. Here, this square is an outline rectangle forming the outline of the finally generated two-dimensional fractal lattice.

Then, as shown in FIG. 17, grid points AB
Grid points E, F, G, and H of the first stage are defined at the midpoints of the grids, BCs, CDs, and DAs, respectively, and at the intersection of the diagonal lines of the four grid points ABCD, another first grid point is defined. Define a grid point I of a stage. Then, scalar values e, f, g, h, and i are defined for these five lattice points, respectively. This is the following arithmetic expression: e = (a + b) /2+T.RND (6) f = (B + c) /2+T.RND (7) g = (c + d) /2+T.RND (8) h = (d + a) /2+T.RND (9) i = (a + b + c + d ) /4+T.RND (10). As in the example of the one-dimensional fractal lattice, T is the maximum half-amplitude value of fluctuation and RND is −1.
It is an arbitrary random number such that ≦ RND ≦ + 1.

Thus, the grid points E, F, G,
Once the scalar values e, f, g, h, i for H and I have been defined, subsequently, as shown in FIG. 18, at the midpoint of each adjacent grid point and the intersection of the diagonals of the four grid points, The grid points J, K, L, M, N, ... Of the second stage are defined respectively (in order to avoid complication, only grid points J, K, L, M, N are displayed with grid point names in FIG. Have been done). Then, for each of these lattice points, scalar values j, k, l, m, n, ... Are defined, respectively. This is the following arithmetic expression (only the arithmetic expressions for j to n are shown) j = (A + e) / 2 + (1/2) .T.RND (11) k = (e + i) / 2 + (1/2) .T.RND (12) l = (i + h) / 2 + (1 / 2) ・ T ・ RND (13) m = (h + a) / 2 + (1/2) ・ T ・ RND (14) n = (a + e + i + h) / 4 + (1/2) ・ T -Calculate by RND (15). In the equation for obtaining the scalar value of the grid point at the second stage, the maximum half amplitude value T is multiplied by a coefficient of (1/2), as in the case of the one-dimensional fractal grid described above.

Similarly, the third step, the fourth step, ...
If the process of the nth stage is repeatedly executed, the scalar value will be defined for a large number of grid points arranged on the two-dimensional plane.

The above processing will be described as a general theory.
First, in the 0th stage, four grid points are defined at the four corner positions of the outer shape rectangle, and predetermined scalar values are defined at each grid point. Then, as the processing of the i-th stage, the following processing may be sequentially executed. That is, first, the minimum rectangle at the current stage that does not include the grid points defined up to the (i-1) th stage is recognized. For example, in the case of the first stage where i = 1, the rectangle AB shown in FIG.
CD is the minimum rectangle (the grid point A defined up to the 0th stage,
B, C, and D are not included in the inside), and in the case of the second stage of i = 2, four rectangles AEIH and E shown in FIG.
BFI, HIGD, and IFCG are the smallest rectangles (first
It is a rectangle that does not include any of the grid points A to I defined up to the stage.

Then, grid points to be defined in the i-th stage are generated at the midpoints of the sides of the minimum rectangle and the center point of the minimum rectangle (for example, in the case of the first stage where i = 1, As shown in FIG. 17, the midpoint E of each side of the minimum rectangle ABCD,
Lattice points to be defined are generated at F, G, H and center point I). Furthermore, among these grid points, the grid point generated at the midpoint of each side has the scalar value of the two grid points defined up to the (i-1) th stage existing at the end points of the side. Gives a scalar value obtained by operating a random number. For example, the grid point E shown in FIG.
, The scalar value a of two grid points A and B,
A scalar value e obtained by applying a random number RND to b is given. In general, if the calculation method of the scalar value s1 with respect to the grid point defined as the midpoint of the adjacent grid points in the nth stage is shown by an equation, s1 = (α + β) / 2 + (1/2 ^(n-1) )・ T ・ RND (16). Here, α and β are scalar values (calculated in the (n−1) th stage) of grid points on both sides of the grid point.

On the other hand, the grid points generated at the center point of the minimum rectangle are the (i) th points at the four corners of the minimum rectangle.
-1) Give a scalar value obtained by applying a random number to the scalar values of the four grid points defined up to the step. For example, for the grid point I shown in FIG. 17, the scalar value a, which has four grid points A, B, C, D,
A scalar value i obtained by applying a random number RND to b, c, and d is given. Generally, if the calculation method of the scalar value s2 about the lattice point defined as the center point of the minimum rectangle in the nth stage is shown by an equation, s2 = (α + β + γ + δ) / 4 + (1/2 ^(n-1) ). It becomes T.RND (17). Here, α, β, γ, δ are 4 of the smallest rectangle.
It is a scalar value of a grid point at one corner (calculated in the (n-1) th stage).

The two-dimensional fractal lattice generated by such a method eventually gives a scalar field spread in a two-dimensional plane. Therefore, if the surface of this two-dimensional fractal grid is placed on a horizontal plane and each scalar value is plotted as a vertical height (elevation) on a graph, a concavo-convex pattern such as a mountain ridge structure can be expressed. It is known that such a raised structure has properties similar to the uneven pattern of the actual mountain raised structure existing in nature.
That is, the complexity of the concavo-convex structure is the same from a microscopic point of view and a macroscopic point of view, and even when a part of the concavo-convex structure is magnified with a magnifying glass, it has the same complexity. In other words, the individual scalar values distributed on the two-dimensional plane are arranged in a self-similar manner, and spatially increase or decrease with natural fluctuations.

§3. Generation of Amorphous Cell Pattern Now, in §2 above, a specific method of generating a two-dimensional fractal lattice was illustrated. Here, a concrete method of generating an amorphous cell pattern using this two-dimensional fractal lattice is described. The general procedure.

The method according to the invention consists of four steps, steps S1 to S4, as shown in the flow chart of FIG. First, in step S1, mother points are regularly arranged. In this embodiment, as shown in FIG.
A large number of identical regular triangles are defined so as to fill up the two-dimensional plane, and mother points are arranged as the vertices of these regular triangles. In this way, the generating points are arranged as vertices of an equilateral triangle that fills the plane, and the Voronoi diagram is created by defining the generating area of the generating points where "Euclidean distance is minimum" with this regular arrangement. Then, as shown in FIG. 4, a Voronoi polygon consisting of regular hexagons filling the plane is formed. However, as polygons that can fill a plane, there are triangles and quadrangles in addition to hexagons, and it is possible to fill a plane by combining pentagons and hexagons. Therefore, in the processing of this step S1, it is sufficient to regularly arrange the generating points on a predetermined plane so that a large number of Voronoi polygons having regularity are formed. It is not limited to the vertex position of the equilateral triangle as shown in.
Specifically, for example, the vertex positions of squares aligned on a plane, the vertex positions of isosceles triangles arranged on a plane so that the top and bottom are alternated, the vertex positions of hexagons aligned on a plane, the plane It is also possible to arrange mother points at the vertex positions of the parallelograms aligned above. However, if the generating points are placed at the vertices of an equilateral triangle as shown in Fig. 3, a Voronoi polygon consisting of regular hexagons (figure close to a circle) can be obtained, which is useful for expressing animal skin or plant cells. Is most preferable.

Then, in step S2, a fractal field is prepared. In this embodiment, two sets of independent two-dimensional fractal lattices are generated by the method described in §2. Then, in step S3, displacement of the generating points is performed using the two sets of two-dimensional fractal grids. FIG.
9 is a conceptual diagram of this mother point displacement processing. The XY plane shown in the upper part of the figure is a plane in which the generating points are regularly arranged in step S1 and has predetermined coordinate values xi, y.
Generatrix point Mi (xi, yi) arranged at the position indicated by i
Are defined in large numbers. On the other hand, the two-dimensional fractal lattice L1 shown in the middle part of the figure and the two-dimensional fractal lattice L2 shown in the lower part of the figure both have step S2.
Is a grid prepared in, and as shown in FIG.
It has a large number of grid points defined in a matrix on a two-dimensional plane, and a predetermined scalar value is defined at each grid point.
As described above, this scalar value distribution is self-similar. The two-dimensional fractal grid shown in FIG. 18 is a very small grid having only 25 grid points in 5 rows and 5 columns, but the number of actually used two-dimensional fractal grids L1 and L2 is larger. It is necessary that the grid points are defined at a density at least as high as the density of the mother points Mi defined on the XY plane. Therefore, in step S2, it is necessary to prepare a two-dimensional fractal grid having a sufficient grid point density in consideration of the population density defined in step S1.

In the displacement processing of the generating point in step S3, the generating point Mi (xi, yi) defined on the XY plane is moved on the XY plane by the displacement amount Δx in the X axis direction to be displaced in the Y axis direction. The mother point Mi after the displacement processing is moved by the amount Δy.
This is a process of obtaining (xi + Δx, yi + Δy). Here, the displacement amounts Δx and Δy are as shown by arrows in FIG.
It is determined based on the grid point corresponding to the position coordinates (xi, yi) of the mother point Mi. That is, the displacement amount Δx is the scalar value S1 of the grid point Q1i arranged at the position corresponding to the position coordinate (xi, yi) of the two-dimensional fractal grid L1.
The displacement amount Δy is determined based on the scalar value S2 of the grid point Q2i arranged at the position corresponding to the position coordinate (xi, yi) of the two-dimensional fractal grid L2. Thus, the two-dimensional fractal lattice L1,
Each of L2 is a fractal field that gives a scalar value by itself, but the two-dimensional fractal lattice L1 shows the displacement amount Δx in the X-axis direction, and the two-dimensional fractal lattice L2 shows the displacement amount Δy in the Y-axis direction. By defining the directionality like this, the vector field can be expressed. In addition,
In this embodiment, the scalar value S defined at each grid point is
1 and S2 are directly used as the values of Δx and Δy.
In other words, the initial condition and the maximum half-amplitude value T are set in the process of step S2 so that a two-dimensional fractal grid having a scalar value suitable for use as the displacement amount of the generating point can be obtained as it is. I will leave it.

FIG. 20 is a flow chart showing in detail the procedure of the mother point displacement process in step S3. First, in step S31, one generating point Mi (xi, yi) is selected, and in step S32, the coordinate (xi, yi) of the selecting generating point Mi is extracted. Then, in step S33, coordinates (x in the first two-dimensional fractal lattice L1
The grid point Q1i adjacent to i, yi) is determined, and the scalar value S1 of this grid point Q1i is extracted. Similarly, in step S34, the second two-dimensional fractal lattice L
The grid point Q2i adjacent to the coordinates (xi, yi) within 2 is determined, and the scalar value S2 of this grid point Q2i is extracted. Then, in step S35, the new coordinates (xi ′, yi ′) of the mother point Mi are calculated as xi ′ = xi + S1, yi ′.
= Yi + S2, and the mother point Mi after displacement is obtained.
(Xi ', yi') is obtained. After all, as shown in FIG. 21, the selected mother point Mi (xi, yi) moves in the direction of the arrow in the figure by Δx (= S1) in the X-axis direction and Δy (= S2) in the Y-axis direction. , The mother point after displacement Mi (xi ′, yi
´) will be obtained. The above processing is repeatedly executed by returning from step S36 to step S31 until all mother points are selected.

In the above-described embodiment, the scalar values S1 and S2 obtained from the grid points are used as displacement amounts Δx in the X-axis direction.
The displacement of the generating point Mi is performed by using the displacement amount Δy in the Y-axis direction and the displacement amount Δy in the Y-axis direction, but the scalar values S1 and S2 may be used as polar coordinate values with the original position of the generating point Mi as the origin. . That is, as shown in FIG.
The polar coordinate system is defined with the position of (xi, yi) as the origin,
The position of the mother point Mi (xi ′, yi ′) after displacement is represented by the polar coordinate value (r, θ). Then, the scalar value S1 obtained from the two-dimensional fractal lattice L1 and the scalar value S2 obtained from the two-dimensional fractal lattice L2 are respectively r
= S1 and θ = S2. In this case, the fractal field of the two-dimensional fractal grid L1 plays a role of giving a natural fluctuation to the displacement amount, and the fractal field of the two-dimensional fractal grid L2 plays a role of giving a natural fluctuation in the displacement direction.

When the displacements of all the generating points Mi defined on the XY plane are completed, the final stage of the flowchart shown in FIG. 6, that is, the Voronoi diagram is created in step S4. In this embodiment, the Voronoi diagram is created under the condition that "an arbitrary point belongs to the sphere of influence of the mother point having the smallest Euclidean distance". The amorphous cell pattern shown in FIG. 7 is a Voronoi diagram pattern created under such conditions with respect to the generating points displaced using a two-dimensional fractal grid. Each cell that constitutes this pattern has a nucleus distributed with fluctuations based on the fractal field, and the Voronoi diagram generated for this nucleus represents an amorphous cell.

As a condition for creating a Voronoi diagram based on a large number of generating points having a specific arrangement, the condition that "Euclidean distance is minimum" was used in the above-mentioned embodiment. Generally speaking, the term "Voronoi diagram" generally refers to the one created under such a condition that "Euclidean distance is minimum". However, in the present invention,
Various other conditions can be set as conditions for creating the Voronoi diagram. For example, in the XY coordinate system shown in FIG. 23, the "Euclidean distance" between the generating point M and the arbitrary point P is represented by (dx ² + dy ² ) ^1/2 , but instead of this "Euclidean distance" For example, a special distance represented by (k1 · dx ² + k2 · dy ² ) ^1/2 may be defined, and the condition “this special distance is minimum” may be set. In this case, the parameters k1,
Various Voronoi diagrams can be obtained by changing the value of k2.

Alternatively, "four adjacent distances" or "eight adjacent distances" may be defined, and the condition "this adjacent distance is minimum" may be set. Here, "four adjacent distances" or "eight adjacent distances" refer to the following distances. Now, defining a pixel array as shown in FIG. 24 (a), four pixels shown by hatching adjacent to the pixel P in the center vertically and horizontally are referred to as "four adjacent pixels". To do. Similarly, the pixel array as shown in FIG. 24 (b) is defined, and the eight pixels shown by hatching the pixel P at the center in the vertical, horizontal, and diagonal directions are referred to as “eight adjacent pixels”. I will call it. Here, considering a pixel array as shown in FIG. 25, a pixel M (corresponding to the mother point M in FIG. 23)
The “four adjacent distance” between the pixel P and the pixel P (corresponding to the point P in FIG. 23) is “move to any one of the four adjacent pixels,
Is defined as "the minimum number of movements required to reach from the pixel P to the pixel M according to the movement condition". Similarly, the "eight adjacent distance" between the pixel M and the pixel P is "always any of eight adjacent pixels". The minimum number of movements required to reach the pixel M from the pixel P according to the movement condition of moving to one. In the example shown in FIG. 25, the “four adjacent distance” between the pixel P and the pixel M is 8, and the “eight adjacent distance” is 5.

Besides this, it is possible to create a Voronoi diagram under various conditions. In short, the "Voronoi diagram" in this specification is obtained by any definition as long as it is a power distribution map obtained by mathematically defining the spatial power zone of the mother point in some form. But it doesn't matter. Mathematically, for example, the “cutting Voronoi diagram”,
Various Voronoi diagrams such as the "farthest point Voronoi diagram" and the "Voronoi diagram of a circle" are known. In addition, all Voronoi diagrams described so far are power distribution maps defined on a two-dimensional plane, but even if power distribution maps defined on a three-dimensional space or more multidimensional space are used. I don't care. For example, in step S1, mother points are arranged in a three-dimensional space, and in step S2, three sets of three-dimensional fractal grids are prepared, and the displacement amounts Δx, Δy, and By determining Δz and performing displacement, a three-dimensional Voronoi diagram can be created based on the generating points distributed in this three-dimensional space. By projecting this three-dimensional Voronoi diagram onto a two-dimensional plane, a two-dimensional amorphous cell pattern can be generated.

§4. Amorphous Cell Pattern Generation Device FIG. 26 is a block diagram showing the configuration of the device used in this embodiment. Here, for convenience of explanation, it is shown as a block component different for each function, but in reality,
Each of these components is realized by an organic combination of computer hardware and software.

The parameter input means 1 is an apparatus for inputting various parameters used in the processing in other means, and is the size of the irregular cell pattern image to be finally generated, the number of generating points, Parameters such as an initial arrangement pattern of points (a pattern for determining a regular arrangement in step S1) and a variation amount of a mother point (maximum displacement amount by the displacement process in step S3) are input. The random number generating means 2 is, for example, a device that generates a random number having a uniform distribution, and the random number generated here is used when generating a fractal field. The generatrix arranging means 3,
It has a function of regularly arranging a large number of generatrix points to be cores of individual cells based on the initial pattern of generatrix points.
For example, when the predetermined vertical and horizontal dimensions are input as the size of the image, and the parameters of the number of generating points: 28 and the initial arrangement pattern of generating points: the position of the vertices of an equilateral triangle are input, this generating point arrangement means 3 is used. , A regular arrangement of generating points as shown in FIG. 3 is obtained.

On the other hand, the fractal field generating means 4 is a device for generating a fractal field capable of expressing a spatially self-similar vector based on the parameter input by the parameter input means 1, and generates a random number. Using the random numbers generated by the device 2, for example, a two-dimensional fractal lattice as shown in FIG. 18 will be generated. Here, the density and number of finally obtained grid points are determined based on the size of the image and the number of generating points input as parameters, and the maximum half-amplitude value T is the fluctuation of the generating points input as parameters. Determined based on quantity.

The generating point displacing means 5 is means for displacing each of the generating points arranged by the generating point arranging means 3 by using the fractal field generated by the fractal field generating means 4. Yes, Voronoi diagram creation means 6
Is a means for performing a process of creating a Voronoi diagram for the mother points after displacement. The contents of each of these processes are as described above. Thus, when the Voronoi diagram is created,
The pattern output means 7 outputs the amorphous cell pattern shown by this Voronoi diagram. If it is used as a texture pattern for computer graphics, it will be output as digital pattern data to an external storage device of the computer, and if it is used as a printed matter, it will be output from the computer to a printing plate device or the like and printed. The steps may be performed.

As described above, when the parameter input means 1 is configured to be able to set various parameters, the irregular cell pattern to be generated, such as fish scales, reptile skin, and plant fiber, can be obtained. Optimal patterns can be generated by appropriately changing the parameter settings according to the type.

The irregular-shaped cell pattern generated by the present invention can be used not only for so-called flat screen display and printed matter but also for three-dimensional printing (for example, embossing). . In this specification, the word "printing" is used to include a so-called "embossing" that includes three-dimensional processing, and the word "printed matter" also includes an embossed article that should be called "three-dimensional printed matter". It is used in a broad sense.

[0057]

As described above, according to the present invention, it is possible to express the "flow" element peculiar to plants and animals, and to generate an atypical cell pattern with a feeling of life.

[Brief description of drawings]

FIG. 1 is a diagram showing a state where six mother points M1 to M6 are defined on a plane.

FIG. 2 is a diagram showing a Voronoi polygon showing the influence zone of each generating point shown in FIG.

FIG. 3 is a diagram showing an example in which a regular generating point Mi is defined as each vertex of an equilateral triangle that fills a plane.

FIG. 4 is a generating point Mi regularly arranged as shown in FIG.
It is a figure which shows the Voronoi diagram created based on.

FIG. 5 is a diagram showing an example of an amorphous cell pattern obtained by a method using a conventional Voronoi diagram.

FIG. 6 is a flowchart showing a basic procedure of a method for generating an irregular cell pattern according to the present invention.

FIG. 7 is a diagram showing an example of an amorphous cell pattern obtained by the method according to the present invention.

FIG. 8 is a diagram showing a state of the 0th stage for generating a one-dimensional fractal lattice.

FIG. 9 is a diagram showing a state of the first stage in which a one-dimensional fractal lattice is generated.

FIG. 10 is a diagram showing a second stage state in which a one-dimensional fractal lattice is generated.

FIG. 11 is a diagram showing specific scalar values defined at each grid point in the 0th stage of generating a one-dimensional fractal grid.

FIG. 12 is a diagram showing specific scalar values defined at each grid point in the first stage of generating a one-dimensional fractal grid.

FIG. 13 is a diagram showing specific scalar values defined at each grid point in the second stage of generating a one-dimensional fractal grid.

FIG. 14 is a diagram showing specific scalar values defined for each grid point in a one-dimensional fractal grid composed of five grid points.

FIG. 15 is a graph showing a natural fluctuation of a one-dimensional fractal grid composed of many grid points.

FIG. 16 is a diagram illustrating a zero-th order for generating a two-dimensional unit fractal lattice.
It is a figure showing a state of a stage.

FIG. 17: First to generate a two-dimensional unit fractal lattice
It is a figure showing a state of a stage.

FIG. 18 is a second diagram for generating a two-dimensional unit fractal lattice.
It is a figure showing a state of a stage.

FIG. 19 is a conceptual diagram of a generating point displacement process shown in step S3 of FIG.

FIG. 20 is a flowchart showing in detail the procedure of generating point displacement processing in step S3 of FIG.

FIG. 21 is a movement amount Δ in the X-axis direction in an XY rectangular coordinate system.
It is a figure which shows the example which displaced the mother point Mi using x and the movement amount (DELTA) y of the Y-axis direction.

FIG. 22 is a diagram showing an example in which the mother point Mi is displaced using the distance r and the angle θ in the rθ polar coordinate system.

FIG. 23 is a diagram showing an example of a method of defining a distance between a generating point M and an arbitrary point P defined when creating a Voronoi diagram.

FIG. 24 is a diagram showing “four adjacent pixels” and “eight adjacent pixels” with respect to a predetermined pixel P.

FIG. 25 is a diagram for explaining “four adjacent distances” or “eight adjacent distances”.

FIG. 26 is a block diagram showing a device configuration according to an embodiment of the present invention.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 ... Parameter input means 2 ... Random number generation means 3 ... Generating point arrangement means 4 ... Fractal field generation means 5 ... Generating point displacement means 6 ... Voronoi diagram creation means 7 ... Pattern output means Hi ... Regular hexagonal Voronoi polygon L1, L2 ... Two-dimensional fractal grid M1 to M6, Mi ... Generating point P ... Arbitrary point Q1i, Q2i ... Grid point of fractal grid S1, S2 ... Scalar value defined by fractal grid XY ... XY plane xi, yi ... Coordinate value Δx, Δy ... Displacement amount dy, dy ... Distance

 ─────────────────────────────────────────────────── ─── Continuation of the front page (72) Inventor Toshio Ariyoshi 1-1-1, Ichigaya-Kagacho, Shinjuku-ku, Tokyo Dai Nippon Printing Co., Ltd. (72) Inventor Yu Okamoto 1-chome, Ichigaya-Kagacho, Shinjuku-ku, Tokyo No. 1 in Dai Nippon Printing Co., Ltd. (72) Inventor Yoshio Sukegawa 311 Takemazawa, Miyoshi-cho, Iruma-gun, Saitama Prefecture

Claims (8)

[Claims] 1. A method for generating a pattern composed of a large number of irregularly shaped cells, the first step of regularly arranging a large number of generating points to be cores of individual cells, and spatially self-similarity. A second step of preparing a fractal field capable of expressing a general vector, a third step of displacing the large number of generatrices using the fractal field, and a Voronoi diagram for the displaced generatrix. A fourth step of creating, and generating a pattern based on the Voronoi diagram. 2. The method according to claim 1, wherein in a first step, the generating points are arranged on a two-dimensional plane, and in a second step, a predetermined scalar value is self-similarly arranged on the two-dimensional plane. A two-dimensional fractal grid defined for each grid point is prepared, and in the third step, the two-dimensional fractal grid is overlaid on the plane where the generatrix is arranged, and the mutual positional relationship between each generatrix and each grid point Based on the above, each grid point is associated with a specific grid point, and each grid point is displaced in a predetermined direction based on the scalar value defined in the corresponding grid point to generate an irregular cell pattern. Method. 3. The method according to claim 2, wherein the generating points are arranged on the XY plane in the first step, and two independent two-dimensional fractal grids are prepared in the second step. In step 3, each generating point is moved in the X-axis direction based on the scalar value defined in the grid point of the first two-dimensional fractal grid, and defined in the grid point of the second two-dimensional fractal grid. A method for generating an irregular cell pattern, which comprises moving in the Y-axis direction based on a scalar value. 4. The method according to claim 1, wherein in the first step, a Voronoi polygon consisting of a triangle, a quadrangle or a hexagon is regularly formed on a predetermined plane. A method for generating an irregular cell pattern characterized by arranging generating points. 5. The method according to claim 1, wherein in the fourth step, a Voronoi diagram is created by making an arbitrary point belong to the sphere of influence of the generating point having the smallest Euclidean distance. A method for generating an amorphous cell pattern characterized by. 6. An apparatus for generating a pattern composed of a large number of irregular cells, comprising parameter input means for inputting a predetermined parameter, random number generation means for generating a random number, and a large number of cores of individual cells. Generating point allocating means for regularly arranging generating points of, based on the parameter, and a fractal field generating means for generating a fractal field capable of expressing a spatially self-similar vector based on the parameter, Generating means for displacing the large number of generating points respectively using the fractal field, Voronoi diagram generating means for generating a Voronoi diagram for the displaced generating points, and generating a pattern based on the Voronoi diagram, An apparatus for generating an irregular cell pattern, comprising: a pattern output means for outputting 7. A printed matter having an amorphous cell pattern produced by the method according to claim 1. 8. A pattern composed of a large number of amorphous cells, characterized in that the cells are distributed with fluctuations based on a fractal field, and an amorphous cell is represented by a Voronoi diagram generated for this kernel. Printed matter having.