JPH09198514A - Method ands device for generating printed matter in shape of non-uniform lattice and non-uniform lattice shape data - Google Patents

Abstract

PROBLEM TO BE SOLVED: To completely match junction parts and to easily change the size or line with of lattice and the level of fluctuations of nonuniformity and feeling of fluctuations by applying new coordinate values to respective lattice points and connecting respective new lattice points and proximately positioned lattice points through line segments. SOLUTION: Based on a fractal lattice generated by fractal lattice generator 3 and the coordinate of an initial image lattice point arranged by a lattice point arranger 4, the coordinate of that initial image lattice point is fluctuated and an image lattice point having the new coordinate value is generated. A lattice point connector 6 connects the image lattice point generated by a lattice point fluctuator 5 and the lattice point proximate to this lattice point through the line segment and generates a lattice image. An output device 8 prints out the non-uniform lattice image having the coordinate fluctuated lattice point based on bit map data transformed by a raster image processor 7. Therefore, the processing of generation can be automatically performed only by changing the setting of parameters.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention belongs to the technical field of generating an image using a digital computer, and the generated image is used for plate making and printing. In particular, the present invention relates to a technique for obtaining data of a non-uniform lattice shape pattern using a vector field having a self-similar fluctuation and forming it on a printed matter. As a result, the non-uniform grid-shaped pattern formed on the printed matter also exhibits self-similar fluctuations. Further, according to the present invention, this non-uniform lattice-shaped pattern can be connected endlessly.

[0002]

2. Description of the Related Art In recent years, images generated and processed by using a computer have been found in printed matter in a wide variety of fields. In particular, the patterns found on building material products such as wallpaper and the packaging of products are often images created using computer graphics technology to some extent. An image captured as digital data in a computer can be enlarged or reduced, and processing such as intentionally distorting the image can be freely performed. It is very expensive and a unique processing method is often used to aim for a special effect.
For example, in games, animations, still images, and textures using CG, or in various texture prints such as resin products, a nonuniform grid pattern may be used aiming at a special design effect.

Such image information is information having a very large amount of data. Therefore, when it is applied to a printed matter having a very large area such as wallpaper, it is general to use a repeating pattern. In addition, the circumference of the gravure cylinder, which is the printing plate of the gravure printing machine, is about 1 m to 2 m, and it is not possible to make a printing plate with an image longer than this.
When making a printing plate, image data that can be connected endlessly around the circumference of the gravure cylinder is required. Therefore, a printing plate is prepared by preparing unit images for an integral fraction of the circumference of the gravure cylinder, and arranging the unit images in a state where they are adjacent to each other in a plane. Since the wallpaper printed by such a printing plate can be connected, theoretically, a wallpaper of any size can be obtained with a continuous pattern. Therefore, normally, at the stage of generating a pattern used as a unit image, consideration is given so that the pattern at the boundary portion is continuous, and a repeatable pattern is generated.

[0004]

However, since the above-mentioned non-uniform grid pattern is conventionally made manually,
When they were repeatedly arranged vertically and horizontally, the alignment was not completely obtained at the joint. Also, when the size of the grid or the line width is changed, the size of the fluctuation of the nonuniformity, or the texture of the fluctuation is changed, it is completely remade, and the load is large and the quality is unstable. Therefore, the object of the present invention is to achieve perfect alignment at the joint, to change the size and line width of the lattice,
An object of the present invention is to provide a printed matter having a non-uniform lattice shape, a method and an apparatus for producing non-uniform lattice shape data, in which the size of the non-uniformity fluctuation and the texture of the fluctuation can be easily changed.

[0005]

The above objects are achieved by the present invention described below. That is, the present invention is a "printed matter having a two-dimensional lattice-shaped pattern, in which a vector value is given to each lattice point of the lattice shape based on a two-dimensional vector field having self-similar fluctuations, A new coordinate value is given to each grid point by calculating the coordinate value of each grid point based on the vector value given to the point, and at each new grid point, with the grid points located in the vicinity. It is a printed matter having an expression of a non-uniform lattice-shaped pattern obtained by connecting the lines with line segments. " According to the printed matter of the present invention, various design effects are expressed by the non-uniform lattice shape pattern.

The present invention also provides that "in the matrix composed of each grid point of the non-uniform grid shape pattern, a specific row and / or
Or a shape formed by a set of grid points belonging to a column and a shape formed by a set of grid points belonging to a row and / or column separated from the specific row and / or column by a predetermined number of rows and / or a predetermined number of columns Are the same and the specific line and /
Alternatively, it is a printed matter having an expression of an endless non-uniform lattice shape pattern in which a plurality of lattice points belonging to a column and a plurality of lattice points belonging to a row and / or a column separated by the predetermined number of rows are overlapped and arranged. According to the printed matter of the present invention, a joint having perfect alignment is obtained, and the joint is not recognized.

Further, the present invention includes "preparing a lattice shape obtained by intersecting a plurality of straight lines parallel to each coordinate axis of two-dimensional coordinates, and preparing a two-dimensional vector field having self-similar fluctuations. , A step of giving a vector value of coordinates of the vector field corresponding to the coordinates of each grid point to each grid point obtained by intersecting the grid-shaped straight line, and based on the vector value given to each grid point Generating a new coordinate value at each grid point by calculating the coordinate value of each grid point, and each new grid point by replacing the coordinate value of each grid point with the new coordinate value. And generating a non-uniform grid shape data by connecting a line segment between adjacent grid points at each of the new grid points. It is the law. " According to the method for generating non-uniform grid shape data of the present invention, the generation process can be automatically performed only by changing the parameter setting, so that the size of the grid or the line width can be changed, and the fluctuation of the non-uniformity can be prevented. It is easy to change the size and texture of fluctuation,
It is possible to generate data having various design effects.

The present invention also provides that "the two-dimensional vector field having the self-similar fluctuation is a vector field defined in a two-dimensional rectangular area, and the opposite sides of the rectangular area of the vector field and / or In the coordinate on the two sides of the left and right, the step of matching the vector value of the corresponding coordinate in the coordinate of the right and left and / or the top and bottom, and each grid point obtained by intersecting the straight line of the grid shape is a two-dimensional rectangular area. The defined grid points, the coordinates on the opposite sides of the rectangular area of the grid points and / or on the left and right sides are defined as the opposite sides of the rectangular area of the vector field and / or on the two sides. Corresponding to the coordinates, and providing a vector value of the coordinates of the vector field corresponding to the coordinates of all the grid points including the grid points on the two sides thereof. A generation method "heterogeneous lattice shape data and symptoms. According to the method for generating non-uniform lattice shape data of the present invention, it is possible to obtain a joint part with perfect matching and avoid recognizing the joint part.

The present invention also relates to the "setting of conditions necessary for generating a two-dimensional vector field having self-similar fluctuations and a lattice obtained by intersecting a plurality of straight lines parallel to each coordinate axis of the two-dimensional coordinate. Parameter input device for setting conditions required to generate a shape and conditions for generating a new coordinate value of a grid point, and a random number for generating a random number for giving a self-similar fluctuation A generator and a vector field generator that inputs a parameter of the vector field from a parameter input device, and that inputs a random number from the random number generator to generate a two-dimensional vector field having self-similar fluctuations, A grid point placement device that inputs the parameters of the grid shape from the parameter input device and generates the coordinates of all grid points, and a vector of the coordinates of the vector field corresponding to the coordinates of each grid point. A new value for each grid point by calculating the coordinate value of each grid point based on the vector value given to each grid point according to the condition for generating a new coordinate value of the grid point. Generate coordinate values,
Generate new grid points by replacing the coordinate values of the grid points with the new coordinate values, and between the grid point changing device and the grid points located in the vicinity of the new grid points. And a grid point connecting device that generates non-uniform grid shape data by connecting line segments, and a non-uniform grid shape data generation device ”. According to the non-uniform grid shape data generation device of the present invention, since the generation process can be automatically performed only by changing the parameter setting, the grid size and the line width are changed, and the non-uniformity fluctuation It is easy to change the size and the texture of fluctuations, and data having various design effects is generated.

According to the present invention, "the two-dimensional vector field having self-similar fluctuation generated by the vector field generator is a vector field defined in a two-dimensional rectangular area, and the rectangular area of the vector field is At the opposite top and bottom and / or the coordinates on the left and right sides,
Alternatively, the vector values of the corresponding coordinates in the vertical coordinates match, and each grid point obtained by intersecting the grid-shaped straight lines generated by the grid point placement device is a grid point defined in a two-dimensional rectangular area. And the opposite top and bottom of the rectangular area of the grid point and / or the coordinates on the two right and left sides are set to the top and bottom of the rectangular area of the vector field
Alternatively, the non-uniform grid shape data generation device is characterized in that the non-uniform grid shape data is generated by associating with the coordinates on the left and right sides. According to the non-uniform lattice shape data generation device of the present invention, a joint part having perfect alignment is obtained, and it is avoided that the joint part is recognized.

[0011]

DESCRIPTION OF THE PREFERRED EMBODIMENTS The present invention will be described below with reference to embodiments. First, a two-dimensional vector field having self-similar fluctuations used in the present invention will be described. This vector field can be defined based on a fractal grid, as described below. It is widely known that so-called fractal figures are suitable for representing many things in the natural world. The feature of this fractal figure is that its complexity is always the same whether it is microscopic or macroscopic. The shape of the coastline, the shape of trees and veins, the shape of snow crystals, etc. found in the natural world are all typical of this fractal figure. It has a complicated shape.

Such a property is generally called self-similarity. The essence of fractal theory lies in this self-similarity, and a more general extension of this theory makes it possible to consider a fractal lattice in which a given scalar value is self-similarly defined at each lattice point. 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.

Here, if the predetermined scalar value is self-similarly defined for each grid point twice completely independently, two independent scalar values are defined for each grid point. become. That is, each lattice point is given a self-similar scalar value as its component, and two independently defined vector values. The two-dimensional vector field in the present invention can be defined as a two-dimensional fractal lattice thus defined by scalar values, that is, a simple extension of the two-dimensional scalar field. Therefore, next, the fractal grid defined by the scalar value will be described.

The fractal lattice has scalar values defined for a large number of lattice points arranged on a two-dimensional plane, and naturally, the fractal lattice has a fractal property. 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 of i = 1, the rectangle ABCD shown in FIG. 1 is the minimum rectangle (the rectangle that does not include the grid points A, B, C, D defined up to the 0th stage). i = 2
In the second stage of, the four rectangles AEIH,
EBFI, HIGD, and IFCG are minimum rectangles (rectangles that do not include any of the grid points A to I defined up to the first 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, 2, the midpoint E of each side of the smallest rectangle ABCD,
Lattice points to be defined are generated at F, G, H and center point I). Furthermore, of these grid points, for the grid point generated at the middle point, a random number is applied to the scalar values of the two grid points defined up to the (i-1) th stage existing at the end points of the side. Gives the scalar value obtained by For example, for the grid point E shown in FIG. 2, a scalar value e obtained by applying a random number RND to the scalar values a and b of the two grid points A and B is given.

In general, the scalar value s for a grid point defined as the midpoint of adjacent grid points in the nth stage
The calculation method of 1 is shown in the following formula 1.

S1 = (α + β) / 2 + (1/2 ^(n-1) ) T RND (1) where α and β are scalar values (the (( n-1) is calculated).

On the other hand, the grid point generated at the center point of the minimum rectangle is located at the four corners of the minimum rectangle (i
-1) Give a scalar value obtained by applying a random number to a scalar value having four grid points defined up to the stage. For example, for the grid point I shown in FIG.
Scalar values a, b, which four grid points A, B, C, D have
A scalar value i obtained by applying a random number RND to c and d is given. Generally, the calculation method of the scalar value s2 for the grid point defined as the center point of the minimum rectangle in the nth stage is shown in the following Expression 2.

S2 = (α + β + γ + δ) / 4 + (1/2 ^(n-1) ) · T · RND (2) where α, β, γ and δ are the lattice points in four directions of the lattice point. It is a scalar value (calculated in the (n-1) th stage).

The two-dimensional fractal lattice generated by such a method eventually gives a scalar field spread over a two-dimensional plane. Therefore, by plotting each scalar value of this two-dimensional fractal grid as the height in the vertical direction (elevation), 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. As explained at the beginning, the above method is independently performed twice, two two-dimensional scalar fields are obtained, and the corresponding scalar value of each two-dimensional scalar field is given to each grid point as a component. The two-dimensional vector field in the present invention can be obtained by performing various extensions.

By the way, it is assumed that the two-dimensional unit fractal lattice 10 as shown in FIG. 3 is generated by the above-mentioned method (called a random midpoint displacement method). This two-dimensional unit fractal grid 10 is composed of a large number of grid points 11 arranged vertically and horizontally (here, one grid point is shown by one grid for convenience), and each grid point 1
A predetermined scalar value is defined in each item. In other words, the two-dimensional unit fractal grid 10 can be considered as a square board in which a large number of tiles each having a predetermined number are arranged in a matrix.

Subsequently, as shown in FIG. 4, when nine such square boards are arranged on a plane, an area of 9 is obtained.
You get a double board. Here, the large fractal lattice thus obtained will be referred to as a two-dimensional synthetic fractal lattice. The word "unit" in the two-dimensional unit fractal 10 shown in FIG. 3 is used in correspondence with the word "synthesis" of the "two-dimensional synthetic fractal lattice 20" shown in FIG.

By the way, the two-dimensional unit fractal lattice 10
The scalar field defined in gives a natural fluctuation as far as it is within this closed region of the unit cell. However, the scalar field defined in the two-dimensional synthetic fractal lattice 20 as shown in FIG. 4 does not always give a natural fluctuation as a whole. Because
This is because the boundary portions shown by hatching in FIG. 4 are not continuously connected. In other words, at this boundary, the scalar field becomes discontinuous and the natural fluctuation is disturbed. In the present invention, even in the case where a plurality of elements are arranged in a spatially adjacent manner, as a whole,
The "unit fractal lattice" that gives a scalar field that gives natural fluctuations is called the "repeatable unit fractal lattice". Therefore, the two-dimensional synthetic fractal grating 20 shown in FIG. 3 can provide a scalar field that gives a natural fluctuation as a whole.

Next, the basic concept for generating a repeatable two-dimensional unit fractal lattice will be described with reference to FIG. Now, as shown in FIG. 5A, a two-dimensional unit fractal lattice 3 in which an outer rectangle that is the outer shape of the lattice is formed by four sides of a left side 31, a right side 32, an upper side 33, and a lower side 34.
Consider 0. At this time, the lower side 3 with hatching in the figure
As a scalar value given to an arbitrary grid point 35 on the grid row along 4 the scalar value given to the grid point 36 at the same lateral position on the grid row along the upper side 33, which is also hatched in the figure, When the same value is given, when the unit fractal lattices are arranged vertically, the scalar field at the boundary becomes continuous. Similarly, in FIG. 5B, as a scalar value given to an arbitrary grid point 37 on the grid row along the right side 32 hatched in the figure, the grid row along the left side 31 also hatched in the figure is shown. When the same value as the scalar value given to the grid point 38 at the same vertical position is given, the scalar field at the boundary becomes continuous when a plurality of unit fractal grids are arranged on the left and right. After all, if the scalar value of the grid point 38 on the left side 31 is diverted, the scalar value of the grid point at the boundary portion hatched in FIG. 4 becomes continuous.

The basic concept of the present invention for generating a repeatable two-dimensional unit fractal lattice is as described above.
This is a method of diverting the scalar value of the grid point on the opposite side of the outer rectangle. However, when the already generated two-dimensional unit fractal grid is modified by diverting the scalar value as described above, the grid point on the outer rectangle and the grid point immediately inside it become discontinuous. turn into. Therefore, in the present invention, it is possible to realize a continuous scalar field even at the boundary portion while maintaining the continuous scalar field inside the fractal lattice. Less than,
A method of generating this repeatable two-dimensional unit fractal lattice will be described with reference to a specific example.

In order to generate a repeatable two-dimensional fractal grid, grid points A, B, C and D are arranged at four vertex positions of the outer shape rectangle as grid points of the 0th stage, as shown in FIG. The same scalar value a is defined for each of these grid points.

Subsequently, in the first stage, as shown in FIG. 7, grid points E, F, G, and H are defined at midpoints between grid points AB, BC, CD, DA. , The smallest rectangle at this point (the same rectangle ABCD as the outer rectangle)
Define another grid point I at the center point of. Scalar values e, f, g, h, and i are defined for these five grid points, respectively. The scalar value f for the grid point F on the right side of the outline rectangle and the grid point on the bottom side of the outline rectangle are defined. When determining the scalar value g for G, the method peculiar to the present invention, which is the diversion of the above-described scalar value, is adopted. That is, if this is expressed by an arithmetic expression,
become that way.

## EQU00003 ## e = (a + a) /2+T.RND (31) h = (a + a) /2+T.RND (32) i = (a + a + a + a) /4+T.RND (33) f = h ( 34) g = e (35) Here, T is the maximum half-amplitude value of the fluctuation, and RND is −1 ≦
It is an arbitrary random number such that RND ≦ + 1. As a result, exactly the same scalar value is defined for each corresponding grid point on the left and right sides of the outer shape rectangle ABCD, and exactly the same scalar value is defined for each corresponding grid point on the upper and lower sides. become.

Thus, the grid points E, F, G,
Once the scalar values e, f, g, h, i for H and I have been defined, then proceed to the second stage, as shown in FIG. 8, to obtain the four smallest rectangles AEIH, EBFI, HIGD, I.
After recognizing the FCG, new grid points J to Y are generated at each of the midpoint positions and the center points of the four sides for each minimum rectangle. Then, scalar values j to y are defined at these grid points J to Y, respectively. In this case, basically, the scalar value defined at each grid point is obtained according to the above-described calculation method (Equation 1 and Equation 2), except that the scalar value for the grid point on the right side of the outer rectangle is calculated. Is
The scalar value for the grid point at the corresponding position on the left side is diverted, and for the scalar value for the grid point on the lower side of the outer shape rectangle, the scalar value for the grid point at the corresponding position on the upper side is diverted.

Specifically, in FIG. 8, the outer shape rectangle AB
For the new grid points N, O defined on the right side of the CD and the new grid points P, Q defined on the lower side, scalar values obtained by diversion should be given instead of scalar values calculated by normal operation. become. That is, the scalar values j to q given to the eight grid points J to Q newly defined on the outer shape rectangle ABCD are given by the following Expression 4.

## EQU00004 ## j = (a + e) / 2 + (1/2) .T.RND (41) k = (e + a) / 2 + (1/2) .T.RND (42) l = (a + h) / 2 + (1/2) · T · RND (43) m = (h + a) / 2 + (1/2) · T · RND (44) n = 1 (45) o = m (46) p = k ( 47) q = j (48)

Scalar values for new grid points J, K defined on the upper side of the outer shape rectangle ABCD and scalar values j for new grid points L, M defined on the left side of the outer shape rectangle ABCD. The arithmetic expressions (41) to (44) for obtaining ~ m are the normal arithmetic expressions already described. On the other hand, the scalar values for the new grid points N and O defined on the right side of the outer shape rectangle ABCD and the scalar values n to q for the new grid points P and Q defined on the lower side of the outer shape rectangle ABCD are obtained. Equations (45) to (48) for simply indicate the diversion of the scalar value of the corresponding grid point. For the scalar values r to y given to the eight newly defined lattice points R to Y inside the outer shape rectangle ABCD, the above-mentioned usual arithmetic expression shown in the following Expression 5 is applied.

[0029]

## EQU00005 ## r = (a + e + i + h) / 4 + (1/2) .T.RND (51) s = (e + i) / 2 + (1/2) .T.RND (52) t = (e + a + f + i) / 4 + (1/2) ・ T ・ RND (53) u = (f + i) / 2 + (1/2) ・ T ・ RND (54) v = (i + f + a + g) / 4 + (1/2) ・ T ・RND (55) w = (g + i) / 2 + (1/2) .T.RND (56) x = (h + i + g + a) / 4 + (1/2) .T.RND (57) y = (h + i) / 2 + (1/2) · T · RND (58)

After all, as shown in FIG. 8, of the 25 grid points A to Y defined up to the second stage, the outer shape rectangle AB
The scalar values of the grid points B, N, F, O, and C on the right side of the CD are the same as the scalar values of the grid points A, L, H, M, and D on the left side, respectively. Since the processing of the third stage is performed in exactly the same manner, finally, a repeatable two-dimensional fractal lattice is obtained. That is,
As shown in FIG. 4, when a plurality of elements are arranged in a plane, the boundary portions are continuously connected. In addition, since the diversion processing of the scalar values for the grid points on the right side and the grid points on the lower side of the outer shape rectangle is performed for each process of each step of generating the fractal grid, the fractal grid finally generated is It becomes natural with a continuous scalar field inside.

By the way, the method of arranging the two-dimensional unit fractal lattice on a plane without a gap is not limited to the method shown in FIG. For example, as shown in FIG. 9, there is also a method of arranging the upper and lower rows by shifting them by an offset amount W in the horizontal direction. In this way, when generating a repeatable two-dimensional fractal grid that is supposed to be arranged with a shift of the offset amount W, the grid points at the same position on the opposite sides of the outer shape rectangle are used as the counterparts to whom the scalar value is diverted. It cannot always be used as is. This can be easily understood by considering the positional relationship of various geometric symbols shown in the boundary portion in FIG. This concept is shown in FIG. As shown in FIG. 10A, for the grid point 12 on the right side, the scalar value of the grid point 13 at the same position on the left side can be diverted as it is, as in the above example, but on the bottom side. It is necessary to consider the grid point 15 at the position where the grid point 14 is shifted by the offset amount W and use the scalar value of the grid point 16 at the same position as the grid point 15 on the upper side. In addition, as shown in FIG. 10B, when the grid point 17 on the lower side is displaced from the unit grid by an offset amount W to the left, the remaining offset amount is shifted from the right end of the unit grid. Considering the grid point 18 at the position, it is necessary to use the scalar value of the grid point 19 at the same position as the grid point 18 on the upper side.

In the above example, the offset direction is the horizontal direction, but the offset direction can be the vertical direction. However, in any case, if the offset amount is determined, the connection corresponding position on the upper side with respect to the predetermined position on the lower side and the connection corresponding position on the left side with respect to the predetermined position on the right side are uniquely obtained. Therefore, if the scalar values for the grid points at the corresponding connection positions are diverted, no matter what array is used,
It is possible to generate a repeatable two-dimensional unit fractal grid.

Now, a general procedure for generating a repeatable two-dimensional unit fractal lattice will be described with reference to the flowchart of FIG. First, in step S1, the lattice size n and the maximum half amplitude value T are set. Here, the grid size n indicates the resolution of the generated fractal grid, that is, the grid density, and in this example, the grid size is determined by the number of steps n indicating how many steps the grid point generating operation is performed. Specified (if n = 1, a 3 × 3 size fractal grid is generated as shown in FIG. 7, and if n = 2, a 5 × 5 size fractal grid is generated as shown in FIG. become).

Next, in step S2, a parameter i indicating the number of stages being processed is set to an initial value 0. That is, the process of the 0th stage is to be performed from now on, and thereafter, each parameter described below is repeatedly executed until i = n while sequentially incrementing the parameter by 1, 2, 3 ,. Will be done.

Step S3 shows the process of the 0th stage. That is, in the 0th stage, as shown in FIG. 6, four grid points A, B, C, D are provided at four corner positions of the outer shape rectangle.
Is defined and a common scalar value is given to these grid points. The scalar value a and the maximum iteration value T set in step S1 are factors that determine the absolute value and fluctuation width of the scalar value of the finally obtained fractal grid. Therefore, in the image generation processing described later, the values of a and T may be appropriately set in consideration of the absolute value and the fluctuation width of the scalar field.

In the next step S4, the parameter i
Is incremented by 1. As a result, the initial stage of i = 0 shifts to the first stage of i = 1, and the process of the first stage is performed thereafter.

Step S5 is the first process in each stage, and is the process of generating grid points in the i-th stage.
A general definition of this processing is as follows. First, the minimum rectangle at the current stage that does not internally include the grid points defined up to the (i-1) th stage is recognized. In the case of the first stage where i = 1, the rectangle ABCD shown in FIG. 6 is recognized as the minimum rectangle that does not include the grid points A, B, C, and D defined up to the 0th stage. Also,
In the case of the second stage of i = 2, the four rectangles AEIH, EBFI, IFCG, and HIG shown in FIG. 7 are set as the minimum rectangles that do not include the grid points A to I defined up to the first stage.
D is recognized. Then, five new grid points are generated for each of the recognized minimum rectangles (note that the grid points generated for the adjacent minimum rectangles are partially overlapped). Specifically, new grid points are generated at the midpoint position of each of the four sides of the minimum rectangle and the midpoint position of the minimum rectangle.

In the following step S6, a scalar value is defined for the new grid point generated in step S5, using the maximum half-amplitude value T and the random number RND set in step S1. At this time, as a general rule, the scalar value s1 obtained by the equation 1 is used for the grid point generated at the midpoint of each side of the minimum rectangle, and the grid point generated at the center point of the minimum rectangle is described above. The scalar value s2 obtained by the equation of Equation 2 is used. However, as an exception, for the grid point on the right side of the outline rectangle, the scalar value of the grid point at the connection corresponding position on the left side is diverted, and for the grid point on the lower side,
Divert the scalar value of the connection corresponding position on the upper side.

Then, in step S7, whether or not the set grid size can be obtained, that is, the parameter i
= N is determined, and if i <n, the processing from step 4 is repeated again. Thus,
When the processing up to the nth stage is executed, the desired repeatable two-dimensional fractal lattice is completed.

In the above description, for the grid points on the right side of the outer shape rectangle, the scalar value of the grid point at the connection corresponding position on the left side is diverted, and for the grid points on the lower side,
The scalar value of the grid point at the connection corresponding position on the upper side is diverted, but conversely, for the grid point on the left side of the outer rectangle, the scalar value of the grid point at the connection corresponding position on the right side is diverted. Alternatively, for the grid point on the upper side, the scalar value of the grid point at the connection corresponding position on the lower side may be diverted.

The method of generating a repeatable two-dimensional fractal lattice by using the random midpoint displacement method has been described above, but this method can generate a one-dimensional fractal lattice or a fractal lattice of three or more dimensions. It can be used similarly when generating. For example, in order to generate a repeatable one-dimensional fractal grid, it is sufficient to set the same scalar value to two grid points in the 0th stage. Further, in order to generate a repeatable three-dimensional fractal lattice, in the 0th stage, the contract points having the same scalar value are defined at the eight corners of the cube, and the three points of this cube are defined.
For the lattice points on the surface, the scalar value of the lattice point on the facing surface may be diverted. For example, even if this cube is used as a dice, the lattice points of the 6th face are diverted for the lattice points of the first eye, and the lattice points of the 5th face are used for the lattice points of the second eye. The grid points of the third surface are diverted, and the grid points of the fourth surface may be diverted.

So far, the method of generating a repeatable unit fractal lattice has been described. This repeatable unit fractal grid is an important concept related to the essence of the present invention, but the substance of the present invention is to utilize the repeatable unit fractal grid to create a printed matter having a repeating pattern. is there. Therefore, FIG.
FIG. 1 is a block diagram showing the basic configuration of the printed matter creating apparatus according to the present invention.

As shown in FIG. 12, this printed matter producing apparatus includes a parameter input apparatus 1, a random number generating apparatus 2, a fractal grid generating apparatus 3, a grid point arrangement apparatus 4, a grid point changing apparatus 5, and a grid point connecting apparatus 6. , A raster image processor 7 and an output device 8. In this configuration,
The parameter input device 1 generates a fractal grid and the conditions necessary for arranging initial grid points (called initial image grid points) before the grid point variation processing of the non-uniform grid according to the present invention. The conditions necessary for changing the coordinates of the grid points are set. The random number generator 2 generates a random number for giving fluctuation to the scalar value given to each lattice point forming this fractal lattice. The fractal lattice generator 3 generates a fractal lattice by a predetermined calculation based on the condition set in the parameter input device 1 and the random number generated by the random number generator 2. The grid point arrangement device 4 calculates the coordinates of the initial image grid points based on the conditions set in the parameter input device 1, and arranges the initial image grid points. Lattice point changing device 5
Is the condition set in the parameter input device 1,
Based on the fractal grid generated by the fractal grid generation device 3 and the coordinates of the initial image grid point arranged by the grid point arrangement device 4, the coordinates of the initial image grid point are changed and the grid point having a new coordinate value ( Image grid points). The grid point connecting device 6 connects the image grid points generated by the grid point changing device 5 to the grid points and neighboring grid points by line segments to generate a grid image. At this time, the lattice image is
For example, even when they are arranged in a plane as shown in FIG.
Make sure the line segments at the boundary are connected. Here, the neighboring grid points are grid points defined in advance as having a connection relationship at the initial image grid points, and in the present embodiment, there are four grid points arranged above, below, to the left and right of a certain grid point. With respect to the image grid points generated by the grid point changing device 5, even if the coordinates of the grid points are changed, connection by line segments is performed with the grid points near this initial image grid point as neighboring grid points. . The raster image processor 7 converts the grid image connected by the grid point connection device 6 into bitmap data. The output device 8 prints out a non-uniform grid image having grid points whose coordinates are changed based on the bitmap data converted by the raster image processor 7.

Here, the parameter input device 1 uses the size n of the unit fractal lattice to be generated and the maximum half amplitude value T.
And a grid point having the same scalar value a, which is arranged at each of the four corners of the outer shape rectangle forming the outer shape of the grid, as a condition, and step S1 in the flowchart shown in FIG. And has a function of performing the setting in step S3. Further, the parameter input device 1 sets the conditions necessary for arranging the initial grid points (called initial image grid points) before performing the grid point variation processing of the non-uniform grid according to the present invention as described above. Set. The initial image grid points are usually defined as a set of points arranged in a matrix at predetermined intervals in a predetermined rectangular range. In other words, it is defined as a set of intersections formed by a set of equidistant parallel lines and another set of parallel equidistant parallel lines. In general, sets of parallel lines may intersect at angles other than orthogonal, and parallel lines need not be evenly spaced, and the initial image grid point may be defined as the set of intersections created thereby. it can. Not only in the normal case but also in the case where the initial image grid points are generally defined as described above, the respective positions of the four corners forming the outline of the unit fractal grid form the outline of the initial image grid points. Set so as to correspond to the four corners. Since the settings are made as described above, when a plurality of initial image grid points are arranged adjacent to each other,
The coordinates of the side grid points can be matched at each initial image grid point, and an endless pattern can be formed. When the above-described method of generating the repeatable two-dimensional unit fractal grid is applied based on the initial image grid points, it is naturally possible to form an endless pattern also by the generated unit fractal grid.

Further, the random number generator 2 has a function of generating a random number RND in the range of -1≤RND≤ + 1 in the case of the embodiments described so far. Further, the fractal grid generator 3 is composed of a scalar value calculation unit, a scalar value diversion unit, and a fractal grid generation unit, and the scalar value calculation unit calculates the basic scalar value shown in step S6 in the flowchart shown in FIG. It has a function to perform arithmetic processing,
The scalar value diversion unit has a function of performing exceptional scalar value diversion processing shown in step S6 in the flowchart shown in FIG. The fractal grid generation unit defines new grid points at the center points of the midpoints of two adjacent grid points and the four grid points forming the minimum rectangle, and in principle, a scalar value calculation unit is provided at each of these grid points. Gives the calculated scalar value obtained by, but when these grid points are on the right side or the bottom side of the outer rectangle, exceptionally, the processing for giving the diversion scalar value found by the scalar value diversion part is performed. .

The parameter input device 1, the random number generator 2 and the fractal lattice generator 3 are the same as those shown in FIG.
The steps in the flow chart shown in Figure 2 are repeated twice to generate independent first and second unit fractal grids. The parameter input device 1 sets the size n of the unit fractal grid to be generated under the condition that the first unit fractal grid and the second unit fractal grid have the same value. On the other hand, the same scalar value A and the maximum half-amplitude value T arranged at each of the four corners of the outline rectangle forming the outline of the lattice may be the same, but different maximum half-amplitude values The initial grid point having t and another scalar value a can be set as a condition. Random number generator 2
Generates, in principle, random numbers of different orders and different numerical values in the first fractal grid and the second fractal grid. However, it is also possible to generate random numbers in the same order and with the same numerical value, aiming at an exceptionally special design effect. The fractal grid generator 3 is the parameter input device 1 described above.
Based on the condition set by and the random number generated by the random number generator 2, the above-described processing is performed to give a scalar value to the first unit fractal grid and the second unit fractal grid.

Since the first unit fractal grid and the second unit fractal grid thus generated have the same size n of the fractal grid, the grid points can be associated with each other. That is, the corresponding grid points are given two scalar values defined by the first unit fractal grid and the second unit fractal grid,
A vector field having the two scalar values as components is constructed. When the first unit fractal lattice and the second unit fractal lattice are fractal lattices in which lattice points are two-dimensionally arranged, the vector field is naturally a two-dimensional vector field.

The grid point changing device 5 has the conditions set in the parameter input device 1, the above-mentioned vector field generated by the fractal grid generating device 3, and the coordinates of the initial image grid points arranged by the grid point arranging device 4. , The coordinates of the initial image grid point are changed to generate an image grid point having new coordinates. The details of the process of changing the coordinates of the initial image grid points performed by the grid point changing device 5 will be described later. By this process, unit grid points composed of image grid points distorted by the change of the coordinates of the grid points are generated. Therefore, the grid point connecting device 6 has grid points and grid points in the vicinity of such distorted unit grid points (grid points having a connection relationship at the initial image grid points, that is, four grid points of the initial image grid points in the embodiment). A process of connecting a line segment with a neighboring grid point) is performed. As a result, the lattice image in which the distorted unit lattice points are connected is given a pattern with natural fluctuation based on a self-similar vector field. FIG. 14 shows an example of the lattice image created in this way. As shown in FIG. 14, this image has a non-uniform grid shape. Moreover, this pattern is such that when a plurality of patterns are arranged on a plane as shown in FIG. 4 or 9, the boundary portions can be continuously connected.

Next, the raster image processor 7 converts the above-mentioned lattice image obtained by performing the processing of connecting the lattice points and the lattice points in the vicinity of the unit lattice points by line segments into bitmap data. After that, the output device 8
By arranging a plurality of the bitmap image data, a composite grid point is generated. The image of this synthetic grid point is composed of a non-uniform grid pattern having natural fluctuations as a whole. Therefore, if the image of the synthetic grid points is printed on, for example, a wallpaper, it becomes possible to create a wallpaper having a non-uniform grid pattern with natural fluctuations. Of the components shown as blocks in FIG. 12, the output device 8 is a component made up of a synthesizing device (or a multi-faceted device) in plate making and a printer or an actual printing machine. All the constituent elements of the above are elements realized by a computer, and each block shows individual processing performed by this computer as a functional block.

Next, the contents of processing of the lattice point changing device 5 will be described. FIG. 13 is a flow chart showing a process of processing performed by the lattice point changing device 5. In FIG. 13, first, in step S101, the initial grid point of the array is selected from the initial image grid points arranged by the grid point arrangement device 4.
Next, in step S102, the coordinate value (x, y) of the selected grid point is read. Next, in step S103, the value of the first fractal grid which is the component of the vector field corresponding to the coordinate value (x, y) of the selected grid point is input and substituted into dx. Next, in step S104, the value of the second fractal grid which is the component of the vector field corresponding to the coordinate value (x, y) of the selected grid point is input and substituted into dy.

Next, in step S105, based on the coordinate value (x, y) of the selected grid point and dx, dy, the following equation 5 is calculated, and the coordinate value (x ', y ′) is updated as a new coordinate value of the selected grid point.

[Mathematical formula-see original document] x '= x + a * dx y' = y + b * dy where a and b are constants. The values of these constants a and b are
The magnitude and direction (positive or negative) of dx and dy given to the fluctuation of the coordinate value are determined. This constant is preset by the parameter input device 1.

Next, in step S106, it is judged whether or not all the grid points of the initial image grid points have been changed, and if there is a grid point that has not been changed, in the array of the initial image grid points, The grid point of the next array is selected, the process returns to step S102, and the above steps are repeated. Further, when the variation is applied to all the lattice points, the processing of the lattice point varying device 5 is finished. By the process shown in FIG. 13, the coordinate values (x, y) of all the grid points of the initial image grid points are new coordinate values (x ′, y ′).
Will be updated to As described above, the image grid points are a set of grid points having the updated coordinate values, and are unit grid points such that the boundary portions are continuously connected when a plurality of grid points are arranged on the plane.

The grid point connecting device 6 generates a composite grid point by arranging a plurality of such unit grid points, and at the same time, connects the grid points to neighboring grid points by line segments. Alternatively, an image in which a plurality of lattice images are arranged on a plane may be generated. Furthermore, after being converted into bitmap data by the raster image processor 7, this image can be printed by the output device 8.

[0054]

As described above, according to the present invention, since the generation processing can be automatically performed only by changing the parameter setting, the lattice size and the line width are changed, and the nonuniformity fluctuation is caused. Provided are a non-uniform grid-shaped printed matter, a method and a device for generating non-uniform grid-shaped data, the size of which is easy to change and the texture of fluctuation. According to the printed matter of the present invention, various design effects are expressed, and a joint portion having perfect alignment can be obtained. According to the non-uniform grid shape data generation method and the generation device of the present invention, it is easy to change the size and line width of the grid, the size of the fluctuation of the non-uniformity, and the texture of the fluctuation, and various It is possible to generate data having a design effect. In addition, a perfectly aligned joint can be obtained and unnatural appearance of the joint can be avoided.

[Brief description of drawings]

FIG. 1 is a diagram showing a state of a 0th stage for generating a two-dimensional fractal lattice.

FIG. 2 is a diagram showing a first stage state in which a two-dimensional fractal lattice is generated.

FIG. 3 is a diagram showing a basic structure of a two-dimensional fractal lattice.

FIG. 4 is a diagram showing a state in which a two-dimensional synthetic fractal lattice is formed by arranging a plurality of two-dimensional unit fractal lattices shown in FIG. 3 on a plane.

FIG. 5 is a diagram illustrating a basic principle of generating a repeatable two-dimensional unit fractal lattice in the present invention.

FIG. 6 is a diagram showing a state of the 0th stage for generating a repeatable two-dimensional unit fractal lattice.

FIG. 7 is a diagram showing a state of a first stage for generating a repeatable two-dimensional unit fractal lattice.

FIG. 8 is a diagram showing a second stage state in which a repeatable two-dimensional unit fractal lattice is generated.

FIG. 9 is a diagram showing another mode of forming a two-dimensional synthetic fractal lattice by arranging a plurality of the two-dimensional unit fractal lattices shown in FIG. 3 on a plane.

FIG. 10 is a diagram illustrating a basic principle of generating a repeatable two-dimensional unit fractal lattice when the arrangement is performed in the mode shown in FIG.

FIG. 11 is a flowchart showing a general procedure for generating a repeatable two-dimensional unit fractal lattice in the present invention.

FIG. 12 is a block diagram showing a basic configuration of a printed matter creating apparatus according to the present invention.

FIG. 13 is a flowchart showing a process of processing performed by the lattice point changing device.

FIG. 14 is a diagram showing an example of a non-uniform lattice lattice shape according to the present invention.

[Explanation of symbols]

 1 Parameter input device 2 Random number generator 3 Fractal grid generator 4 Lattice point arrangement device 5 Lattice point changing device 6 Lattice point connection device 7 Raster image processor 8 Output device

 ──────────────────────────────────────────────────続 き Continuation of the front page (72) Inventor Tetsuo Shinriki 1-1-1, Ichigaya-Kagacho, Shinjuku-ku, Tokyo Inside Dai Nippon Printing Co., Ltd. (72) Inventor Yu Okamoto 1-1-1, Ichigaga-cho, Shinjuku-ku, Tokyo No. 1 Inside Dai Nippon Printing Co., Ltd.

Claims (6)

[Claims] 1. A printed matter having a two-dimensional lattice shape pattern, wherein a vector value is given to each lattice point of the lattice shape based on a two-dimensional vector field having self-similar fluctuations, and each lattice point A new coordinate value is given to each grid point by calculating the coordinate value of each grid point on the basis of the vector value given to, and at each new grid point, between the grid points located in the vicinity. A printed matter characterized by having an expression of a non-uniform grid-shaped pattern obtained by connecting with a line segment. 2. The printed matter according to claim 1, wherein a matrix composed of grid points of the non-uniform grid shape pattern,
A shape formed by a set of grid points belonging to a specific row and / or column, and a grid point belonging to a row and / or column separated from the specific row and / or column by a predetermined number of rows and / or a predetermined number of columns. The shape of the set is the same, and a plurality of grid points belonging to the specific row and / or column and grid points belonging to the row and / or column separated by the predetermined number of rows are overlapped with each other to form an endless pattern. A printed material having an expression of a uniform lattice-shaped pattern. 3. A step of preparing a grid shape obtained by intersecting a plurality of straight lines parallel to each coordinate axis of the two-dimensional coordinate, a step of preparing a two-dimensional vector field having a self-similar fluctuation, and a grid shape. To each grid point obtained by intersecting the straight line of, the step of giving a vector value of the coordinates of the vector field corresponding to the coordinates of the respective grid points, and respectively based on the vector value given to each grid point Generating new coordinate values for each grid point by calculating the coordinate values of each grid point; and generating new grid points by replacing the coordinate values of each grid point with the new coordinate values. And a step of generating non-uniform grid shape data by connecting a line segment between adjacent grid points at each of the new grid points, the non-uniform grid shape data. Generation method. 4. The non-uniform grid shape data generation method according to claim 3, wherein the two-dimensional vector field having self-similar fluctuations is a vector field defined in a two-dimensional rectangular area, At the coordinates on the opposite vertical and / or right and left sides of the rectangular area of the field, the step of matching the vector values of the corresponding coordinates at the right and left and / or the vertical coordinates, and the straight line of the grid shape are obtained. Each of the grid points defined is a grid point defined in a two-dimensional rectangular area, and the coordinates on the opposite sides of the rectangular area of the grid point and / or on the two left and right sides are defined as the opposite sides of the rectangular area of the vector field. Of the coordinates of the vector field corresponding to the coordinates of all the grid points including the grid points on the two sides. Method of generating a non-uniform grid shape data, comprising the steps of partake a vector value. 5. A condition required for generating a two-dimensional vector field having self-similar fluctuations and a lattice shape obtained by intersecting a plurality of straight lines parallel to each coordinate axis of the two-dimensional coordinate are generated. Parameter input device for setting the conditions necessary to generate the new coordinate values and generating the new coordinate values for the grid points, and the random number generator for generating the random numbers used to add self-similar fluctuations. A device and a vector field generator for inputting the parameter of the vector field from a parameter input device, and a random number from the random number generator for generating a two-dimensional vector field having self-similar fluctuations; A grid point arrangement device that inputs the parameters of the grid shape from an input device and generates coordinates of all grid points, and a vector of the coordinates of the vector field corresponding to the coordinates of each grid point. Value is given to each grid point, and the coordinate value of each grid point is calculated based on the vector value given to each grid point according to the condition for generating a new coordinate value of the grid point. A grid point changing device that generates coordinate values and generates new grid points by replacing the coordinate values of the grid points with the new coordinate values, and is located near each of the new grid points. A grid point connecting device that connects grid points with a line segment to generate non-uniform grid shape data, and a non-uniform grid shape data generation device. 6. The non-uniform grid shape data generation device according to claim 5, wherein the two-dimensional vector field having self-similar fluctuations generated by the vector field generation device is a vector defined in a two-dimensional rectangular region. Field, the vector values of the corresponding coordinates in the left and right and / or the top and bottom of the rectangular area of the vector field on the opposite two sides of the top and bottom and / or the left and right are the same, and the grid point Each grid point obtained by intersecting the grid-shaped straight lines generated by the placement device is a grid point defined in a two-dimensional rectangular area, and the top and bottom facing the rectangular area of the grid point and / or the two left and right sides. The non-uniform grid shape data is generated by associating the coordinates on the sides with the coordinates on the opposite sides of the rectangular area of the vector field and / or the coordinates on the left and right sides. Generator heterogeneous lattice shape data, characterized in that.