JP3254659B2 - Pattern generation method and apparatus - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

The present invention relates to tiles, wallpapers,
The present invention relates to a method and an apparatus for generating a pattern of a building material, an interior material, and an exterior material to be continuously arranged on a plane such as a tile carpet.

[0002]

2. Description of the Related Art In industrial products such as tiles, it is important to provide a pattern in order to enhance the value of the product. By the way, when arranging tiles, if the pattern is continuous at the boundary between two adjacent tiles and the boundary is not visible, the viewer will not be conscious of each tile, so it can be seen as a smooth pattern over the whole . Also, simply arranging tiles with the same pattern (basic tile pattern) in the same direction will cause the same pattern habit to appear repeatedly at each tile interval. If the patterns can be connected at the boundary even when they are pasted or when a small number of tiles with different patterns are pasted, the whole pattern can be regarded as one and the aesthetic appearance can be increased.

Further, a plurality of types of tiles having a continuous pattern extending over the boundary between adjacent tiles and having different patterns in the side areas of the tiles are prepared. If these can be randomly combined and arranged on a plane, they are arranged. This is preferable in increasing the variety of tile patterns. However, it is difficult to generate a plurality of patterns that are continuous at a boundary, except for a simple geometric pattern or an approximate pattern created manually. Moreover, even if it can be generated, there are only about two types, and since the boundaries of the tiles can be easily understood, at least about four types of basic tile patterns having different inner patterns of the tiles are required. However, preparing a plurality of tiles has problems in terms of mass production effect of production cost, distribution cost, complexity of handling, and the like.

[0004]

SUMMARY OF THE INVENTION An object of the present invention is to solve the above-mentioned problem, and to automatically generate a tile pattern whose pattern is continuous at a boundary even if the tiles are connected and arranged at arbitrary sides that can be adjacent to each other. And an apparatus. Another object of the present invention is that the density of the pattern elements is substantially uniform in the boundary area of the arranged tiles and the area inside the tiles.
Accordingly, it is an object to provide a method and apparatus for automatically generating a tile pattern that reduces the individual presence of a tile.
It is another object of the present invention to provide a method and an apparatus that can generate a different tile pattern that is continuous at a boundary with the generated tile pattern.

[0005]

According to a first aspect of the present invention, a polygon having at least two axes of symmetry such that a pattern is continuous at a boundary when tiles are sequentially arranged adjacent to each other. A method of writing pixel values of a pattern in a tile area pixel by pixel, including the following steps: (a) writing pixel values of a pattern pixel by pixel in the tile area; (C) If the pixel written in step (b) is adjacent to any of the sides, it is determined whether or not the pixel is adjacent to any of the sides of the polygon. Determine the position of the pixel adjacent to the writing pixel on the polygonal area, determine the position of the adjacent pixel when the adjacent polygon is overlapped with the tile area as a shift position of the adjacent pixel, (d) The position of the write pixel and the shift position are Around the center of the square according to the connection direction of the condition of the tile is rotated by a predetermined angle by at least one obtains the rotational position, writes the pixel value (e) the shift position and the rotational position.

According to a second aspect of the present invention, there is provided a method for generating a tile pattern by repeatedly writing a predetermined pattern element in a polygonal tile area, and forming a square including the pattern element in advance in a stamp area. When the stamp area is placed, the stamp area always crosses the boundary of the tile area, and when the stamp area is placed, the stamp area does not straddle the boundary. Defining an inner region within the tile region, the method includes the steps of: (a) randomly generating a center position of the stamp region within the tile region; It is determined whether the designated stamp area is in the boundary area or the inner area. (C) If the stamp area is in the inner area, the finger of the stamp area is determined. (D) If the stamp area is within the boundary area, the part protruding from the boundary of the pattern element into the adjacent polygon area, and the adjacent polygon area into the tile area The pattern element that shifts to a position on the tile area when overlaid on the tile, and that does not protrude from the boundary of the pattern element that straddles the boundary and the shifted part are divided according to the connection condition of the tile. At least one predetermined angle around the center of the area
Additional writing is performed at the rotated position. (E) When the additional writing is performed, additional writing is performed at least once in the inner area.

According to a third aspect of the present invention, the second aspect
In view of the above, the number of additional writes to the inner region may be determined so that the density of the pattern elements in the boundary region is substantially equal to the density of the pattern elements in the inner region. According to a fourth aspect of the present invention, in the second aspect, the orientation of the pattern element is changed every time the pattern element is written, irrespective of any of the steps (c), (d), and (e). The polygon tile may be rotated by an angle corresponding to a predetermined possible connection direction.

According to a fifth aspect of the present invention, the second aspect
In view of the above, at the time of generating the first tile pattern, the step (b) includes a step of writing the write position of the stamp area determined to straddle the boundary into the memory means, and the generation of the second tile pattern is performed as follows. (F) reading the writing position from the memory means; (g) writing the pattern element at the read writing position in the boundary area; (h) area ratio of the inner area to the boundary area Is S _I / S _B , the center position of the stamp area is randomly generated in the inner area with the number of writing times of about S _I / S _B times the number of writing to the boundary area in step (g). Then, the pattern element is written at that position.

According to a sixth aspect of the present invention, the fifth aspect is provided.
In view of the above, the writing in the step (g) and the writing in the step (h) are mixed and executed.
According to the seventh aspect of the present invention, the pixel value of the pattern is written for each pixel in the polygon tile area so that the pattern is continuous at the boundary when the tiles are sequentially arranged adjacent to each other to generate the pattern. The pattern data source means; coordinate address generating means for specifying a position where the pattern data from the pattern data source means is to be written into the polygon area for each pixel; Determining means for determining whether or not the pixel is adjacent to any side of the polygonal area; and, if the written pixel is adjacent to any of the sides, the determination is made on an adjacent polygonal area adjacent to the side. The position of a pixel adjacent to the writing pixel is obtained, and the position of the adjacent pixel when the adjacent polygon is overlapped with the tile area is obtained as a shift position of the adjacent pixel. Position rotating means for rotating the shift position at least once about a center of the polygon by a predetermined angle to obtain a rotation position, and additional writing means for additionally writing the pixel value at the shift position and the rotation position .

According to an eighth aspect of the present invention, there is provided an apparatus for generating a tile pattern by repeatedly writing a predetermined pattern element in a polygonal tile area, and forming a square including the pattern element in a stamp area in advance. When the stamp area is placed, the stamp area always crosses the boundary of the tile area, and when the stamp area is placed, the stamp area does not straddle the boundary. An inner area is defined in the tile area, and the apparatus includes: a pattern element source means for outputting the pattern element; and a center position of the stamp area for specifying a position for writing the pattern element in the square area. Means for randomly generating center coordinates in the tile area, and whether the stamp area whose position is designated by the center position is within the boundary area. Or, in response to a result of the determination by the area determining means, the pattern element is written at a designated position of the stamp area if the stamp area is within the inner area. When the stamp area is within the boundary area, a portion of the pattern element that protrudes from the boundary into the adjacent polygon area is displayed on the tile area when the adjacent polygon area is superimposed on the tile area. A portion that does not protrude from the boundary of the pattern element that is shifted to a position and straddles the boundary and the shifted portion are at least once a predetermined angle around the center of the tile area according to the connection condition of the tile. Additional writing is performed at the rotated position.
Writing means for additionally writing at least once in the inner area.

According to the first and nineteenth aspects of the present invention, when writing occurs in a pixel adjacent to the boundary, the corresponding tile of the own tile is connected to adjacent pixels on all sides where the connection of the adjacent tile is predicted. Since writing is performed on the pixel at the position, continuity at the boundary of the tile pattern is guaranteed. Claims 6 and 2
According to the second aspect of the present invention, when additional pattern elements are written in the boundary area in order to ensure continuity of the pattern elements across the boundary, the pattern elements are additionally written also in the inner area, so that the density of the pattern elements is uniform. Performance can be improved.

According to the twelfth, thirteenth, and twenty- third aspects of the present invention, the pattern density of the inner region and the boundary region can be made equal by controlling the number of times of writing. According to the fourteenth and twenty-fourth aspects of the present invention, even if the pattern element has directionality, the direction of the pattern is changed for each writing, so that the pattern is changed over the tile boundary area and the inner area. The directions are dispersed and the individual tiles are less conscious.

According to the fifteenth and twenty-fifth aspects of the present invention, the writing position in the boundary area stored in the memory when the original tile pattern is generated is read out when the second tile pattern is generated, and the writing is performed at the same position in the boundary area. Since writing is performed at random positions in the inner area, a second tile pattern that is continuous with the original tile pattern and different from the original tile pattern can be generated.

[0014] Claim 16, 17, 18, according to the 26 and 27 invention, with respect to the inner region and the boundary region at the time of generation of the second tile pattern according to claim 15 and 25, the writing alternates its area ratio Therefore, a pattern in which the boundary area is not conscious even when writing in which the exchange rule is not satisfied can be generated.

[0015]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS For the sake of simplicity, when a square tile is arranged in a matrix, a basic principle is described in which a pattern of an arbitrary tile always generates a pattern that is always continuous with a pattern of tiles adjacent to the top, bottom, left and right of the tile. I do. Generally, a rectangle includes a square. One side adjacent the T _a and T _b of square W as shown in FIG. 1A, it is assumed that the pattern contains a line portion L for continuous across the boundary B is depicted. The most close to each other pixel P _a across the boundary B on the curve portion L, and the coordinates of P _b, respectively (x _a, y _a), and (x _b, y _b). To the pixel P _a tile T _a, for adjacent tiles T _b throat pixel P _b that one side is adjacent the continuous also the pixel P _a and is present in the tile P _b 90 °,
180 °, when rotating 270 degrees, there must be a pixel P _b1, P _b2, P _b3 matching position of P _b. Tiles T _a in order to reverse the tile T _b of the pixel P _b to the tile T _a pixel P _a to be one side of the throat are adjacent contiguous to the pixel P _b is present
90 °, 180 °, when rotating 270 degrees, there must be a pixel P _a1, P _a2, P _a3 matches the position of P _a. To satisfy these two conditions in any two tiles, pixel T _a which satisfies the above two conditions the four sides on the same square superimposed tiles T _a and T _b, T _a1, T _a2 ,
It suffices that T _a3 , T _b , T _b1 , T _b2 , and T _b3 exist. From this, even if two tiles arbitrarily selected are made adjacent to each other on an arbitrary side, the generation of the pattern of each tile such that the pattern crossing the boundary is continuous may be performed as follows.

[0016] (a) in a sequential writing process the pixel value to a pixel position for forming a pattern on the tile, a position adjacent to one of the sides of the tile as shown in FIG. 1B (x _a, y _a) pixel value If the writing has occurred, the position of the pixel P _b that is adjacent to the pixel P _a on the tile T _b to assume adjacent to the side (x _b,
y _b ). the position of the pixel P _b when superimposed on the tile T _a (b) to adjacent tiles T _b as described above assuming shifted to an adjacent direction
P _b ′ is obtained, for example, as in the case of FIG. 1B (x _b -w, y _b ).

[0017] (c) the center O of the tile T _a, as shown in FIG. 1C
_C coordinates (X _c, Y _c) centered on the pixel P _a and P _b 'and 90 ° for 18
Pixels P _a , P _a1 , P _a2 , when rotated by 0 ° and 270 °, respectively
The positions of P _a3 , P _b ′, P _b1 ′, P _b2 ′, and P _b4 ′ are determined, and the pixel values are written to the determined pixel positions. Such processing is performed when _a pixel Pa adjacent to the boundary occurs.
According to (a), (b), and (c), additional writing is performed on the pixel adjacent to the boundary, and a tile obtained by generating a pattern extending from these pixels adjacent to the boundary is a tile that is adjacent to the tile. Is continuous.

In the above description, the case of a square tile has been described. However, in the case of a rectangular tile having adjacent pieces having different lengths, the angle to be rotated in the above step (c) may be only 180 °. The tiles and one end O _X center 90 ° counterclockwise rotation tiles T _b in the adjacent sides in FIG. 1B instead overlap to translate the adjacent tiles T _b is, for example, step (b) when a square tile T superimposed over _a, it may obtain the position of the pixel P _b "at that time.

The same principle can be applied to regular triangles and regular hexagons. Figure 2 is a case of applying an equilateral triangle, connection direction of tile 0 °, 120 °, if so it is possible to 240 °, for example the pixel P _a which is adjacent to one side of the triangle T _a occurs, adjacent triangles pixel P _b that is adjacent to the pixel P _a on T _b
Seek position, the pixel P _b 'superimposed on the triangle T _a rotating 60 degrees left triangle T _b around the end O _X sides adjacent
Find the position of Then a triangle T _a around its center O _C
By rotating by 120 ° and 240 °, P _a1 , P _a2 , and P _b1 ′, P _b2 ′ can be obtained.

FIG. 3 shows a pixel A generated so as to satisfy the pattern continuity condition at the boundary shown in FIG. 2 when the triangle tiles are laid on a plane, and a pixel B adjacent to the pixel A across the boundary. FIG. 4 shows writing of a pattern that guarantees continuity of the pattern at the boundary of the tile when the regular hexagon tiles are laid on a plane. If there is a write to a pixel P _a which is adjacent to the boundary of the tile T _a, in this example, determine the coordinates of the pixel P _b on adjacent tiles T _b which sandwich the boundary around the one end O _X of the boundary edges obtaining the position coordinates of P _b 'on the tile T _a of the rotated pixel P _b when superimposed on the tile T _a and the tile T _b is 120 ° clockwise. Tile connection direction is 0 °, 60
°, 120 °, 180 °, 240 °, 300 ° are possible, so tile
T _a 60 °, 120 °, 180 °, seek 240 °, 300 ° sequential coordinates of the rotated pixel P _a time (expressed in A) and P _b '(represented by B), their coordinate positions Write a value to the pixel. Even if the side of the tile obtained in this way is adjacent to any side of another tile formed in the same manner, the continuity of the pattern at the boundary is ensured.

In the above description, the pattern continuity condition when the tile is a regular polygon has been described. However, even if the tile is a rectangle having sides of different lengths, for example, the tiles are connected by the sides of the same length as the adjacent tiles. If the condition of the connection direction of the tile is determined as follows, the angle according to the connection direction, that is, 1 for rectangular
What is necessary is just to perform additional writing in the position rotated by 80 degrees. In general, when writing to a pixel adjacent to a boundary occurs as a pattern continuation condition of a desired polygonal tile having at least two axes of symmetry, the pixel and its own tile corresponding to the pixel of the adjacent tile continuous thereto May be additionally written at a position rotated by an angle corresponding to the condition of the connection direction of the tile.

Next, an apparatus for drawing a circle, for example, on a large number of tiles, which is predetermined by applying the above-described method of the present invention, is shown in FIG.
This will be described with reference to FIG. It is assumed that a square tile having a side of W is defined on the coordinate systems X and Y shown in FIG. 6A. In this embodiment, the position of the pattern element to be written on the tile is randomly generated as the center coordinates ( _Xc , _Yc ) of the element, and the generated center coordinates ( _Xc , _Yc ) are used as a center in FIG.
A circle of radius R shown in B is written on the tile. Here, it is assumed that the data to be written to the tile is written to the pattern data memory 18.

Each pixel value on one circle (referred to as a pattern element) having a radius R shown in FIG. 6B is previously written in the element memory 11 at an address corresponding to the coordinates (x, y) of the pixel. . Each time the center coordinate generation unit 13 generates one center coordinate (X _c , Y _c ) of a pattern element to be written, the address generation unit 12 generates a square area R _{S including} the pattern element C in the element memory 11.
Sequentially generate all addresses (x, y). Central coordinate generator 1
3 is the center coordinates (X _c , X _c) within the range of 0 ≦ X _c ≦ W and 0 ≦ Y _c ≦ W
Y _c ) is generated randomly. The coordinate synthesizing unit 14 synthesizes the read address (x, y) generated by the address generation unit 12 and the center coordinates ( _Xc , _Yc ) from the center coordinate generation unit 13, and generates synthesized coordinates (x + _Xc , y + _Yc ). Is output. Circle C in this embodiment is a pattern element to be written in the tile T _a, as shown in FIG. 6A
If is located on the tile boundary, writes arc portion C _b which goes out of the tile T _a is the tiles so as to be continuous on adjacent tiles at the boundary. Its domain converter 15 for the calculation _{X = (x + X c)} modW, Y = (y + Y c) perform ModW, coordinates of each pixel on the arc portion C _b to out of the tile T _a, as shown in FIG. 6A X = (x + X _c ) mod W = x + X _c −W, Y = (y
+ Is converted to _{Y c) modW = y + Y} c -W. Area determination unit 16
From the radius R and the center coordinates of the circle, it is determined whether the circle C is on the boundary (or any of the four sides) of the tile T _a. That _{W-X c <R, W} -Y c < if least be satisfied one of the R, the circle is determined to be on the boundary. Coordinate rotation unit 17
When the circle C is not on the boundary according to the judgment of the area judging unit 16, the given coordinate (X, Y) is read as an address from the memory 11 using the coordinates (x, y) in the pattern data memory 18. Write the pixel value. However, when the pixel value is 0, writing is not performed. When it is determined that the circle C is on the boundary, the coordinate rotating unit 17 stores the pixel value read from the address (x, y) of the memory 11 in the same manner as described above, using the composite coordinates (X, Y) as an address. 18 and the coordinates (X ₁ , X ₁ , Y 2) rotated by 90 °, 180 °, and 270 °.
Y ₁ ), (X ₂ , Y ₂ ), (X ₃ , Y ₃ ) are calculated, and the same pixel value as above is written to the memory 18 using them as addresses (when the pixel value is 0, no writing is performed). .

The above processing is performed by the square area R _{S of the} element memory 11.
Is executed for all the addresses (x, y) to be scanned, the pattern generation for one center coordinate generated by the center coordinate generation unit 18 is completed, and then a new center coordinate is randomly generated, and the same processing is repeated. . As shown in FIG. 6C, one complete circle C ₀ is written in the memory 18 for the center coordinate determined by the area determination unit 16 as not being on the boundary, but the circle is on the boundary. For the center coordinates determined as, two arcs C _a and C _b divided by the boundary and arcs C _a1 and C _b1 obtained by rotating them, C _a2 , C _b2 ; C
_{The set of a3} and _Cb3 is written to the data memory 18. As is clear from FIG. 6C, the tile having the pattern generated in this way has a continuous pattern regardless of which side of the tile is in contact with a similar tile.

The conversion unit 15 shown in FIG. 5 shows a case where a portion of a pattern element protruding from one side of a tile is written by performing a modulo operation so that the side is parallel-shifted to the opposite side. As explained in
The portion that protrudes around one end of the side where the pattern protrudes may be shifted by 90 ° around the one end to move into the tile. In that case is converted to C _b3 in Figure 6C the arc portion C _b which protrudes from one side of the tile T _a in FIG. 6A for example centered on 90 ° counterclockwise rotation of the O _X. This transformation, the coordinates of the pixels of the run-off pattern from the tile (X, Y) coordinate that is rotated 90 degrees around the O _x When becomes (WY, XW).

The procedure for generating a tile pattern by the apparatus shown in FIG. 5 is shown in the flowchart of FIG. First, to set the total number of occurrences N of the center coordinates at step S1, the rotation flag F _C is set to 0, then generating center coordinate in the step S2 (X _C, Y _C) to random. In step S3, the current occurrence number n is incremented by one, and in step S4, it is determined whether or not the pattern element crosses the boundary. If it does not cross the boundary, the read address (x,
y) is generated, and the corresponding pixel value is read from the pattern element memory 11. In step S6, the address (x, y) and the center coordinates
(X _C , Y _C ) and the coordinates X = x + X _C , Y = y + Y _C are synthesized, and in step S7, the synthesized memory is used as an address with the synthesized coordinates as an address.
Is written in step S5. In step S8, reading has been completed for all addresses (x, y), but it is checked. If not, steps S5, S6,
S7 is repeated. When reading has been completed for all addresses, it is determined in step S9 whether the number n of occurrences of center coordinates has reached N. If not, the process returns to step S2, and if so, the process ends.

If it is determined in step S4 that the pattern element straddles the boundary, the read address (x,
generating a y), read out the pixel values from the pattern element memory 11, the address in step 11 (x, y) and the center coordinates (X _C, Y _C)
Are combined, and a remainder operation modulo W is performed on the combined address (x + X _C , y + Y _C ), thereby obtaining coordinates (X, Y).
Step S12 in the coordinate (X, Y) are 0 ° if the rotation flag F _C is 0,1,2,3 hand, 90 °, 180 °, 270
The rotation of ゜ is given to the coordinates (X ′, Y ′), and the pixel values read in the step 10 are written to the data memory 18 using the coordinates (X ′, Y ′) as addresses in step S13. Step S14
It is checked whether reading has been completed for all addresses (x, y), and if not, steps S10 to S13 are repeated. All addresses (x, y) is checked whether the flag F _C becomes 3 in step S15 if the completed reading the flag in step S16 if not become F _C
, And returns to step S10. If the flag F _C is reached 3 at step S15, resets the flag F _C to 0 in step S17, the procedure proceeds to step S9.

In the embodiment described with reference to FIGS. 5, 6A, 6B and 6C, the coordinate rotating unit 17 sets the composite coordinates (X, Y) to 0.
In the case where each of the pattern elements is rotated by {, 90}, 180 °, and 270 ° to be a write address to the pattern data memory 18, the pattern element itself written to the memory 18 is also set to 0.
゜, 90 ゜, 180 ゜, 270 ゜. To achieve a similar result, the center coordinates (X _C , Y _C ) are set to 0.
゜, 90 ゜, 180 ゜, and 270 ゜, respectively, and the addresses (x, y) to be combined with the rotated center coordinates are 0 ゜, 90 を
It is also possible to rotate {180} and 270 ° respectively (that is, rotate the pattern), and combine these rotated center coordinates and addresses.

That is, as shown in FIG. 8, for example, instead of the coordinate rotating unit 17 in FIG. 5, a central coordinate rotating unit 17A for rotating the central coordinate and an address rotating unit 17B for rotating the address are separately provided to determine the area. When the pattern element C to be written is determined to cross the boundary by the unit 16, the center coordinate rotating unit 17A sets the center coordinates (X _C , Y _C ) to the center O of the tile.
Rotate 90 ° around _C , for example, as shown in FIG.
(X _C ′, Y _C ′), and the address (x, y) to be combined with the rotation center coordinate is rotated by 90 ° by the address rotation unit 17B, and FIG.
The memory 18 is rotated 90 ° from the position indicated by the broken line.
May be written at a position centered on the rotation center coordinates (X _C ′, Y _C ′). The same applies to other rotation angles of 0 °, 180 °, and 270 °.

In this case, the procedure for generating the tile pattern simply needs to change steps S11 and S12 in FIG. 7 to FIG. That is, as shown in FIG. 10, in step S11, the address (x, y) is rotated by an angle corresponding to the value of the flag F _C to (x ′, y ′), and the center coordinates (X _C , Y _C ) To the flag F
_By rotating by an angle corresponding to the value of _C to (X _C ′, Y _C ′), these composite coordinates X = x ′ + X _C ′, Y = y ′ + Y _C ′ are obtained. However,
Flag F _C each rotation angle of 0 ° when the 0,1,2,3, 90 °, 180 ° and 270 °. Next, step S1
In step 2, the remainder operation modulo W is performed on the combined coordinates X and Y, and the obtained remainders X ′ and Y ′ are used as addresses, and the process proceeds to step S13 in FIG.

FIG. 11A shows a tile pattern generated by writing a black circle as a pattern element in a square area (tile area) using the method described in FIG. 5 or 8. When these tiles are arranged, the pattern continues at the boundary as shown in FIG. 11B. By the way, according to the method described with reference to FIGS. 5 and 8, when a black circle to be written takes a change in one tile, three black circles are additionally written in order to guarantee the continuity of the pattern at the boundary. When the center coordinates of the black circles are generated randomly, the density of the black circles increases along the boundary. Therefore, FIG.
As the number of black circles in 1A increases, the black circles concentrate around the boundaries of the tiles arranged as shown in FIG. 12A, resulting in an unnatural border pattern near the boundaries.

The number of times of additional writing depends on the connection condition of the tile. For example, under the connection condition where the pattern is continuous at the boundary when tiles are uniquely determined and arranged, no problem occurs because additional writing is not required, but the pattern is continuous at the boundary even if tiles are rotated by 180 ° The number of additional writes is 1 under the connection condition, and the number of additional writes is 3 under the connection condition where the pattern is continuous at the boundary even if the tiles are rotated 90 °, 180 °, and 270 °.

Therefore, the tile pattern is improved by additionally writing the pattern in the inner region so that the writing density in the boundary region where the pattern extends over the boundary and the writing density in the inner region where the pattern does not extend over the boundary are close. The generation method will be described below. The basic configuration of the pattern generating apparatus that performs this method is the same as that shown in FIG. 5 or 8, and therefore, will be described with reference to FIG. In the element memory 11, a desired pattern element C,
For example, it is assumed that an elliptical pattern element C having a major axis D in the x direction as shown in FIG. 13A is stored in advance. A square region R _S (which will be referred to as a stamp region) containing the pattern element is defined. Defining a square tile having a width W as shown in FIG. 13B, further, the inner area R _I was D / 2 retract from the sides of the tile inwardly, predefining the outer boundary region R _B.

[0034] Thus, the center coordinates (X _c of the stamp area R _S,
If Y _c ) is inside the inner area R _I , the stamp area R _I does not go out of the side of the tile, so the pattern element C does not go out of the tile boundary, but the center coordinates (X _c , Y _c ) are When the boundary area R in _B part of the stamp area R _S falls outside of the boundary. In the latter case, if the pattern element C is a circle inscribed in the square stamp region R _S , a part of the circle will always go outside the boundary, but as shown in FIG. Is used, the center coordinates (X _c ,
Even Y _c) is in the on boundary area R _B, is that the element C is not out of the tile. Even in such a case, the center coordinates generated by the center coordinate generating section 13 in this embodiment is determined by the region determining unit 16 to be in the boundary area R in _B,
As long as a part of the stamp area R _S is outside the tile, the processing that satisfies the above-described pattern continuity condition at the boundary is executed. That is, in the conversion unit 15, the divided stamp area portion divided at the boundary and projected to the adjacent tile area in the same manner as in the case of FIG. the on the tile T _a, transferred by writing the pixel values in the divided stamp area R _S in the data memory 18, a further 90 ° to the divided stamp area R _S,
The pixel values in the divided stamp area are written to the data memory at positions sequentially rotated by 180 ° and 270 °.

Even if a part of the stamp area R _S is outside, the element C is not divided unless the pattern element C in it is outside. Therefore, the center coordinates (X
_c , Y _c ), writing element C to memory 18 and moving element C 90 °, 180 °, 270 around the center of the tile.
(4) Additional writing of the element C to the memory 18 at each rotated position is performed. Although these additional writes do not contribute to the continuity of the pattern at the tile boundaries, they do not have any particular visual adverse effect. In addition, there is the convenience that the unified processing can be performed by defining the square including the pattern element. Embodiment differs from the embodiment of Figure 5, with respect to the additional write of three elements of the boundary region R _B by such rotation, at least one or more, the pattern elements C here the same number (three) the center coordinates (X _c, Y _c) is able to add writing to be within the inner area R _I. For this purpose, the center coordinate generation unit 13 determines the center coordinates (X _c, Y _c ) limited to the inside region R _I after or before additional writing to the boundary region or alternately based on the determination of the region determination unit 16. Randomly generated inside area R _I
Add the writing of the pattern inside.

FIG. 14 shows a flowchart of the above-described pattern generation method. In step S2, the number of center coordinates generated is set to N,
The area flag F _B and the rotation flag F _C are set to 0 in advance. In step S1, the center coordinates (X) satisfying W> X _c > 0 and W> Y _c > 0 in the tile area by the center coordinate generation unit 13.
_c, Y _c ) are generated randomly, and the number n is set to 1 in step S3.
In step S4, the center coordinates ( _{Xc, Yc} ) are shown in FIG.
Determining whether the inner area R or boundary region is within the _I R _B of B, determines that if it is within the boundary area R _B stamp area R _S spans border, area flag F in step S5 Set _B to 1. Address read in step S6 if it is within the inner area R _I (x, y) generates and reads the pixel value from the element memory 11. In step S7, the coordinates (X, Y) at which the pixel value is to be written are synthesized by the coordinate synthesizing unit 14,
In step S8, the pixel value is written to the pattern data memory 18. However, when the pixel value is 0, writing is not performed because the address (x, y) is not on the pattern. All addresses (x, y) of the component memory 11 in step S9 determines whether generated on has finished, repeat steps S6~S9 until the end of one pattern element is written in the inner area R _I. Next area flag F _B is determined whether or not 1 at step S10, again the center coordinates back to not 1 step S2
(X _c , Y _c ) is generated, n is incremented in step S3, and the stamp area R _S containing the pattern to be written is written in step S4.
Is determined on the boundary. If on the boundary is set to 1 to flag F _B in step S5, step S11
Generates a read address (x, y) and reads out a pixel value from the element memory 11. Since F _B = 1, a part of the stamp area R _{S to} be written is outside the tile boundary.
The composite coordinates (x + _Xc , y + _Yc ) are shifted by the length W of one side of the tile to convert the composite coordinates onto the tile.

Next, in step S13, it is detected whether the value of the rotation flag F _C is 0, 1, 2, or 3, and F _C =
If 0, the transformed coordinates (X, Y) obtained in step S12 are represented by X
← X, Y ← Y (0 ° rotation), and if F _C = 1, X ← W−
Y, Y ← X (90 ° rotation), and if F _C = 2, X ← W−
X, Y ← WY (180 ° rotation), and if F _C = 3, X ←
Y, Y ← WX (270 ° rotation), and the address (X, Y) is obtained by any of these conversions. In step S14, the pixel value read in step S11 is written to the data memory 18 by using this address.
It is determined that the generation of all addresses (x, y) has been completed. Steps S11 to S15 until generation of all addresses is completed.
Is repeated, and if the end of generation of all addresses is detected in step S15, it is determined in step S16 whether or not F _C = 3. If not, the value of the rotation flag F _C is incremented by 1 in step S17, and Steps S11 to S15
Execute

When these operations are completed, in step S18, the center coordinates (X _c , Y _c ) are randomly selected in the inner region R _I of FIG. 13B.
Was generated, repeat steps S6 to S9, the write pixel values read for all addresses in the same manner as described above in the data memory, the F _B = 1 is detected at step S10, the rotation flag by 1 in step S19 It subtracted, again returns to step S18 if not become F _C is 0 at step S20, a series of steps until F _C becomes 0 S1
8, S6 to S10, S19 and 20 are repeated. This three pattern elements C are added to the inner area R _I. If F _C = 1 is detected in step S20, step S2
1 in the flag F _B is reset to 0, the number of occurrences n in step S22, it is checked whether becomes N, it have unless the same processing as described above returns to the step S2 is repeated a desired number of times.

Although the case where an ellipse is written as the pattern element C has been described above, when the black circles described with reference to FIGS. 11A, 11B and 12A are written, tiles to which the method of FIG. Thus, the pattern is continuous at the boundary of the tile. In addition, since the effect of pattern elements being concentrated along the boundary is reduced, the presence of individual tiles is reduced. The number of pattern elements to be added to the inner area R _I was the same as the number of pattern elements added to the boundary area R _B, not necessarily the same, depending on the number of pattern elements to be added to the boundary area R _B You may decide. FIG. 14 illustrates the case where a square tile is used and each side can be continuously connected to any side of the adjacent tile in a pattern. If continuous connection is possible, only one pattern element rotated by 180 ° is added if the pattern element straddles the boundary.
The rotations of 0 ° and 270 ° are omitted, and the rotation of 180 ° is performed. In the determination in step S16, it is determined whether or not F _C = 1. Also, since only one pattern element is added to the inner area, steps S19 and S20 are omitted. In this case, the tile may be any rectangle, including a square.

Next, an example of a tile pattern generated by using a shape having a directionality such as a wedge as a pattern element and writing it into a tile area using the method described with reference to FIG. 14 is shown in FIG.
It is shown in FIG. When arranging this tile, tile boundaries as shown in FIG. 15B although pattern leads to continuous, a statistical near the boundary to the different distribution of the orientations of the pattern elements in the tile boundary region R _B and the inner area R _I An unnatural border pattern occurs.

This is because, in the above-described embodiment, the writing center coordinates (Xc, Yc) of the pattern element are set in the inner region R of the tile.
If within _I always whereas writing the pattern elements in a certain direction, when the center coordinate is in the boundary area R _B is
This is because a pattern rotated by 180 ° or rotated by 90 °, 180 °, or 270 ° is written. To solve this problem,
May write a pattern element having a center coordinate in the inner area R _I, alternating 0 ° 180 ° rotation in response to the pattern continuous conditions used, or 0, 90, 180, rotated 270 ° May be sequentially switched to perform writing. An embodiment based on such a concept will be described with reference to FIGS.

The continuous pattern generation device shown in FIG. 16 is different from the device shown in FIG. Instead, the pattern element is written to the temporary memory 21 in the designated rotation direction,
Read an element from the temporary memory 21, for each writing element inside the region R _I tiles, the address converter 19
, The read address is converted, thereby changing the rotation direction of the element of the temporary memory 21 to rewrite.

More specifically, in this embodiment, similarly to the above, a predetermined pattern element is stored in the pattern element memory 11, and a square stamp area including the pattern element is defined. The address generator 12 sequentially generates a series of addresses (x, y) for all pixels in the stamp area. At the start of the operation, the address from the address generation unit 12 is directly supplied to the element memory 11 through the address conversion unit 19 and read out, and the read pixel value of the element is written to the corresponding address in the temporary memory 21. (FIG. 17, step S2). Center coordinate generating section 13 generates the center coordinates (X _c, Y _c) in the same manner tile regions that shown in FIG. 13B a random (step S3), and the area determining portion 16 that the central coordinate boundary area R on _B It is determined whether or not the stamp area straddles the boundary based on whether the stamp area is on the inner area RI (step S5). If it does not extend over the boundary, the address (x, y) is generated from the address generator 12 and given to the temporary memory 21 to read out the pixel value (step S7).
In step 4, the address (x, y) is synthesized with the center coordinates (X _C , Y _C ) (step S8).

The composite coordinates (X, Y) are represented by a tile area (W × W)
Therefore, the conversion unit 15 is not converted and is not rotated by the coordinate rotation unit 17 and is provided to the pattern data memory 18 as it is, and the pixel value from the temporary memory 21 is written to the data memory 18 (step S9). . However, when the pixel value is 0, writing is not performed. When the above reading and writing are completed for all addresses in the stamp area (step S10), the address generation unit 12 sequentially generates all addresses (x, y) for rewriting the temporary memory 21, and the address conversion unit 19 generates the addresses. (x, y) is rotated by 90 ° and given as a read address to the pattern element memory 11 as (-y, x),
By sequentially writing the read pixel values into the addresses (x, y) of the temporary memory 21, the pattern elements rotated by 90 ° are written in the temporary memory (step S11). Accordingly, then when writing a pattern element having a center coordinate in the inside area R _I in the data memory 18, will be 90 ° rotated pattern elements from the temporary memory 21 is written, after the writing, FIG. 17 In step S11, the pattern element memory 1
One pattern element is rotated 180 ° and rewritten in the temporary memory 21. Therefore, in the address conversion unit 19, the address (x, y)
To (-x, -y). More after then writing to the inner area R _I, performs rewriting the pattern elements of the temporary memory 21 to 270 ° rotated pattern elements. The read address (x, y) in the memory 11 at that time is converted to (y, -x). Hereinafter, similarly, rewriting of the memory 21 with the elements rotated by 0 °, 90 °, 180 °, and 270 ° is repeated.

The generated center coordinates (X _C , Y _C ) correspond to the boundary region R
_B is determined by the area determination unit 16 to be within
_B is set to 1 (step S6), and the coordinates X = x + X _C , Y = composed by the coordinate composition unit 14 as in the embodiment of FIG.
The portion outside of the y + Y _C tile is translated into the tile by remainder operation (step S14), and the combined coordinates are rotated by 0 °, 90 °, 180 °, and 270 ° around the center of the tile, respectively. Thus, the pattern element is rotated by 0 °, 90 °, 180 °, and 270 ° and written into the pattern data memory 18 (steps S13 to S13).
S19). When the stamp area straddles the boundary, the pattern is written by rotating the pattern by 0 °, 90 °, 180 °, and 270 ° so as to satisfy the boundary continuation condition in steps S13 to S19. and write pattern which centered coordinates in the inner area R _I by S11 0 °, 90
゜, 180 ゜, and 270 毎 are changed every time writing is performed. For example, when a plurality of tiles are arranged as shown in FIG. 15C, the direction of the pattern element written in the boundary area and the inner area is 0.
゜, 90 ゜, 180 ゜, 270 ゜ are almost uniformly dispersed.

In the embodiment shown in FIGS. 16 and 17, the case where the pattern continuity condition is satisfied even when each side of the square tile is adjacent to any side of the other tile has been described. It is easily understood that it is also possible to make only two opposing sides (0 ° and 180 °) of the same length of another tile continuous with each side of the tile. FIG.
In the embodiment of the present invention, in order to combine a plurality of types of tile patterns satisfying the pattern continuity condition at the boundary, the region determination unit 16
Is provided with a coordinate memory 16M indicated by a broken line, and at the time of generating the first tile pattern,
A center coordinate storage step S4a indicated by a broken line is provided on the YES side. In the first tile pattern generation, the center coordinate generation unit 1
3 is the center coordinates (X _C ,
Y _C) each time is determined to be on the boundary region R _B by the region determining unit 16 (step S4 in FIG. 7), center coordinate generating section 13 the center coordinates (X _C to, Y _C) to coordinate memory 16M (step S4a). The generation of the first tile pattern is completed through step S9, all the center coordinates (X _C, Y _C) on which it boundary area generated by R _B is held in the coordinate memory 16M.

[0047] Figure 18 shows a flow diagram for generating the second and subsequent tile pattern, in the drawing, the step S2 is obtained by simplified representation in one block to the same process as step S10~S14 in Figure 7, Similarly, step S7 in FIG. 18 is a simplified representation of the same processing as steps S5 to S8 in FIG. First read the center coordinates located at the boundary region R in _B held in the coordinate memory 16M in step S1. In step S2, the center coordinates (X
_C , Y _C ), the pattern element read from the element memory 11 is arranged, and the portion outside the boundary is translated by W by the area conversion unit 15, and the pattern element divided by 0 °,
The patterns rotated by 90 °, 180 °, and 270 ° are written in the data memory 18. In step S3, it is determined whether or not the processing has been completed for all the center coordinates (assuming that there are K) in the memory 16M. If not, the process returns to step S1 to read the next center coordinate from the memory 16M, and step S2 Performs the same processing. If it is determined in step S3 that the processing for the K center coordinates has been completed, in step S4, the number of center coordinates K in the boundary area is calculated from the total number N of center coordinates generated.
Is subtracted to obtain the number L of center coordinates in the inside area. Pattern then center coordinates (X _C, Y _C) within the inner region R _B in step S5 randomly to generate the number of occurrences m 1 increased in step S6, the read out from the parameter memory 11 in step S7 The element is placed at the position of the coordinates (X _C , Y _C ) and written to the data memory 18. Center coordinates number m in the inner region R _B is determined whether the L-number in step S8, it returns to step S5 if not, similar processing S6, S7 repeatedly, termination if the m = L in step S8 I do.

The write pattern elements using coordinates read as center coordinates of similarly perimeter R _B also in the generation of the third and subsequent tile pattern from the memory 16M (step S1 to S3), the inside area R _I Are generated randomly to generate pattern elements (steps S4 to S4).
8). According to this method shown in FIG. 18, in the generation of the second and subsequent tile pattern read center position coordinates in the generated border region R _B at the time of generation of the first tile pattern from the coordinate memory 16M Te, their division coordinate elements and their 90 ° to position 180 °, the pattern connection conditions at the boundary because it generates a 270 ° rotated pattern is always satisfied, and random in the inner area R _I Since a pattern element is written at an appropriate position, a different pattern can be generated for each tile.

[0049] To apply to the embodiment of FIG. 14 A similar approach is the center coordinates in area determination step S4 in the first round of the flowchart tile pattern generator shown FIG 14 is determined to be on the boundary region R _B In this case, the center coordinates are stored in the memory 16M in step S4a indicated by a broken line.
In the generation of the second and subsequent tile patterns, if processing is performed as L = N−K + 3K = N + 2K in step S4 in FIG.
Rotated by now possible to add write pattern element in the inner area R _I in the same number as pattern elements added border region at step S2, the density of the pattern element is close in the inner area R _I and the boundary region R _B . Similarly, in the case of the embodiments of FIGS. 16 and 17, a coordinate memory 16M is provided in the area determination unit 16, and FIG.
The processing step S5a provided shown in YES side of the decision step S5 by the broken line in the procedure, as in FIG. 14 in the tile pattern generation of the first round, the center coordinates (X _C generated on the boundary area R _B, Y _C ) Is stored in the coordinate memory 16M. Second
In the subsequent generation of the tile pattern, L = N + 2K in step S4 of FIG. 18 as in the embodiment of FIG.
And step S7 indicated by a broken line after step S7
a , and the inner region R as in step S11 of FIG.
Every time the element is written in _I , the pattern element in the temporary memory 21 (FIG. 16) is rotated by 90 °.

[0050] Normally often the size of the pattern elements is sufficiently smaller than the size of the tile, hence is sufficiently large area of the inner area R _I than the area of the boundary area R _B 14, FIG. 1
In the embodiment of 6,17, pattern element density and the inner region in only the boundary area R _B number pattern elements were added to the rotational position R _I
As the inner pattern element density is almost the same, are adding pattern elements at random positions into the inner area R _I. When generating a different type of tile pattern a pattern continuous conditions are the same at the interface accordingly in the procedure of FIG. 18, the write count L to the inner area R _I in the boundary region R _B as described above in step S4 L = N + 2K depending on the number of additional writes of 3K
Although the case where the writing processes S5 to S8 are repeated has been described, the following may be performed.

The border area described in FIG. 13B R _B respectively S _B the area of the inner region, and S _I. Center coordinates generated in the boundary area R _B in the generation of the first tile pattern (X _C, Y _C)
When the number of the K pieces, including the number 3K added the written pattern elements seemed continuous conditions, the number of elements that are written in the border area R in _B is 4K. Therefore, the inner region R _I
Assuming that the number of pattern elements to be written in L is L, in order to make the element density the same in the boundary area and the inner area, 4K / S _B = L / S _I should be satisfied. The number of writes L can be determined as L = 4KS _I / S _B. Since L must be an integer, if the value of 4KS _I / S _B is not an integer, it is converted to an integer by a predetermined method such as rounding off, rounding down, or rounding up.

In each of the above-described embodiments, when a pattern element to be written to the data memory 18 has a closed area, and all the pixels in the area have non-zero pixel values, a certain pattern previously written When a pattern element is written so as to partially overlap the element, the overlapping portion is overwritten by the pattern element written later. As described above, when a pattern is generated by the method of each of the above-described embodiments, the writing method of the designated pattern element may not satisfy the exchange rule between the pixel value to be written and the pixel value at the writing position. here,
The exchange rule is satisfied when the pixel value on the tile area before writing is A, the pixel value of the pattern element to be written is B, and the pixel value after writing is C. And writing method in which C does not change even if B is exchanged. The exchange rule does not hold if A and B are exchanged and C
Is changed, and, for example, post-writing priority writing (so-called overwriting) corresponds to this.

When a different tile pattern that satisfies the pattern continuity condition at the boundary is generated from the original tile pattern,
Writing all the divided pattern on the first boundary area according to the center coordinates read from the memory 16M to R _B is in the process of FIG. 18 (step S1 to S3), then writes the pattern elements at random positions within the interior region (Step S4 ~
S8). FIG. 19A shows an example of a tile pattern generated by overwriting in the method of FIG. Since the postscript is prioritized, the pattern elements written in the inner area after writing at the four rotational positions in the boundary area always overlap the pattern elements written in the boundary area, and thus, in the vicinity of the boundary, An unnatural border pattern occurs.

In order to solve such a problem, when a writing method that does not satisfy the exchange rule is specified, writing of a pattern element over a boundary and writing of a pattern element that does not cross a boundary are alternately mixed. May be written to For example, as the ratio of the total write number N _I that do not span the entire write number N _B and the boundary across the boundary is an area S _B and the inner area R _I ratio of the area S _I of the boundary area R _B, i.e. two The pattern elements are written alternately while selecting the writing so that the pattern element densities of the areas become equal.

FIGS. 20 and 21 show the processing procedure of the second and subsequent different tile pattern generation methods for the original tile pattern when the above-described concept is implemented. For example, FIG.
The first round of tile pattern generation by 6 of the apparatus, the coordinate memory 16M is the rotation center coordinates of all patterns elements written to the rotational position of the boundary area R _B (0 including ° the rotation), their written It is assumed that the orientation of the set pattern element is stored. The number center coordinates in the boundary region detected by the region determining unit 16 R _B and C _B, pattern to be written in the border area R in _B including the pattern elements added writing to the rotational position in accordance with the pattern continuous conditions at the boundary The total number of elements
And N _B = 4C _B, the total number of elements to be written into the inner area R _I and N _I. Also the area of the boundary area R _B and the inner area R _I S _B, respectively, and S _I. In order for the pattern element densities to be substantially the same in the boundary region and the inner region, N _I is determined so that N _B / S _B = N _I / S _I substantially holds. That is, _{N I = N B S I /} S B. Therefore, in this embodiment, for example, the well-known D
By repeating the DA method determines whether to either (Differential Digital Analysis Method) boundary area for each once with R _B and the inner area R _I perform a pattern element writing executes element write, write Number of times
N _B : Control to be N _I.

[0056] Figure 20 is N _I> N shows a processing procedure based on the idea of the above-described case of _{B, N I, N I /} 2, N respectively variable RG ₁ the value of _B at step S1, RG _2, RG ₃ Initialize to. Determines whether RG _2> 0 in step S2, if satisfied, randomly center coordinates in the inner area R _I in step S3 (X _C,
Y _C ) is generated, and in step S4, 12 flow steps 6 to
S9 and read from the element memory 11 to the pattern element in the same manner as the position of the data memory 18 (X _C, Y _C) is written to. In step S5, RG ₂ -RG ₃ is calculated, and its value is updated to RG ₂
Value. In step S6, the number of processes n is incremented by one. In step S7, it is checked whether n has reached the total number of elements to be written in the tile area.
Return to If it is determined in step S2 that RG ₂ > 0 is not established , one center coordinate and direction are sequentially read from the memory 16M in step S8, and FIG.
Similarly to steps S11 to S15 of the four flows, the pattern element is rotated in the designated direction, and the center coordinates (X _C , Y _C ) read by the angle specified by the read direction are set around the tile center. Rotate, and write the rotated pattern element at the rotated position. Then calculate the RG ₂ + RG ₁ in step S10, it updates the RG ₂ at that value. In step S6, the number of processes n is incremented by one, and when the number of processes n reaches the total number of elements in step S7, the process ends. When the processing of FIG. 20 is performed, the writing of elements to the boundary area and the inner area is performed alternately with the probability of N _B : N _I.

[0057] N basic processing procedure in the case of _B ≧ N _I Figure 20
Is similar to, is different from each N _B to RG _1, RG _2, RG ₃ at step S1 as shown in FIG. 21, N _B / 2, the value of N _I initializes, at step S2 RG ₂ If> 0 is satisfied, writing to the boundary area is performed in steps S8 and S9,
Update the RG ₂ with the value of RG ₂ -RG ₃ at step S10, by writing to the interior region in step S3, S4 when the determination in step S2 is NO, the value of RG ₂ + RG ₁ in step S5 The point is that RG ₂ is updated.

In the embodiments shown in FIGS. 20 and 21, the case where the DDA method is used as an example of a method of alternately writing at a ratio such that the density of written pattern elements in the boundary area and the inner area becomes substantially the same is shown. But the number of writes
If N _B <N _I , writing to the inner area first (N _I -N _B ) times consecutively and then alternately writing to both areas once may be repeated N _B times . Conversely, when N _B > N _I , writing is continuously performed (N _B -N _I ) times on the boundary area first, and then alternately writing once on both areas is repeated N _I times. If N _B = N _I , it is sufficient to simply repeat writing once to both areas N _B times.

FIG. 19B shows an example of a second tile pattern generated using the method according to the embodiment of FIG. 20 based on the original tile pattern generated at the first time. Since the writing order of the pattern elements in the inner region and the boundary region is alternated, it can be seen that an unnatural border pattern near the boundary as shown in FIG. 19A does not occur. Each of the above four embodiments is
Although the pattern generation using the type of pattern elements has been described, it is needless to say that a pattern can be generated by individually applying each of the above-described embodiments to each of the pattern elements even when a plurality of types of pattern elements are written.

In each of the above-described embodiments, a pattern is generated in a square or rectangular area (tile area) using a two-dimensional pattern element, but the two-dimensional pattern element is extended to a three-dimensional three-dimensional pattern element. A square stamp area including a pattern element is defined as a cubic stamp area, a square or rectangular tile area is defined as a cubic area (eg, a brick area), and (X, Y)
Just extend the coordinate calculation to the (X, Y, Z) coordinate calculation, and when cuboid bricks are stacked in exactly the same procedure, a solid pattern that is continuous at the boundary surface, that is, a solid used in computer graphics Needless to say, the texture can be easily generated.

Incidentally, in the case of industrial products such as tiles and carpets, it is important to form a pattern on a rectangular area in order to increase the value of the product. In the tile pattern generation method that satisfies the boundary pattern continuity condition in each of the above-described embodiments, the case where a predetermined pattern element is repeatedly written in the tile area has been described. The pattern in each tile area formed by these methods is basically a repetition of a predetermined pattern element, and is insufficient in the variety of obtained patterns. If the fractal method can be used to generate a tile pattern that satisfies the pattern continuity condition at the boundary, the diversity of the pattern can be further enhanced. Below, in the square area for reference
Will be described.

The fractal method, which is one of the pattern generation methods, is a powerful pattern generation method capable of generating a complex and natural pattern, and easily generates a 1 / f fluctuation pattern whose spatial frequency attenuates at -6 dB / Oct. In recent years, it has been gaining more and more attention in the point that it can be made (for example, the literature James D. Foley et.
ics, ISBN 0-201-12110-7). This fractal method is
In the area defined by equilateral triangles or their set,
First, determine the pixel value of each vertex of the equilateral triangle appropriately,
The equilateral triangle area is divided into four parts by giving, as the pixel value of the midpoint of each side of the equilateral triangle, a value obtained by adding the amount of noise to the average of the pixel values at both ends (two vertices) of the side of the equilateral triangle. The above operation is repeatedly applied to each divided triangular area to further divide it into 16 regular triangular areas. Less than,
This is a method of generating a pattern in an area defined by an original equilateral triangle and a set thereof by repeating this operation until values are written to all pixels in the original equilateral triangle area.

However, this existing fractal generation technique can generate a pattern only in an area defined by an equilateral triangle and a set thereof as described above. When a fractal pattern is generated in a rectangular area, the rectangular area is included. A fractal pattern is generated in a region defined by a large equilateral triangle or a set thereof, and a pattern is generated in a rectangular region by cutting out the rectangular region after the generation. However, in this method, a work area having a larger area than a target pattern is required in the memory, so that the amount of memory used by the computer and the calculation time unnecessarily increase. This is particularly problematic when generating high-definition patterns. In addition, there is a method of generating a pattern in which a pattern is connected continuously at a boundary when a rectangular area is arranged by devising the coordinate calculation at the time of drawing as described above. Must be performed in units of rectangular areas, and it is difficult to apply the conventional fractal generation method. Therefore, it is considered that a fractal pattern is generated in a square area by the following method.

First, as shown in FIG. 22A, first, the coordinates of the pixels at the four vertices of the original square area are appropriately determined. Then obtain the pixel value V _C of the center point P _C of the four vertices of the original square area. At this time, if the definition of the conventional fractal generation method for a triangular area is simply extended and applied, the average value of the pixel values at the four vertices is obtained, and the value obtained by adding the noise amount to the average value is used as the center point P _C spots is a common idea that to the pixel value V _C, small pixel value distribution of fractal pattern has been generated under rapidly becomes smaller such generation condition in accordance with the divided number of operations the amount of noise in this manner It produces sharp bright and dark spots. Therefore, if a color pattern is generated by, for example, mapping a color according to the pixel value, these bright or dark points become stains whose colors are significantly different from those of the surroundings, and the texture of the pattern is significantly impaired. Would.

[0065] Therefore, a set of two sets of vertices located on the respective diagonal of the four vertices of the square area to avoid the above mentioned problems chosen randomly, the average of the selected set of two vertices the pixel value V _C of the center point P _C a value obtained by adding the amount of noise to the value. This method is equivalent to obtaining the midpoint of the hypotenuse of a right-angled isosceles triangle from two vertices as shown in FIG. 22A, so the fractal pattern obtained is based on the original fractal method of dividing an equilateral triangle and the texture. It is very close and does not produce significant light or dark spots.

[0066] After obtaining the pixel value V _C of the center point P _C, each side just before the original square as diagonal, one side of the center point P _C and one common vertex W / 2 ^1/2 four Fig. 22 shows the square area.
Defined as B. These four small squares whose diagonal directions are inclined by 45 ° with respect to the diagonal direction of the original square are hereinafter referred to as rhombic regions. Next, for each rhombic region, one of two pairs of vertices located on the diagonal is selected at random, and the value obtained by adding the noise amount to the average value of the two vertices of the pair is the center of the rhombic region. Is the pixel value of the part. However, for a rhombic region having a vertex indicated by a white circle generated outside the original square region, a pair of diagonal vertices not including the vertex outside the region is forcibly selected, and the noise amount is added to the average value of these two vertices. And ask for it. That is, when one of the diagonal lines of the rhombic region crosses one side of the original square region, the other diagonal line is selected.

When the rhombic region is divided by the above method, FIG.
As shown in (1), a set of square areas each having a side of W / 2 is completed. This is equivalent to dividing the square area of FIG. 22A into four. In other words, when the two steps of dividing the square area into the rhombic area and dividing the rhombic area into the square area are performed, the original square area is converted into a set of square areas divided into four. Therefore, these two procedures are repeatedly applied alternately until the length of one side of the divided square area becomes one pixel. As a result, writing is performed on all the pixels in the square area, and the generation of the fractal pattern is completed. According to this method, a fractal pattern can be generated in a square area of a square of a given size.

FIG. 23 is a block diagram of an apparatus for implementing the above-described fractal pattern generation method. Reference numeral 51 denotes a square area pixel value storage memory for storing the generated pattern; 52, a control unit for controlling the movement of the apparatus; 53, a square area vertex for calculating coordinate values of four vertices of any square area existing in the memory The calculating unit 54 calculates a coordinate value of four vertices of an arbitrary rhombic region having at least three vertices in the memory 51. A rhombus region vertex calculating unit 55 calculates four vertices defined by the vertex calculating unit 53 or 54. A diagonal vertex selector that divides into two sets of vertices located on the diagonal and selects one of them, calculates a V _C pixel value of the midpoint of the two vertices selected by the diagonal vertex selector 55 Reference numeral 57 denotes a random number generator for selecting a diagonal vertex at random, reference numeral 58 denotes a noise generator, and reference numeral 59 denotes a writing unit for writing the calculated pixel value to the memory 51. In FIG. 23, thick arrows indicate the flow of pixel values, and thin lines indicate the flow of coordinate values, other data values, or control signals.

A fractal pattern generating device having the configuration shown in FIG.
The arrangement will be described next with reference to the processing procedure of FIG. First, appropriate pixel values are written in advance at four vertices of the original square area of the memory 51. The length of one side of this original square area is W
And W can be any length, but here, the simplest operation is a power of 2 times the length between pixels, for example, 1
6, 32, 64, 128, 256...

The controller 52 instructs the square area vertex calculator 53 to calculate the coordinates of four vertices of the original square area from the length W of one side of the original square area defined in the memory 51. The vertex calculating unit 53 calculates the coordinates (0,0), (W, 0), (W, W), (4) of the four vertices of the square area (see FIG.
(0, W) is calculated and sent to the diagonal vertex selector 55 (step S1).

The selector 55 classifies the four vertices sent from the vertex calculator 53 into two sets of diagonal vertices,
Select either set of vertices based on the values sent from the send their coordinates to the center point pixel value calculating section 56 (step S2), and followed by the midpoint P _SC coordinates of the set of vertices And sends it to the writing section 59 as an address. The random number generation section 57 generates a random number used by the selection section 55 to randomly select a set of vertices. For example, the random number generation unit 57
Generates a random number R from 0 to 1, and the selecting unit 55 outputs R <0.
If 5, a pair of diagonal vertices rising to the right with respect to the square
If it is 0.5, either diagonal vertex set can be selected with the same probability by selecting the diagonal vertex set that descends to the right with respect to the square area.

Next, in step S3, the center point pixel value calculation unit 5
6 reads the pixel values V ₁ and V ₂ at the coordinate values of the selected pair of vertices sent from the selection unit 55 from the memory 51, calculates an average value of them, and adds the average value to the noise generation unit. adding the sent come noise value N from 58 sends to the write section 59 as the pixel value V _C of the center point P _SC square region. The intensity N of the noise generated by the noise generator 58 changes according to an instruction from the controller 52.

The writing section 59 includes a center point pixel value calculating section 56.
In writing to the memory 51 according to the coordinates instructed the pixel value V _C obtained by the selection unit 55. With the above operation, the first division from the square area to the rhombic area is completed, and the number of divisions n is advanced by one in step S4. Next, in step S5, the control unit 5
2 is obtained by dividing the length W stored therein by ^21/2 , and four sides each having a diagonal line of a rhombic region whose one side is W / ^21/2 shown in FIG. The coordinates of the four vertices of each rhombus of the rhombus region are instructed to the rhombus region vertex calculation unit 54, and the noise generation unit 58 is instructed on the noise intensity N. The rhombus region vertex calculation unit 54 calculates the coordinates of the four vertices of each rhombus region (FIG. 25B) having a side length of W / 2 ^1/2 designated by the control unit 52, and sends the coordinates to the selection unit 55. Send.

In step S 6, the diagonal vertex selection unit 55 classifies the four vertices of each diamond-shaped region sent into two sets of diagonal vertices. For example, if R <0.5, a set of vertical diagonal vertices of the rhombic region is selected based on the obtained random number R, and if R ≧ 0.5, a set of horizontal diagonal vertices is selected, and their coordinate values are used as the center point pixel values. If one vertex is outside the original square area, the two vertices select a set of diagonal vertices on the sides of the original square area and send their coordinate values to the center point pixel value calculation section 56. Send to Then send the midpoint P _RC of the coordinates of a set of vertices and the selected 59 asking.

In step S7, the center point pixel value calculation unit 56 reads out the pixel values V ₃ and V ₄ at the coordinates of the two diagonal vertices sent for each rhombic region from the memory 51, and averages these values. Is calculated, and the noise generating unit 58 is added to the average value.
Adding the noise value N from the sending to the write section 59 as the pixel value V _C of the center point P _RC with. The write unit 59 has selected pixel value V _C obtained in the pixel value calculation unit 56 by the selection unit 55 2
One of the following central point P _RC of the coordinates of the vertices written to the memory 51, by one increment the number of divisions n at step S8.

In step S9, each side of the rhombic region is defined as a diagonal line, as shown in FIG. 26A. finish. Next, in step S10, it is determined whether or not the length W / ^{2n / 2} of one side of the divided square area is equal to or less than the distance d between adjacent pixels. If not, the process returns to step S2 and the side obtained in step S7 is W Again one side of the square area of / 2
^By dividing by ^1/2 , the length W / 2 ^3/2 of one side of the rhombic region having the side of the length W / 2 shown in FIG. 26B as a diagonal line is obtained, and the square region (FIG. 27A ) Into a diamond-shaped area (FIG. 27B), and a diamond-shaped area (FIG. 27B) into a square area (FIG. 28B).
Continuing with the division into A), the rhombus region vertex calculation unit 54 extracts the four vertices of the rhombus region according to the length, and according to the k-th process, as shown in FIG. (2 ^1/2 2
All the rhombic regions of ^k ) are extracted, and the coordinates of each of the four vertices are calculated (step S5). When selecting the four vertices of the square area according to the length, the square area vertex calculation unit 53 selects the same side length W / 2 ^k as shown in FIG. 28A according to the (n / 2 = k) th process.
Are extracted, and the coordinates of each of the four vertices are calculated (step S9). In step S10, the operation is stopped when the value obtained by dividing the length W by 2 ^{n / 2} becomes equal to or less than the distance d between pixels.

When the above-described division operation is repeated and the control unit 52 stops operating, the memory 51 stores the generated fractal pattern. As described above, according to this embodiment, fractal generation can be efficiently made on a rectangular area defined by a square area and a set of square areas, and waste in terms of calculation memory amount and calculation time as in the conventional method. There is no. In addition, since the center point is obtained by using only two vertices located on the diagonal in spite of the quadrangle division, it is substantially a right isosceles triangle division as shown in FIG. 22A or FIG. The texture is very similar to the pattern based on the triangulation, and there is no unnatural pattern peculiar to the fractal pattern based on the quadrilateral.

[0078] For a square or rectangular area of the tile and carpets, etc. which were generated by fractal pattern generation method of this the materials given above, when line it many, pattern leads to a continuous in adjacent portions, seen as a smooth pattern throughout Hopefully you can. In addition, simply arranging tiles with the same pattern in the same direction will cause the same pattern habit to appear repeatedly at each tile interval, so you will be aware of each tile from the pattern interval, but if you change the tile orientation and paste it, Even if tiles of different patterns are pasted, if the patterns can be connected at the boundary, the entire pattern can be regarded as one, and the aesthetic appearance can be increased. Similar to the case of the above-described pattern element, a pattern can be generated so as to satisfy the pattern continuity condition at the boundary described with reference to FIGS. 1A, 1B, and 1C. However, if the above-described continuity condition is used as it is, continuous connection of pixel values on the boundary is guaranteed, but continuity of the rate of change of the pixel value cannot be guaranteed. Natural pattern changes occur. FIG. 29A is a diagram in which six fractal patterns generated in a square area are arranged, and three-dimensionally displayed assuming pixel values as heights. Although the heights of adjacent patterns at the boundary are equal, the slope at the boundary changes discontinuously. Next, FIG. 29B shows a pattern generated by mapping all densities (pixel values) below a certain value as white and mapping densities above the certain value. This stripe information has the same meaning as the contour drawn on a map or the like. If the density gradient is not continuous at the boundary, the contour of the pattern does not smoothly continue at the boundary, and corners are formed at the connection of the pattern at the boundary.
Therefore, as shown in FIG. 29B, only a low-quality pattern in which the position of the boundary is conspicuous can be generated. Conversely,
If the density gradient is continuous at the boundary, the contour of the pattern there is also smoothly continuous.

Therefore, in order to make not only the pixel value but also the slope, that is, the change rate of the pixel value at the boundary continuous, the pixel value calculation considering the information of the adjacent pattern may be performed in the division procedure in the fractal generation. Such an embodiment will now be described. When dividing the area described with reference to FIGS. 22A to 22C, the division from the square area to the rhombic area uses only the information inside the square area, so the processing is the same as the above-described processing. Since there is a diamond-shaped area that straddles the boundary of the original square area, division is performed here in consideration of information on the pattern of the adjacent tile.
That is, when one of the four vertices detects a rhombic area outside the original square area, a point inside the square area of an adjacent tile corresponding to the position of this vertex is connected by rotating the adjacent tile. For example, four sides that can be selected are sequentially selected. The number selected depends on the connection conditions and the number of different patterns to be generated. When the pattern is aligned and aligned, one piece is connected under the condition where the pattern is continuous at the boundary. When the pattern is connected with the pattern whose orientation is changed by 180 °, two pieces are connected under the condition where the pattern is continuous at the boundary, 90 °, 180 °, Under the condition that the pattern is continuous at the boundary even if it is arranged with the pattern whose orientation has been changed by 270 °, four pixels are selected. When continuous connection with a plurality of patterns is considered, the number is a multiple of the number determined by the connection conditions. When the number of the points selected in this way is Q, an inner vertex of the original square area, a Q set of the selected point of the adjacent tile, and another one of the rhombic areas on the side of the original square area One set is randomly selected from the total Q + 1 sets of the diagonal vertices of the set, and the value obtained by adding the noise amount to the average value of the pixel values of the two vertices of the set is used as the pixel value at the center of the rhombic region. Divides a set of rhombic regions into a set of square regions. Then, a pattern is generated by alternately repeating the procedure of dividing the square area into the rhombic area and the procedure of dividing the diamond area into the square area until the length of one side of the divided square area becomes equal to the length between pixels. I do.

FIG. 30 shows an example of a fractal pattern generating apparatus based on the above idea. Components having the same names and operations as those in the embodiment of FIG. 23 are given the same numbers as in FIG. The configuration added to the configuration of FIG. 23 is a flag storage memory 61 indicating that a pixel value has already been written in the memory 51, a reference used when generating a plurality of tile patterns in which patterns are continuous at boundaries. A pattern pixel value storage memory 62, an area determining unit 63 that determines whether all vertices of the rhombic area calculated by the rhombic area vertex calculating unit 54 are within the original square area or a part thereof is outside the original square area, Out-of-area vertex selection unit 6 that selects a plurality of pixels in the pattern of an adjacent square area located at a vertex outside the area, and outputs the selected number, their coordinate values, and which pattern they are in.
4. A written determination unit 65 that determines whether the midpoint coordinates calculated by the opposing vertex selection unit 55 have already been written. The thick arrows in FIG. 30 indicate the flow of pixel values, and the thin lines indicate the flow of coordinate values, other data values, or control signals.

When a single tile pattern is generated, first, the same appropriate pixel values are already written in the four vertices of the original square area of the memory 51, and are written in the four vertices of the original square area of the flag storage memory 61. Flag is set. The length of one side of the original square area is W. When generating a plurality of tile patterns that are continuous with the previously generated tile pattern at the boundary, first, the pixel values of the reference pattern are written to all the pixels belonging to the sides of the square area of the memory 51, and the flag storage memory 6
All pixels belonging to the side of the square area 1 are set with the written flag. The memory 62 may be omitted if it is not necessary to generate a plurality of continuous patterns at the boundary.

The control unit 52 instructs the square area vertex calculation unit 53 to calculate the coordinates of the four vertices of the original square area. The square area vertex calculation unit 53 calculates the coordinates of the four vertices of the square area from the length W of one side of the square area predefined in the memory 51 as shown in FIG. Send.

The selecting section 55 classifies the four vertices sent from the square area vertex calculating section 53 into two sets of diagonal vertices in the same manner as in the above embodiment, and Then, one of the sets of vertices is selected, and their coordinate values are sent to the writing unit 65. Then, the midpoint coordinates of the set of vertices are obtained and sent to the writing unit 59. The writing unit 65 refers to the flag storage memory 61 to check whether writing has already been performed on the writing coordinates sent from the selecting unit 55, and if the writing has been completed, stops writing to the coordinates. If it has not been written, the coordinate value is sent to the center point pixel value calculation unit 56.

The center point pixel value calculation unit 56 receives the
The pixel values V ₁ and V ₂ at the two coordinate values are read from the memory 51, the average value is calculated, the noise value N given from the noise generation unit 58 is added to the average value, and the result is sent to the writing unit 59. The intensity N of the noise generated by the noise generator 58 changes according to an instruction from the controller 52. Writing unit 59
Writing into the memory 51 in accordance with the indicated coordinate of the center point P _SC for the selected diagonal vertex pixel values of the diagonal center point obtained at the center point pixel value calculating unit 56 by the selection unit 55, the flag storage memory 61 Set the written flag in the coordinate value.
At this time, if the same coordinate value is on the side of the square area having the length W, the position shifted to the side facing the side and the positions of both sides are determined according to the pattern continuation condition described with reference to FIGS. 1A and 1B. The same pixel value is written into a total of eight coordinates at positions sequentially rotated by 90 °, 180 °, and 270 °, and a flag is set at the corresponding coordinate in the flag storage memory 61. With the above operation, the first division from the square area to the diamond area is completed.
The pixel value on the side of the original square area is determined by the above-described calculation only for one predetermined side, and the determined pixel value is copied to another side in accordance with the above-described continuity condition to obtain the other side. The pixel value shall be determined.

Next, the control unit 52 determines the length W stored therein.
Is divided by 2 ^1/2 , and the coordinates of four vertices of the rhombic region whose one side length is W / 2 ^1/2 are instructed to the rhombus region vertex calculating unit 54,
The noise intensity N is designated to the noise generator 58. The rhombus region vertex calculator 54 calculates the length W / 2 specified by the controller 52.
The coordinates of the four vertices of the ^1/2 diamond region are calculated as shown in FIG. 25B, and the coordinate values are sent to the region determination unit 63.

The area judging unit 63 checks whether the four vertices represented by the coordinate values are in the original square area of length W or one vertex is outside the square area, and selects the vertices in the original square area. The coordinates are sent to the section 55. For the vertices outside the square area, the coordinates are sent to the outside area vertex selection section 64.
If one vertex of the diamond area is outside the original square area, the other two vertices are on the sides of the original square area, the other vertices are inside the original square area, and the coordinates of these vertices are P _X , P _B1 , P _B2 , P _I will be represented. In the state shown in FIG. 25B, the vertex P _I coincides with the center point P _SC .

[0087] The coordinates P _X sent from the area outside the vertex selection unit 64 area determination section 63, of the adjacent tiles satisfying the continuous condition, the own tile as shown in Figure 31 is regarded as coordinates corresponding with the own tile The four coordinates P of the position where it is superimposed and the position where it is rotated 90 °, 180 °, and 270 ° sequentially on its own tile
Select _R1 , _PR2 , _PR3 , _PR4 . Alternatively, the coordinates PX are regarded as positions on the adjacent tiles, and the positions P _R2 ′, P _R3 ′, and P _R4 ′ obtained by rotating the coordinates PX by 90 °, 180 °, and 270 ° around the center point of the adjacent tiles are obtained. , When their neighboring tiles are shifted and overlapped on the original square area, their positions P _X ,
Coordinates P _R1 , P _R2 , P on the original square area of P _R2 ', P _R3 ', P _R4 '
_The same _holds true for _R3 and _PR4 . In the state of FIG. 25B, P
_{Since X} coincides with the center point of the adjacent square area, these four positions also coincide with the center point P _SC , but in the state of FIG. 26B, these four points are obtained as shown in FIG.
However, when generating the fractal original fractal different pattern has the memory 62 a pattern of adjacent tiles as fractal pattern of the original tile, 90 ° point P _X in its original tile, 180 °, 270 ° Rotated position P _R2 ', P _R3 ',
Select P _R4 ′ with P _X. When the first tile pattern (original pattern) is generated, those four coordinates are stored in the memory 51.
In the case of generating information representing the coordinates in the second and subsequent different patterns, those four coordinates are stored in the memory 6.
The selection unit 5 attaches information representing the coordinates in 2 to those coordinates.
Give 5

When the area judging section 63 judges that all four vertices of the rhombic area are present in the original square area, the selecting section 55 sets two sets of the four vertices given from the rhombic area vertex calculating section 54 to two sets. Are selected at random according to the random number R from the random number generator 57, and the selected set of coordinate values is provided to the center point pixel value calculator 56. When one vertex is determined to be outside the original square area by the area determination unit 63, the four coordinates P _X , P _B1 , P _B2 , and P _I from the rhombus area vertex calculation unit 54 and the vertex outside the area are determined. Selector 64
Receive four coordinates P _R1 , P _R2 , P _R3 , P _R4 from. Former 4
Two sets of diagonal vertices (P _X , P _I ) and (P _B1 , P _B2 ) are defined from the two coordinates, and the pixel values of the latter four coordinates are selected as possible pixel values of the vertex P _X outside the area. I do. That is, as a selectable diagonal vertex of the rhombic area, a set of two vertices (P _B1 , P _B2 ) on the sides of the original square area, and a set of vertices P _I inside the sides of the square area and the selected coordinates ( Five sets of P _I , P _R1 ), (P _I , P _R2 ), (P _I , P _R3 ), (P _I , P _R4 ) are defined. One of these five sets is selected in accordance with the random number R, and the selected set of coordinate values is selected together with information indicating whether the set of coordinate values is a point on the memory 51 or a point on the memory 62. Give to 56. Further, in any of the above cases, the coordinates of the midpoint of the selected set of coordinates are obtained and given to the write determination unit 65. These selectable 5
Of the set of coordinates, four sets is given as the coordinates of the selectable pixel for a set of opposite corners including vertex P _X got out of the original square area, by a random number R of these five sets of coordinates Selecting one set means that the probability of selecting a set of diagonal vertices (P _X , P _I ) including vertices outside the original square region is a set of diagonal vertices on the boundary (P _B1 , P _B2 ) is four times the probability of selecting. This makes it possible to increase the influence of the pattern of the adjacent tile on the determination of the pixel value of the center point to be performed next, thereby realizing smooth continuity of the pattern.

The write judging section 65 checks whether writing has already been performed on the writing coordinates sent from the selecting section 55 with reference to the flag storage memory 61, and if the writing has been completed, stops writing to the coordinates. If it has not been written, the coordinate value is sent to the center point pixel value calculation unit 56. The center point pixel value calculation unit 56 reads out the pixel values on the memory 51 or 62 in the two coordinate values of the set given by the selection unit 55, calculates the average value of the read out pixel values, and calculates the average value thereof. Is sent to the writing unit 59 as the pixel value of the center point of the diagonal vertex (therefore, the center point of the diamond-shaped area).

The writing section 59 includes a center point pixel value calculating section 56.
Is written into the memory 51 in accordance with the coordinates selected by the selection unit 55. With the above operation, the first division from the rhombic region to the square region is completed, and the square region becomes a set of square regions divided into four. Next, the control unit 52 divides again ^21/2 length W / 2 ^1/2 held therein previously. As a result, the length W / 2 of one side of the square area divided into four is obtained. Based on this length W / 2, the square area is again divided into a rhombic area,
Further, division is performed from a rhombic region to a square region with one side being W / 2 ^3/2 , and the processing procedure of this pair is repeated, and the length W / 2 ^{n / 2} of one side of the retained divided square region is determined as an adjacent pixel. Stop the operation when the length between them becomes equal. When selecting the four vertices of the square area having the diagonal length of W / 2 ^{n / 2} (n = 1, 3, 5,...), The square area vertex calculation unit 53 performs the processing of FIG. The coordinates of four vertices of all the square areas having the same length of one side are calculated as in k. The rhombus region vertex calculation unit 54 calculates the diagonal length.
When four vertices of the rhombic region according to W / 2 ^{n / 2} (n = 2, 4, 6,...) Are selected, the same side is controlled by the control unit 52 as shown in FIG. A plurality of all rhombic regions of length are selected, and the coordinates of each of the four vertices are calculated.

When the above dividing operation is repeated and the control unit 52 stops operating, a fractal pattern in which the pattern is continuous at the boundary is generated and stored in the memory 51.
The fractal pattern generated in this manner is based not only on the continuity of the pixel values at the boundary but also on the continuity of the change rate of the pixel values. No unnatural pattern habit occurs at the boundary. In addition, a fractal pattern in which the pattern is continuous at the boundary can be generated by referring to not only the pattern to be referred to when selecting a pixel located at the vertex outside the rhombic region but also other fractal patterns.

In the above description, when determining the pixel value of the center point of the diamond-shaped area, if one vertex is outside the original square area, five pairs of two diagonal vertices are selectable. Selectable pixels were determined, one set was randomly selected from them, and the pixel value of the central point of the rhombus region was determined from the pixel values of the two selected pixels and noise. In this case, if the smoothness of the connection pattern at the tile boundary can be reduced to some extent, the above four coordinates P _X , P _R2 ′, P _R3 ′, which can be selected as pixels corresponding to vertices outside the original square area Select any one of P _R4 ′ and set the pixel on the own tile corresponding to the selected position or the pixel on the reference original tile as the pixel of the outside vertex, and select one of the two sets of diagonal vertices. May be randomly selected, and the pixel value of the center point of the rhombus region may be determined from the pixel values of the two diagonal vertices of the selected set and the noise.

In this embodiment, the method and apparatus for generating a fractal pattern in a square tile area have been described. However, in general, a fractal pattern is generated in a rectangular area defined by a set of square areas. It can be realized with a simple application. For example, when generating a fractal pattern having an aspect ratio of 1: 2, a square area fractal pattern that is continuous at two types of boundaries is generated according to the above-described embodiment, and a desired pattern can be obtained simply by connecting the fractal patterns. Further, even in the case of a rectangular area having an arbitrary aspect ratio, it can be created by compressing and expanding the generated pattern in the horizontal direction.
In this case, if the compression and elongation ratios are extremely large, the texture of the pattern has a directionality, which is not preferable. Therefore, the pattern is generated in advance in a rectangular area defined by a set of square areas having the closest aspect ratio. May be slightly compressed and decompressed to be converted into a rectangular area having a desired aspect ratio.

In the above embodiment, the case where a fractal pattern is generated on a two-dimensional plane has been described.
By extending the processing of x, y to the processing of x, y, z, and making the mutual division of the square area and the rhombic area into the mutual division of the cubic area and the octahedral area, the solid pattern is continuous at the boundary surface. It goes without saying that it can be easily applied to the generation of fractal patterns.

In each of the above-described embodiments, the case where the tile pattern is written in the tile area defined in the pattern data memory 18 or 51 has been described. Alternatively, the data may be written on a floppy disk, an IC card, or another removable recording medium, read out from the recording medium when necessary, and printed. Alternatively, instead of performing printing, a pattern may be processed on the surface of the plate-like material by a numerical control processing device in accordance with the pattern data thus read.

[0096]

According to the first and nineteenth aspects of the present invention, when writing occurs in the pixel adjacent to the boundary, the connection of the adjacent tile is continued to the adjacent pixels on all sides where the connection is predicted.
Since writing is performed to the pixel at the corresponding position of the tile,
Continuity at the boundaries of the tile pattern is guaranteed.

According to the sixth and twenty-second aspects of the present invention, when additional pattern elements are written in the boundary area to ensure continuity of the pattern elements across the boundary, the additional pattern elements are written in the inner area. Thereby, the uniformity of the density of the pattern elements can be improved. According to the twelfth, thirteenth, and twenty- third aspects, by controlling the number of times of writing, the pattern density of the inner region and the boundary region can be made equal.

According to the fourteenth and twenty-fourth aspects of the present invention, even if the pattern element has directionality, the direction of the pattern is changed every writing, so that the direction of the pattern can be changed over the tile boundary area and the inner area. Dispersed, less conscious of individual tiles. According to the invention of claims 15 and 25 , the writing position in the boundary area stored in the memory at the time of generation of the original tile pattern is read out at the time of generation of the second tile pattern, and written at the same position of the boundary area. Since writing is performed at random positions in the area, it is continuous with the original tile pattern,
In addition, a second tile pattern different from the original tile pattern can be generated.

[0099] Claim 16, 17, 18, according to the 26 and 27 invention, with respect to the inner region and the boundary region at the time of generation of the second tile pattern according to claim 15 and 25, the writing alternates its area ratio Therefore, a pattern in which the boundary area is not conscious even when writing in which the exchange rule is not satisfied can be generated.

[Brief description of the drawings]

FIG. 1A is a diagram showing a square region of a tile and a square region adjacent thereto for explaining the principle of the present invention, FIG. 1B is a diagram for further explaining the principle of the present invention, and C is a diagram further illustrating the principle of the present invention. FIG.

FIG. 2 is a diagram for explaining the principle of applying the present invention to an equilateral triangle tile.

FIG. 3 is a diagram for explaining a pattern continuation condition in an equilateral triangle tile.

FIG. 4 is a diagram for explaining a pattern continuation condition in a regular hexagon tile.

FIG. 5 is a block diagram showing an embodiment of a pattern generating apparatus according to the present invention.

6A is a diagram for explaining a pattern element continuity condition in a square tile, FIG. 6B is a diagram for explaining a pattern continuation condition, and FIG. 6C is a diagram showing a stamp area including the pattern element.

FIG. 7 is a block diagram showing a tile pattern generation procedure according to the embodiment of FIG. 5;

FIG. 8 is a block diagram showing a modified example of FIG. 5;

FIG. 9 is a view for explaining coordinate synthesis in the embodiment of FIG. 7;

FIG. 10 is a diagram showing a main part of a pattern generation procedure according to the embodiment of FIG. 8;

11A is a diagram showing an example of a tile pattern that satisfies continuation conditions using a black circle as a pattern element, and FIG. 11B is a diagram showing an example in which a plurality of tiles in FIG. 11A are connected.

12A is a diagram illustrating an example of a tile pattern in which the density of pattern elements is high in a boundary region, and FIG. 12B is a diagram illustrating an example of a tile pattern generated by the processing procedure of FIG. 14;

13A is a diagram illustrating a pattern element and a stamp area including the pattern element, and FIG. 13B is a diagram illustrating a relationship between a tile area in which the pattern element is written and a stamp area.

FIG. 14 is a flowchart showing a processing procedure for generating a pattern with a uniform pattern element density.

15A is a diagram showing an example of a tile pattern in which pattern elements having directivity are written, FIG. 15B is a diagram showing an example in which tiles of FIG. 15A are arranged, and FIG. 15C is a tile pattern generated by the processing of FIG. FIG.

FIG. 16 is a block diagram showing an embodiment of a pattern generating device for dispersing the writing direction of a directional pattern element.

FIG. 17 is a flowchart showing a processing procedure for generating a tile pattern by the apparatus of FIG. 16;

FIG. 18 is a flowchart showing a processing procedure for generating a tile having a different pattern by satisfying a continuation condition on a second sheet.

FIG. 19A is a diagram showing an example of a tile pattern by writing in which the exchange rule is not satisfied;

[20] N _I> N flowchart showing a write process performed by the DDA method when the _B.

[Figure 21] Flow chart showing a write process performed by the DDA method when the N _I ≦ N _B.

22A is a diagram for explaining a first processing procedure of fractal generation according to the present invention, FIG. 22B is a diagram for explaining a second processing procedure of fractal generation according to the present invention, and C is a fractal according to the present invention. FIG. 9 is a diagram for explaining a third processing procedure of generation.

Figure 23 is a block diagram showing an embodiment of a fractal pattern generator.

FIG. 24 is a flowchart showing a processing procedure for generating a fractal pattern by the apparatus of FIG. 23;

FIG. 25A is a diagram showing an original square region in the fractal pattern generation procedure of the present invention, and FIG. 25B is a diagram showing the formation of a rhombic region in fractal generation.

26A is a diagram illustrating a first divided square region in fractal generation, and FIG. 26B is a diagram illustrating a first divided diamond region in fractal generation.

FIG. 27A is a diagram showing a second divided square region in fractal generation, and FIG. 27B is a diagram showing a second divided diamond region in fractal generation.

FIG. 28A is a diagram illustrating a third divided square region in fractal generation, and FIG. 28B is a diagram illustrating a k-th divided diamond region in fractal generation.

29A is a diagram schematically showing a density distribution of a connected fractal pattern, and FIG. 29B is a diagram showing an example of a fractal pattern in which an edge occurs in the connection of the pattern at the boundary.

Figure 30 is a block diagram showing the generation instrumentation 置例 fractal pattern concentration gradient at the boundary is continuous.

FIG. 31 is a view for explaining selection of a pixel when a vertex of a rhombus region is outside a square region;

Continuation of front page (56) References JP-A-7-281409 (JP, A) JP-A-5-242256 (JP, A) JP-A-8-30664 (JP, A) JP-A-7-200844 (JP) , A) JP-A-7-220006 (JP, A) (58) Fields investigated (Int. Cl. ⁷ , DB name) G06F 17/50 620

Claims (27)

(57) [Claims] 1. A method of writing pixel values of a pattern for each pixel in an area of a polygonal tile so that a pattern is continuous at a boundary when tiles are sequentially arranged adjacent to each other. Is the pixel of the pattern element memory means
It is stored in advance at the address corresponding to the coordinates, and
The pixel values of the pattern should be stored in the pattern data memory means.
You can define a polygonal tile area, comprising the steps of: (a) reading a pixel value pattern from the pattern element memory means for each pixel, the tile territory of the pattern data memory means
Writing to pass, (b) the pixels of the written pattern of the polygonal-shaped tile territory
Whether determined located on either side of the range, the pixel is the tie written above (c) step (b)
If located on either side of Le area, obtains the position of a pixel adjacent to the write pixel on regions of adjacent polygons adjacent the edge, the adjacent polygon regions of the tile The position of the adjacent pixel when overlapped is determined as a shift position of the adjacent pixel. (D) The position of the write pixel and the shift position are rotated at least once by a predetermined angle around the center of the polygon. (E) in the tile area of the pattern data memory means.
That writing the pixel value in the shift position and the rotational position. 2. The method of claim 1, wherein said polygon is a rectangle and said predetermined angle comprises 180 °. 3. The method of claim 1, wherein said polygon is a square and said predetermined rotation angle is 90 °, 180 °.
° and 270 °. 4. The method of claim 1, wherein said polygon is an equilateral triangle and said predetermined rotation angles are 120 ° and 240 °.
°. 5. The method of claim 1, wherein said polygon is a regular hexagon and said predetermined rotation angle is 60 °, 120 °.
°, 180 °, 240 ° and 300 °. 6. A method of repeatedly writing a predetermined pattern element in a polygonal tile area to generate a tile pattern, wherein a square including the pattern element is defined in advance as a stamp area, and the stamp area is placed. When the stamp area is placed, the boundary area where the stamp area always straddles the boundary of the tile area, and the inner area where the stamp area does not straddle the boundary when the stamp area is placed, are included in the tile area. Stipulate that each pixel value of the pattern element is
The address corresponding to the coordinates of the pixel in the memory means
The tiles stored and stored in the pattern data memory means
There is a tile area where pixel values of the pattern are to be stored.
And the method includes the steps of: (a) randomly generating a center position of the stamp area in the tile area; and (b) determining a stamp area whose position is specified by the center position in the boundary area. (C) If the stamp area is within the inner area , the pattern is determined .
The specified position of said stamp area of the tile area of the data memory means, stored in said pattern element memory means
Reads the pattern elements are writing, (d) the stamp area is in the case of the border region, a portion protruding into an adjacent polygonal area from the boundary of the pattern elements, the adjacent polygonal region of the tile region The part of the pattern element that is shifted to the position on the tile area when it is superimposed on the boundary and that does not protrude from the boundary of the pattern element and the shifted part is read from the pattern element memory means.
To the tile area of the pattern data memory means.
Kicking, depending on the connection conditions of the tiles additional writing in a position rotated at least once by a predetermined angle around the center of the tile area, if there is (e) the additional writing, the pattern Detame
In the above-mentioned inner area of the tile area of the mower means , at least one
Each time , the pattern element stored in the pattern element memory means is read out and additionally written. 7. The method according to claim 6, wherein said polygon is a rectangle and said predetermined angle in said step (d) is 180.
Including °. 8. The method of claim 7, wherein said rectangle is a square, said predetermined angle in step (d) further includes 90 ° and 270 °, and said additional writing is said predetermined angle of 90 °, 180 °. ° and 270 ° at each rotational position. The method of claim 9 claim 8, upper Symbol step
(d) sequentially generating an address for reading a pixel value from the stamp area in the pattern element memory means, and sequentially accessing an address of the stamp area of the pattern element memory means with the address to read the pixel value Steps. 10. The method according to claim 9, further comprising the step of combining the coordinates specifying the center position with the read address to generate a combined coordinate, wherein the step (d) comprises the step of: of the length of one side produces a remainder operation treated modulo, the remainder generated as write address coordinates rotated by said rotational angle, the upper Symbol said pattern element memory in the pattern data memory means as a write address The pixel read from the means
Writing the value . 11. The method of claim 9, wherein said step (d) comprises rotating said address around said center of said stamp area by said rotation angle to generate a rotation address, and said center coordinate of said tile area. A rotation coordinate is generated by rotating about the center by the rotation angle, and the rotation address and the rotation coordinate are combined to generate a combined coordinate.The length of one side of the tile area is modulo to the combined coordinate. Generating a remainder obtained by performing the remainder calculation processing as a write address, and writing the pixel value to the write address position of the pattern data memory means. 12. The method according to claim 6, wherein the number of additional writes to the inner area is the same as the number of additional writes to the boundary area. 13. The method according to claim 6, wherein the number of additional writings in the inner area is determined so that the density of the pattern elements in the boundary area is substantially equal to the density of the pattern elements in the inner area. Number. 14. The polygonal tile according to claim 6, wherein the orientation of the pattern element is changed every time the pattern element is written, regardless of any of the steps (c), (d), and (e). Is rotated by an angle corresponding to the predetermined possible connection direction. 15. The method according to claim 6, wherein, when the first tile pattern is generated, the step (b) stores the writing position of the stamp area determined to straddle the boundary in the coordinate memory means. The step of writing, the generation of the second tile pattern includes the following steps: (f) reading the write position from the coordinate memory means; and (g) reading the boundary area in the pattern data memory means . (H) Assuming that the area ratio between the inner region and the boundary region is S _I / S _B , the number of times of writing to the boundary region in the step (g) is approximately S _I / S _B. / S generates the center position of the stamp area randomly at _B times in the inner region in the write count, writing the pattern elements to the position in the pattern data memory means. 16. The method according to claim 15, wherein the writing in step (g) and the writing in step (h) are performed in a mixed manner. 17. The method according to claim 15, wherein said step (g) and said step (h) are performed by using a difference digital analysis method such that the number of writes is the ratio S _I / S _B. Execute (g) and (h) together. 18. The method according to claim 15, wherein the larger of the difference between the number of times of writing in step (g) and the number of times of writing in step (h) is executed first, and the rest are alternately executed. 19. An apparatus for generating a pattern by writing a pixel value of a pattern for each pixel in an area of a polygonal tile so that a pattern is continuous at a boundary when tiles are sequentially arranged adjacent to each other. Including: pattern data source means; coordinate address generating means for specifying a position to write the pattern data from the pattern data source means in the polygon area for each pixel; and wherein the coordinate address is any of the polygon area Determining means for determining whether or not the written pixel is adjacent to any of the sides; and if the written pixel is adjacent to any of the sides, the written pixel is adjacent to the written pixel on an adjacent polygonal area adjacent to the side. The position of the pixel to be obtained is obtained, the position of the adjacent pixel when the adjacent polygon is overlapped with the tile area is obtained as the shift position of the adjacent pixel, and the position of the write pixel and the shift position are obtained. Position rotating means for determining the rotational position is rotated by a predetermined angle by at least once around the serial polygonal center, additional writing means for adding writing the pixel value in the shift position and the rotational position. 20. The apparatus of claim 19 , wherein said polygon is a rectangle and said predetermined angle is 180 °. 21. The apparatus of claim 19 , wherein said polygon is a square and said predetermined rotation angle is 90 °, 18 °.
0 ° and 270 °. 22. An apparatus for repeatedly writing a predetermined pattern element in a polygon tile area to generate a tile pattern, wherein a square including the pattern element is defined in advance as a stamp area, and the stamp area is placed. When the stamp area is placed, the boundary area where the stamp area always straddles the boundary of the tile area, and the inner area where the stamp area does not straddle the boundary when the stamp area is placed, are included in the tile area. The apparatus comprises: a pattern element source means for outputting the pattern element; and randomly generating a center position of the stamp area in the tile area for specifying a position at which the pattern element is written in the square area. A center coordinate generating means for determining whether the stamp area specified by the center position is in the boundary area or in the inner area Responding to the determination result of the area determining means, if the stamp area is within the inner area, writing the pattern element at a designated position of the stamp area, and setting the stamp area to the boundary area In the case of, the portion of the pattern element that protrudes from the boundary into the adjacent polygon area is shifted to a position on the tile area when the adjacent polygon area is overlaid on the tile area, and the boundary is shifted. The part of the pattern element straddling that does not protrude from the boundary and the shifted part are
Additional writing at a position rotated at least once by a predetermined angle around the center of the tile area according to the connection condition of the tile, and if the additional writing has occurred, writing to the inner area at least once means. 23. The apparatus according to claim 22 , wherein the number of additional writings in the inner area is a number determined so that the density of the pattern elements in the boundary area is substantially equal to the density of the pattern elements in the inner area. It is. 24. The apparatus according to claim 22 , further comprising a pattern rotating means for rotating the direction of the pattern element by an angle corresponding to a predetermined possible connection direction of the polygonal tile each time the pattern element is written. Have been. 25. The apparatus of claim 22 or 24,
At the time of generating the first tile pattern, there is provided a memory means for writing a write position of the stamp area determined to straddle the boundary, and the center coordinate generating means sets the inside of the inner area at the time of generating the second tile pattern. Means for randomly generating a center position of the stamp area, wherein the writing means reads a writing position from the memory means when the second tile pattern is generated, writes the pattern element at that position, and The area ratio of the boundary area
When S _I / S _B, to number of writes to the boundary region, including means for writing said pattern element to that location at approximately S _I / S _B times the number of writes. 26. The apparatus according to claim 25 , wherein said writing means includes means for executing writing to said boundary area and writing to said inner area in a mixed manner when said second tile pattern is generated. 27. The apparatus according to claim 25 , wherein a difference digital analysis method is used for both areas so that the number of times of writing to the inner area and the number of times of writing to the boundary area become the ratio S _I / S _B. Includes means for performing mixed writing.