JPH11149561A - Method and device for generating non-fractal scalar place - Google Patents

Abstract

PROBLEM TO BE SOLVED: To easily generate a non-fractal scalar place having an optional characteristic by using a scalar value which is given as fluctuation width at the time of calculating the scalar value of a grid point which is defined by means of a middle point displacing method. SOLUTION: An operator inputs a numerical string consisting of the scalar value of fluctuation width by which one-dimensional scalar place having the desired characteristic is obtained from an input device. A controller 3 temporarily stores the inputted value in a memory part 4. When arithmetic execution is indicated, a grid point generating part 5 generates the grid point of a 0-th stage. When the scalar value of the 0-th stage grid point is decided, the grid point generating part 5 generates a first stage grid point secondly. A scalar value arithmetic part 7 fetches the value which is decided as the fluctuation width of the first stage grid point from the numerical string stored in the memory part 14, generates one random number in a random number generating part 6 so as to fetch the value and operates the scalar value as against the first stage grid point. This kind of processing is executed to the designated stage.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method and an apparatus for generating a non-fractal scalar field having a desired fluctuation component.

[0002]

2. Description of the Related Art In recent years, computer graphics (C)
It is widely practiced to use the technique G) to perform design by performing various processings on an original image. An n-dimensional scalar field having a fluctuation component of 1 / f ^k is widely used as a tool for performing desired processing on an original image.

An n-dimensional scalar field having such a 1 / f ^k fluctuation component is called a fractal, and a fractal n
The midpoint displacement method is widely used as a method for generating a dimensional scalar field.

Hereinafter, a method of generating a fractal one-dimensional scalar field (one-dimensional fractal lattice) and a method of generating a fractal two-dimensional scalar field (two-dimensional fractal lattice) by the midpoint displacement method will be described.

[One-dimensional fractal grid] As shown in FIG. 2, two grid points A and B (indicated by a double circle in the figure) are defined on a single line at a predetermined distance from each other. Scalar values a and b are defined for these grid points A and B, respectively.
The two grid points A and B defined in this way are the grid points in the initial stage (hereinafter referred to as the 0th stage), and the scalar values a and b are set to these two grid points A and B. This is an initial condition.

Next, as shown in FIG. 3, a first-stage grid point C is defined at the midpoint between the two grid points A and B. At this time, a scalar value c is also defined for the grid point C, and the scalar value c is defined by a predetermined operation based on the scalar values a and b. FIG. 3 shows a grid point C
Indicates a state in which the scalar value c has not been determined yet.
Here, the grid points in the state where the scalar value is undefined are indicated by single circles, and the grid points in the state where the scalar values are defined are indicated by double circles. Hereinafter, the same applies.

The scalar value c of the grid point C is calculated by the following equation: c = (a + b) / 2 + T · RND (1) Here, a and b are grid points A
And B are scalar values defined for T, T is the maximum half-amplitude value of fluctuation, and RND is a random number. This random number is normally a random number in the range of −1 ≦ RND ≦ + 1.

As described above, a random number is used for the definition of the scalar value c, which depends on an accidental element.
However, the scalar value c is not defined as a completely random value, but is limited by the scalar values a and b of the adjacent grid points A and B and the maximum half-amplitude value T. That is, as shown in the above equation (1), a value obtained by adding an arbitrary value (determined by a random number) in the range of −T to + T to the average value of the scalar values a and b is a scalar value. It becomes the value of c. Therefore, the maximum half-amplitude value T is a parameter that limits the degree of fluctuation that deviates from the average value.

After the scalar value c for the grid point C at the first stage has been defined in this way, subsequently, as shown in FIG. 4, the middle point of the grid points A and C and the middle point of the grid points C and B are set. ,
The grid points D and E of the second stage are defined respectively. And
For these grid points D and E, scalar values d and e respectively
D = (a + c) / 2 + (1/2) · T · RND (2) e = (c + b) / 2 + (1/2) · T · RND (3) Here, as described above, T
Is a maximum half-amplitude value of fluctuation, and RND is a random number. formula
(2) and (3) are very similar to equation (1), but it should be noted that the maximum half-amplitude value T is multiplied by (1/2).

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

Hereinafter, the same operations as in the fourth, fifth,... Steps are repeatedly executed. Such an operation is performed by n
If (n is a natural number) iteratively, a number of grid points are defined between the grid points A and B in the 0th stage, and a predetermined scalar value is defined for each of these grid points. In addition, if the calculation method of the scalar value s for the grid point at the n-th stage is expressed by a general formula, s = (α + β) / 2 + (1/2 ⁿ⁻¹ ) · T · RND (5) Here, α and β are the scalar values of the grid points on both sides of the grid point, that is, the scalar values calculated for the grid points defined in the (n-1) th step. T is the maximum half-amplitude value of the fluctuation, and RND is a random number.

When a number of grid points having a predetermined scalar value are defined by such a method, these grid points become 1
This constitutes a dimensional fractal lattice.

[Two-dimensional fractal lattice]
The method of generating a two-dimensional fractal lattice by the midpoint displacement method has been described. Next, a method of generating a two-dimensional fractal lattice by the midpoint displacement method will be described.

In order to generate a two-dimensional fractal grid, as shown in FIG.
Grid points A, B, C, and D are arranged at vertices, and scalar values a, b, c, and d are defined, respectively. Here, the size of this square is the size of the finally generated two-dimensional fractal lattice.

Next, as shown in FIG. 6, between grid points AB,
The first stage grid points E, F, G, and H are defined at the middle points between BC, CD, and DA, and another first stage is formed at the intersection of the diagonal lines of the four grid points ABCD. Is defined. Then, scalar values e, f, g, h, and i are defined for these five grid points, respectively, which are calculated by the following equations.

E = (a + b) / 2 + T · RND (6) f = (b + c) / 2 + T · RND (7) g = (c + d) / 2 + T · RND (8) h = (d + a) / 2 + T · RND (9) i = (a + b + c + d) /4+T.RND (10) As in the example of the one-dimensional fractal lattice, T is the maximum half-amplitude value of fluctuation, and RND is a random number. This random number is normally a random number in the range of −1 ≦ RND ≦ + 1.

Thus, the first stage grid points E, F, G,
After the scalar values e, f, g, h, and i for H and I have been defined, subsequently, as shown in FIG. 7, at the midpoint of each adjacent grid point and the intersection of the diagonal lines of the four grid points, The grid points J, K, L, M, N,... Of the second stage are defined.
In FIG. 7, grid point names are displayed only for grid points J, K, L, M, and N in order to avoid complication. Then, for each of these grid points, a scalar value j,
k, l, m, n,... are calculated by the following equations. Here, only equations for j to n are shown.

J = (a + e) / 2 + (1/2) · T · RND (11) k = (e + i) / 2 + (1/2) · T · RND (12) l = (i + h) / 2 + (1/2) · T · RND (13) m = (h + a) / 2 + (１ ／) · T · RND (14) n = (a + e + i + h) / 4 + (1/2) · T · RND (15) In the equation for obtaining the scalar value of the grid point at the second stage, the maximum half-amplitude value T is multiplied by a factor of (1/2), as in the case of the one-dimensional fractal grid described above.

Hereinafter, similarly, the third stage, the fourth stage,.
By repeatedly executing the processing of the n-th stage, a scalar value is defined for a large number of grid points arranged on a two-dimensional plane.

The above processing will be described in general terms.
First, in the 0th stage, four grid points are defined at four corner positions of a rectangle of a desired size, and a predetermined scalar value is defined at each grid point. Then, the following processes may be sequentially executed as the process at the i-th stage.
That is, first, the smallest rectangle at the current stage that does not include the lattice points defined up to the (i-1) th stage is recognized.
For example, in the case of the first stage where i = 1, the rectangle ABCD shown in FIG. 5 is the minimum rectangle (a rectangle that does not include the grid points A, B, C, and D defined up to the zeroth stage), i = 2
In the case of the second stage, four rectangles AEIH, shown in FIG.
EBFI, HIGHD, and IFCG are the minimum rectangles (rectangles that do not include any of the lattice points A to I defined up to the first stage).

Then, a grid point to be defined in the i-th stage is generated at the midpoint of each side of the minimum rectangle and the center point of the minimum rectangle. For example, in the case of the first stage where i = 1, FIG.
As shown in the figure, the middle points E, F,
Grid points to be defined are generated at G, H and the center point I. Further, among these lattice points, the lattice point generated at the midpoint of each side is represented by the scalar value of the two lattice points defined by the (i-1) th stage existing at the end point of the side. Gives a scalar value obtained by applying a random number. For example, for the grid point E shown in FIG.
The random numbers RND are added to the scalar values a and b of the two grid points A and B.
Is given as a scalar value e. In general, a scalar value s ₁ for a grid point defined as the midpoint of adjacent grid points in the nth stage
S ₁ = (α + β) / 2 + (1/2 ⁿ⁻¹ ) · T · RND (16) Here, α and β are scalar values of grid points on both sides of the grid point (calculated in the (n-1) th step)
It is.

On the other hand, with respect to the grid point generated at the center point of the minimum rectangle, the (i)
-1) A scalar value obtained by applying a random number to the scalar value of the four grid points defined up to the stage is given. For example, for grid point I shown in FIG.
Scalar values a, b, c, and
A scalar value i obtained by applying a random number RND to d is given. In general, the method of calculating the scalar value s2 for the grid point defined as the center point of the minimum rectangle in the n-th stage can be expressed by the following equation: s ₂ = (α + β + γ + δ) / 4 + (1/2 ⁿ⁻¹ ) · T RND: (17) Here, α, β, γ, and δ are 4
Is the scalar value of the grid point at one corner (calculated in the (n-1) th step).

The two-dimensional fractal lattice generated by such a method eventually gives a scalar field spread two-dimensionally.

The method of generating a two-dimensional fractal lattice has been described above. It is known that a three-dimensional,..., N-dimensional fractal lattice can be generated by such a method.
For example, Minoru Okada et al. “Texture expression of heterogeneous materials using three-dimensional random fractals”
(Transactions of Information Processing Society of Japan Nov.1987 Vol.29 No.11 No.1146
Page below) are famous.

[0025]

According to the above method, an arbitrary n-dimensional fractal scalar field can be generated.
Such a scalar field is processed by acting on the original image. However, the fractal scalar field generated by the above-mentioned midpoint displacement method lacks variations because its characteristics are all the same. That is, the characteristic of the fractal scalar field generated by the midpoint displacement method is a hyperbolic curve as schematically shown in FIG. The horizontal axis in FIG. 8 indicates the spatial frequency f, and the vertical axis indicates the fluctuation power.
That is, what is shown in FIG. 8A can be called a fluctuation power spectrum of a fractal scalar field expressed by 1 / f ⁿ .

However, if the characteristics of the fractal scalar field acting on the original image are always as shown in FIG.
The state of the image obtained by processing is always the same.

The power spectrum of the fluctuation is shown in FIG.
As shown by (b), if the frequency becomes smaller rapidly as the spatial frequency f increases, or as shown by (c) in FIG. , The variation of the scalar field can be increased. A scalar field that cannot be represented by 1 / f ⁿ having the characteristics shown in FIGS. 8B and 8C in FIG. 8 cannot be said to be a fractal scalar field, and will be referred to as a non-fractal scalar field in this specification.

Now, such a non-fractal scalar field cannot be generated by the ordinary midpoint displacement method, but a non-fractal scalar field having an arbitrary characteristic can be obtained by using a method generally called an inverse Fourier transform method. It is known that scalar fields can be generated. That is, first, a frequency distribution having desired characteristics is given on an arbitrary n-dimensional space, and the obtained frequency distribution is subjected to inverse Fourier transform to obtain a scalar field.

However, in the inverse Fourier transform method, the fluctuation component can be set arbitrarily, as is apparent from the above description. However, a program for generating a scalar field when multidimensionally expanded is very difficult. It is complicated and not realistic.

The present invention has been made in view of the above problems, and a method and apparatus for easily generating a non-fractal scalar field having arbitrary characteristics by applying the midpoint displacement method. The purpose is to provide.

[0031]

According to a first aspect of the present invention, there is provided a method for generating a non-fractal scalar field, comprising the steps of: providing a predetermined number of arbitrary scalar values; The above-mentioned given scalar value is used as a fluctuation width when calculating a scalar value of a grid point defined by a method.

In the method for generating a non-fractal scalar field according to a second aspect, a function representing a desired characteristic curve is provided, and a scalar value of a grid point defined by a midpoint displacement method is calculated. The fluctuation width in the case is determined based on the function.

According to a third aspect of the present invention, there is provided an apparatus for generating a non-fractal scalar field, input means, grid point generating means for generating grid points based on a midpoint displacement method, and grid points generated by the grid point generating means. And a scalar value calculating unit that uses a scalar value input by the input unit as a fluctuation width when calculating the scalar value of (1).

According to a fourth aspect of the present invention, there is provided an apparatus for generating a non-fractal scalar field, comprising: input means; grid point generating means for generating grid points based on a midpoint displacement method; and grid points generated by the grid point generating means. And a scalar value calculating means for calculating a fluctuation width in calculating the scalar value of the scalar value based on a function input by the input means.

[0035]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, embodiments will be described with reference to the drawings. First, a fluctuation width Z is defined. Here, a coefficient to which a random number is applied when determining a scalar value to be given to each grid point by the midpoint displacement method is defined as a fluctuation width Z. For example, as shown in the above equation (5), when generating a one-dimensional fractal scalar field by the midpoint displacement method, the scalar value s of the grid point at the n-th stage is s = (α + β) / 2 + (1 ^{/ 2 n-1) · T} · RND ... (5) in it given, wherein a coefficient random RND is acting "(1/2 ^n-1) · T" is from the fluctuation width. Therefore, in the method for generating a non-fractal scalar field according to the present invention, when generating a one-dimensional non-fractal scalar field, the scalar value s of the grid point at the n-th stage is generally s = (α + β) / 2 + Z · RND (18) Here, α and β are (n
Naturally, it is a scalar value calculated for the grid point defined in step -1). The same applies to a two-dimensional scalar field.

Now, an embodiment of a method for generating a non-fractal one-dimensional scalar field and a method for generating a non-fractal two-dimensional scalar field by the method for generating a non-fractal scalar field according to the present invention will be described. I do.

[Generation Method of One-Dimensional Scalar Field] First, a sequence of fluctuation width Z consisting of the following scalar values is given. _{Z 10, Z 11, ...,} Z 1m, ... ... (19) Here, the value of each fluctuation width can be arbitrarily determined.
The first two Z ₁₀ and Z ₁₁ are scalar values given to the grid points defined in the 0th stage, Z ₁₃ is the fluctuation width used in calculating the grid points defined in the first stage, Z ₁₄ , Z ₁₅ is the fluctuation width used when calculating the grid points defined in the second stage, and Z _{16 to} Z ₁₉ are the fluctuation widths used when calculating the grid points defined in the third stage. Therefore, assuming that grid points are defined up to the n-th stage, the number K of scalar values in the sequence represented by (19) is as follows: K = 2 + 2 ⁰ +2 ¹ +2 ² +... +2 ^n-1 (20)

Accordingly, assuming that two grid points A and B are defined on a single line at a predetermined distance from each other as shown in FIG. supply a scalar value Z ₁₀ of the lattice point B so as to provide a scalar value Z ₁₁ of the second term in the above sequence.

Next, as a first stage, as shown in FIG.
A grid point C is defined at the midpoint between the two grid points A and B, and a scalar value c is calculated for this grid point C. In this case, the fluctuation width is defined as supply a scalar value Z _12, calculated by _{c = (Z 10 + Z 11} ) / 2 + Z 12 · RND ... (21). Here, RND is a random number. A random number having an appropriate distribution may be used.

Next, as a second stage, as shown in FIG.
The grid points D and E in the second stage are defined at the midpoints of the lattice points A and C and the midpoints of the lattice points C and B, respectively, and the scalar value for each of the lattice points D and E is calculated. But,
Section 4 of the sequence as a fluctuation range in this case, gives a scalar value Z _13, Z ₁₄ of Section _{5, d = (Z 10 + c} ) / 2 + Z 13 · RND ... (22) e = (c + Z 11) / 2 + Z ₁₄ · RND is calculated by ... (23). Here, RND is a random number as described above.

Hereinafter, if the calculations are similarly performed from the third stage to the n-th stage, a non-fractal one-dimensional scalar field having desired characteristics can be generated. It should be noted that the scalar value of each term in the above sequence is naturally a value that can obtain a scalar field having desired characteristics.

Further, as is apparent from the above description, when a plurality of grid points are defined at a certain stage, scalar values of the number of grid points defined at that stage fluctuate from the above sequence. Although it is used as the width, the order in which these scalar values correspond to which grid points may be arbitrarily determined in advance. In the example described above, correspondence is made in order from the grid point on the left side of the figure.

As described above, in the conventionally used midpoint displacement method, the fluctuation width when calculating the scalar value of the grid point defined after the first stage is automatically determined by the maximum half amplitude value T. In contrast, according to the method for generating a non-fractal scalar field, the fluctuation width when calculating the scalar value of the grid point defined after the first stage can be arbitrarily determined. A non-fractal scalar field with the following characteristics can be generated.

[Method of Generating a Two-Dimensional Scalar Field] The method of generating a non-fractal one-dimensional scalar field has been described above. Next, a method of generating a non-fractal scalar field according to the present invention will be described. An embodiment of the generation method will be described.

First, similarly to the above-described method of generating a non-fractal one-dimensional scalar field, a sequence of fluctuation width Z consisting of the following scalar values is given. _{Z 20, Z 21, ...,} Z 2m, ... ... (24) where the values of the fluctuation width may be arbitrarily determined.
This sequence is a scalar value given to a grid point defined in the 0th stage, a scalar value used as a fluctuation width used when calculating a scalar value given to a grid point defined in the first stage,.
This is a sequence of scalar values that are used as fluctuation widths when calculating scalar values given to grid points defined in the n-th stage.

Therefore, assuming that grid points A, B, C, and D are defined at the four vertices of the square at the 0th stage as shown in FIG. 5, for example, the grid point A has the scalar value Z of the first term of the above-mentioned sequence. ₂₀
At the lattice point B, the scalar value Z ₂₁ of the second term of the above sequence
At the lattice point C, the scalar value Z ₂₂ of the third term of the above sequence
At the lattice point D, the scalar value Z ₂₃ of the fourth term in the above sequence
To give.

Next, as a first stage, as shown in FIG.
The grid points E, F, G, and H are defined at the middle points between the grid points AB, BC, CD, and DA, and another first step is performed at the intersection of the diagonal lines of the four grid points ABCD. Is defined, and a scalar value is calculated for these lattice points E to I. In this case, the scalar values of the fifth to ninth terms in the above sequence are given as the fluctuation width. ,
It is calculated by the following formula.

E = (Z ₂₀ + Z ₂₁ ) / 2 + Z ₂₄ · RND (25) f = (Z ₂₁ + Z ₂₂ ) / 2 + Z ₂₅ · RND (26) g = (Z ₂₂ + Z ₂₃ ) / 2 + Z ₂₆ · RND ... (27) h = (Z 23 + Z 20) / 2 + Z 27 · RND ... (28) i = (Z 20 + Z 21 + Z 22 + Z 23) / 4 + Z 28 · RND ... (29) where, RND is a random number . A random number having an appropriate distribution may be used.

Hereinafter, if the calculations are similarly performed from the second stage to the n-th stage, a non-fractal two-dimensional scalar field having desired characteristics can be generated. It should be noted that the scalar value of each term in the above sequence is naturally a value that can obtain a scalar field having desired characteristics.

Further, as is apparent from the above description, when a plurality of grid points are defined at a certain stage, the scalar values of the number of grid points defined at the corresponding stage fluctuate from the above sequence. Although it is used as the width, the order in which these scalar values correspond to which grid points may be arbitrarily determined in advance.

As described above, in the conventionally used midpoint displacement method, the fluctuation width when calculating the scalar value of the grid point defined after the first stage is automatically determined by the maximum half amplitude value T. In contrast, according to this non-fractal scalar field generation method, the fluctuation width when calculating the scalar value of each grid point defined after the first stage can be arbitrarily determined. A non-fractal scalar field with the desired properties can be generated.

For example, it is assumed that an appropriate scalar value is given to a grid point defined first in the 0th stage, and a scalar which is a fluctuation width used when calculating a scalar value given to a grid point defined in the 1st stage. An arbitrary value α is given as a value, and a scalar value which is a fluctuation width used when calculating a scalar value given to a grid point defined in the second stage is α /
3 gives, when a scalar value which is a fluctuation range used for calculating the scalar value given to the lattice point defined in the third step so as giving the alpha / n ^n, as shown by B in FIG. 8 It is possible to generate a scalar field having such a characteristic that the power of fluctuation rapidly decreases as the spatial frequency increases.

The fluctuation width used when calculating the scalar value given to the grid points defined in the first to i-th stages is set to 0, and the scalar value given to the grid points defined in the (i + 1) -th and subsequent stages is set. As the fluctuation width used when calculating the value
By giving an appropriate value other than 0, a scalar field having characteristics as shown by C in FIG. 8 can be generated.

[Other Embodiments] The embodiment of the method for generating a non-fractal scalar field according to the present invention has been described above. Next, another embodiment will be described. In this embodiment, a desired characteristic curve, that is, a power spectrum of fluctuation is first given as a mathematical expression as a function of a spatial frequency. Then, as a fluctuation width used in calculating a scalar value given to a grid point defined in a certain stage, a function value obtained when a value of a spatial frequency corresponding to the stage is substituted into this function is used. For example, assuming that a desired characteristic curve is given by a function F (f) and a spatial frequency corresponding to a certain stage is f _i , when calculating a scalar value to be given to a grid point defined at that stage, The fluctuation width used is F (f _i ). In this case, an arbitrary scalar value may be given to the grid point defined in the 0th stage.

It is clear that this method can be applied to the case where an arbitrary n-dimensional scalar field is generated. As described above, according to this method, when a desired characteristic curve is given, a fluctuation width used when calculating a scalar value to be given to a grid point defined at each stage is automatically obtained from the characteristic curve. Will be done.

The embodiment of the method for generating a non-fractal scalar field according to the present invention has been described above. Next, referring to FIG. 1 for an embodiment of an apparatus for generating a non-fractal scalar field according to the present invention. I will explain. In FIG. 1, 1 is an input device, 2 is a display device, 3 is a control device,
Denotes a memory unit, 5 denotes a grid point generation unit, 6 denotes a random number generation unit, and 7 denotes a scalar value calculation unit.

The input device 1 is composed of a keyboard or the like, and constitutes an interactive man-machine interface together with the display device 2 composed of a color CRT or the like. The control device 3 is composed of an appropriate processing unit, and includes a memory unit 4, a grid point generation unit 5, a random number generation unit 6, and a scalar value calculation unit 7.

Next, the operation will be described. Here, a case where a non-fractal one-dimensional scalar field is generated will be described for easy understanding. First, a case will be described in which a sequence shown in Expression (19) is given, and a scalar value of a grid point at each stage is obtained based on the sequence.

In this case, the operator first sets the size of the one-dimensional scalar field generated from the input device 1, the number of grid points to be operated, and the one-dimensional scalar having desired characteristics. A sequence consisting of scalar values having a fluctuation width to obtain a field is input to instruct execution of a scalar field.

When these are input, the control device 3 temporarily stores the value input by the input device 1 in a predetermined area of the memory unit 4. Then, when the execution of the operation is instructed, first, the grid point generating unit 5 generates a grid point of the 0th stage. When the grid point of the 0th stage is generated, the scalar value calculation unit 7 is started, and the values of the first term and the second term are fetched from the sequence stored in the memory unit 4, and are respectively stored in the grid points of the 0th stage. assign.

When the scalar value of the grid point at the 0th stage is determined in this way, the grid point generator 5 next generates the grid point at the first stage. When the grid point generator 5 generates the first-stage grid points, the scalar value calculator 7 calculates a value determined as the fluctuation width of the first-stage grid points from the sequence stored in the memory unit 4. At the same time, one random number is generated by the random number generator 6 and its value is captured, and the scalar value for the first-stage grid point is calculated by the above equation (21).

The above processing is performed up to the designated stage. Thus, a non-fractal one-dimensional scalar field having desired characteristics can be generated. The operation in the case of generating a non-fractal one-dimensional scalar field has been described above, but the same applies to the case of generating a two-dimensional or more non-fractal scalar field.

Next, a description will be given of the operation in the case where a desired characteristic curve, that is, a fluctuation power spectrum is given as a function of a spatial frequency and is given as a formula, and a scalar value of a grid point at each stage is obtained based on the function. even here,
A case where a non-fractal one-dimensional scalar field is generated for easy understanding will be described.

In this case, the operator first sets the size of the one-dimensional scalar field generated from the input device 1, the number of grid points to be calculated, and the 0 th order.
A scalar value for a grid point defined in a step is input, and a function of a spatial frequency representing a one-dimensional scalar field having desired characteristics is input to instruct execution of a scalar field.

When these are input, the control device 3 temporarily stores the values and functions input by the input device 1 in a predetermined area of the memory unit 4. Then, when the execution of the operation is instructed, first, the grid point generating unit 5 generates a grid point of the 0th stage. When the grid point of the 0th stage is generated, the scalar value calculation unit 7 is started, and the scalar value of the 0th stage stored in the memory unit 4 is fetched and assigned to the grid point of the 0th stage.

When the scalar value of the grid point at the 0th stage is determined in this way, the grid point generator 5 next generates the grid point at the first stage. When the grid point generator 5 generates the first-stage grid points, the scalar value calculator 7 takes in the function stored in the memory 4 and substitutes the value of the spatial frequency corresponding to the first stage into the function. The value of the function is obtained as the fluctuation width of the grid point at the first stage, and one random number is generated by the random number generator 6 and the value is taken in. Computes a scalar value for.

The above processing is performed up to the designated stage. Thus, a non-fractal one-dimensional scalar field having desired characteristics can be generated. The operation in the case of generating a non-fractal one-dimensional scalar field has been described above, but the same applies to the case of generating a two-dimensional or more non-fractal scalar field.

As described above, according to the method and apparatus for generating a nonfractal scalar field, it is possible to easily generate an n-dimensional scalar field having a desired fluctuation component.

The embodiments of the method and apparatus for generating a non-fractal scalar field according to the present invention have been described above.
The present invention is not limited to the above embodiment, and various modifications are possible. For example, the present invention can be applied to a case where a scalar field generally called a scalar field having a similarity ratio of √2 is generated. In addition, the present applicant has disclosed in
Repeatable n as proposed in US Pat.
The present invention can be applied to the case where a dimensional scalar field is generated.

[Brief description of the drawings]

FIG. 1 is a diagram showing an embodiment of an apparatus for generating a non-fractal scalar field according to the present invention.

FIG. 2 is a diagram illustrating a state of a 0th stage when a one-dimensional fractal lattice is generated by a midpoint displacement method.

FIG. 3 is a diagram showing a state of a first stage when a one-dimensional fractal lattice is generated by a midpoint displacement method.

FIG. 4 is a diagram illustrating a state of a second stage when a one-dimensional fractal lattice is generated by a midpoint displacement method.

FIG. 5 is a diagram showing a state of a 0th stage when a two-dimensional fractal lattice is generated by the midpoint displacement method.

FIG. 6 is a diagram showing a state of a first stage when a two-dimensional fractal lattice is generated by a midpoint displacement method.

FIG. 7 is a diagram showing a state of a second stage when a two-dimensional fractal lattice is generated by the midpoint displacement method.

FIG. 8 is a diagram illustrating characteristics of a fractal scalar field generated by a midpoint displacement method and illustrating an object of the present invention.

[Explanation of symbols]

 REFERENCE SIGNS LIST 1 input device 2 display device 3 control device 4 memory unit 5 lattice point generation unit 6 random number generation unit 7 scalar value calculation unit

Claims (4)

[Claims] 1. A method according to claim 1, wherein a given number of arbitrary scalar values are given, and said given scalar value is used as a fluctuation width when calculating a scalar value of a grid point defined by a midpoint displacement method. Characteristic non-fractal scalar field generation method. 2. A function representing a desired characteristic curve is provided, and a fluctuation width in calculating a scalar value of a grid point defined by a midpoint displacement method is determined based on the function. To generate non-fractal scalar fields. 3. An input means, a grid point generating means for generating grid points based on a midpoint displacement method, and an input as a fluctuation width when calculating a scalar value of a grid point generated by the grid point generating means. A non-fractal scalar field generation device, comprising: a scalar value calculation unit that uses a scalar value input by the unit. 4. An input means, a grid point generating means for generating grid points based on a midpoint displacement method, and a fluctuation width for calculating a scalar value of a grid point generated by the grid point generating means. A non-fractal scalar field generation device, comprising: a scalar value calculation unit that obtains a scalar value based on a function input by the unit.