JP2792539B2 - 3D data creation system from contour lines - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a system for creating three-dimensional data from contour lines, and more particularly, to applying a grid on a two-dimensional plane of contour line data, which is a series of points constituting a contour line, to thereby form each mesh on the grid. The present invention relates to a three-dimensional data creation system that creates three-dimensional data such as a smooth terrain model that is close to actual by obtaining altitude data of points.

[0002]

2. Description of the Related Art When generating three-dimensional data from contour data, a sequence of points obtained by approximating a contour line as a curve by a continuous straight line is used as input data by a process called vectorization (hereinafter referred to as points on the contour line). In this case, indicate the points included in the point sequence data.) A grid is applied to this input data as shown in FIG. 12, and the altitude of each grid point (hereinafter referred to as a mesh point) is obtained by some processing, and is used as output data.

A conventional method for generating three-dimensional data from contour data is performed according to the flow shown in FIG. An example of such a conventional method for generating three-dimensional data from high-contour data is “Method for Creating Three-Dimensional Data for Terrain Model” (Japanese Patent Laid-Open No. 4-293078) (hereinafter referred to as Prior Art 1). is there. In the prior art 1, the altitude is calculated by linear interpolation from the altitudes of two contour lines at a point to be obtained. As shown in FIG. 14, two points a is the nearest two higher lines in the mesh point c to be obtained, searching b, altitude h _a from the ratio of the distance d _a, d _b to the two points, h _{Find b} .

[0004] Although linear interpolation is easy to calculate, it is assumed that the altitude changes linearly. Therefore, in actuality, tertiary terrain such as mountains and valleys or terrain where the slope changes rapidly is actually used. When the original data is generated, a result different from the actual terrain is often obtained.

On the other hand, as a method of performing interpolation closer to the actual terrain, it is conceivable to use an interpolation method such as curve interpolation or curved surface interpolation. Curve interpolation can express a smoother slope than linear interpolation, but since the terrain, which is originally a plane, can only be captured as a line,
The result may differ from the actual terrain. On the other hand, curved surface interpolation can be regarded as a surface as compared with linear interpolation or curve interpolation, and therefore, theoretically, smoother three-dimensional data can be generated.

As another prior art related to the present invention, Japanese Patent Application Laid-Open No. Hei 5-274418 (hereinafter referred to as Prior Art 2)
A "contour line drawing method" is disclosed in which, when contour lines are drawn with respect to height data having noise, noise below an arbitrary frequency is removed and global characteristics are extracted. That is, in the prior art 2, the entire region is divided into partial regions by the region dividing device, the height data on the sides forming the boundaries of the partial regions are respectively approximated by the curve approximating device, and the surface is approximated by the function interpolating device. . Contour lines approximated by a curved surface are traced by a contour line tracking device, and contour lines extending over partial regions are smoothly connected by a smoothing device, thereby removing noise and drawing contour lines.

Japanese Patent Laid-Open Publication No. Hei 1-231180 (hereinafter referred to as Prior Art 3) discloses that the values of three-dimensional information, the number of intersecting contour lines, and the interpolation within the contour region are performed, and the grid points are interpolated. A "three-dimensional data interpolation device" has been disclosed which is capable of obtaining an interpolation value of an altitude value which is extremely close to a true value as compared with a simple linear interpolation by obtaining an interpolation value of an elevation value. I have. That is, in Prior Art 3, it is assumed that grid point data is given on a grid as three-dimensional information. The image data is a digital image of an actual topographic map corresponding to the grid point data. The CPU calculates a conversion formula for aligning the three-dimensional information of the grid point data with the digital image of the image data. For positioning, the position coordinates of four points around the picture frame are measured in the digital image, and a conversion formula is created by the least square method using the corresponding position coordinates of the three-dimensional information. The intersection detection circuit calculates the address of the image corresponding to the adjacent point to be interpolated by the above conversion formula, extracts the corresponding area, and counts the number of intersections with the contour lines in the area. The CPU also obtains the coordinates of adjacent intersection contours of the interpolation point and performs interpolation calculation in the contour region by linear interpolation.

[0008]

When three-dimensional data is generated from curved surface data by surface interpolation, a curved surface passing through a plurality of designated points is generated. The designated point through which the surface passes is called a sample point. Surface interpolation of an arbitrary point requires data of a plurality of sample points surrounding the point. These sampling points can be set in any way, but the accuracy is greatly affected by the setting method.

For example, in a terrain where the contour lines are curved, the point sequence data representing the contour lines is usually set finely. Therefore, if a sample point is selected from a point close to a point to be interpolated, the curve interpolation is performed infinitely. Approaching (Fig. 15
(A)). Further, when the sample point is selected as shown in FIG. 15B, the information indicating the curvature of the contour line is not reflected, and the line representing the slope of the terrain is largely bent at a portion where the contour line intersects with the contour line, thereby reflecting the continuity of the slope. It is difficult to obtain high accuracy because it is not performed. In FIG. 15, a curve indicates a contour line, a black point indicates a sample point, a straight line indicates a line connecting the sample points, and P is a mesh point.

At present, there is no established sample point setting method. Therefore, even if curved surface interpolation is used, accuracy may be poor or erroneous interpolation may be performed depending on the sample point setting. is there.

Therefore, the present invention proposes a method for solving the above-mentioned problem as a method of setting sample points for performing the surface interpolation, and makes it possible to create a smooth terrain model utilizing the characteristics of the surface interpolation. It aims to provide a data creation system.

Further, each point constituting adjacent contour lines is associated with each other, and based on the corresponding points obtained by the association,
Even if sample points are set, if a locally optimum set is set as a corresponding point, the entire area will be as shown in FIG. 16, and a corresponding point that is not necessarily optimum may be set. is there. Since the sample points are based on the corresponding points, if the setting of the corresponding points is not appropriate, the set sample points are not suitable for the curved surface interpolation, and the accuracy of the curved surface interpolation is reduced. That is, a result different from the actual terrain may be obtained.

In view of the above, the present invention proposes a method for solving the above-mentioned problem as a method for setting corresponding points, and provides a three-dimensional data creation system capable of creating a smooth terrain model utilizing the features of curved surface interpolation. That is the other purpose.

The prior art 2 discloses a technical idea of globally drawing contour lines by removing noise having a frequency equal to or less than a certain value from height data having noise. This is a technical idea which is completely different from the technical idea of the present invention for obtaining the height data of the mesh points. Prior Art 3 is based on the premise that grid point data is given on a grid using three-dimensional information, and discloses a technical idea for obtaining an interpolated value of an elevation value between grid points. Similarly to the above, the technical idea of the present invention relating to the technical idea of obtaining the altitude data of each mesh point on the grid from the contour data is a technical idea completely different from the present invention.

[0015]

According to a first aspect of the present invention, a grid is formed on a two-dimensional plane of contour data, which is data of a series of points forming a contour line, thereby forming each of these grids. seeking elevation data of the mesh points a three-dimensional data creation system for creating three-dimensional data, the corresponding point searching means for searching the corresponding points between the contour data constituting the contour of adjacent, the corresponding point searching unit Sample point setting means for setting a plurality of sample points surrounding the mesh points for interpolation based on the corresponding points searched by the method, and interpolation using a curved surface using the sample points set by the sample point setting means. and an altitude calculating means for performing altitude processing to obtain altitude data of the mesh points.

According to a second aspect of the present invention, in the above-described three-dimensional data creation system, the corresponding point searching means determines a degree of correspondence with each point on the contour line constituting the adjacent contour line. A correspondence degree calculation unit that calculates a correspondence degree that is an evaluation function to be represented, and a corresponding point selection unit that selects a set of corresponding points such that the evaluation function represented by the sum of the correspondence degrees is minimized as a whole A three-dimensional data creation system characterized by the following is obtained.

[0017]

According to the first aspect of the present invention, when point sequence data constituting a contour line is given, a corresponding point between adjacent contour line data is searched, and a sampling point optimal for surface interpolation is searched based on the corresponding point. By selecting and setting a plurality of three-dimensional data, and performing three-dimensional data by performing surface interpolation including mesh points using the data of the plurality of sample points, it is possible to obtain three-dimensional data of a smooth terrain model closer to the actual one. Can be

According to the second aspect of the present invention, when point sequence data constituting a contour line is given, an evaluation function value representing the degree of correspondence of each point between adjacent contour line data is calculated,
A corresponding point is set based on the result. By selecting and setting a plurality of optimal sample points for surface interpolation based on the corresponding points, and performing three-dimensional data by performing surface interpolation including mesh points using data of the plurality of sample points, Three-dimensional data of a smooth terrain model close to the actual one can be obtained.

[0019]

Next, the present invention will be described in detail with reference to the drawings.

FIG. 1 shows a functional block diagram of a system for creating three-dimensional data from contour lines according to a first embodiment of the present invention as a processing flow chart. The system for generating three-dimensional data from contour lines according to the present embodiment is provided with an evaluation function indicating a distance, an inclination, or the like for adjacent contour data, and a corresponding point searching means 10 for searching for a corresponding point based on the value of the evaluation function.
A sample point setting unit 11 for setting sample points for surface interpolation based on the corresponding points searched by the corresponding point search unit 10; and a curved surface using the sample points set by the sample point setting unit 11. Altitude calculation means 12 for performing interpolation to obtain altitude data of mesh points on a two-dimensional plane. Hereinafter, each means will be described.

The corresponding point searching means 10 associates arbitrary points on two adjacent contour lines. "Any point on two adjacent contour lines corresponds" refers to a case where the distance between the two points is the shortest, a case where the inclination direction and the curvature of the contour line match, or the like. (Hereinafter, the corresponding points are called corresponding points). As means for searching for the corresponding point, the processing of FIG. 2 is performed on two adjacent contour lines.

First, as shown in FIG. 3, two adjacent contour lines A and B are selected (step 100), and two sets of corresponding points are set ([a _s , b _s ], [a _e ,
b _e]). In FIG. 3, as an example, the closest point in a section having a distance is selected as two sets of corresponding points. This 2
An area between the set of corresponding points is set as a corresponding point search area (step 101).

In the corresponding point search area, a point on the contour line A is a _i (i = 0,..., N), and a point on B is b _j (j = 0,
..., m). When points a _i and b _j are corresponding points,
Evaluation function values representing the degree of correspondence between points a _i and b _{j + 1} , a _{i + 1} and b _j , a _{i + 1} and b _{j + 1} , f (a _i , b _{j + 1} ), f
(A _{i + 1} , b _j ) and f (a _{i + 1} , b _{j + 1} ) are calculated (step 102).

In this embodiment, as an example of an evaluation function, f (a, b) = d (a, b) × a (a, b) f = (a, b): evaluation function d of points a and b (A, b): Euclidean distance between points a, b a (a, b): Expression of angle difference (θ _a −θ _b ) between straight line ab and two contour lines is used.

Since the smaller the value of the evaluation function is, the stronger the correspondence between the two points is, the two points having the smallest evaluation function are regarded as the corresponding points.

Next, let the corresponding points be a _i and b _j ,
That is, when f (a _{i + 1} , b _j ) is minimum, only i is obtained, and when f (a _i , b _{j + 1} ) is minimum, only j is obtained.
When f (a _{i + 1} , b _{j + 1} ) becomes the minimum, i and j are incremented by one, and the next corresponding point is similarly obtained (steps 103 to 105).

This process is repeated to obtain all the corresponding points in the corresponding point search area (steps 106 and 107). Similarly, corresponding points of all adjacent contour lines are obtained (step 108).

Next, the operation of the sample point setting means 11 will be described. For example, in the case of performing a spline surface interpolation using a Coons bicubic patch as the surface interpolation method, twelve sample points indicated by black points in FIG. 6 are required. For details of the spline surface interpolation using the Koons bicubic patch, see “Basic Graphics”, published by Shokodo Co., Ltd. on October 25, 1985, by Prof. Kawai, a professor at the University of Tokyo. 137-147.

In this embodiment, it is assumed that a spline surface interpolation method using this Coons bicubic patch is used.
One setting method in the case of setting 12 points surrounding the mesh point P as shown in FIG. 4 as the sample points of the curved surface interpolation will be described.

The corresponding points are shown in FIGS.
There are three types of correspondence (c), which are called one-to-one, one-to-many, and many-to-one correspondences, respectively. First, the nearest point a on the contour line on both sides of the mesh point is searched. FIG.
When the point a has a one-to-one correspondence as in (a), the point a is defined as a sample point T ₀₀ and the corresponding point of the point a is defined as a sample point T ₀₁ .

As shown in FIG. 5 (b), when the correspondence is one-to-many, the point a is set to the sampling point T ₀₀ , and among the corresponding points of the point a, when the number of the corresponding points is an odd number, the corresponding point in the middle is set. In the case of an even number, the corresponding point closer to the mesh point P in the middle is set as the sample point _T01 .

As shown in FIG. 5C, in the case of a many-to-one correspondence, among the corresponding points of the corresponding point b of the point a, when the number of the corresponding points is an odd number, the center corresponding point is replaced with the even number of the corresponding points. In this case, the corresponding point closer to the mesh point P in the middle is a sample point T ₀₀ , and the point b is a sample point T ₀₁ .

Assuming that two of the twelve sample points have been set in this way, a method of setting the remaining ten points will now be described with reference to FIG.

[0034] There is seen from the sample point T ₀₀ to mesh point P side, to search for re-neighboring points with corresponding points other than the sample point T _01,
The sample point T _10. In a manner similar to the set sample points T ₁₀ corresponding to the sample point T _00, set to select the sample point T ₁₁ from outside the T ₁₀ of the corresponding point T _10.

Next, the nearest point having a corresponding point other than the sample points T ₀₁ and T ₁₁ and located on the opposite side of the mesh point P when viewed from the sample points T ₀₀ and T ₁₀ is searched. _-10, and T _20. Sample point T _-11 in the same manner as described above, sets the T _21.

Finally, similarly, sample points T ₀₀ , T ₁₀ , T ₀₁ , T
Sampling points T _0-1 , T _1-1 , T ₀₂ , and T ₁₂ corresponding to ₁₁ are respectively set on outer adjacent contour lines. In this way, twelve sample points surrounding the mesh point P are set.

Next, the operation of the altitude calculation means 12 will be described. Surface interpolation is performed using the 12 sample points set by the sample point setting means 11 to calculate the height of the mesh points. As an example of the curved surface interpolation, as described above, the spline curved surface interpolation using the Coons bicubic patch is used. FIG. 7 shows a calculation formula in this case, and FIG. 6 shows the relationship between the variables in FIG.

In the present embodiment, the corresponding point setting means sets the corresponding point search area manually. However, as a modification, two sets of nearest neighbors are searched, and the set is searched for the start point and end point of the corresponding point search area. For example, it is possible to set automatically.

As an example of the calculation result according to the prior art 1 ("Method of creating three-dimensional data for terrain model" in Japanese Patent Application Laid-Open No. 4-297878), the altitudes of points X and Y in FIG. FIG. 9 shows the results. FIG. 9A shows the prior art 1 and FIG. 9B shows the present invention, and shows a cross section taken along a straight line 1 in FIG.

The terrain assumed is indicated by a dotted line in FIG. According to FIG. 9, in the case of the prior art 1, the height of the point Y is lower than that of the point X. Although the altitude is 100 m, if this value is correct, a contour line should be drawn here, which contradicts the contour line data in FIG. On the other hand, in the present invention, it is found that a value close to the estimated terrain (altitude) is obtained.

In the first embodiment, when setting the corresponding points, as shown in FIG. 3, [a _i ,
b _{j + 1} ], [a _{i + 1} , b _j ], [a _{i + 1} , b _{j + 1} ]
Only one set of points is considered. Therefore, among these three sets of points, a locally optimum set is set as a corresponding point. However, as described above, when the entire area is viewed, FIG.
6 and a corresponding point that is not always optimal may be set.

Referring to FIG. 10, in order to solve this problem, the system for creating three-dimensional data from contour lines according to the second embodiment of the present invention is different from that of the first embodiment except that the corresponding point searching means is changed. , Has the same configuration as that shown in FIG. Accordingly, the corresponding point searching means is denoted by reference numeral 10A, and those having the same functions are denoted by the same reference numerals and description thereof is omitted.

The corresponding point searching means 10A is provided with an evaluation function using distance and inclination as parameters for adjacent contour data, and a corresponding degree calculating means 10-1 for calculating an evaluation function value of each point on the contour data. , The correspondence degree calculating means 10
And corresponding point selecting means 10-2 for selecting a set of corresponding points that minimizes the sum of the evaluation functions as a whole based on the value of the evaluation function calculated by -1. Hereinafter, each means will be described.

The corresponding point searching means 10A obtains a set of associated points on two adjacent contour lines.
"Any associated point on two adjacent contours"
The term refers to either a pair of points at which the distance between two points is closest (the contour lines are closest) or a pair of points at which the slope direction and the curvature of the contour lines match at that point (hereinafter, referred to as a pair). The pair of two associated points is called a corresponding point), and the value of the evaluation function representing the degree of correspondence is called the degree of correspondence.

In the correspondence degree calculating means 10-1, two adjacent
The degree of correspondence of an arbitrary point on one contour line is calculated.

First, as shown in FIG. 11, two adjacent contour lines A and B are selected, and two sets of corresponding points are set ([a
_{s, b s], [a} e, b e]). In FIG. 11, the closest point in a certain section of the contour line is determined as a corresponding point, and
In this example, the corresponding points in one section are paired. An area between the two sets of corresponding points is defined as a corresponding point search area.

[0047] The points on the contour A in the corresponding point search area _{a i (i = 0, ...} , n, a 0 = a s, a n = a e), B
Let the upper point be b _j (j = 0,..., M, b ₀ = b _s , b _m = b
_e ), and an evaluation function f (a _i , bj) representing the degree of correspondence
) Is calculated.

In the present embodiment, as the evaluation function f, f (a, b) = d (a, b) × a (a, b) f = (a, b) as in the first embodiment. : Evaluation function of points a and b d (a, b): Euclidean distance between points a and b a (a, b): Expression of acute angle difference | θ _a −θ _b | between straight line ab and two contour lines Is used. The smaller the value of the evaluation function (evaluation degree), the stronger the correspondence between the two points.

The corresponding point selecting means 10-2 selects a set of corresponding points based on the corresponding degree calculated by the corresponding degree calculating means 10-1.

Since the smaller the degree of correspondence, the stronger the correspondence between the two points, the set of corresponding points that minimizes the sum of the degrees of correspondence in the entire corresponding point search area is the optimal corresponding point in this area. Is obtained as a set of

When the sum of the degrees of correspondence is calculated for all combinations, the amount of calculation becomes enormous. Therefore, in this embodiment, a dynamic algorithm known as an algorithm for solving such a minimization problem with a smaller amount of calculation is used. We will use the principle of programming. For details on dynamic programming, see
"Pattern Recognition and Learning Algorithm" published by Bunichi Sogo Publishing Co., Ltd.
University of Electro-Communications by Kazuhiko Ozeki) 94-97. Specifically, the sum of the degrees of correspondence is calculated by solving the following recurrence formula.

[0052] g (i, j) = f (a i, b j) + g (i-1, k) g (i, j): point a _i, region when the b _j and a corresponding point ([a ₀ , b ₀ ], [a _i , b _j ]), where g (0, 0) = f (a ₀ , b ₀ ) f (a _i , b _j ): points a _i , b The correspondence degree of _j : k that gives min {g (i-1, k) | 0 ≦ k ≦ j} In the above recurrence formula, [a _i−1 , b _k ] is the corresponding point.

The processing of the correspondence calculating means 10-1 and the corresponding point selecting means 10-2 is repeated to obtain the correspondence of all adjacent contour lines in all regions.

In the present embodiment, the corresponding point calculating area is set manually by the corresponding degree calculating means. However, as a modified example, two sets of nearest neighbor points are searched, and the closest point is searched for the starting point and the ending point of the corresponding point searching area. For example, it is possible to set automatically.

[0055]

As described above, according to the first aspect of the present invention, by providing the corresponding point searching means and the sample point setting means, it is possible to realize more accurate curved surface interpolation. There is an effect that it is possible to generate smooth three-dimensional data close to the terrain.

Further, according to the second aspect of the present invention, by providing the correspondence degree calculating means and the corresponding point selecting means,
It is possible to prevent the setting of a corresponding point that is locally optimal but inappropriate from a global perspective. In addition, by setting appropriate corresponding points, sample points more suitable for curved surface interpolation can be set, and more accurate curved surface interpolation can be realized. As a result, there is an effect that smooth three-dimensional data close to the actual terrain can be generated.

[Brief description of the drawings]

FIG. 1 is a flowchart showing a configuration of a system for generating three-dimensional data from contour lines according to a first embodiment of the present invention.

FIG. 2 is a flowchart showing a process in a corresponding point search means of the first embodiment.

FIG. 3 is a diagram illustrating a method of obtaining a corresponding point by a corresponding point search unit according to the first embodiment.

FIG. 4 is a diagram showing a positional relationship between sample points set by a sample point setting unit of the first embodiment.

FIG. 5 is a diagram illustrating types of corresponding points in a corresponding point search unit according to the first embodiment.

FIG. 6 is an explanatory diagram of an equation for curved surface interpolation in the altitude calculation means of the first embodiment.

FIG. 7 is a diagram showing a calculation formula for curved surface interpolation.

FIG. 8 is a diagram illustrating an example of contour line data.

FIG. 9 is an explanatory diagram showing calculation results of the related art (prior art 1) and the present invention.

FIG. 10 is a flowchart illustrating a configuration of a system for generating three-dimensional data from contour lines according to the second embodiment of this invention.

FIG. 11 is an explanatory diagram illustrating a correspondence search area in a correspondence calculation unit according to the second embodiment;

FIG. 12 is an explanatory diagram showing a method of setting mesh points.

FIG. 13 is a flowchart showing the configuration of a conventional method for generating three-dimensional data from contour lines.

FIG. 14 is an explanatory diagram showing a method of obtaining an altitude by a conventional method.

FIG. 15 is an explanatory diagram showing an example of setting sample points.

FIG. 16 is an explanatory diagram illustrating an example of setting corresponding points in the method of generating three-dimensional data from contour lines according to the first embodiment.

[Explanation of symbols]

 10, 10A Corresponding point searching means 11 Sampling point setting means 12 Altitude calculating means 10-1 Corresponding degree calculating means 10-2 Corresponding point selecting means

Claims (7)

(57) [Claims] 1. A cubic method for generating three-dimensional data by obtaining altitude data of each mesh point on a two-dimensional plane of contour data, which is data of a series of points constituting a contour line, on a two-dimensional plane. An original data creation system, comprising: a corresponding point searching means for searching for a corresponding point between contour data forming mutually adjacent contour lines; and surrounding the mesh point based on the corresponding point searched by the corresponding point searching means. Sample point setting means for setting a plurality of sample points for interpolation, and music using the sample points set by the sample point setting means.
An altitude calculation means for performing altitude interpolation to obtain the altitude data of the mesh points. 2. A method according to claim 1, wherein the corresponding point search means displays each of the points on the adjacent contour lines as a product of a Euclidean distance and an angle formed by a line segment connecting the corresponding points and the contour line. 2. The three-dimensional data creation system according to claim 1, wherein the correspondence is made by an evaluation function to be performed. 3. The correspondence point search means, wherein: a correspondence degree calculation means for calculating a correspondence degree, which is an evaluation function representing a degree of correspondence with respect to each point on the contour lines constituting the adjacent contour lines; 2. The three-dimensional data creation system according to claim 1, further comprising: a corresponding point selecting unit that selects a set of corresponding points such that an evaluation function represented by a sum is minimized as a whole. 4. The correspondence degree calculating means calculates, for each point on the contour line forming the adjacent contour line, a product of a Euclidean distance and an angle formed by a line segment connecting the two points and the contour line. 4. The three-dimensional data creation system according to claim 3, wherein the degree of correspondence, which is a value of the evaluation function to be performed, is calculated. 5. The corresponding point selecting means, based on the degree of correspondence at each point calculated by the corresponding point calculating means, determines a combination of points that minimizes an evaluation function represented by the sum of the degrees of correspondence. 4. The three-dimensional data creation system according to claim 3, wherein a corresponding point is selected. 6. The method according to claim 1, wherein the sample point setting means is arranged such that, when an arbitrary point on the contour line has a plurality of adjacent contour lines associated with each other by the corresponding point search means, a middle corresponding point exists when the number is an odd number. The three-dimensional data creation system according to claim 1, wherein, when there are a plurality of points, a corresponding point of a point close to the mesh point is selected in the middle. 7. The height calculation means is configured to calculate the height of the mesh point by a spline surface interpolation process using a Coons bicubic patch, and the sample point setting means is configured to calculate twelve points surrounding the mesh point. The three-dimensional data creation system according to claim 1, wherein the system is configured to set sample points.