JP2007264952A - Ground-analyzing mesh generation method and ground-analyzing mesh generation program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a method for generating a highly accurate ground-analyzing mesh approximating a stratum boundary face on the basis of stratum boundary altitude data of sampling points arranged on a plurality of sampling lines set inside an analysis target area. <P>SOLUTION: This ground-analyzing mesh generation method has: a step S3 for classifying the sampling line comprising a set of a plurality of sampling points each having the data related to an in-horizontal face position and a height of the stratum boundary face in the position, nearly arranged on a straight line inside the horizontal face into two sampling line groups according to a direction of the sampling line; a step S4 for generating a temporary mesh on the basis of a first sampling line group; a step S5 for generating a temporary mesh on the basis of a second sampling line group; and a step S6 for composing the temporary mesh obtained from the first sampling line group and the temporary mesh obtained from the second sampling line group to generate the mesh approximating the stratum boundary face. <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

  The present invention relates to a mesh generation method and a mesh generation program, and in particular, generates a mesh that approximates a boundary surface extending over an analysis target area in a three-dimensional space in which the analysis target area is specified on a horizontal plane, and performs ground analysis, etc. The present invention relates to a mesh generation method and a mesh generation program that enable execution of simulation.

  Here, the boundary surface means a boundary surface between layers having different characteristics in a three-dimensional space. Examples of such a boundary surface include a ground surface that is a boundary between the atmosphere and the crust, and a stratum boundary surface between layers having different characteristics. Furthermore, the outer surface of a tangible object is included in the category of the boundary surface. Further, the term “mesh” means an aggregate of unit elements given as, for example, a quadrilateral element.

  A technique for generating a mesh that approximates a curved surface extending over a range in a three-dimensional space in which the range on the horizontal plane is specified is described in, for example, Japanese Patent Laid-Open No. 9-305746. In this publication, the simple average is used for altitude data at other points in the target area based on the data on the height or depth at the sampling points existing in the target area (hereinafter referred to as altitude data). A terrain data interpolating apparatus that generates a mesh that approximates the ground surface of a target area by obtaining the calculated interpolation operation has been disclosed.

  When generating a mesh that approximates the ground surface in the target area, first, an orthogonal lattice is generated by equally dividing a rectangular region on the horizontal plane that specifies the target area in the X direction and the Y direction, respectively. An initial mesh is generated by assigning corresponding altitude data to each lattice point existing in the orthogonal lattice. Sampling points are set to coincide with these lattice points, and altitude data obtained for each sampling point is used for generating an initial mesh.

  Second, regarding the initial mesh, altitude data at a position corresponding to the midpoint of the line segment connecting the lattice points, that is, the sampling points, is given as an average value of the altitude data of the two sampling points. Also, for each quadrilateral element constituting the initial mesh, altitude data at a position corresponding to the center point is given as an average value of altitude data of four adjacent sampling points. As a result, a primary divided mesh is generated. Furthermore, terrain data having a desired data density is configured by repeating similar mesh division processing.

JP-A-9-305746

  In the ground survey, several sampling lines are set according to the geographical characteristics of the survey target, and sampling points are selected at regular intervals or unequal intervals for each sampling line. By carrying out a boring survey for each sampling point, it is possible to obtain altitude data or the like at the boundary between different geological layers immediately below the sampling point. Due to topographical or economic constraints, it is extremely difficult to conduct many boring surveys with sampling points coincident with grid points, which is advantageous when performing ground analysis simulation after the survey. Therefore, when generating a mesh that approximates the formation boundary surface, if a conventional mesh generation method is used, the quadrilateral element that is a unit for data interpolation can be made dense and sufficient interpolation accuracy can be obtained. There is a problem that it is difficult to obtain an effective mesh suitable for ground analysis.

  In an actual boring survey, each sampling line tends to be classified into a main-direction sampling line group that requires detailed analysis and a sub-direction sampling group. In the sampling line group in the main direction, the number of sampling lines is large and sampling line points arranged on the sampling lines are densely arranged. In the sub-direction sampling line group, the number of sampling lines is relatively small, and the sampling line points arranged on the sampling lines are relatively coarsely arranged. The setting of the sampling line oriented in the sub direction is intended to supplement analysis in the main direction and efficiently obtain analysis data in the entire analysis target area. In a conventional mesh generation method, new height data is calculated by a simple average of height data determined at adjacent grid points. That is, altitude data obtained based on sampling lines in the main direction and expected to have a relatively high accuracy, and altitude data obtained based on sampling lines in the sub direction and expected to have a relatively low accuracy. There is a problem that an optimal mesh cannot always be obtained in consideration of the overall accuracy.

  The present invention has been made to solve the above-described problems, and has an accuracy of approximating a boundary surface based on altitude data at sampling points arranged on a plurality of sampling lines set in an analysis target area. An object is to provide a mesh generation method and a mesh generation program capable of generating a high mesh. Further, the present invention can generate a mesh with improved overall accuracy by reflecting the direction of each sampling line group set in the analysis target area in the calculation related to the calculation of altitude data. An object is to provide a generation method and a mesh generation program.

  In order to solve the above technical problems, the ground analysis mesh generation method (ground analysis mesh generation program) according to the present invention is based on the data on the horizontal plane position and the height of the formation boundary surface at the position. And having a plurality of sampling lines composed of a set of a plurality of sampling points arranged substantially linearly in a horizontal plane for each of two sampling line groups obtained by classifying each sampling line according to the direction of the sampling line, The first step (first step) to the fifth step (fifth step) are performed, and in the first step (first step), the sampling lines included in each sampling line group are specified, In the second process (second step), at each sampling line, at the sampling point included in the sampling line. The formation boundary line extending in the sampling line direction is generated by obtaining an interpolation curve connecting the formation boundary points based on the height of the formation boundary surface. In the third step (third step), each sampling line is generated. Every time, the height of the formation boundary line extending in the sampling line direction at the intersection of the sampling line on the horizontal plane and each lattice line in the predetermined direction is calculated. In the fourth step (fourth step), the predetermined height is calculated. For each grid line in the direction, the formation boundary line extending in the grid line direction in a predetermined direction by obtaining an interpolation curve connecting the formation boundary points based on the height of the formation boundary line extending in the sampling direction at the intersection In the fifth step (fifth step), for each grid line in a predetermined direction, the height of the formation boundary line extending in the grid line direction at the grid point is calculated, Temporary mesh obtained from sampling line group and is obtained so as to generate a mesh that approximates the geological boundary surface by combining the temporary mesh obtained from the second sampling line group. Thereby, it is not necessary to make the sampling points coincide with the lattice points, and the flexibility of the ground analysis system can be improved. In addition, since it was configured to generate a formation boundary line composed of a plurality of formation boundary points using an interpolation curve, the conventional method used to calculate the height of the formation boundary surface at the lattice points by simple averaging Compared with the method, a mesh that approximates the formation boundary surface can be obtained with high accuracy. Furthermore, since the main operations necessary to generate a mesh that approximates the formation boundary surface are operations related to calculation of interpolation curves, operations related to calculation of altitude data related to intersections of sampling lines and grid lines, etc. Compared with the case where an interpolation curved surface is generated based on sampling points, the mesh generation processing can be performed at high speed.

  Moreover, the mesh generation method for ground analysis according to the present invention includes a height in the temporary mesh obtained from the first sampling line group and a height in the temporary mesh obtained from the second sampling line group for each lattice point. The mesh that approximates the formation boundary surface is generated by setting the weighted average value of the values to the height at the lattice point. Thus, by setting appropriate weight values according to the difference between the number of investigations and investigation accuracy in the direction of the first sampling line group and the number of investigations and investigation accuracy in the direction of the second sampling line group, respectively. The mesh that approximates the formation boundary surface can be obtained with higher accuracy.

  In addition, the ground generation mesh generation method according to the present invention is the shortest distance to the sampling line included in the first sampling line group and the sampling line included in the second sampling line group for each lattice point. The weight value for the height in the temporary mesh obtained from the first sampling line group and the weight value for the height in the temporary mesh obtained from the second sampling line group are calculated on the basis of the ratio to the shortest distance. It is a thing. As a result, the weight value for the height in the temporary mesh obtained from the sampling line group to which the closer sampling line belongs can be increased appropriately according to the ratio of the distance to the sampling line, so the stratum boundary is approximated. The mesh to be obtained can be obtained with higher accuracy.

  In addition, the ground analysis mesh generation method according to the present invention provides a new weight value by multiplying the weight value for the height in the temporary mesh obtained from the first sampling line group by a predetermined constant for each grid point. In addition, a value obtained by subtracting the weight value obtained by multiplying the constant by 1 is set as a new weight value for the height in the mesh obtained from the second sampling line group. Thus, by setting the above constant based on the difference between the number of investigations and investigation accuracy in the direction of the first sampling line group and the number of investigations and investigation accuracy in the direction of the second sampling line group, the ratio of the shortest distance is set. Thus, the weight value calculated based on can be appropriately corrected, and a mesh approximating the formation boundary surface can be obtained with higher accuracy.

  The ground analysis mesh generation method according to the present invention uses a spline curve as an interpolation curve. Thereby, it is possible to generate a smooth and highly accurate formation boundary line that passes through a plurality of formation boundary points, and a mesh that approximates the formation boundary surface can be obtained with higher accuracy.

  The ground analysis mesh generation method according to the present invention enables an arbitrary rectangular analysis target area to be set on a screen on which a topographic map is displayed. As a result, the target range to be analyzed can be clearly grasped on the topographic map, and the size and shape of the analyzed range can be arbitrarily changed to generate a ground analysis mesh suitable for analysis. Convenience can be improved.

  In addition, the mesh generation method (mesh generation program) according to the present invention has a plurality of data arranged on a substantially straight line in the horizontal plane, each having data on the horizontal plane position and the height of the boundary surface at the position. A first step (first step) is performed for each of one or a plurality of sampling line groups obtained by classifying a plurality of sampling lines composed of a set of sampling points into one or a plurality of groups according to the direction of the sampling lines. ) To 5th step (fifth step), the first step (first step) identifies the sampling lines included in each sampling line group, and the second step (second step). ) For each sampling line, the boundary point is set based on the height of the boundary surface at the sampling point included in the sampling line. A boundary line extending in the sampling line direction, which is an intersection line between the cross section along the sampling line and the boundary surface, is generated by obtaining a continuous interpolation curve. In the third step (third step), each sampling line is generated. In addition, the height of the boundary line extending in the sampling line direction at the intersection of the sampling line on the horizontal plane and each lattice line in the predetermined direction is calculated. In the fourth step (fourth step), the height of the predetermined direction is calculated. For each grid line, a grid that is an intersection line between the cross section along the grid line in a predetermined direction and the boundary surface by obtaining an interpolation curve that connects the boundary points based on the height of the boundary line at the intersection A boundary line extending in the line direction is generated, and in the fifth step (fifth step), for each lattice line in a predetermined direction, the height of the boundary line extending in the lattice line direction at the lattice point is calculated. Generating a temporary mesh at each sampling line group, it is obtained so as to generate a mesh that approximates the boundary surface by combining the temporary mesh obtained from two or more sampling line group. Thereby, it is not necessary to make the sampling points coincide with the lattice points, and the flexibility of the mesh generation system can be improved. In addition, since the formation boundary layer composed of a plurality of boundary points is generated using an interpolation curve, the height of the boundary surface at the lattice point is calculated based on the interpolation curve. Compared with the conventional method that calculates the height of the boundary surface at the lattice point by averaging, a mesh that approximates the boundary surface can be obtained with high accuracy. Furthermore, since the main operations required to generate the boundary surface are operations related to the calculation of the interpolation curve and operations related to the calculation of the height of the boundary surface at the intersection of the sampling line and the grid line, the sampling point Compared with the case where an interpolation curved surface is generated based on this, mesh generation processing can be performed at high speed.

  According to the present invention, for the first sampling line group and the second sampling line group, a formation boundary line formed by connecting a plurality of formation boundary points is generated using an interpolation curve in which a spline curve is suitable. Then, a temporary mesh is generated by calculating the height of the formation boundary surface at the lattice point based on these formation boundary lines, and a mesh that approximates the formation boundary surface is generated by combining the two temporary meshes. Since it comprised as mentioned above, there exists an effect that the mesh which approximates a formation boundary surface can be obtained with high precision.

  According to the present invention, for each lattice point, the weighted average value of the height of the temporary mesh obtained from the first sampling line group and the height of the temporary mesh obtained from the second sampling line group is calculated as the height at the lattice point. With this configuration, a mesh that approximates the formation boundary surface is generated, so the number of surveys and survey accuracy in the direction of the first sampling line group and the number of surveys and survey accuracy in the direction of the second sampling line group By setting an appropriate weight value according to the difference, it is possible to generate a more accurate mesh reflecting the investigation mode in each direction.

DESCRIPTION OF EMBODIMENTS Hereinafter, preferred embodiments of a ground analysis mesh generation method and a ground analysis mesh generation program according to the present invention will be described in detail with reference to the accompanying drawings.
Embodiment 1 FIG.
FIG. 1 is a diagram showing an example of the configuration of a ground analysis system that uses the mesh generation method according to the present invention. In FIG. 1, 1 is a ground analysis system realized by a workstation or a personal computer, 2 is a program execution unit constituted by a CPU of a computer, 3 is a storage unit provided as a hard disk, for example, and 4 is provided as a display, for example. Display unit, 5 is a shape modeling program, 6 is a mesh generation program, 7 is an analysis program, 8 is a display program, 9 is a systematic collection of various data such as map data, geological data, topographic data, and earthquake data. Database. The various programs described above are downloaded from an external server via an information storage medium such as a CD-ROM or DVD-ROM or via a network and installed in the storage unit 3 included in the ground analysis system 1. By executing the predetermined mesh generation program by the program execution unit 2, the mesh generation function in the ground analysis system is realized.

  FIG. 2 is a flowchart showing a mesh generation method according to Embodiment 1 of the present invention. If the topographic map of the surrounding area including the analysis target area for executing the ground analysis is displayed on the display unit 4, the analysis target area is set in the topographic map (step S1). If the analysis target area is set, a sampling point including a sampling point at which the boring survey has been performed and a set of a plurality of sampling points arranged on a substantially straight line in the horizontal plane is set (step S2).

  For the setting of the sampling point, the horizontal coordinate of the sampling point and the altitude data of the formation boundary surface at the position, the data from the storage means storing the sampling line to which the sampling point belongs and the type of the direction of the sampling line are stored. Can be read and a symbol or the like indicating the sampling point is displayed at the corresponding position. Further, it is possible to use a method of specifying the position of the sampling point on the screen of the display unit 4 using an input means such as a mouse or a keyboard and displaying a symbol or the like indicating the sampling point at the corresponding position.

  Regarding the setting of the sampling line, when the information of the sampling line to which the sampling point belongs is stored in the storage means for each sampling point, the data related to the sampling line is read from the storage means and belongs to the same sampling line A method of displaying a straight line segment that almost passes through the sampling point can be adopted. Further, it is possible to use a method of specifying a sampling point belonging to the same sampling line using the input means and displaying a linear line segment that almost passes through the sampling point belonging to the same sampling line.

  As already mentioned, a boring survey is usually performed on sampling points arranged on a sampling line that faces a direction categorized as either the main direction or the sub-direction. That is, the direction of each sampling line is classified into either the main direction or the sub direction. If all the sampling lines are set, according to the direction of the sampling line, each sampling line is classified into either a sampling line group in the main direction or a sampling line group in the sub direction. (Step S3). When the type related to the direction of the sampling line is stored in the storage unit for each sampling line, data related to the direction of the sampling line is read from the storage unit, and the sampling line is displayed on the screen according to the direction of the sampling line. Is changed so that the main-direction sampling line and the sub-direction sampling line can be identified. Further, the direction of the sampling line may be specified using the input means, and the color, form, etc. of the line segment representing the sampling line on the screen may be changed according to the direction of the sampling line.

  FIG. 3 is a diagram showing an analysis target area set in the topographic map. In FIG. 3, circles indicate sampling points located on the sampling line in the main direction, and crosses indicate sampling points located on the sampling line in the sub direction. If a sampling point is set in the analysis target area, an appropriate straight line is generated as a sampling line using, for example, the least square method. Further, an intersection of a line segment that defines the range of the analysis target area and a straight line representing the sampling line is obtained and used as an end point of the sampling line. FIG. 4 is a diagram illustrating sampling lines set in the analysis target area. In FIG. 4, the sampling lines included in the sampling line group in the main direction are indicated by solid lines, and the sampling lines included in the sampling line group in the sub direction are indicated by broken lines.

  In the main direction, the sampling line LA given as a line segment between the end points PA1 and PA2, the sampling line LB given as a line segment between the end points PB1 and PB2, and between the end points PC1 and PC2 A sampling line LC given as a line segment and a sampling line LD given as a line segment between the end points PD1 and PD2 are set. In the sub direction, the sampling line LE given as a line segment between the end points PE1 and PE2, the sampling line LF given as a line segment between the end points PF1 and PF2, and the end points PG1 and PG2 A sampling line LG given as a line segment between them is set.

  If the sampling lines included in the sampling line group in the main direction and the sampling lines included in the sampling line group in the sub direction are identified, the formation boundary surface is approximated based on the sampling lines included in the sampling line group in the main direction. To generate a temporary mesh (hereinafter referred to as a first temporary mesh as appropriate) (step S4). FIG. 5 is a diagram illustrating a temporary mesh generated based on a sampling line group in the main direction. The analysis target area is specified on the horizontal plane. Based on the orthogonal grid obtained by equally dividing the long and short sides of the rectangle as shown in FIG. By giving altitude data of the formation boundary surface at the corresponding position, such a temporary mesh or a synthesized mesh described later can be generated.

  Next, based on the sampling lines included in the sub-direction sampling line group, a temporary mesh that approximates the formation boundary surface (hereinafter referred to as a second temporary mesh as appropriate) is generated (step S5). FIG. 6 is a diagram illustrating a temporary mesh generated based on a sampling line group in the sub direction. Here, the orthogonal lattice that is the basis of the first temporary mesh and the orthogonal lattice that is the basis of the second temporary mesh have the same form. That is, each orthogonal lattice has the same number of divisions in the long side direction and the short side direction, and the first temporary mesh and the second temporary mesh are associated with each lattice point. Note that a method of generating a temporary mesh that approximates the formation boundary surface based on either the main direction or the sub-direction sampling line group will be described later. Moreover, about the process of step S4 and the process of step S5, any process may be performed first and you may make it perform both processes in parallel.

  If the first temporary mesh and the second temporary mesh are generated, the first temporary mesh and the second temporary mesh are combined to generate a mesh that approximates the formation boundary surface (step S6). When the first temporary mesh and the second temporary mesh are combined, a weighted average value of the height data of the first temporary mesh and the height data of the second temporary mesh is combined for each lattice point. The altitude data at the corresponding grid point.

The lattice point on the orthogonal lattice on which the first temporary mesh and the second temporary mesh are commonly used is represented by K (i, j), and corresponds to the lattice point K (i, j) in the synthesized mesh. The altitude data is represented by H (i, j), the altitude data corresponding to the grid point K (i, j) in the first temporary mesh is represented by H1 (i, j), and the grid point K in the second temporary mesh. The altitude data corresponding to (i, j) is represented by H2 (i, j). When synthesizing the first temporary mesh and the second temporary mesh, if the weight value indicating the contribution of the first temporary mesh at the lattice point K (i, j) is α (i, j), the altitude data H (i, j) is obtained by the following equation 1.
[Formula 1]
H (i, j) = α (i, j) * H1 (i, j) + (1−α (i, j)) * H2 (i, j)
By performing the above calculation for all lattice points, a mesh that approximates the formation boundary surface can be generated.

Regarding the weight value α, the same value may be set for all grid points, or the weight value α may be set appropriately for each grid point. One method for setting the weight value for each grid point is to calculate the shortest distance from the grid point to the sampling line in the main direction and the shortest distance from the sampling line in the sub direction, and the ratio of these shortest distances. It is conceivable to calculate the weight value based on the above. FIG. 7 is a diagram illustrating a weight value calculation method. In FIG. 7, K (i, j) is a grid point in i row and j column, L1a and L1b are sampling lines in the main direction, L2a and L2b are sampling lines in the sub direction, and l1 is from the grid point K (i, j). A distance to the sampling line L1a, l2 indicates a distance from the lattice point K (i, j) to the sampling line L2b. In this case, the weight value α (i, j) related to the first temporary mesh is obtained from the following Expression 2.
[Formula 2]
α (i, j) = l2 / (l1 + l2) (2)
The weight value (1-α (i, j)) related to the second temporary mesh is naturally l1 / (l1 + l2). The first temporary mesh and the second temporary mesh are synthesized by substituting the weight values obtained in this way into Equation 1 and calculating the altitude data H (i, j) for all lattice points. The resulting mesh is generated. FIG. 8 is a diagram showing the synthesized mesh.

  As described above, there are differences in the number of sampling lines in each direction, the density of sampling points in the sampling lines, and the like between the main direction and the sub direction. Due to this, the first temporary mesh often approximates the formation boundary surface with higher accuracy than the second temporary mesh. Therefore, it is conceivable to introduce a coefficient reflecting such a difference in approximation accuracy into the calculation of the weight value. For example, if the ratio of the approximation accuracy of the first temporary mesh to the approximation accuracy of the second temporary mesh is β (β> 1), it approximates the above weight value α obtained based on the shortest distance to the sampling line. The altitude data of each grid point may be calculated using a numerical value obtained by multiplying by the accuracy ratio β as a new weight value. In this case, altitude data is calculated using αβ as a weight value instead of α in Equation 1. Note that sampling points that do not belong to any sampling line may appear in the step of setting the sampling line. When such a sampling point is close to the lattice point K (i, j), a new weight data is calculated by calculating a weighted average value of the height data at the sampling point and the height data obtained by the equation (1). By obtaining the above, it becomes possible to generate a more accurate mesh.

  Next, a method for generating a temporary mesh that approximates the formation boundary surface based on the sampling lines included in the sampling line group will be described. In the following description, the generation of the first temporary mesh based on the sampling line group in the main direction will be described as an example. FIG. 9 is a flowchart illustrating a method for generating a temporary mesh. If the sampling line group used for generating the temporary mesh is specified, the sampling line included in the sampling line group is specified (step S11). When the first temporary mesh is generated based on the sampling line group in the main direction, the sampling lines LA, LB, LC, and LD shown in FIG. 4 are used for generating the temporary mesh.

  If a sampling line for generating a temporary mesh is specified, an interpolation curve for connecting the formation boundary point is obtained for each sampling line based on the altitude data of the formation boundary surface at the sampling point included in the sampling line. Thus, the formation boundary line in the cross section along the sampling line is generated (step S12). Here, the formation boundary line means an intersection line between a section along a predetermined straight line extending in the horizontal direction and the formation boundary surface. The formation boundary point means an intersection of a perpendicular extending from a predetermined point such as a sampling point whose position is specified on the horizontal plane and the formation boundary surface.

  Taking the sampling line LA as an example, generation of a formation boundary line extending in the sampling line direction will be described. FIG. 10 is a diagram illustrating a formation boundary line extending in the sampling line direction. In FIG. 10, a circle indicates a sampling point, and a triangle indicates a point on the formation boundary surface immediately below the sampling point, that is, a formation boundary point. The position of the formation boundary point is specified by obtaining the altitude data of the formation boundary surface by the boring survey at the sampling point. 11 is the ground surface, 12 is the stratum boundary line I-II between the stratum I and the stratum II, and 13 is the stratum boundary line II-III between the stratum II and the stratum III. According to FIG. 10, there are two formation boundary surfaces, formation boundary surface I-II and formation boundary surface II-III, in the analysis target area, but in the following description, formation boundary surface I-II An example of generating an approximate temporary mesh will be described. It will be clear that the generation of a temporary mesh approximating the formation boundary surface II-III can be realized in a similar manner.

  The formation boundary line is generated by obtaining a smooth curve that passes through the formation boundary point indicated by the triangle mark and whose height position is fixed. Specifically, an interpolation curve expressed by a different polynomial is assigned to each section given as a section between the stratum boundary points and a section between the stratum boundary points and the end of the analysis target area. For example, a spline curve or a Bezier curve is preferably used as the interpolation curve. When the spline curve is used, the boundary of the formation is a node, and the connection of the interpolation curve at the node and the continuity of the first and second derivatives are guaranteed. Mathematically, a boundary condition is given to a polynomial representing a spline function, and a simultaneous linear equation related to the coefficient of the polynomial is solved, thereby obtaining a curve that smoothly connects the boundary points of each layer. In addition, when the calculation speed is required to be increased even if the accuracy is lowered, the formation boundary line may be generated by linearly interpolating formation boundary points.

  In order to generate a temporary mesh, based on an orthogonal grid formed by dividing a rectangle that specifies the analysis target area on the horizontal plane, the altitude data of the formation boundary surface at the position corresponding to each grid point is obtained. It is necessary to calculate. If a formation boundary line extending in the sampling line direction is generated, for each sampling line, an intersection between the sampling line on the horizontal plane and each grid line extending in a direction substantially transverse to the main direction is obtained, and The altitude data of the formation boundary line extending in the sampling line direction is calculated (step S13). FIG. 11 is a diagram showing orthogonal lattices and sampling lines in the main direction set in the analysis target area. As shown in FIG. 11, the grid lines are classified into a row direction and a column direction. The grid lines extending in the row direction are m0, m1, m2,. In addition, grid lines extending in the column direction are denoted as n0, n1, n2,. For the sampling lines LA, LB, LC, and LD in the main direction, the grid lines in the row direction extend in a direction that substantially crosses. Here, for each sampling line, intersections with grid lines m0, m1, m2,..., M13 extending in the row direction are calculated. In FIG. 11, black circles indicate the intersections between the sampling lines and the grid lines.

  Taking the sampling line LA as an example, calculation of altitude boundary level data extending in the sampling line direction at the intersection of the sampling line and each grid line will be described. FIG. 12 is a diagram illustrating a formation boundary line extending in the sampling line direction. As shown in FIG. 12, the formation boundary line extending in the sampling direction in the analysis target area is divided by the number obtained by subtracting 1 from the number of grid lines in the row direction (in this case, 13). By calculating the intersection of the dividing line and the formation boundary line 12, altitude data at the position where the formation boundary line 12 intersects the respective grid lines m0, m1, m2,..., M13 in the row direction can be calculated. it can. Similarly, for the sampling line LB, the sampling line LC, and the sampling line LD, the formation boundary line extending in the direction of each sampling line is at a position intersecting with the respective grid lines m0, m1, m2,. Altitude data can be calculated.

  If the altitude data at the intersection of each grid line in the row direction and each sampling line is calculated, the stratum boundary point is connected for each grid line in the row direction based on the altitude data at the intersection with each sampling line. By obtaining the interpolation curve, the formation boundary line in the cross section along the grid line in the row direction is generated (step S14). FIG. 13 is a diagram showing formation boundary lines extending in the lattice line direction. Here, a description will be given by taking the formation boundary line along the grid line m6 as an example. In step S13, the altitude data of the formation boundary line at the intersection of the grid line m6 and each sampling line is calculated. In FIG. 13, PAU and PAD are formation boundary points on the intersection with the sampling line A, PBU and PBD are formation boundary points on the intersection with the sampling line B, and PCU and PCD are formation boundaries on the intersection with the sampling line C. Points, PDUs, and PDDs are formation boundary points on the intersection with the sampling line D. Further, 21 is a formation boundary line I-II between the formation I and the formation II, and 22 is a formation boundary line II-III between the formation II and the formation III.

  Based on the horizontal position coordinates of the intersection of each sampling line and the grid line m6 and the altitude data of the stratum boundary points PAU, PBU, PCU and PDU, the section between the stratum boundary points and the end of the stratum boundary point and the analysis target area An interpolation curve expressed by a different polynomial is assigned to each section given as a section with a part. The generation of the interpolation curve can be realized in the same manner as the interpolation curve used when generating the formation boundary line extending in the sampling line direction, and the description thereof is omitted.

  If a formation boundary line extending in the lattice line direction is generated, altitude data at the position of the lattice point is calculated for each lattice point in the formation boundary line (step S15). Here, the calculation of altitude data at each lattice point of the formation boundary line extending in the direction of the lattice line m6 will be described using the lattice line m6 as an example. As shown in FIG. 13, the formation boundary line extending in the direction of the grid line m6 in the analysis target area is divided into a number obtained by subtracting 1 from the number of grid lines in the column direction (16 in this case). By obtaining the intersections of these dividing lines and the formation boundary line 21, the lattice points K (m6, n0), K (m6, n1), K (m6, n2),. , K (m6, n16), altitude data can be calculated. Similarly, for the grid lines m0, m1,... M5, m7,... M16, altitude data at the positions of the respective grid points can be calculated for the formation boundary lines extending in the respective grid line directions. As a result, altitude data relating to all grid points in the basic orthogonal grid is calculated, and a first temporary mesh is generated.

  It will be apparent that the second temporary mesh generated based on the sub-direction sampling line group can also be generated using the same method as the first temporary mesh. However, regarding the second temporary mesh, unlike the first temporary mesh, the intersections with the grid lines as shown in FIG. 11 are obtained between the grid lines extending in the column direction. Thereby, for each lattice line extending in the column direction, a formation boundary line as shown in FIG. 13 is generated. As described above, the first temporary mesh and the second temporary mesh generate the formation boundary lines along lattice lines extending in different directions in principle. However, depending on the direction of the sampling line group in the main direction and the sampling line group in the sub direction, the formation boundary line may be generated along the grid lines that extend in the same direction.

  As described above, according to the mesh generation method according to the first embodiment, the first step of setting the sampling lines included in each sampling line group for each sampling line group in the main direction and the sub direction, Generating a formation boundary line extending in the sampling line direction by obtaining an interpolation curve connecting the formation boundary points based on altitude data of the formation boundary surface at the sampling points included in the sampling line A third step of calculating height data of a formation boundary line extending in the sampling line direction at the intersection of the sampling line on the horizontal plane and each lattice line in a predetermined direction for each sampling line; For each grid line in the direction of A fourth step of generating a formation boundary line extending in a grid line direction in a predetermined direction by obtaining an interpolation curve connecting the formation boundary points based on altitude data of the formation boundary line extending to A fifth step of calculating altitude data of the formation boundary line extending in the lattice line direction at the lattice point for each line, and performing sampling in the sub-direction and the first temporary mesh obtained from the sampling line group in the main direction Since it is configured to generate a mesh that approximates the formation boundary by combining the second temporary mesh obtained from the line group, there is no need to match the sampling points to the grid points, and the flexibility of the ground analysis system Can be improved. In addition, since it is configured to generate a formation boundary line that is formed by connecting a plurality of formation boundary points using an interpolation curve, altitude data related to the lattice points is calculated based on the interpolation curve. Compared with the conventional method which calculated the altitude data related to the grid points, a mesh that approximates the formation boundary surface can be obtained with high accuracy. Furthermore, since the main operations necessary to generate a mesh that approximates the formation boundary surface are operations related to calculation of interpolation curves, operations related to calculation of altitude data related to intersections of sampling lines and grid lines, etc. Compared with the case where an interpolation curved surface is generated based on sampling points, the mesh generation processing can be executed at high speed.

  In addition, for each grid point, by making the altitude data the weighted average value of the altitude data in the temporary mesh obtained from the sampling line group in the main direction and the altitude data in the temporary mesh obtained from the sampling group in the sub direction, Since it is configured to generate a mesh that approximates the stratum boundary, an appropriate weight value must be set according to the difference between the number of surveys and survey accuracy in the main direction and the number of surveys and survey accuracy in the sub-direction. Thus, a mesh approximating the formation boundary surface can be obtained with higher accuracy.

  In addition, for each lattice point, a weighted average is used based on the ratio of the shortest distance to the sampling line included in the sampling line group in the main direction and the shortest distance to the sampling line included in the sampling line group in the sub direction. Since the weight value is determined, the weight value for altitude data in the temporary mesh obtained from the sampling line group to which the closer sampling line belongs can be appropriately increased according to the ratio of the distance to the sampling line. Therefore, a mesh that approximates the formation boundary surface can be obtained with higher accuracy.

  In addition, since the new weight value is calculated by multiplying the weight value determined for each grid point by a predetermined constant, the number of investigations and investigation accuracy in the main direction and the number of investigations and investigation accuracy in the sub-direction By setting the above constant based on the difference in the weight, the weight value calculated based on the ratio of the shortest distance to the sampling line can be corrected appropriately, and the mesh that approximates the formation boundary surface has higher accuracy. Can be obtained at

  In addition, since a spline curve is used as the interpolation curve, it is possible to generate a smooth and accurate formation boundary line that passes through multiple formation boundary points, and to improve the approximation accuracy of the mesh to the formation boundary surface There is an effect that can be.

  In addition, since an arbitrary rectangular analysis target area can be set on the screen on which the topographic map is displayed, the target range to be analyzed can be clearly understood on the topographic map, and the size of the analysis range can be determined. Since a ground analysis mesh suitable for analysis can be generated by arbitrarily changing the shape, user convenience can be improved.

  A mesh generation program comprising program codes for executing the steps in the flowcharts shown in FIGS. 2 and 9 is obtained by obtaining an information storage medium such as a CD-ROM or DVD-ROM in which the mesh generation program is stored. Or it can utilize by downloading from the external server in which the said mesh production | generation program was stored. The mesh generation program read from the information storage medium or downloaded from an external server is installed in the storage unit 3 of the ground analysis system 1. By executing the mesh generation program installed in the storage unit 3 by the program execution unit 2, the mesh generation method described above can be realized.

  Note that the mesh generation method and the mesh generation program described in the first embodiment are not intended to limit the present invention, but are disclosed for the purpose of illustration. The technical scope of the present invention is defined by the description of the scope of claims, and various design changes can be made within the technical scope described in the scope of claims. For example, the mesh generation method and the mesh generation program according to the present invention are not limited to generation of a mesh for ground analysis, but are arbitrary extending over the range in a three-dimensional space in which the range is specified on a horizontal plane. It can be widely applied to the generation of a mesh that approximates the boundary surface of. In this case, a plurality of sampling lines each including a set of a plurality of sampling points arranged in a substantially straight line in the horizontal plane are set, each having data on the horizontal plane position and the height of the boundary surface at the position. The Further, one or a plurality of sampling line groups obtained by classifying these sampling lines into one or a plurality of groups according to the direction of the sampling lines are set. Also, the number of sampling line groups is not limited to two. For example, when three sampling line groups are set, three temporary meshes are generated based on the respective sampling line groups, and a weighted average operation related to the generated three temporary meshes is performed, whereby a boundary is obtained. A mesh approximating the surface can be generated.

  In the above embodiment, calculation processing such as mesh generation and ground analysis and processing such as screen display and user input are executed on the same computer. In addition to such a configuration, a ground analysis system may be configured from a host computer and a terminal computer. In this case, calculation processing such as mesh generation and ground analysis is executed by the host computer, and processing such as calculation result display and user input is executed by the terminal computer. For example, using a server on the Internet as a host computer, a ground analysis service is provided to a user terminal accessed via the Internet.

  The present invention can be widely applied to generation of a mesh that approximates a boundary surface extending over a range in a three-dimensional space in which the range in the horizontal plane is specified, including generation of a mesh for ground analysis.

It is a figure which shows an example of a structure of the ground analysis system which uses the mesh production | generation method which concerns on this invention. It is a flowchart which shows the mesh production | generation method by Embodiment 1 of this invention. It is a figure which shows the analysis object area set in the topographic map. It is a figure which shows the sampling line set in the analysis object area. It is a figure which shows the temporary mesh produced | generated based on the sampling line group of the main direction. It is a figure which shows the temporary mesh produced | generated based on the sampling line group of the sub direction. It is a figure which shows the calculation method of a weight value. It is a figure which shows the synthesize | combined mesh. It is a flowchart which shows the method of producing | generating a temporary mesh. It is a figure which shows the stratum boundary line extended in a sampling line direction. It is a figure which shows the orthogonal lattice set in the analysis object area, and the sampling line of the main direction. It is a figure which shows the stratum boundary line extended in a sampling line direction. It is a figure which shows the stratum boundary line extended in a lattice line direction.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Ground analysis system, 2 Program execution part, 3 Storage part, 4 Display part, 5 Shape modeling program, 6 Mesh generation program, 7 Analysis program, 8 Display program, 9 Database, 11 Ground surface, 12, 13, 21, 22 Stratum boundary

Claims (9)

In the three-dimensional space in which the analysis target area is specified on the horizontal plane, a mesh generation method for ground analysis that generates a mesh that approximates the formation boundary surface extending over the analysis target area.
A plurality of sampling lines each including a set of a plurality of sampling points arranged in a substantially straight line in the horizontal plane, each having data on the horizontal plane position and the height of the formation boundary surface at the position, For each of the two sampling line groups obtained by classifying according to the direction,
A first step of identifying sampling lines included in each sampling line group;
For each sampling line, by generating an interpolation curve that connects the formation boundary points based on the height of the formation boundary surface at the sampling points included in the sampling lines, a formation boundary line extending in the sampling line direction is generated. And the process of
A third step of calculating, for each sampling line, the height of the formation boundary line extending in the sampling line direction at the intersection of the sampling line on the horizontal plane and each lattice line in a predetermined direction;
For each grid line in a predetermined direction, the formation extending in the grid line direction in the predetermined direction by obtaining an interpolation curve connecting the formation boundary points based on the height of the formation boundary line extending in the sampling direction at the intersection A fourth step of generating a boundary line;
Performing a fifth step of calculating the height of the formation boundary line extending in the lattice line direction at the lattice point for each lattice line in a predetermined direction;
Generating a ground analysis mesh characterized by generating a mesh that approximates the formation boundary by combining a temporary mesh obtained from the first sampling line group and a temporary mesh obtained from the second sampling line group Method. For each grid point, the weighted average value of the height in the temporary mesh obtained from the first sampling line group and the height in the temporary mesh obtained from the second sampling line group is set as the height at the grid point. 2. The method for generating a mesh for ground analysis according to claim 1, wherein a mesh that approximates the formation boundary surface is generated. For each grid point, the first sampling is performed based on the ratio of the shortest distance to the sampling line included in the first sampling line group and the shortest distance to the sampling line included in the second sampling line group. The ground analysis mesh generation method according to claim 2, wherein a weight value for the height in the temporary mesh obtained from the line group and a weight value for the height in the temporary mesh obtained from the second sampling line group are calculated. . For each grid point, the weight value for the height in the temporary mesh obtained from the first sampling line group is multiplied by a predetermined constant to obtain a new weight value, and the weight value obtained by multiplying the constant from 1 is obtained. The ground analysis mesh generation method according to claim 3, wherein a value obtained by subtracting the weight value is used as a new weight value for the height in the mesh obtained from the second sampling group. 2. The ground analysis mesh generation method according to claim 1, wherein a spline curve is used as the interpolation curve. 2. The ground analysis mesh generation method according to claim 1, wherein an arbitrary rectangular analysis target area can be set on a screen on which a topographic map is displayed. A plurality of sampling lines each including a set of a plurality of sampling points arranged in a substantially straight line in the horizontal plane, each having data on the horizontal plane position and the height of the formation boundary surface at the position, Categorizing into either a first sampling line group or a second sampling line group depending on the direction;
Generating a temporary mesh approximating the formation boundary surface based on the first sampling line group;
Generating a temporary mesh approximating the formation boundary surface based on the second sampling line group;
A step of generating a mesh that approximates the formation boundary surface by combining the temporary mesh obtained from the first sampling line group and the temporary mesh obtained from the second sampling line group;
The step of generating a temporary mesh that approximates the formation boundary surface based on the sampling line group,
A first step of identifying sampling lines included in the sampling line group;
For each sampling line, by generating an interpolation curve that connects the formation boundary points based on the height of the formation boundary surface at the sampling points included in the sampling lines, a formation boundary line extending in the sampling line direction is generated. And the steps
A third step of calculating the height of the formation boundary line extending in the sampling line direction at the intersection of the sampling line on the horizontal plane and each lattice line in a predetermined direction for each sampling line;
For each grid line in a predetermined direction, the formation extending in the grid line direction in the predetermined direction by obtaining an interpolation curve connecting the formation boundary points based on the height of the formation boundary line extending in the sampling direction at the intersection A fourth step of generating a boundary line;
A ground generation mesh generation program comprising: a fifth step of calculating a height of a formation boundary line extending in a lattice line direction at a lattice point for each lattice line in a predetermined direction. In a mesh generation method for generating a mesh approximating a boundary surface extending over a range on a specified horizontal plane in a three-dimensional space in which the range on a horizontal plane is specified,
A plurality of sampling lines each comprising a set of sampling points arranged in a substantially straight line in the horizontal plane, each having data relating to the position in the horizontal plane and the height of the boundary surface at the position, and the direction of the sampling line For each sampling line group or groups obtained by classifying into one or more groups according to
A first step of identifying sampling lines included in each sampling line group;
For each sampling line, an intersection curve between the cross section and the boundary surface along the sampling line is obtained by obtaining an interpolation curve that connects the boundary points based on the height of the boundary surface at the sampling points included in the sampling line. A second step of generating a boundary line extending in the sampling line direction;
A third step of calculating, for each sampling line, the height of the boundary line extending in the sampling line direction at the intersection of the sampling line on the horizontal plane and each lattice line in a predetermined direction;
For each grid line in a predetermined direction, an intersection curve between the cross section and the boundary surface along the grid line in the predetermined direction is obtained by obtaining an interpolation curve that connects the boundary points based on the height of the boundary line at the intersection. A fourth step of generating a boundary line extending in a lattice line direction to be a line;
For each grid line in a predetermined direction, perform a fifth step of calculating the height of the boundary line extending in the grid line direction at the grid point,
Generate a temporary mesh for each sampling line group,
A mesh generation method characterized by generating a mesh that approximates a boundary surface by synthesizing temporary meshes obtained from two or more sampling line groups. A plurality of sampling lines each comprising a set of sampling points arranged in a substantially straight line in the horizontal plane, each having data relating to the position in the horizontal plane and the height of the boundary surface at the position, and the direction of the sampling line Categorizing into one or more sampling line groups according to
For each sampling line group, generating a temporary mesh that approximates the boundary surface based on the sampling line group;
Generating a mesh that approximates the boundary surface by combining temporary meshes obtained from two or more sampling line groups,
Generating a temporary mesh approximating the boundary surface based on the sampling line group,
A first step of identifying sampling lines included in the sampling line group;
For each sampling line, an intersection curve between the cross section and the boundary surface along the sampling line is obtained by obtaining an interpolation curve that connects the boundary points based on the height of the boundary surface at the sampling points included in the sampling line. A second step of generating a boundary line extending in the sampling line direction;
A third step of calculating, for each sampling line, the height of the boundary line extending in the sampling line direction at the intersection of the sampling line on the horizontal plane and each lattice line in a predetermined direction;
For each grid line in a predetermined direction, an intersection curve between the cross section and the boundary surface along the grid line in the predetermined direction is obtained by obtaining an interpolation curve that connects the boundary points based on the height of the boundary line at the intersection. A fourth step of generating a boundary line extending in a lattice line direction to be a line;
A mesh generation program comprising: a fifth step of calculating a height of a boundary line extending in a lattice line direction at a lattice point for each lattice line in a predetermined direction.

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