JPH09282490A - Generating method and display method for geographic simulation model - Google Patents

Abstract

PROBLEM TO BE SOLVED: To simulate topography with different precision according to areas. SOLUTION: The methods for generating and displaying a topography simulation model divide a simulated area into two triangles and finds a topographic simulation error with the triangles, further redivides the triangles each into two triangles when the topographic simulation error exceeds a permissible error and finds a topographic simulation error with the respective triangles, and repeats the fractionation of the triangles until the topographic simulation error becomes less than the permissible error to finds a view angle error by dividing the topographic simulation error by the distance from the triangle to a viewpoint, thereby selecting and displaying triangles which are closer to the viewpoint when the view angle error from the viewpoint is within the permissible error. The topographical simulation error is weighted into an error at the altitude point in the triangle by a weight function defined by a coordinate system assumed In the simulation area.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method of generating a terrain simulation model in computer graphics and a method of displaying the same, and relates to the development of those disclosed in JP-A-5-290148 and JP-A-4-276761, and more particularly, , (1) A method of simulating the terrain with different accuracy depending on the region, (2) A method of simulating the boundaries of areas with different attributes, (3) A method of simulating the moving attention area more precisely than other areas. , (4) A method of simulating the ridgeline of the terrain more finely than other parts, and (5) A method of generating and displaying the terrain simulation at high speed.

[0002]

2. Description of the Related Art FIG. 7 is a diagram for explaining an evaluation range of a triangular terrain simulation error for explaining a conventional terrain simulation generation method and its display method. As shown in the figure, in the conventional method of generating a terrain simulation and its display method, a given simulated coverage area of a square is divided into two diagonal lines, and two right-angled isosceles triangles (hereinafter simply referred to as triangles) T and Td. Approximate the terrain with, and the approximation error e (T) of the isosceles right triangle T into two triangles T, Td
The maximum value of the half-approximation error err (T) and err (Td) of the half-approximation error err (T) is the maximum elevation difference from the triangle T to the ground surface.
Let error (T), e (Te), e (Tr) be the approximation errors of the inscribed triangles Te, Tr with the hypotenuses being the two sides that intersect the triangle T at right angles. error (T), e (Te), e The maximum of (Tr),
If the approximation error e when the terrain is approximated by the triangle is within the specified tolerance, the division of the triangle is terminated, and if the approximation error e (T) is not within the tolerance, the triangle T is set to 2
Divide into two right-angled isosceles triangles Te and Tr and divide the triangle after division until the approximation error e falls within the allowable error.
The recurrence target of the approximation error of the divided right-angled isosceles triangle is not only that of the triangle itself but also those of the right-angled isosceles triangle that inscribes or circumscribes each side of the triangle and makes that side a hypotenuse. , It is guaranteed that the approximation error of the triangles touching them will be less than those, and the terrain simulation will be performed with the minimum number of triangles within the allowable error.

In displaying a triangle, the approximation error of the divided triangle is made to correspond to the node of the binary tree by the division, and the hypothetical viewpoint in the simulated field of view starts from the root of the binary tree and its child node is viewed. Approximate error is obtained in order from the node closer to, and the angle of view error is calculated for each child node in sequence until the angle of view error is within the specified angle of view error.
Display the triangle. The view angle error is a value obtained by dividing the approximation error by the distance from the viewpoint to the triangle.

[0004]

However, according to the conventional method of generating a terrain simulation model and its display method, the first method is used.
In addition, since the entire simulated coverage area is simulated with the same accuracy,
Both important and unimportant areas are simulated with the same accuracy,
There is a problem that the less important area is simulated by many triangles and the amount of data is large, and the terrain simulation generation time is long. For example, the terrain around the approach route around the airport should be simulated with high accuracy, but the distant mountainous terrain, which never approaches, was simulated in the same way although the accuracy could be reduced.

Secondly, since there is not much difference in elevation, it is simulated by a large triangle, so that there is a problem that a boundary between regions having different attributes such as sea and land is not precisely simulated.
In order to solve this, it is necessary to simulate the boundary of the area with another polygon that closely simulates the boundary of the area. Thirdly, since the simulation is performed so that the angle of view error is constant, the undulation of small terrain at a distance cannot be simulated, and the state in which a target such as a moving object is visible and hidden due to the undulation of the terrain cannot be accurately simulated. There's a problem. If the accuracy of terrain simulation is increased to accurately simulate this, the number of triangles on the entire screen increases, which is a further problem.

[0006] In the fourth case, since the view angle error is simulated to be constant, a relatively small triangle is simulated near, but a large triangle is simulated in the distant, and the ridge line of a distant mountain is linear. There is a problem that the reality is lost. Further, for the same reason, there is a problem that an object that should be blocked by the topographical relief appears unblocked.
If the permissible value of the angle-of-view error is reduced in order to improve these, the number of triangles on the entire screen increases, which becomes a further problem.

Fifth, when calculating the simulation error of a triangle, adjacent triangles are calculated recursively, so that there is a portion where the calculation overlaps and there is a problem that the calculation time becomes long. In addition, in order to simulate the ridgeline of the terrain more finely than other parts in the display, the periphery of the triangle to be displayed, as shown in this figure, that is, the terrain simulation error evaluation range (scope) of the triangle There is a problem that it is necessary to calculate the visibility of the child triangles in, and they are calculated redundantly, which reduces the display speed.

Therefore, in view of the above problems, the present invention can simulate the terrain with different accuracy depending on the region, finely simulate the boundaries of regions having different attributes, and make the movable region of interest finer than other parts. It is an object of the present invention to provide a method of generating and displaying a terrain simulation model capable of simulating the terrain, simulating the ridgeline of the terrain more finely than other parts, and generating and displaying the terrain simulation at high speed.

[0009]

In order to solve the above problems, the present invention divides a simulated coverage area into two triangles and obtains a terrain simulation error for each triangle, and the terrain simulation error exceeds an allowable error. Then, each triangle is subdivided into two triangles and a terrain simulation error is calculated for each triangle, and the triangles are subdivided repeatedly until the terrain simulation error is within the allowable error. The angle of view error divided by the distance is calculated and the triangle whose view angle error from the viewpoint is within the permissible error is selected and displayed from the triangles closer to the viewpoint, and the terrain simulation error is the elevation point in the triangle. A method of generating and displaying a terrain simulation is characterized in that the error in is weighted by a weighting function defined in the coordinate system assumed for the simulated coverage. By this means, the terrain is simulated with a relatively small number of relatively large triangles or with a relatively large number of relatively small triangles depending on the region, thereby simulating a predetermined region with higher or lower accuracy than other regions with arbitrary accuracy. be able to.

When the attributes of the three vertices of the divided triangle are not the same, the weighting function of the terrain simulation error has a sufficiently large value as compared with the case where the attributes are the same. By this means, it becomes possible to simulate in detail the boundaries of regions having different attributes such as land and sea, city and suburbs, airport premises and fields. When the evaluation area of the terrain simulation error and the attention area overlap,
The perspective angle error of the triangle to be displayed is weighted to improve the simulation accuracy compared to other areas. By this means, the vicinity of a moving object that is important in training, the vicinity of a dynamically movable area such as the laser distance measurement target point, the pilot's attention point, etc. can be simulated more finely than other areas.

When there are invisible divided triangles within the evaluation range of the above-mentioned terrain simulation error, the prospective angle error is weighted to improve the accuracy of the ridge line. By this means, it is possible to precisely simulate the ridgeline of the terrain. In order to generate and display the terrain simulation model at high speed,
The data structure is a lattice structure, and among the divided triangles, the terrain simulation error of the dual triangles that share the hypotenuses and circumscribe each other, the error-calculated flag, and the visible flag of the triangle within the evaluation range of the terrain simulation error are set. Store in the grid. By this means, it becomes possible to display the terrain at high speed without duplicating calculations for the dual triangles.

[0012]

BEST MODE FOR CARRYING OUT THE INVENTION A first embodiment of the present invention, which is a method for simulating a terrain with different simulation accuracy depending on the region, will be described below with reference to the drawings. Here, the method of simulating the terrain with different simulation accuracy depending on the terrain, which is the first embodiment, assigns weights with the coordinate in the assumed coordinate system as a variable to the simulated coverage area so that it can be changed depending on the area. It simulates terrain with accuracy and without flags.

FIG. 1 is a diagram for explaining the definition of triangles in the triangulation of the ground surface according to the present invention, FIGS. 2 and 3 are flowcharts for explaining a terrain simulation model generation algorithm, and FIG. It is a flowchart explaining the display of the triangle generated using the algorithm. In the flowcharts shown in FIGS. 2 and 3, the simulation error of the triangular terrain is calculated by the following equations (1) and (2).

[0014]

[Equation 1]

[0015]

[Equation 2]

That is, the error of the triangular terrain simulation error
In the calculation of (T), the error at each elevation point is weighted by the weighting function w (x, y) defined in the coordinate system assumed for the simulated coverage. Where the intrinsic error error (T) is the triangle T
Any numerical value can be used as long as it is determined only by the error in the grid (lattice point) which is the elevation point inside. Here, the maximum value of the difference between the elevation in the grid in the triangle T and the plane formed by the triangle T is set.

More specifically, using the triangular terrain simulation error calculated by the equations (1) and (2), it becomes possible to triangulate the terrain, that is, to generate a terrain simulation model according to the flowchart shown in FIG. Then, by displaying the triangles in the flowchart of FIG. 4, it is possible to simulate a predetermined area with an arbitrary accuracy higher (or lower) than other areas. That is, since the original error of the grid is weighted by the value of the weighting function w (x, y) defined on the simulated coverage area in the grid, the determination of the stop of the triangulation can be made soft or strict. Depending on the region, it is possible to simulate the terrain with a relatively small number of relatively large triangles or with a relatively large number of relatively small triangles.

Therefore, according to the embodiment of the present invention, in the calculation of the terrain simulation error of the triangle in the generation of the terrain simulation model, if the coordinates of the simulated coverage area are changed, the terrain simulation error is weighted by the weighting function. Therefore, there is an effect that the simulation accuracy can be arbitrarily set depending on the region. That is, in a flight simulator, the area of operational importance such as the vicinity of an airport is simulated with high accuracy, and the area of operational importance that is far from the flight course is simulated with low accuracy to reduce the capacity of the terrain database, Can be displayed at high speed.

Next, a second embodiment of the present invention, which is a method for simulating a boundary between regions having different attributes with high accuracy, will be described. Here, the method of highly accurately simulating the boundaries of regions having different attributes, which is the second embodiment, uses a normal error calculation when the attributes of the three vertices of the triangle are the same in the calculation of the terrain simulation error of the triangle. And the error is maximized at other times to finely simulate the boundaries of regions having different attributes. Specifically, the terrain triangulation is performed according to the flowcharts shown in FIGS. 2 and 3, and the terrain simulation error of the triangle is calculated by the equation (1) and the following equation (3).

[0020]

(Equation 3)

That is, the error of the triangle terrain simulation error
In the calculation of (T), when the attributes of the three vertices of the triangle are the same, the normal error calculation is performed, and otherwise the error is set to a sufficiently large value. More specifically, using the terrain simulation error of the triangle calculated by the formulas (1) and (3), the terrain is triangulated, that is, the terrain simulation model is generated according to the flowcharts shown in FIGS. By processing the terrain simulation according to the flowchart and displaying the triangles, the boundaries of regions having different attributes can be simulated with the highest degree of detail. That is, when the attributes of the three vertices of the triangle are not the same, the terrain simulation error of the triangle is maximum, so
Where the boundary of the region passes through the triangle error evaluation scope, the triangulation proceeds, and the boundary of the region can be simulated with the highest degree of detail and without cracks.

Therefore, according to the embodiment of the present invention, when the attributes of the three vertices of the triangle are different, the terrain simulation error of the triangle is largely evaluated, so that the boundaries of the regions having different attributes of the ground surface are simulated in detail. There is an effect that can be done. That is,
Since the boundaries of regions with different attributes such as land and sea, urban areas and suburbs, airport premises and fields can be simulated in detail, there is an effect that a terrain database can be efficiently generated without separately modeling with polygons.

Next, a third embodiment of the present invention, which is a method of simulating a movable region of interest with higher accuracy than other regions, will be described. Here, the third embodiment of the present invention, which is a method of simulating a movable region of interest with higher accuracy than other regions, uses a method of simulating a view angle error from a terrain simulation error of a triangle. If the triangular terrain simulation error evaluation range (scope) overlaps with the dynamically movable area of interest such as the pilot's gazing point, moving object, or distance measurement point, the weight determined for the area of interest is used for estimation. By weighting the angular error, the moving target area and its vicinity are more accurately simulated than other areas. Specifically, the terrain simulation display is performed according to the flowchart shown in FIG. 4, and the view angle error of the triangle is calculated by the equation (1) and the following equation (4).

[0024]

(Equation 4)

[0025] That is, in the calculation of the terrain simulated errors of the triangle e (T), when the evaluation range of the terrain simulated error triangle to be displayed and (scope) and region of interest of a radius s _m overlap, trying to display The viewing angle error of the existing triangle is weighted by the degree of improvement in simulation accuracy w _m in that region. Specifically, in the process of processing the terrain simulation and displaying the triangle according to the flowchart shown in FIG. 4, by using the equation (4) as the evaluation formula of the angle of view error of the triangle, the moving area such as the vicinity of the moving object can be determined. It can be simulated with higher accuracy than other areas. In other words, when the error evaluation range of the triangle overlaps the moving area, the terrain can be advanced and the terrain can be simulated in more detail by strictly evaluating the prospective angle.

Therefore, according to the embodiment of the present invention, when the triangle error table and the region of interest overlap, the view angle error of the triangle is weighted by the weight determined by the region of interest. Therefore, there is an effect that the moving attention area can be simulated with arbitrary accuracy. In other words, the vicinity of a moving object that is important for training and the vicinity of a dynamically moving point such as a laser distance measurement target point or the point of interest of the pilot can be simulated more precisely than in other areas, and the generation and display of a terrain simulation is efficient. Can be done. This has the effect of finely simulating a state in which a moving object is hidden by an obstacle with a relatively small number of polygons.

Next, a fourth embodiment of the present invention, which is a method of simulating the ridgeline of the terrain with high accuracy, will be described.
Here, the fourth embodiment of the present invention, which is a method of simulating a ridgeline of a terrain with high accuracy, calculates a view angle error from a terrain simulation error of a triangle, and when calculating a view angle error of the triangle, the terrain simulation error evaluation range of the triangle ( Compared with the case where all the child triangles are visible, the view angle error is evaluated when there is at least one invisible child triangle in the terrain simulation error evaluation range (scope). Is tougher, and the ridgeline of the terrain is simulated more finely than other parts. Specifically, the terrain simulation display is performed according to the flowchart shown in FIG. 4, and the view angle error of the triangle to be displayed is evaluated by the following formula (5).

[0028]

(Equation 5)

That is, when calculating the view angle error from the terrain simulation error of the triangle, the visibility of the child triangles within the terrain simulation error evaluation range (scope) of the triangle is judged to be visible and all the child triangles are visible (scope visible). Compared to (T) = true), if there is at least one invisible child triangle in the terrain simulation error evaluation range (scope) of the triangle,
It is weighted by _e and simulates the ridgeline of the terrain more finely than other parts.

More specifically, in the process of processing the terrain simulation to represent the triangle according to the flowchart shown in FIG.
By using the formula (5) as the evaluation formula of the angle of view error of the triangle, the ridgeline of the terrain can be simulated with higher accuracy than other parts. In other words, if there is at least one invisible child triangle within the triangle error evaluation range (scope), the angle of view error is rigorously evaluated by the weighting w _e set in advance to advance the triangulation and determine the ridgeline of the terrain. It can be simulated in more detail. Here, the visible and invisible triangle error evaluation ranges (scope) are recursively recursively calculated by the following equation (6).
It can be obtained by calculating the visible and invisible values of.

[0031]

(Equation 6)

Therefore, according to the embodiment of the present invention, when there is at least one child triangle which cannot be seen from the viewpoint within the evaluation range (triangle) of the terrain simulation error of the triangle, the likelihood of the triangle is larger than that in the case where it is not. Since the angle error is strictly evaluated, it has the effect of finely simulating the ridgeline of the terrain. That is, it is possible to closely simulate the characteristics of a mountain range in the distance with a relatively small number of triangles. Further, it is possible to accurately simulate a state in which an object is hidden by the undulations of a relatively small topography with a small number of triangles. Also, this has a complementary relationship with the texture mapping, and the texture mapping can be effectively performed. That is, in texture mapping, large irregularities on the ground surface, that is, the contour of the terrain cannot be simulated, but small irregularities are simulated by the shaded pattern, so that the terrain can be simulated with a small number of triangles.

Next, a fifth embodiment of the present invention, that is, a method for generating and displaying a terrain simulation at high speed will be described. Here, the fifth embodiment of the present invention, which is a method of generating and displaying a terrain simulation at high speed, uses a grid structure instead of a binary tree structure as the terrain data structure, and sets a hypotenuse at each grid point. Corresponds to a right-angled isosceles triangle that is shared and circumscribes each other (hereafter referred to as a dual triangle), and indicates that the terrain simulation error, the error-calculated flag, and the child triangles of the terrain simulation error evaluation scope are all visible. The terrain simulation error evaluation range visible flag is stored in the grid point. As a result, in the generation of the terrain model, the terrain simulation error of two dual triangles is not calculated twice, the surrounding triangles are not redundantly processed, and the terrain simulation error evaluation range is displayed in the display of the terrain simulation. It enables high-speed processing without duplicating visible / invisible calculation of child triangles in (scope).

FIG. 5 is a diagram showing a conventional terrain simulation data structure (binary tree structure). Specifically, in order to generate and display the terrain simulation model at high speed, as shown in FIG.
The data structure is not a binary tree structure but a lattice structure described below. The following information is stored in each grid. (1) Elevation at that point (2) Terrain simulation error of the dual triangle associated with the grid Here, the grid and the dual triangle are associated as follows. When the endpoints of the hypotenuse of a dual triangle are ≪q ₁ ≫, ≪q ₂ ≫, let ≪ q _d ≫ = ｜ (≪q ₁ ≫ + ≪q ₂ ≫) / 2 ｜ be the corresponding grid of the dual triangle. . here,
<<>> means vector display.

(3) Error-computed flag of dual triangle (4) Error evaluation range of dual triangle (scope) Visible flag Further, in order to speed up the display, dual cell triangles are added to the grid as grids. Correlate and store each normal vector in the corresponding grid.
Specific examples are shown in the table below.

[0036]

[Table 1]

More specifically, the terrain simulation data structure is a grid structure, and the terrain data in which each grid point has the data structure shown in the above table is subjected to elevation data processing according to the flowcharts shown in FIGS. The terrain simulation can be generated at high speed. That is, since two dual triangles are associated with one grid point, the dual triangle is not calculated twice separately as described above. In addition, since the error of the child triangle is recursively calculated in the calculation of the dual triangle error, the triangles will be calculated in duplicate, but the triangle already-calculated flag is prepared and referenced, When it is on, it does not need to calculate again, and it can be calculated only once for a triangle by using the already calculated error. Also,
Fig. 4 shows the topographic data having the data structure shown in the table above.
By performing the processing shown in, it is possible to display the terrain simulation model at high speed. That is, when performing edge emphasis,
Visibility of the error evaluation scope of the triangle to be displayed
(visibility) must be calculated, the visibility of child triangles must be recursively calculated, and the visibility of triangles must be calculated multiple times.
e) By providing a flag, duplicate calculations can be avoided and triangles can be displayed at high speed.

Therefore, according to the embodiment of the present invention, the data structure for terrain simulation is made into a grid structure, and two triangles which are dual to each other are associated with one grid point and the error-calculated flag is stored at the grid point. Therefore, the terrain simulation errors of two triangles that are dual to each other are stored in one place, and only one calculation is required.When calculating the terrain simulation error of triangles, the terrain simulation errors of the surrounding triangles are duplicated. There is an effect that it is possible to generate the terrain simulation at high speed without calculating. In addition, since a visible flag of the dual triangle terrain simulation error evaluation range (scope) is prepared, it is possible to calculate without overlapping in the visible and invisible calculation of the surrounding triangle when simulating the ridgeline of the terrain in detail, so high speed terrain There is an effect that it can be displayed. Further, since the structure of the terrain database is not a hierarchical structure based on the degree of detail but a flat lattice structure, it is possible to easily calculate the address of the triangle and to easily fetch the data from the external storage device.

FIG. 6 is a block diagram of an apparatus used in the above method. In this device, a visual object is numerically modeled and simulated as a combination of polygons, polygonal surfaces (polygons) and light spots. In this figure, the view calculation device 101 is
Information such as positions of all visual objects included in the assumed three-dimensional scene, positions of vertices forming a surface, and colors is stored. For example, in the case of an airplane simulator, the direction of the airplane,
According to the viewpoint information such as the height and the viewpoint position of the pilot, the visual target object within the field of view is selected and sent to the geometric calculation device described later and the matrix calculation for the coordinate conversion used in the geometric calculation device is performed. The database generation device 1011 creates a database off-line, that is, creates the data of the terrain model and the three-dimensional object created by the above method and stores them in the memory 1012. The terrain model data and the object data are read from the memory in order to respond to the change in the appearance of the terrain and the object due to the change of the viewpoint.

The geometric calculation device 102 is the view calculation device 101.
Priorities are given to the objects in the visual field sent from the robot in the order closer to the viewpoint according to the positional relationship with the viewpoint. Geometric calculations such as calculation of a perspective view of the visual object viewed from a specified viewpoint, brightness of each surface when illuminated by a specified light source, calculation of haze, and the like are performed. Further, coordinate conversion, perspective conversion, calculation of intersection brightness, etc. regarding the light spots are performed, and the result is output together with the priority order to a video signal generator described later. Also, parameters such as coordinate conversion for mapping the texture pattern onto polygons are calculated and transferred to the video signal generating circuit. Further, the geometric calculation device 102 determines whether the triangle of the topographical data read from the view calculation device 101 has a predetermined allowable error, and if the triangle is within the allowable error and further correction is necessary, the correction is performed by the above method. To do.

The video signal generator 103 calculates the position of the intersection of the scanning line and the edge, the brightness and haze at the intersection, the brightness and fade calculation, and the hidden surface on the basis of the signal output from the geometric calculator 102. Erasure is performed to generate a video signal, which is displayed in color on the display device 104.

[Brief description of drawings]

FIG. 1 is a diagram illustrating the definition of a triangle in the terrain triangulation according to the present invention.

FIG. 2 is a flowchart illustrating a terrain simulation model generation algorithm.

FIG. 3 is a flowchart illustrating a terrain simulation model generation algorithm.

FIG. 4 is a flow chart illustrating the display of triangles processed using the algorithms of FIGS.

FIG. 5 is a diagram showing a conventional terrain simulation data structure (binary tree structure).

FIG. 6 is a block diagram of an apparatus used in the above method.

FIG. 7 is a diagram illustrating a triangular terrain simulation error evaluation range for explaining a conventional terrain simulation generation method and a display method thereof.

[Explanation of symbols]

 101 ... Visibility calculation device 102 ... Geometric calculation device 103 ... Video signal generation device 104 ... Display device

Claims (5)

[Claims] 1. A simulated coverage area is divided into two triangles, and a terrain simulation error is obtained for each triangle. If the terrain simulation error exceeds an allowable error, each triangle is further subdivided into two triangles, and the terrain is divided by each triangle. The simulation error is calculated, the triangle is subdivided repeatedly until the terrain simulation error is within the allowable error, and the view angle error obtained by dividing the terrain simulation error by the distance from the triangle to the viewpoint is calculated. Is selected and displayed from the triangle closer to the viewpoint, and the terrain simulation error is defined as an error at an elevation point in the triangle in the coordinate system assumed for the simulated coverage area. A method for generating and displaying a terrain simulation model characterized by being weighted by a weighting function. 2. The terrain simulation error weighting function is set to a sufficiently large value when the attributes of the three vertices of the divided triangle are not the same as when the attributes are the same. A method of generating and displaying a terrain simulation according to claim 1. 3. When the evaluation range of the terrain simulation error and the region of interest overlap, the perspective angle error of the triangle to be displayed is weighted to increase the simulation accuracy compared to other regions. The method for generating and displaying a terrain simulation model according to claim 1, which is characterized. 4. If the invisible divided triangle exists within the evaluation range of the terrain simulation error of the triangle, the prospective angle error is weighted to improve the accuracy of the ridge line. The method for generating and displaying the terrain simulation model described in 1. 5. In order to generate and display the topographical simulation at high speed, the data structure is a lattice structure, and the topographical simulation error of the dual triangles which share hypotenuses and circumscribe each other among the divided triangles, A method of generating and displaying a terrain simulation model, characterized in that an error-calculated flag and a visible flag of a triangle within the evaluation range of the terrain simulation error are stored in the grid.