CN107067446B - Contour line proximity relation judgment and direction automatic adjustment method - Google Patents

Contour line proximity relation judgment and direction automatic adjustment method Download PDF

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CN107067446B
CN107067446B CN201710039603.6A CN201710039603A CN107067446B CN 107067446 B CN107067446 B CN 107067446B CN 201710039603 A CN201710039603 A CN 201710039603A CN 107067446 B CN107067446 B CN 107067446B
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contour line
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CN107067446A (en
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李成名
郭沛沛
殷勇
武鹏达
方驰宇
印洁
吴政
马照亭
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Chinese Academy of Surveying and Mapping
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Abstract

The invention discloses a contour line proximity relation judgment and direction automatic adjustment method, which comprises the following steps: A. determining the structural characteristics, topological characteristics and attribute characteristics of contour lines according to the organization mode of the contour lines in the topographic map; B. determining the proximity relation between the closed contour line and the broken contour line according to the characteristics of the contour lines; C. establishing a tree structure to express the adjacent relation of the closed contour line and the broken contour line, and fusing the two tree structures; D. and based on the fused tree structure, combining altitude information and directional properties of the contour line to realize automatic adjustment of the direction of the contour line. The invention establishes a loose spatial adjacent hierarchical relationship for the contour lines, forms a contour line tree structure expressing the relationship, and realizes automatic adjustment of the contour line direction according to the hierarchical relationship, when the method is adopted for judging the adjacent relationship and adjusting the direction, the time consumption is short, the working efficiency is high, the directions of closed and broken contour lines in an area are adjusted, and the accuracy rate reaches 100 percent.

Description

Contour line proximity relation judgment and direction automatic adjustment method
Technical Field
The invention relates to the field of map synthesis, in particular to a method for judging contour line proximity relation and automatically adjusting direction.
Background
The contour lines express the terrain in a grouped manner, and the spatial relationship of the contour lines plays an important role in the aspects of topographic map reading, map synthesis and the like. In terms of storage and presentation, contours can be divided into closed contours and broken contours. The closed contour is more standard and complete when the contour is expressed, and the spatial relationship of the closed contour generally comprises two types: the common tool for representing these two spatial relationships, including and adjacent, is the tree structure in graph theory. At present, many scholars research contour trees, mostly on the premise that all contours are closed contours or broken contours are correctly connected and closed, the elevation attributes of the contours and the spatial inclusion relationship are combined, and a tree structure is used for expression, for example, Guo Qingsheng et al analyze the spatial relationship rules of the contours and establish a tree structure model; the Joker fly et al establishes a contour line spatial relationship formalized expression tree structure based on graph theory; in addition, some researchers have studied methods for creating contour trees including broken contours, including a closed-connection method, a triangulation method, a scanning line method, an elevation comparison method, and the like.
Observing the application of the contour lines, the broken contour lines and the closed contour lines have the same important application proportion, and a considerable part of the application is realized by not including the relation between the contour lines but only the spatial proximity relation between the contour lines. If the direction of a certain contour line is known in the contour line direction adjustment process, the correctness judgment and processing can be carried out on the contour line direction directly adjacent to the contour line according to the contour line property; in the process of extracting the geological structure line, the connection of the feature points only needs to be carried out on the adjacent contour lines.
Therefore, the invention provides a contour line proximity relation judgment method which is wide in application range and easy to operate, and provides a contour line direction automatic adjustment method with high accuracy on the basis.
Disclosure of Invention
The present invention provides a method for determining a contour line proximity relationship and automatically adjusting a direction, so as to solve the problems in the background art.
In order to achieve the purpose, the invention provides the following technical scheme:
a method for judging contour line proximity relation and automatically adjusting direction comprises the following specific steps:
A. determining the structural characteristics, topological characteristics and attribute characteristics of contour lines according to the organization mode of the contour lines in the topographic map;
B. determining the proximity relation between the closed contour line and the broken contour line according to the characteristics of the contour lines;
C. establishing a tree structure to express the adjacent relation of the closed contour line and the broken contour line, and fusing the two tree structures to realize the integrated expression of the adjacent relation;
D. and based on the fused tree structure, combining altitude information and directional properties of the contour line to realize automatic adjustment of the direction of the contour line.
As a further scheme of the invention: the structural characteristics of the contour lines in the step A comprise region independence, relative closeness and absolute disjointness.
As a further scheme of the invention: the topological characteristics of the contour lines in the step A comprise an inclusion relation and a phase-separation relation.
As a further scheme of the invention: the attribute characteristics of the contour lines in the step A comprise directionality and contained elevation.
The structural characteristics of the contour lines in the step A refer to:
region independence: the contour lines express the topographic features of valleys, ridges and the like in a grouped manner, the topographic line extraction needs to be established on the grouped continuous contour lines with consistent directions, but the contour lines express the continuous topographic surfaces in a discrete manner, and the structural features show that the expression of the contour lines cannot focus on the integrity in a wireless space, and more, an area-independent contour line expression structure needs to be established.
Meanwhile, the storage form of the contour lines is mostly in a frame storage mode, contour line data in a certain space range can be stored in a frame, and the contour line characteristics in the map frame area need to be considered more when the contour lines are applied in the storage mode.
Relative closeness: in theory any contour must be closed. This means that on an infinite plane, for a map of limited format, the partially closed contour lines will be cut by the map format boundary lines and become broken contour lines.
Absolute disjointness: for contour lines of different elevations, no intersection can occur on the topographic map (except for cliff terrain).
The topological characteristics of the contour lines in the step A refer to:
due to the non-intersection of the structural features of the contour lines, the topological feature classification is simple. If the contour lines are taken as line targets, the topological relations of the contour lines are only 1-phase-separated relations; if the contours are considered as planar objects, the contour topological relationships can be divided into 2 categories — inclusion and separation relationships. A disjointed relationship may be considered a proximity relationship.
The attribute characteristics of the contour lines in the step A refer to:
directionality: for a set of contours, the contours appear "high left right low" in elevation along the direction of advance, i.e., the closed contour of the positive landscape appears counterclockwise and the closed contour of the negative landscape appears clockwise. Similar rules also exist for the fracture contour, although the closed surface of the fracture contour is formed by means of partial figure boundary lines.
The content of the elevation: the contour lines are curves formed by connecting adjacent points with equal height on the topographic map, but the points with the same altitude do not necessarily lie on the same contour line. The height difference between adjacent contours within the contour is generally the same.
Compared with the prior art, the invention has the beneficial effects that: the invention provides a method for judging contour line proximity relation and automatically adjusting direction, which summarizes a contour line proximity relation judgment rule on the basis of analyzing the structure, topology and attribute characteristics of a contour line by a system, tries to establish a loose spatial proximity hierarchical relation to the contour line (closed and broken), forms a fused contour line tree structure capable of expressing the proximity relation and accordingly realizes automatic adjustment of the contour line direction. When the method provided by the invention is adopted for judging the proximity relation and adjusting the direction, the time consumption is short, the working efficiency is high, the directions of the closed and broken contour lines in the area are adjusted, the accuracy rate reaches 100 percent, and the using effect is good.
Drawings
Fig. 1 is a schematic flow chart of a method for determining a contour proximity relationship and automatically adjusting a direction according to an embodiment of the present invention.
Fig. 2 is a schematic diagram of the adjacent relationship of closed contour lines and broken contour lines of the present invention, wherein fig. 2(a) is a schematic diagram of the adjacent relationship of closed contour lines, and fig. 2(b) is a schematic diagram of the adjacent relationship of broken contour lines.
Fig. 3 is a schematic diagram of a tree structure showing a contour line adjacency relationship according to the present invention, in which fig. 3(a) is a tree structure showing a closed contour line adjacency relationship shown in fig. 2(a), and fig. 3(b) is a tree structure showing a broken contour line adjacency relationship shown in fig. 2 (b).
FIG. 4 is a schematic diagram of the fusion of contour proximity tree structures according to the present invention.
FIG. 5 is a schematic view of a "pseudo-closed contour" of a fracture contour of the present invention.
Fig. 6 is a schematic diagram of the comparison of valley points extracted before and after contour direction adjustment according to the present invention, in which fig. 6(a) shows the valley points extracted without direction adjustment, fig. 6(b) shows the valley points extracted after direction adjustment, and fig. 6(c) shows the valley lines generated according to b).
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 2-4, as shown in fig. 2(a), for the closed contour, the proximity relationship can be divided into three types:
(1) inner adjacent: if the closed surface formed by the contour line L1 is included in the closed surface formed by the contour line L2, the closed surface is called adjacent to the contour line L2 in the contour line L1.
(2) Outer adjacent: the closed surface formed by contour line L1 includes the closed surface formed by contour line L2, which is called contour line L1 is externally adjacent to contour line L2.
(3) Parallel and adjacent: the contour line L1 and the contour line L2 are included in a closed surface of the same contour line, and the contour lines L1 and L2 are juxtaposed and adjacent to each other.
In fig. 2(a), contour L1 is internally adjacent to L2, while externally adjacent to contour L3. The contour line L4 and the contour line L1 are located in the closed plane of the contour line L2, and they are in a juxtaposed relationship.
FIG. 2(b) is a schematic diagram showing the adjacency of fracture contours.
The premise of the contour line proximity relation judgment is that the contour lines form a closed surface, so that the broken contour lines caused by framing or other factors need to be subjected to closing treatment to form pseudo-closed contour lines. According to the characteristic that the fracture contour lines have two intersection points with the boundary of the map frame certainly, the invention makes the following provisions on the fracture contour lines and designs a map frame boundary intersection point method to judge the proximity relation according to the definition:
provision 1: the two intersections of the fracture contour lines and the map sheet divide the map sheet boundary into two parts, and if the intersection of other contour lines does not exist on the map sheet boundary of one part, the two intersections are called as adjacent;
provision 2: if two intersections of the contour and the map frame boundary are adjacent, the fracture contour is considered to be the minimum, and is called as a seed contour;
provision 3: the partial graph frame boundary without other contour line intersection points is called as the directed auxiliary graph frame boundary;
provision of 4: the oriented auxiliary map frame boundary surrounds the whole map frame boundary in a counterclockwise direction, the starting node of the oriented auxiliary map frame boundary is the starting intersection point of the seed contour line, and the ending node of the oriented auxiliary map frame boundary is the ending intersection point of the seed contour line.
As shown in FIG. 2(b), contour lines L1-L6 are broken contour lines. Wherein L1, L3, L4 and L5 are the contour lines of seeds.
There are also three adjacent relationships between fracture contours:
(1) inner adjacent: a contour L1 is said to be adjacent to L2 if the start or end intersection of L1 is adjacent to the start or end intersection of L2, or the start or end intersection of some juxtaposed adjacent contour of L1 is adjacent to the start or end intersection of L2, while the auxiliary map frame boundary of contour L1 is part of the auxiliary map frame boundary of contour L2.
(2) Outer adjacent: the case corresponding to the inner adjacency is called L2 outer adjacency to L1.
(3) Parallel and adjacent: the juxtaposition and adjacency of the fracture contours can be divided into two categories: if the starting point of L2 is adjacent to the starting point (or the end point) of L1, or the end point of L2 is adjacent to the end point (or the starting point) of L1, and the boundary of the auxiliary map frame does not overlap, the contour lines L1 and L2 are directly adjacent in parallel. If L2 and L1 are directly juxtaposed and adjacent, L1 and L3 are directly juxtaposed and adjacent, and the contour lines L1 and L3 are indirectly juxtaposed and adjacent.
As shown in fig. 2(b), adjacent to L2 within contour L1; the contour lines L3, L4 and L5 are adjacent in parallel, and L6 is adjacent to the contour lines.
FIG. 3 is a schematic diagram of a tree structure showing the adjacency relationship of contour lines according to the present invention.
The contour neighborhood tree is composed of nodes and edges connecting the nodes. Where nodes represent contours and edges represent proximity relationships between contours. The tree has a unique root node (Rootnode) to represent the whole image; each of the remaining nodes represents a contour: leaf nodes represent contours without adjacent contours inside; the middle node represents a contour line with inner and outer adjacent contour lines; the relationship between nodes implies a neighborhood of contours: edges between parent and child nodes represent an inside-outside adjacent relationship, namely the contour line of the parent node (Parentnode) is adjacent to the contour line of the child node (Childrenode) outside; respective sibling nodes (sibingnodes) having the same parent node indicate that the contours have a side-by-side proximity relationship therebetween.
FIGS. 3(a) and (b) are schematic representations of tree structures of contour proximity relations in FIGS. 2(a) and (b), respectively. Each node in the graph represents a contour, and the nodes in the tree structure have only adjacent relations, so that the concept of 'layer' (representing elevation) and 'path' (representing inclusion relation) included in the traditional contour tree structure is not expressed. As in fig. 3(a), contour line L1, as a child node, is internally adjacent to L2; as a parent, the outer neighbor is L3; as sibling nodes, it is juxtaposed adjacent to L4.
FIG. 4 is a schematic diagram of the fusion of contour proximity tree structures according to the present invention.
To realize the expression of the spatial proximity relation between all the contours in the whole graph, the closed contour tree and the broken contour tree need to be combined. Because broken contour lines cannot exist in the closed contour lines, tree structure fusion is completed by inserting branches of the closed contour line tree into the broken contour line tree, and the insertion position is determined by whether a closed surface formed by the contour lines has an inclusion relation.
Suppose that the child nodes of the closed contour tree are { N }1,N2…,Nm}. The sub-node of the fractured contour is { M }1,M2,…,MnJudge NiAnd MiThe method comprises the following steps of firstly carrying out auxiliary closure on the fracture contour line to form a 'pseudo-closed contour line', and carrying out the following process: for each node Mi(i ═ 1, 2.. multidot.n), a fracture contour line represented by the fracture contour line is taken, a clockwise closed curve formed from the contour line to the boundary of the drawing sheet from the starting intersection point of the contour line and the boundary of the drawing sheet to the ending intersection point along the contour line, and then from the boundary of the drawing sheet to the starting node is called a 'pseudo closed curve', a closed surface formed by surrounding is called a 'pseudo closed surface', and the number P is represented by PiAnd marks such as a closed face p1 enclosed by DL1ED, a closed face p2 enclosed by BL2CB and the like in FIG. 5.
The fusion process is as follows:
step 1: taking the maximum child node N of the closed contour linejClosed plane Q formed by (child nodes of root node)j(ii) a Take each MiThe represented fracture contour line is calculated to form a closed surface P of a' pseudo closed curvei. First time of judgment MiIs the largest child node of the fractured contour tree (child node of the root node).
Step 2: judging whether a closed plane P existsiComprising a closed surface Qj
And step 3: if not, then node NjAs MiInserting the brother nodes into the broken contour tree;
and 4, step 4: if there is one node MkThe closed surface of its pseudo-closed curve "comprises QjThen take MkOfAnd (5) returning to the step 1 if the child node exists.
And 5: when all nodes NjWhen (j ═ 1.. m) is inserted into the fractured contour tree, the fusion process ends.
Fig. 4 is a schematic structural fusion diagram of a contour line proximity relationship tree, and in the fused contour line proximity relationship tree, a root node represents the whole map frame and does not represent any contour line. The leaf nodes represent the "minimum contours" of the fracture or the closed contours of the innermost layer. Unlike traditional contour tree node relationships, in a contour neighborhood relationship tree, spatial direct neighborhood relationships between contours are represented between nodes, and neighborhood relationships exist between each node and the parent and child nodes and sibling nodes with which it is directly associated.
In the actual production process, most contour line data are generated by digitalizing raster images, the consistency of contour line directions cannot be ensured, and the contour line directions have very important significance for characteristic line extraction and contour line synthesis. By means of the tree structure representing the proximity relation of the contour lines and combining the elevation information and the direction property of the contour lines, the direction automatic adjustment of the contour lines can be quickly and accurately realized.
The basic principle of contour direction adjustment is as follows: in a forward landform, a counterclockwise closed surface (pseudo closed surface) formed by high-altitude contours is contained inside a counterclockwise closed surface (pseudo closed surface) formed by low-altitude contours, and one contour cannot intersect with a counterclockwise closed surface (pseudo closed surface) formed by a contour of the same altitude. For this purpose, an Automatic Contour Direction Adjustment Model (acdma) is designed as shown in the following formula:
ACDAM=FA(MContour,FContour,NContour)
in the formula, FAA finger automatic Adjustment Function (Function Adjustment); mContourThe group of the highest contour lines is the contour line with the highest elevation in the area of the map, and the contour line may be one contour line or a plurality of contour lines; fContourThe former contour group, i.e. the one whose contour direction adjustment has been completed during the treatment processA set of contours; n is a radical ofContourThe latter contour group, i.e. a group of contours to be subsequently processed, is referred to.
From the characteristics of the contour lines, N of a certain contour line is knownContourThree cases are involved: (1) low elevation adjacent equal height wire set, NContour<FContourI.e. contour lines having a lower elevation than the contour line and no processing mark, using LContourTo identify; (2) same-altitude adjacent contour group, NContour=FContourI.e. contour lines of the same elevation as the one and without processing mark, using EContourTo identify; (3) high-altitude adjacent contour group, NContour>FContourI.e. contour lines with an elevation higher than this and without processing marks, using RContourAnd (5) identifying.
The adjustment of the contour line direction is a continuous iterative process, the adjustment sequence is carried out according to the altitude from high to low, firstly, the contour line with the highest altitude is processed, and when N is in the processing processContour>FContourAnd performing reverse processing according to the sequence of the elevation from low to high until the elevation is empty, and finishing the cycle processing. The contour direction adjustment comprises the following five parts:
100: contour line closed surface
For a closed contour, the surface surrounded by the closed contour is the closed surface of the contour, and a broken contour needs to form a 'pseudo-closed contour' by means of a map frame boundary to form the closed surface, which is as follows:
single break contour: and connecting partial map frame boundaries along the direction of the contour lines to form a counterclockwise pseudo-closed contour line.
Multiple fracture contours: (1) solving two intersection points of each contour line and the boundary; (2) calculating the distance from the intersection point to the lower left corner point of the boundary, and performing ascending arrangement to obtain the sequence of contour lines; (3) if the first point and the second point belong to the same contour line after sorting, connecting the contour lines in sequence; if the first point and the second point do not belong to the same contour, the connection is made starting from the second contour. And (3) enclosing the two contour lines by using a boundary line segment, namely forming a pseudo-enclosed contour line in the counterclockwise direction.
As shown in fig. 4, intersections of the contour lines L1, L2, L3 with the boundaries are D, E, B, C, and A, F, respectively. Starting from L2, L2 and L1, L1 and L3, and L3 and L2 are connected by line segments CD, EF and AB, respectively, so that a closed curve ABL2CEL1EFL3 is formed, which is shown as a dark portion in the figure.
200: highest contour group (M)Contour) Of (2) a
If there is only one contour, then: (1) the line is a closed contour line, whether the line is in a counterclockwise sequence is judged, if so, the line is not processed, otherwise, the direction of the line is adjusted to be in a counterclockwise direction; (2) the line is a fracture contour line, and obviously, the line is certainly a 'minimum contour line', and a 'pseudo-closed contour line' of the line is adjusted to form a counterclockwise closed surface.
If there are several contour lines, then: (1) if only the contour lines are closed, the processing conditions are the same as above; 2) if the closed contour line and the broken contour line exist, the closed contour line is processed to be in the anticlockwise direction, and then the relation between the closed surfaces formed by the closed contour line and the high-range contour line is judged according to the proximity relation tree, and the trend of the contour line is determined; (3) if all the broken contours are broken contours, at least one 'minimum contour' is necessary, the correct direction of the broken contours is determined according to the rule that the highest contour only has one broken contour, and the rest highest-elevation broken contours are determined according to the relation between closed surfaces formed by the broken contours and the high-altitude contours.
After the direction of the contour line with the highest elevation is determined, the adjacent contour line is obtained according to the adjacent relation tree and is divided into E with the same elevation as the adjacent contour lineContourAnd L in a lower elevation than itContourTwo kinds.
300: adjacent contour lines of same height (E)Contour) Of (2) a
If E isContourEach contour line in the two-dimensional space is closed, and the closing direction is ensured to be anticlockwise; if the contour is broken, a counterclockwise "pseudo closed surface" is formed when the counterclockwise "pseudo closed surface" and F are formedContourWhen the formed surfaces are intersected, the direction of the contour line needs to be reversed and adjusted, otherwise, the contour line needs to be reversed and adjustedNo adjustment is made.
400: adjacent high altitude contour (R)Contour) Of (2) a
For RContourIf each contour line is closed, the direction is ensured to be anticlockwise; if R isContourIs broken, and the resulting counterclockwise "false seal" is calculated when EContourThe counter-clockwise closure profile formed in the correct direction comprising RContourIn the case of counterclockwise "pseudo-closed surface", RContourThe direction of (a) does not need to be adjusted, otherwise the reverse adjustment is performed.
500: adjacent low elevation contour lines (L)Contour) Of (2) a
To LContourThe closed contour line in (1) ensures that the direction is counterclockwise. To LContourFor each of which the resulting counter-clockwise "pseudo-occlusion face" is calculated as it is and FContourWhen the anticlockwise pseudo-closed surfaces formed in the correct direction are intersected, the trend of the contour line does not need to be adjusted, otherwise, the L is adjustedContourThe contour lines are reversed and adjusted.
Examples
The contour lines of part of Ankang city, Shanxi province are taken as an example, the range of the whole region is about 15605 square kilometers, the scale is 1:25 thousands, the contour distance is 100m, the region contains topography forms such as mountain tops, hollow areas, saddles and the like, and a contour line proximity relation judgment rule and a direction automatic adjustment model provided by the invention are embedded by relying on a WJ-III map workstation of a NewMap software platform developed by China research institute of surveying and mapping science.
To ensure the richness of the data samples and the reliability of the experiment, 5 sets of data were cut out from the whole area. These data incorporate both closed and broken contours and contain typical topographical features, with data processing and elapsed time as shown in table 1. It can be seen that the whole automatic treatment is short in time consumption and high in efficiency, the directions of the closed contour lines and the broken contour lines in the area are adjusted, and the accuracy rate reaches 100%.
TABLE 1 statistical table of experimental data
Figure GDA0002806676570000131
Fig. 6(a) and (b) show the valley point sets calculated before and after the adjustment of the direction of the contour line in the data 1, respectively, and fig. 6(c) shows the valley lines formed by connecting the valley points in fig. 6 (b). It can be seen from the figure that the valley points taken out on the premise of direction adjustment are relatively disordered, obvious errors exist, and correct terrain lines cannot be obtained; the valley point obtained after the direction adjustment is correct and effective, and an obvious topographic characteristic line can be generated. Due to the limited range of display, only the results of data 1 are shown here, and the same results are shown for the other sets of data in the experiment. It will be evident to those skilled in the art that the invention is not limited to the details of the foregoing illustrative embodiments, and that the present invention may be embodied in other specific forms without departing from the spirit or essential attributes thereof. The present embodiments are therefore to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. Any reference sign in a claim should not be construed as limiting the claim concerned.

Claims (1)

1. A method for judging contour line proximity relation and automatically adjusting direction is characterized by comprising the following specific steps:
A. determining structural features, topological features and attribute features of the contour lines according to the organization mode of the contour lines in the topographic map, wherein the structural features of the contour lines comprise area independence, relative closeness and absolute disjointness, the topological features of the contour lines comprise inclusion relation and phase separation relation, and the attribute features of the contour lines comprise directivity and elevation;
B. determining the proximity relation between the closed contour line and the broken contour line according to the characteristics of the contour lines;
C. establishing a tree structure to express the adjacent relation of the closed contour line and the broken contour line, and fusing the two tree structures to realize the integrated expression of the adjacent relation;
D. based on the fused tree structure, combining altitude information and directional properties of the contour line to realize automatic adjustment of the direction of the contour line;
the basic principle of the automatic adjustment process is as follows: in a forward landform, a counterclockwise closed surface formed by high-altitude contour lines is contained in the interior by a counterclockwise closed surface formed by low-altitude contour lines, and one contour line cannot be intersected with the counterclockwise closed surface formed by the contour line with the same altitude; the contour direction automatic adjustment model is as follows: ACDMA (AcDMA-F)A(MContour,FContour,NContour),FAAn automatic adjustment function is pointed out; mContourThe group of the highest contour lines is the contour line with the highest elevation in the area of the map, and the contour line may be one contour line or a plurality of contour lines; fContourThe former contour group is the contour group which is the group of contours with the contour direction adjusted in the processing process; n is a radical ofContourThe latter contour group, i.e. a group of contours to be subsequently processed, is referred to.
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