CN113032888A - Section interpolation encryption method based on dichotomy and layered lowest point - Google Patents
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Abstract
The invention discloses a section interpolation encryption method based on dichotomy and layered lowest point, which comprises the following steps: finding out respective lowest points of the upstream and downstream section data of the position to be interpolated; dividing the section data into a left group and a right group according to the lowest point, and finding out the lowest point of each group; repeating the process, and simultaneously defining the topological attribute of the lowest point of each layer until the segmentation cannot be continued; establishing a corresponding relation between two data points which are positioned in the same segmentation depth layer, have a corresponding relation between parent data points and are positioned on the same side of the respective parent data points; establishing a corresponding relation between end data points of the upstream and downstream sections, and correcting or supplementing the corresponding relation; and performing linear interpolation at the position to be interpolated based on the corresponding relation to generate a new section. The invention fully considers the fact that water is used as fluid and is influenced by gravity, and the lower point is more important to water flow, and is more suitable for hydrodynamics calculation.
Description
Technical Field
The invention relates to the technical field of hydraulic engineering, in particular to a section interpolation encryption method based on a dichotomy and a layered lowest point.
Background
In the practice of water conservancy projects, particularly in the aspects of engineering design, flood forecasting, reservoir scheduling and the like, a one-dimensional hydrodynamic model based on a natural river channel is often required to be constructed to provide data support. Among elements of model construction, cross-sectional data is important. The quality of the river channel section data is reflected in two aspects, namely the degree of the real shape of the section and the section distance.
A profile is generally characterized by a set of discrete data points (e.g., (y 1, z 1), (y 2, z 2) …, where y generally represents distance from the left bank and z represents elevation). In early hydraulic applications, rectangles or trapezoids were used instead of true cross-sectional shapes to simplify calculations, with a corresponding smaller number of data points. With the continuous development of numerical calculation level, it is more and more common to apply the actually measured and irregular section data to model calculation. Theoretically, the more the section data points are, the more the real water level-flow relation can be reflected, and the higher the calculation accuracy is.
From the aspect of section spacing, the more uniform the section distribution, the more favorable the stability and accuracy of numerical calculation. However, the actual data often cannot meet the requirement, so that interpolation is needed to supplement a new section in the missing segment based on the existing section data at the upstream and downstream. For simple regular sections such as trapezoids or rectangles, interpolation encryption can be completed without a special method. However, to satisfy universality, the interpolation encryption method should also be able to cope with complex measured cross-section data.
The existing section interpolation technology generally adopts the following method: firstly, normalizing the upstream and downstream sections, for example, taking the left bank as a starting point, calculating the ratio of the cumulative length of each data point to the total length of the section (the ratio has monotonicity relative to the y value) along the wet circumferential direction, and the ratio is called as a position factor; then, the position factor calculated based on the upstream and downstream sections is integrated to determine the position of the data point of the new section (theoretically, the data point of the new section is more than the data points of the upstream and downstream sections); then, respectively supplementing and generating new data points at the same positions on the upstream and downstream sections according to the position factor of the new section, so that the upstream and downstream sections have the same number of data points in one-to-one correspondence; and finally, interpolating the upstream and downstream section points according to the corresponding relation to generate a new section. The above technology fully considers the overall shape of the section, but does not consider certain key information in the section data, such as the river bottom elevation.
Disclosure of Invention
In order to solve the technical problem, the invention provides a section interpolation encryption method based on a dichotomy and layered lowest points, which is used for finding out the respective lowest points according to upstream and downstream section data of a position to be interpolated; dividing the section data into a left group and a right group according to the lowest point, and finding out the lowest point of each group; repeating the process, and simultaneously defining topological attributes of the lowest points of each layer, including data point numbers, segmentation depths, parent data point numbers and relative positions (left or right) of the parent data points, until segmentation cannot be continued; establishing a corresponding relation between two data points which are positioned in the same segmentation depth layer, have a corresponding relation between parent data points and are positioned on the same side of the respective parent data points; establishing a corresponding relation between end data points of the upstream and downstream sections, and correcting or supplementing the corresponding relation; and performing linear interpolation at the position to be interpolated based on the corresponding relation to generate a new section. Compared with the prior art, the method fully considers the fact that water is used as fluid and is influenced by gravity, and always preferentially occupies a lower point position, so that the lower point is very important for the water flow movement phenomenon, and is realized by utilizing the dichotomy principle without expanding the composition points of the upstream and downstream sections, the steps are simple and clear, the sections generated by interpolation can accurately reflect the basic information of the upstream and downstream sections, and the method is more suitable for hydrodynamics calculation.
The invention aims to provide a section interpolation encryption method based on dichotomy and layered lowest point, which comprises the following steps of obtaining upstream section data and downstream section data:
step 1: traversing the upstream section data points of the position to be interpolated to find out the lowest elevation point of the upstream data;
step 2: segmenting the upstream section data points by using a data segmentation method to obtain an upstream segmentation data table;
and step 3: traversing the downstream section data points of the position to be interpolated to find out the lowest elevation point of the downstream data;
and 4, step 4: segmenting the downstream section data points by using the data segmentation method to obtain a downstream segmentation data table;
and 5: establishing a corresponding relation between the upstream segmentation data table and the downstream segmentation data table;
step 6: and performing linear interpolation at the position to be interpolated based on the one-to-one correspondence between the upstream section data points and the downstream section data points to obtain a new section.
Preferably, the data segmentation method includes the sub-steps of:
step 21: dividing the section data point into a left group of data and a right group of data according to the lowest elevation point, and defining the division depth as 1;
step 22: traversing the newly obtained left and right groups of data points, and respectively finding out respective lowest elevation points;
step 23: repeatedly executing the step 21 and the step 22 until the segmentation cannot be continued;
step 24: and generating a segmentation data table.
In any of the above solutions, it is preferable that the step 22 includes defining topological properties of the two newly found lowest elevation points, including data point number, segmentation depth, parent data point number and relative position to the parent data point.
In any of the above schemes, preferably, the segmentation data table is composed of the lowest elevation point numbers and topology attributes thereof at different segmentation depths.
In any of the above schemes, preferably, the divided data table includes at least four columns, a first column is a data point number, a second column is a division depth, a third column is a parent data point number, and a fourth column is a relative position to the parent data point.
In any of the above solutions, preferably, the step 5 includes the following sub-steps:
step 51: establishing a corresponding relation between the lowest elevation points of the upstream segmentation data table and the downstream segmentation data table;
step 52: establishing a corresponding relation between two data points in the upstream segmentation data table and the downstream segmentation data table which meet corresponding conditions;
step 53: step 52 is repeated until all correspondences are found.
In any of the above aspects, preferably, the corresponding condition includes at least the following:
(1) the two data points are at the same segmentation depth layer;
(2) a corresponding relationship exists between parent data points of the two data points;
(3) the two data points are on the same side of the respective parent data point.
In any of the above schemes, preferably, the step 5 further includes supplementing or changing the corresponding relationship by using a supplementing method.
In any of the above schemes, preferably, the supplementing method is:
(1) establishing a corresponding relation between the leftmost data point of the upstream section and the leftmost data point of the downstream section directly;
(2) and establishing a corresponding relation between the rightmost data point of the upstream section and the rightmost data point of the downstream section.
In any of the above schemes, preferably, the step 5 further includes performing ascending order arrangement according to the upstream or downstream sections to generate a final correspondence table.
The invention provides a section interpolation encryption method and system based on dichotomy and layered lowest point, which fully consider the following facts when section interpolation encryption is carried out: firstly, water is used as fluid and is influenced by gravity, and always preferentially occupies a lower point position, so that the lower point is crucial to the water flow movement phenomenon; secondly, in the one-dimensional river channel hydrodynamic calculation, the processing of the river channel bottom slope item is an important part of momentum calculation, so that the lowest point (corresponding to the river channel bottom elevation) is the most important point in the section data points; and thirdly, the leftmost data point and the rightmost data point (the left bank and the right bank) of the river cross section are key points for analyzing whether overflow occurs or not, so that independent consideration is needed. Compared with other methods, the new section obtained based on the method is more suitable for hydrodynamics calculation.
Drawings
Fig. 1 is a flow chart of a preferred embodiment of a section interpolation encryption method based on dichotomy and layered lowest point according to the present invention.
Fig. 2 is a flowchart of an embodiment of a data segmentation method based on a bisection method and a hierarchical nadir cross-section interpolation encryption method according to the present invention.
Fig. 3 is a flowchart of an embodiment of a method for establishing a correspondence relationship between a bisection method and a cross-sectional interpolation encryption method based on a layered lowest point according to the present invention.
Fig. 4 is a schematic diagram of an embodiment of a hierarchical lowest point-based dichotomy of a cross-sectional interpolation encryption method based on dichotomy and hierarchical lowest points according to the present invention.
Fig. 5 is a flowchart of another preferred embodiment of a section interpolation encryption method based on dichotomy and layered lowest point according to the present invention.
Fig. 6 is a schematic cross-sectional view of an upstream channel of a cross-sectional interpolation encryption method based on bisection and layered lowest point according to an embodiment of the present invention.
Fig. 7 is a schematic cross-sectional view of a downstream river channel according to an embodiment of the cross-sectional interpolation encryption method based on the bisection method and the layered lowest point in the invention.
Fig. 8 is a schematic diagram of an embodiment of a river section generated by a section interpolation encryption method based on dichotomy and layered lowest point according to the present invention.
Fig. 9 is a schematic diagram of an embodiment of a river section generated according to the prior art of the section interpolation encryption method based on dichotomy and layered lowest point of the present invention.
Detailed Description
The invention is further illustrated with reference to the figures and the specific examples.
Example one
As shown in fig. 1, step 100 is performed to obtain upstream cross-sectional data and downstream cross-sectional data.
Step 110 is executed to traverse the upstream section data point of the position to be interpolated, and find out the lowest elevation point of the upstream data.
Step 120 is executed, the upstream fracture surface data point is segmented by using a data segmentation method, and an upstream segmentation data table is obtained.
As shown in fig. 2, the data segmentation method includes the following sub-steps:
step 121 is executed to divide the section data point into a left group of data and a right group of data according to the lowest elevation point, and the division depth is defined as 1.
And step 122 is executed, the newly obtained left and right groups of data points are traversed, respective lowest elevation points are found out, and topology attributes of the newly found two lowest elevation points are defined, wherein the topology attributes comprise data point numbers, segmentation depths, parent data point numbers and relative positions of parent data points.
Step 123 is executed to determine whether the division is completed. If the segmentation can be continued, step 121 is executed again, and if the segmentation cannot be continued, step 124 is executed to generate a segmentation data table, wherein the segmentation data table is composed of the lowest elevation point numbers and the topology attributes thereof at different segmentation depths. The split data table includes at least four columns, the first column being the data point number, the second column being the split depth, the third column being the parent data point number, and the fourth column being the relative position to the parent data point.
Step 130 is executed to traverse the downstream section data point of the position to be interpolated, and find the lowest elevation point of the downstream data.
Step 140 is executed, the data segmentation method is used to segment the downstream fracture surface data points, and a downstream segmentation data table is obtained.
Step 150 is executed to establish a corresponding relationship between the upstream split data table and the downstream split data table.
As shown in fig. 3, in this step, step 151 is executed to establish a correspondence relationship between the lowest elevation points of the upstream divided data table and the downstream divided data table.
Step 152 is executed to establish a corresponding relationship between two data points in the upstream and downstream segmented data tables that satisfy the corresponding condition. The corresponding conditions include at least the following: (1) the two data points are at the same segmentation depth layer; (2) a corresponding relationship exists between parent data points of the two data points; (3) the two data points are on the same side of the respective parent data point.
Step 153 is executed to determine whether all the corresponding relationships are found. If not, re-executing step 152; if all the correspondences have been found, step 154 is executed to supplement or modify the correspondences by a supplement method. The supplement method comprises the following steps: (1) establishing a corresponding relation between the leftmost data point of the upstream section and the leftmost data point of the downstream section directly; (2) and establishing a corresponding relation between the rightmost data point of the upstream section and the rightmost data point of the downstream section.
Step 155 is executed to perform ascending order arrangement according to the upstream or downstream sections to generate a final correspondence table.
And step 160 is executed, linear interpolation is carried out at the position to be interpolated based on the one-to-one correspondence relationship between the upstream section data points and the downstream section data points, and a new section is obtained.
Example two
Aiming at the defects in the prior art, the invention provides a section interpolation encryption method based on dichotomy and layered lowest point. The theoretical basis of the invention is as follows: the water as a fluid is influenced by gravity and always preferentially occupies a lower point, so that the lower point is crucial to the water flow movement phenomenon and should be fully considered; in addition, in the one-dimensional river hydrodynamic calculation, the processing of the river bottom slope term is an important part of the momentum calculation, so the lowest point (corresponding to the river bottom elevation) is the most important point in the section data points, and must be considered separately in the generation of a new section.
The invention provides a section interpolation encryption method based on a dichotomy and a layered lowest point, and the specific technical scheme is as follows.
As shown in fig. 4 and 5, a section interpolation encryption method based on the dichotomy and the layered lowest point includes the following steps:
the method comprises the following steps: and traversing the upstream section data points of the position to be interpolated to find out the lowest elevation point.
Step two: dividing the upstream section data point into a left group of data and a right group of data (not including the lowest elevation point) according to the lowest elevation point; defining the segmentation depth as 1; traversing the newly obtained left and right groups of data points, and respectively finding out respective lowest elevation points; topology attributes of the newly found two lowest elevation points are defined, including data point number, depth of segmentation, parent data point number, and relative position to the parent data point (left or right).
Step three: aiming at the two lowest elevation points newly obtained in the step two, continuing to divide downwards according to the step two, and finding the lowest elevation point of the divided depth layer; and repeating the process until the segmentation cannot be continued. Thus, for the upstream cross section, a data table (or matrix) consisting of the lowest elevation point numbers and the topological attributes thereof at different segmentation depths can be obtained. The first column is the data point number, the second column is the depth of segmentation, the third column is the parent data point number, and the fourth column is the relative position to the parent data point.
Step four: and (4) completely treating the downstream cross section according to the steps from the first step to the third step.
Step five: aiming at two newly obtained data tables, firstly establishing a corresponding relation between the lowest elevation points (the data points in the first row of each data table) of the two data tables; then, the data points are positioned in the same segmentation depth layer by layer, corresponding relations exist among the parent data points, and the corresponding relations are established between two data points positioned on the same side of the respective parent data points; until all correspondences are found.
Step six: in view of the importance of the leftmost data point and the rightmost data point (left bank and right bank) of the section, the corresponding relation is directly established between the leftmost data point and the rightmost data point of the upstream and downstream sections respectively; and accordingly, supplementing or changing the corresponding relation in the fifth step.
Step seven: and performing linear interpolation at the position to be interpolated based on the one-to-one correspondence relationship between the data points of the upstream and downstream sections to obtain a new section.
Compared with the prior art, the technical scheme adopted by the invention fully considers the following facts when the section interpolation encryption is carried out: firstly, water is used as fluid and is influenced by gravity, and always preferentially occupies a lower point position, so that the lower point is crucial to the water flow movement phenomenon; secondly, in the one-dimensional river channel hydrodynamic calculation, the processing of the river channel bottom slope item is an important part of momentum calculation, so that the lowest point (corresponding to the river channel bottom elevation) is the most important point in the section data points; and thirdly, the leftmost data point and the rightmost data point (the left bank and the right bank) of the river cross section are key points for analyzing whether overflow occurs or not, so that independent consideration is needed. Compared with other methods, the new section obtained based on the method is more suitable for hydrodynamics calculation.
EXAMPLE III
The invention provides a section interpolation encryption method and device based on a dichotomy and a layered lowest point. The theoretical basis of the invention is as follows: the water as a fluid is influenced by gravity and always preferentially occupies a lower point, so that the lower point is crucial to the water flow movement phenomenon and should be fully considered; in addition, in the one-dimensional river hydrodynamic calculation, the processing of the river bottom slope term is an important part of the momentum calculation, so the lowest point (corresponding to the river bottom elevation) is the most important point in the section data points, and must be considered separately in the generation of a new section.
The section interpolation encryption method and device based on the dichotomy and the layered lowest point comprise the following implementation steps:
step one, as shown in fig. 6, traversing the upstream section data points, and finding out a point with the lowest elevation, wherein the number is 8 (if two or more points meeting the condition are the leftmost point); defining the division depth as 0, the parent point number as null and the relative position as null.
And step two, dividing the section data point into a left data group and a right data group according to the lowest point found in the step one, namely the number 8, wherein the left data group comprises data points 1 to 7, and the right data group comprises data points 9 to 19. The current segmentation depth is defined as 1 and the parent point number is 8. Traversing the newly obtained left and right groups of data, and respectively finding out respective lowest elevation points: for the left data set, the lowest point number is 7; for the right data set, the lowest point is numbered 9.
Step three, aiming at the two newly obtained lowest points in the step two, continuously dividing downwards according to the step two, and finding the lowest point of the divided depth layer; and repeating the process until the segmentation cannot be continued. Thus, as shown in table 1, a data table including the nadir numbers and the topology attributes thereof at different division depths can be obtained, and the maximum division depth level is 10.
TABLE 1 lowest point number and topology Properties for different segmentation depths of upstream section
Step four, as shown in fig. 7, the same processing is performed on the downstream cross section according to steps one to three, and a data table composed of the lowest point numbers and the topology attributes thereof at different division depths as shown in table 2 can be obtained, where the maximum division depth level is 8.
TABLE 2 lowest point number and topology attributes thereof at different segmentation depths of downstream section
Step five, aiming at the two newly obtained data tables, firstly establishing a corresponding relation between the lowest points (data points in the respective first row) of the two data tables; then, the layers are positioned in the same segmentation depth layer by layer, corresponding relations exist among the parent-level points, and the corresponding relations are established between two data points positioned on the same side of the respective parent-level data points; until all correspondences are found, as shown in table 3.
TABLE 3 data point correspondence between upstream and downstream sections
Step six, directly establishing corresponding relations between the leftmost data point and the rightmost data point of the upstream and downstream sections respectively; and accordingly, supplementing or changing the corresponding relation in the step five, and performing ascending arrangement according to the upstream or downstream sections. The final correspondence obtained is shown in table 4.
TABLE 4 Final correspondence of data points for upstream and downstream sections
And seventhly, performing linear interpolation at the position to be interpolated based on the corresponding relation in the table 4 to obtain a new section. If the position to be interpolated is located at the midpoint of the upstream and downstream sections, the generated new section is as shown in fig. 8.
Compared with the river cross-section diagram generated by adopting the prior art as shown in fig. 9, the cross section generated by the method can keep more consistent in shape of the upstream and downstream cross sections, and the bottom elevation of the new cross section is more reasonable.
Description of the drawings: in the example, although the number of the upstream and downstream section data points is coincidentally consistent, the invention does not require this, and the invention can process section data of any shape. For the section types shown by the examples, the section generated by adopting the prior art does not reflect the real conditions of the upstream and the downstream in terms of the form and the lowest point information, and the section generated by adopting the invention can intuitively reflect the conditions of the upstream and the downstream sections.
For a better understanding of the present invention, the foregoing detailed description has been given in conjunction with specific embodiments thereof, but not with the intention of limiting the invention thereto. Any simple modifications of the above embodiments according to the technical essence of the present invention still fall within the scope of the technical solution of the present invention. In the present specification, each embodiment is described with emphasis on differences from other embodiments, and the same or similar parts between the respective embodiments may be referred to each other. For the system embodiment, since it basically corresponds to the method embodiment, the description is relatively simple, and for the relevant points, reference may be made to the partial description of the method embodiment.
Claims (10)
1. A section interpolation encryption method based on dichotomy and layered lowest point comprises the steps of obtaining upstream section data and downstream section data, and is characterized by further comprising the following steps:
step 1: traversing the upstream section data points of the position to be interpolated to find out the lowest elevation point of the upstream data;
step 2: segmenting the upstream section data points by using a data segmentation method to obtain an upstream segmentation data table;
and step 3: traversing the downstream section data points of the position to be interpolated to find out the lowest elevation point of the downstream data;
and 4, step 4: segmenting the downstream section data points by using the data segmentation method to obtain a downstream segmentation data table;
and 5: establishing a corresponding relation between the upstream segmentation data table and the downstream segmentation data table;
step 6: and performing linear interpolation at the position to be interpolated based on the one-to-one correspondence between the upstream section data points and the downstream section data points to obtain a new section.
2. A section interpolation encryption method based on bisection and hierarchical nadir according to claim 1, wherein the data segmentation method comprises the sub-steps of:
step 21: dividing the section data point into a left group of data and a right group of data according to the lowest elevation point, and defining the division depth as 1;
step 22: traversing the newly obtained left and right groups of data points, and respectively finding out respective lowest elevation points;
step 23: repeatedly executing the step 21 and the step 22 until the segmentation cannot be continued;
step 24: and generating a segmentation data table.
3. A method of section interpolation encryption based on bisection and hierarchical nadir as claimed in claim 2 wherein said step 22 comprises defining topological attributes of the newly found two lowest elevation points including data point number, depth of segmentation, parent data point number and relative position to parent data point.
4. A section interpolation encryption method based on bisection and hierarchical nadir as claimed in claim 3, wherein the segmentation data table is composed of the lowest elevation point numbers and topology attributes thereof at different segmentation depths.
5. A method of section interpolation encryption based on bisection and hierarchical nadir according to claim 4, wherein the table of partitioned data includes at least four columns, a first column being a data point number, a second column being a depth of partition, a third column being a parent data point number, and a fourth column being a relative position to the parent data point.
6. A section interpolation encryption method based on dichotomy and layered lowest point as defined in claim 5, wherein the step 5 comprises the substeps of:
step 51: establishing a corresponding relation between the lowest elevation points of the upstream segmentation data table and the downstream segmentation data table;
step 52: establishing a corresponding relation between two data points in the upstream segmentation data table and the downstream segmentation data table which meet corresponding conditions;
step 53: step 52 is repeated until all correspondences are found.
7. A section interpolation encryption method based on dichotomy and layered lowest point according to claim 6, wherein the corresponding conditions at least comprise the following:
(1) the two data points are at the same segmentation depth layer;
(2) a corresponding relationship exists between parent data points of the two data points;
(3) the two data points are on the same side of the respective parent data point.
8. A section interpolation encryption method based on dichotomy and layered lowest point as claimed in claim 7, wherein said step 5 further comprises supplementing or modifying said correspondence by a supplementing method.
9. A section interpolation encryption method based on dichotomy and layered lowest point as claimed in claim 8, wherein the complementary method is:
(1) establishing a corresponding relation between the leftmost data point of the upstream section and the leftmost data point of the downstream section directly;
(2) and establishing a corresponding relation between the rightmost data point of the upstream section and the rightmost data point of the downstream section.
10. The section interpolation encryption method based on dichotomy and layered lowest point as claimed in claim 9, wherein said step 5 further comprises generating a final correspondence table by ascending order according to upstream or downstream sections.
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| JIAN OU等: "River 3D Visualization and Analyzing Technique Using DEM", 《IEEE》 * |
| 余伟等: "河道流动水体三维仿真方法研究", 《测绘通报》 * |
| 李丽: "分布式水文模型的汇流演算研究", 《中国博士学位论文全文数据库 基础科学辑》 * |
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