CN102567439A - SRG (sphere rhombus grid) subdivision code and geographic coordinate converting algorithm - Google Patents

Abstract

The invention relates to a conversion algorithm between subdivision coding and latitude and longitude coordinates based on the SRG subdivision method. This algorithm inherits the advantages of the SRG subdivision method. The SRG address code itself has a fixed directionality, which is beneficial to the proximity search. The SRG subdivision method does not involve any projection transformation, and the conversion process does not involve projection. The calculation process only uses Add, subtract, multiply and divide simple arithmetic operations with fast calculation speed. And the coordinate system is used to assist in distinguishing some difficult-to-distinguish rhombus blocks, thereby improving the conversion accuracy.

Description

SRG Subdivision Coding and Geographic Coordinate Conversion Algorithm

technical field

The invention relates to a conversion algorithm between subdivision coding and latitude and longitude coordinates based on the SRG subdivision method.

Background technique

At present, the vast majority of spherical geographic data is based on latitude and longitude coordinates. In the SRG structure, the grid coordinates are implicitly expressed by address codes. The data information in is mapped to the traditional latitude and longitude coordinates, in order to conform to people's thinking habits, the mutual conversion between these two address codes must be realized.

Sphere Rhombus Grid (SRG) is a subdivision method based on geographic coordinates combined with latitude and longitude lines and using the idea of regular polyhedron recursion step by step to directly subdivide the spherical surface.

At present, the vast majority of spherical geographic data is based on latitude and longitude coordinates. In the SRG structure, the grid coordinates are implicitly expressed by address codes. The data information in is mapped to the traditional latitude and longitude coordinates, in order to conform to people's thinking habits, the mutual conversion between these two address codes must be realized.

Sphere Rhombus Grid (SRG) is a subdivision method based on geographic coordinates combined with latitude and longitude lines and using the idea of regular polyhedron recursion step by step to directly subdivide the spherical surface. "Row-column approximation method" only uses simple arithmetic operations of addition, subtraction, multiplication and division in specific calculations, and the corresponding conversion speed is fast, but the conversion accuracy is not high enough.

Contents of the invention

In view of the above problems, the present invention proposes a conversion algorithm between subdivision coding and latitude and longitude coordinates based on the SRG subdivision method.

SRG segmentation method

SRG combines the spherical grid based on the geographic coordinate system and the spherical grid based on the regular polyhedron. It makes full use of the longitude and latitude lines, does not need to inscribe the regular polyhedron, and does not need projection. It can be recursively connected directly on the spherical surface with arcs. Diamond split.

1. SRG coding scheme

After n-level subdivision, the whole world can be divided into 4×4 ⁿ rhombus spheres. The code length of the diamond-shaped sphere produced by n-level subdivision is n+1, and the code is composed of several digits in 0, 1, 2, and 3. The subdivision is organized sequentially, and there is hierarchy between different levels. Each rhombus sphere can be divided into four small rhombus spheres, and the four small quadrilaterals correspond to 0, 1, 2, and 3 respectively in the order of up, down, left, and right. The number of the first digit of the code represents the number of the spherical surface on which the patch is located, and each subsequent digit is coded one more on the basis of the rhombus spherical surface coding of the previous level. Assume that the code of a subdivided patch on the kth layer is a ₀ a ₁ a ₂ L a _n L a _k , where a ₁ ~ a _k is the quarter code of the k layer, and the values are 0, 1, 2, 3; a ₀ is generated by level 0 subdivision, and the values are also 0, 1, 2, 3. Each subdivision patch has a unique code corresponding to it, the length of the code reflects the subdivision level, and the subdivision unit code has a spatial position correlation. For example, the code generated after the No. 0 sphere is divided into two levels is shown in Fig. 2 . The whole encoding process is similar to DUTTON's QTM encoding.

2. Conversion algorithm between latitude and longitude coordinates and SRG subdivision address code

For the convenience of calculation, the position coordinates (latitude and longitude or address code) of the other 1 to 3 units are first converted to unit 0, and then converted. Next, take the upper part of the sphere of No. 0 as an example to analyze the steps and accuracy of the algorithm in detail. Let the rhombus subdivision level be k and the address code be a ₀ a ₁ a ₂ L a _n L a _k . And when subdivided to a certain level, the spherical surface can be treated as a plane. In this conversion process, the spherical surface can be treated as a plane.

2.1 Transformation of latitude and longitude coordinates to SRG code

The principle of "coordinate recursion method": according to the SRG subdivision method, first define the rows and columns of the spherical SRG grid (rows correspond to latitude lines, the number of rows defining the equator is 0, and there are 2 ⁿ rows north of the equator in n-level subdivision; the columns are Starting from longitude 0, the number of rhombuses along the same latitude, that is, the same row, especially, the number of columns at the pole is 1).

The basic principle of the algorithm is:

(1) For any point P, if you want to convert the latitude and longitude to the address code, first convert the latitude and longitude coordinates (φ, λ) into the number of rows and columns (i, j) of the point in the SRG grid, and finally according to ( i, j) perform recursion level by level to obtain SRG code level by level.

(2) For the determination of the n-level SRG of point P, as shown in Figure 3, the blank area is easy to determine, and the order of up, down, left, and right is 0, 1, 2, 3 respectively. The shaded part in the middle is difficult to distinguish, such as points P and Q with the same number of rows and columns, but in different rhombuses, and coded differently. In this method, a hierarchical coordinate system is used to assist in distinguishing the attribution of the points in the middle shadow part. As shown in Figure 4, the center point of point P in the n-1 rhombus is used as the origin, the horizontal diagonal is the x axis, and the vertical diagonal is the x axis. The angular line is the y-axis, and the expressions of the dividing line generated by the n-level subdivision in this coordinate system are y+ax=0 (left), y-ax=0 (right). Substituting the coordinates (α, β) of point p relative to the coordinate system into y+ax or y-ax according to the different values of α and β, and comparing the obtained value with 0, and then determining which n-level rhombus the point P belongs to , and determine n-level subdivision coding.

(3) Determination of the coefficient a value

After 0-level subdivision, the longitudinal diagonal of the generated rhombus is a meridian, and the horizontal diagonal is 1/4 of the length of the equator (assuming the earth is a perfect circle), so the longitudinal diagonal is twice the length of the horizontal diagonal , it is obtained that a=2, and the rhombuses of each level of subdivision are approximately similar, so each level of subdivision has a=2.

(4) The subdivision code of each level is determined on the basis of the upper level, which is a recursive process, so as long as the initial value is known and the recursive formula is known, the entire SRG code can be obtained.

The conversion of latitude and longitude coordinates to SRG codes, the specific conversion process:

(1) Calculate the maximum number of rows and columns (I, J) according to the subdivision level k of the grid: I=2 ^k , J=2 ^k

(2) Determine the number of rows and columns (i, j) of the latitude and longitude coordinates P (φ, λ) in the grid

$\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; \&phi;</span>}}{\mathrm{<span\; class="notranslate">\; 90</span>}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}}$

$\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}{\mathrm{<span\; class="notranslate">\; 90</span>}<span\; class="notranslate">\; /</span><span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; int</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>}$

(3) Determination method of n+1 level SRG code

In the n-level rhombus where point P is located, a coordinate system is established with the center point as the origin, the horizontal diagonal as the x-axis, and the vertical diagonal as the y-axis.

There are 2 ^kn rows above and below the x-axis, and the maximum number of columns on the left and right of the y-axis is 2 ^kn-1 . The number of rows on the x-axis is recorded as I _n , and the number of columns on the y-axis is recorded as J _n .

The coordinates of point P in this coordinate system are marked as (α _n+1 , β _n+1 )

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}\\ {\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; J</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}\end{array}\right.$

when $\left\{\begin{array}{c}-2^{k-\mathrm{no}-2}\&le;{\mathrm{\&alpha;}}_{\mathrm{no}+1}\&le;2^{k-\mathrm{no}-2}\\ -2^{k-\mathrm{no}-1}\&le;{\mathrm{\&beta;}}_{\mathrm{no}+1}\&le;2^{k-\mathrm{no}-1}\end{array}\right.$ , the coordinate system is used to assist in distinguishing, as shown in Figure 5, the expression of the two dividing lines produced by the n+1 level subdivision in the coordinate system is y+2x=0 (two and four quadrants), y-2x=0 (one and three quadrants).

When α>0, β>0, substitute (α, β) into y-2x, then $\left\{\begin{array}{c}\mathrm{\&beta;}-2a>0,a_{\mathrm{no}+1}=0\\ \mathrm{\&beta;}-2a<0,a_{\mathrm{no}+1}=3\end{array}\right.$

When α>0, β<0, substitute (α, β) into y+2x, then $\left\{\begin{array}{c}\mathrm{\&beta;}+2a>0,a_{\mathrm{no}+1}=3\\ \mathrm{\&beta;}+2a<0,a_{\mathrm{no}+1}=1\end{array}\right.$

When α<0, β>0, substitute (α, β) into y+2x, then $\left\{\begin{array}{c}\mathrm{\&beta;}+2a>0,a_{\mathrm{no}+1}=0\\ \mathrm{\&beta;}+2a<0,a_{\mathrm{no}+1}=2\end{array}\right.$

When α<0, β<0, substitute (α, β) into y-2x, then $\left\{\begin{array}{c}\mathrm{\&beta;}-2a>0,a_{\mathrm{no}+1}=2\\ \mathrm{\&beta;}-2a<0,a_{\mathrm{no}+1}=1\end{array}\right.$

(4) Determination of the number of rows and columns where the coordinate axis is located

The n-level coordinate axis is based on the n-1 level coordinate axis, and moves according to certain rules according to the different values of a _n , summarized as follows:

when a _n =0, $\left\{\begin{array}{c}{I}_{\mathrm{no}}=I_{\mathrm{no}-1}+2^{k-\mathrm{no}}\\ J_{\mathrm{no}}=J_{\mathrm{no}-1}-2^{k-\mathrm{no}-1}\end{array}\right.$

When a _n =1, $\left\{\begin{array}{c}{I}_{\mathrm{no}}=I_{\mathrm{no}-1}-2^{k-\mathrm{no}}\\ J_{\mathrm{no}}=J_{\mathrm{no}-1}+2^{k-\mathrm{no}-1}\end{array}\right.$

When a _n = 2, $\left\{\begin{array}{c}{I}_{\mathrm{no}}=I_{\mathrm{no}-1}\\ J_{\mathrm{no}}=J_{\mathrm{no}-1}-2^{k-\mathrm{no}-1}\end{array}\right.$

When a _n = 3, $\left\{\begin{array}{c}{I}_{\mathrm{no}}=I_{\mathrm{no}-1}\\ J_{\mathrm{no}}=J_{\mathrm{no}-1}+2^{k-\mathrm{no}-1}\end{array}\right.$

(5) Determination of SRG complete coding

The number of rows and columns of the diagonals of the No. 0 rhombus generated after the 0-level subdivision is I ₀ = 0, J ₀ = 2 ^k-1. Using the recursive formula in the third step, a ₁ can be obtained; a ₁ , I ₀ and J ₀ can be substituted into the fourth step to obtain I ₁ , J ₁ , and then substituted into the recursive formula of the third step to obtain a ₂ ..., so that a ₀ a ₁ a ₂ L a _n L can be obtained recursively a _k .

For the conversion of the lower half of the 0 sphere, you can first change the latitude to north latitude, and then convert to the upper half to calculate. After finding the result, change the SRG code except for a ₀ , and replace the 0 on the other bits with 1, 1 All can be replaced with 0. Other spherical surfaces can be converted to spherical surface No. 0 for calculation, and a ₀ of the calculation result is replaced with codes 1 to 3 corresponding to spherical surfaces.

2.2 Conversion of SRG codes to latitude and longitude coordinates

Conversion algorithm: the latitude and longitude of a rhombus at a certain level are calculated on the basis of the previous level, and according to certain rules according to the difference in the encoding value of this level. It is a recursive process, so as long as the initial value and the recursive formula are known, the Different levels of SRG codes are converted into latitude and longitude coordinates.

Specific conversion process

The code of each quadrilateral is unique, and its corresponding geographic coordinates take the coordinates of its center point. Taking the No. 0 sphere as an example, the corresponding coordinates of the four quadrilaterals generated by the first-level subdivision are: 00 quadrilateral (45 north latitude, 45 east longitude ), 01 quadrilateral (45 south latitude, 45 east longitude), 02 quadrilateral (equator, 22.5 east longitude), and 03 quadrilateral (equator, 67.5 east longitude) are shown in Table 1.

latitude Longitude 00 45 90/1/2 01 -45 90/1/2 02 0 90/2/2 03 0 90/2+90/2/2

Table 1 Coordinate conversion of first-level subdivision of No.0 spherical surface

The 00 sphere is subdivided into two levels, and the coordinate transformation is shown in Table 2:

latitude longitude 000 45+45/2 90/1/2 001 45-45/2 90/3+90/3/2 002 45 90/2/2 003 45 90/2+90/2/2

Table 2 00 sphere two-level subdivision coordinate conversion

The 00 sphere is subdivided into three levels, and the coordinate transformation is shown in Table 3:

latitude Longitude 0000 45+45/2+45/2^2 90/1/2 0001 45+45/2-45/2^2 90/3+90/3/2 0002 45+45/2 90/2/2 0003 45+45/2 90/2+90/2/2 0010 45-45/2+45/2^2 2×(90/5)+90/5/2 0011 45-45/2-45/2^2 3×(90/7)+90/7/2 0012 45-45/2 2×(90/6)+90/6/2 ... ... ...

Table 3 00 spherical three-level subdivision coordinate conversion

Based on the subdivision process and the above tables, the conversion relationship between codes and geographic coordinates can be obtained through summary analysis.

(1) Latitude conversion

Denote the latitude of a quadrilateral of level n as W, and the latitude calculation method of the four quadrilaterals of level n+1 corresponding to the quadrilateral is as follows:

a _n+1 =0, W ₀ =W+45/2 ⁿ

a _n+1 =1, W ₁ =W-45/2 ⁿ

a _n+1 =2, W ₂ =W

a _n+1 =3, W ₃ =W

From Table 1, we know the latitude of the first-level subdivision quadrilateral, w ₀₀ =45, w ₀₁ =-45, (in this paper, the south latitude is represented by a negative sign), w ₀₂ =0, w ₀₃ =0. On this basis, the latitude of the quadrilateral generated by each level of subdivision of the No. 0 sphere can be obtained by recursive calculation level by level using the above formula.

(2) Longitude conversion

For the 00 quadrilateral spherical surface, it can be obtained from the inductive analysis of the above table that for a certain quadrilateral produced by n-level subdivision, its longitude is J=a×(90/x)+45/x, and its corresponding n+1 level four The longitude of the quadrilateral is:

a _n+1 =0, J ₀ =2a×[90/(2x-1)]+45/(2x-1)

a _n+1 =1, J ₁ =(2a+1)×[90/(2x+1)]+45/(2x+1)

a _n+1 =2, J ₂ =2a×[90/(2x)]+45/(2x)

a _n+1 =3, J ₃ =(2a+1)×[90/(2x)]+45/(2x)

It can be known from Table 1 that the longitude j ₀₀ of the 00 quadrilateral = 0×(90/1)+45/1, according to the above formula, it can be obtained:

j ₀₀₀ = (2×0)×[90/(2×1-1)]+45/(2×1-1)

＝0×(90/1)+45/1＝45

j ₀₀₁ = (2×0+1)×[90/(2×1+1)]+45/(2×1+1)

＝1×(90/3)+45/3＝45

j ₀₀₂ = (2×0)×[90/(2×1)]+45/(2×1)

＝0×(90/2)+45/2＝22.5

j ₀₀₃ = (2×0+1)×[90/(2×1)]+45/(2×1)

＝1×(90/2)+45/2＝67.5

Each subsequent level can be calculated step by step on the basis of 00 to obtain the longitude coordinates. The longitude conversion calculation method of 01 and 00 spheres is the same. It can be seen from Table 1 that j ₀₁ = 0×(90/1)+45/1, and the longitude conversion of quadrilateral spheres starting with 01 can be based on j ₀₁ , using the 00 sphere formula to calculate.

The 02 and 03 quadrilateral spheres are respectively symmetrical about the equator, and the quadrilaterals generated after subdividing 02 and 03, some quadrilaterals are symmetrical about the equator, and the coding of the quadrilateral symmetrical about the equator, the first two digits are 02 or 03, and the last digit is 0, 1, 2 or 3, the middle bits are all made up of 2 and 3. If these quadrilaterals have a tail number of 1, the longitude calculation method is the same as that of their corresponding sibling quadrilaterals with a tail number of 0. If the tail number is 0, 2, or 3, the calculation method is the same as the above formula. details as follows:

A quadrilateral of level n, its longitude is J=a×(90/x)+45/x, and the longitude of the four quadrilaterals corresponding to level n+1 is:

a _n+1 =0, J ₀ =2a×[90/(2x-1)]+45/(2x-1)

a _n+1 =1, J ₁ =2a×[90/(2x-1)]+45/(2x-1)

a _n+1 =2, J ₂ =2a×[90/(2x)]+45/(2x)

a _n+1 =3, J ₃ =(2a+1)×[90/(2x)]+45/(2x)

The above is about the encoding and coordinate conversion of sphere 0. The latitude conversion of sphere 1, 2, and 3 is the same as the corresponding quadrilateral of sphere 0, except that the first digit of the code is changed from 0 to 1, 2 or 3. For the longitude conversion of the quadrilateral generated by the subdivision of the No. 1 sphere, add 90 to the longitude of the quadrilateral corresponding to the No. 0 sphere (only the first digit is different). Similarly, add 180 to the longitude of the quadrilateral corresponding to the No. 2 sphere and No. 0 sphere. 3 Number sphere plus 270.

In addition, for some special quadrilaterals, coordinate conversion also has a simple calculation method, such as 000...0x, the tail number is uncertain, except for the tail number, the rest of the position codes are 0, and the code of the n-level subdivision is converted to geographic coordinates. The formula is (latitude Denoted by W and longitude by J):

If the last bit is 0:

W=45×(2-0.5 ^n-1 ), J=45;

If the last bit is 1:

W=45×(2-0.5 ^n-2 )-45/2 ^n-1 , J=45;

If the last digit is 2:

W=45×(2-0.5 ^n-2 ), J=22.5;

If the last digit is 3:

W=45×(2-0.5 ^n-2 ), J=67.5.

This algorithm is based on the SRG subdivision method and SRG subdivision code, and inherits the advantages of the SRG subdivision method. The SRG address code itself has a fixed directionality, which is beneficial to the proximity search. The SRG subdivision method does not involve any projection. Transformation, projection is not involved in the conversion process, and the calculation process only applies simple arithmetic operations of addition, subtraction, multiplication and division, and the calculation speed is fast. And a great improvement has been made on the basis of the "row-column approximation method", and the coordinate system is used to assist in distinguishing some difficult-to-distinguish rhombus blocks, thereby improving the conversion accuracy.

Description of drawings

Figure 1 SRG3 level subdivision

Figure 2 SRG2-level subdivision coding

Figure 3 Determination of n-level SRG at point P

Figure 4 Auxiliary distinction of coordinate system

Figure 5 The dividing line in the auxiliary coordinates

Detailed ways

Examples of conversion between latitude and longitude coordinates and SRG subdivision address codes

Conversion of SRG codes to latitude and longitude coordinates

For example, the quadrilateral numbered 0012301 is generated by 6-level subdivision, its latitude is recorded as w _0112301 , longitude is recorded as j _0012301 , and the calculation process is as follows:

w _0012301 = w ₀₀₁₂₃₀ -45/5 ⁵

=w ₀₀₁₂₃ +45/2 ⁴ -45/2 ⁵

=w ₀₀₁₂ +45/2 ⁴ -45/2 ⁵

=w ₀₀₁ +45/2 ⁴ -45/2 ⁵

=w ₀₀ -45/2+45/2 ⁴ -45/2 ⁵

＝45-45/2+45/2 ⁴ -45/2 ⁵

＝24.25

j ₀₀₁ =1×(90/3)+45/3

j ₀₀₁₂ =2×(90/6)+45/6

j ₀₀₁₂₃ = 5×(90/12)+45/12

j ₀₀₁₂₃₀ = 10×(90/23)+45/23

j _0012301 = 21 × (90/47) + 45/47 = 41.17

Conversion of latitude and longitude coordinates to SRG code

Given the latitude and longitude coordinates (24.25, 41.17) of point P, find its 6-level subdivision SRG code.

Firstly, according to the latitude and longitude coordinates, it is determined that the point P is on the 0th sphere, so a ₀ =0;

K=6, so I=2 ⁶ , J=2 ⁶

$j=\frac{\mathrm{\&lambda;}}{90/[2^k-\mathrm{int}\left(i\right)]}=\frac{41.17}{90/[2^6-\mathrm{int}\left(i\right)]}=21.5$ So a ₁ =0

I ₀ =0, J ₀ =2 ^k-1

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 17.24</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 17.24</span>}\\ {\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="J"\; filenames="HDA0000097186970000012.png,HDA0000097186970000021.png"\; state="\{\{state\}\}">J</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 21.5</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 5</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 17.24</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1.88</span>}\end{array}\right.$

I ₁ , J ₁ can be obtained from a ₁ , then β ₂ , α ₂ , and then a ₂ can be obtained, and so on, recursively, and finally a ₀ a ₁ a ₂ a 3 _{a 4 a 5} a ₆ = 0012301.

The process of converting SRG codes to latitude and longitude coordinates is only a simple arithmetic operation, which is a recursive process. The known SRG code 0012301 can be calculated as latitude w ₀₁₂₃₀₁ = 24.25 and longitude j _0012301 = 41.17. And in the conversion process of latitude and longitude coordinates to SRG code, according to the number of ranks and the coordinate system where the point is located to assist in distinguishing, known point latitude w ₀₁₂₃₀₁ =24.25, longitude j _0012301 =41.17, can draw SRG code to be 0012301 through calculation, and The SRG code itself has strict directionality, and 0, 1, 2, and 3 represent up, down, left, and right, respectively. The algorithms for mutual conversion are different, but the conclusions obtained mutually verify their correctness. It can be seen from this example that the calculation process is only simple addition, subtraction, multiplication and division, the process is simple and the speed is fast.

Claims (2)

1. The conversion algorithm of SRG subdivision coding and geographical coordinates is characterized in that, specifically comprises: (1) SRG coding scheme After n-level subdivision, the world can be divided into 4×4 ⁿ rhombic spheres. The code length of the rhombus sphere produced by n-level subdivision is n+1, and the codes are composed of several digits in 0, 1, 2, and 3. Combination, each subdivision level rhombus sphere coding is organized according to the sequence from low-level subdivision to high-level subdivision, there is hierarchy between different levels, each rhombus sphere can be divided into four small rhombus The order of up, down, left, and right corresponds to 0, 1, 2, 3 respectively. The number of the first digit of the code represents the number of the spherical surface on which the patch is located. bit; (2) Conversion algorithm between latitude and longitude coordinates and SRG subdivision address code (2.1) Transformation of latitude and longitude coordinates to SRG codes, including: (2.1.1) If any point P is to be converted from latitude and longitude to an address code, the latitude and longitude coordinates (φ, λ) are first converted to the number of rows and columns (i, j) of the point in the SRG grid; (2.1.2) For the determination of the n-level SRG of point P, the order of up, down, left, and right is 0, 1, 2, and 3 respectively, and the center point of point P in the n-1 level rhombus is used as the origin, and the horizontal diagonal is the x-axis, the longitudinal diagonal is the y-axis, and the expressions of the dividing line generated by the n-level subdivision in this coordinate system are y+ax=0 (left), y-ax=0 (right), and point The coordinates (α, β) of p relative to the coordinate system are substituted into y+ax or y-ax according to the different values of α and β, and the obtained value is compared with 0 to determine which n-level rhombus the point P belongs to, and Determine the n-level subdivision code; (2.1.3) Determination of coefficient a value After 0-level subdivision, the longitudinal diagonal of the generated rhombus is a meridian, and the horizontal diagonal is 1/4 of the length of the equator. Assuming that the earth is a perfect circle, the longitudinal diagonal is twice the length of the horizontal diagonal , draw a=2, and the rhombuses of all levels of subdivision are approximately similar in the future, so all levels of subdivision have a=2; (2.1.4) The subdivision code of each level is determined on the basis of the upper level, which is a recursive process. As long as the initial value is known and the recursive formula is known, the entire SRG code can be obtained; (2.2) Conversion of SRG codes to latitude and longitude coordinates, including: (2.2.1) Latitude conversion Denote the latitude of a quadrilateral of level n as W, and the latitude calculation method of the four quadrilaterals of level n+1 corresponding to the quadrilateral is as follows: a _n+1 =0, W ₀ =W+45/2 ⁿ a _n+1 =1, W ₁ =W-45/2 ⁿ a _n+1 =2, W ₂ =W a _n+1 =3, W ₃ =W (2.2.2) Longitude Conversion For a certain quadrilateral generated by n-level subdivision, its longitude is J=a×(90/x)+45/x, and the longitude of the four quadrilaterals corresponding to level n+1 is: a _n+1 =0, J ₀ =2a×[90/(2x-1)]+45/(2x-1) a _n+1 =1, J ₁ =(2a+1)×[90/(2x+1)]+45/(2x+1) a _n+1 =2, J ₂ =2a×[90/(2x)]+45/(2x) a _n+1 =3, J ₃ =(2a+1)×[90/(2x)]+45/(2x) 2. the conversion algorithm of SRG subdivision coding and geographic coordinates according to claim 1, it is characterized in that, the transformation of latitude and longitude coordinates to SRG coding, concrete process is: (1) Calculate the maximum number of rows and columns (I, J) according to the subdivision level k of the grid: I=2 ^k , J=2 ^k (2) Determine the number of rows and columns (i, j) of the latitude and longitude coordinates P (φ, λ) in the grid $\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; \&phi;</span>}}{\mathrm{<span\; class="notranslate">\; 90</span>}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}}$ $\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}{\mathrm{<span\; class="notranslate">\; 90</span>}<span\; class="notranslate">\; /</span><span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; int</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>}$ (3) Determination method of n+1 level SRG code In the n-level rhombus where the point P is located, the center point is the origin, the horizontal diagonal is the x-axis, and the vertical diagonal is the y-axis to establish a coordinate system. There are 2 ^kn rows above and below the x-axis, and the maximum number of columns on the left and right of the y-axis is 2 ^kn-1 . The number of rows on the x-axis is recorded as I _n , and the number of columns on the y-axis is recorded as J _n . The coordinates of point P in this coordinate system are marked as (α _n+1 , β _n+1 ) $\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}\\ {\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; J</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}\end{array}\right.$

(4) Determination of the number of rows and columns where the coordinate axis is located The n-level coordinate axis is based on the n-1 level coordinate axis, and moves according to certain rules according to the different values of a _n , summarized as follows: when a _n =0, $\left\{\begin{array}{c}{I}_{\mathrm{no}}=I_{\mathrm{no}-1}+2^{k-\mathrm{no}}\\ J_{\mathrm{no}}=J_{\mathrm{no}-1}-2^{k-\mathrm{no}-1}\end{array}\right.$ When a _n =1, $\left\{\begin{array}{c}{I}_{\mathrm{no}}=I_{\mathrm{no}-1}-2^{k-\mathrm{no}}\\ J_{\mathrm{no}}=J_{\mathrm{no}-1}+2^{k-\mathrm{no}-1}\end{array}\right.$ When a _n = 2, $\left\{\begin{array}{c}{I}_{\mathrm{no}}=I_{\mathrm{no}-1}\\ J_{\mathrm{no}}=J_{\mathrm{no}-1}-2^{k-\mathrm{no}-1}\end{array}\right.$ When a _n = 3, $\left\{\begin{array}{c}{I}_{\mathrm{no}}=I_{\mathrm{no}-1}\\ J_{\mathrm{no}}=J_{\mathrm{no}-1}+2^{k-\mathrm{no}-1}\end{array}\right.$ (5) Determination of SRG complete coding The number of rows and columns of the diagonals of the No. 0 rhombus generated after the 0-level subdivision is I ₀ = 0, J ₀ = 2 ^k-1. Using the recursive formula in the third step, a ₁ can be obtained; a ₁ , I ₀ and J ₀ can be substituted into the fourth step to obtain I ₁ , J ₁ , and then substituted into the recursive formula of the third step to obtain a ₂ ..., so that a ₀ a ₁ a ₂ L a _n L can be obtained recursively a _k .

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