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

Abstract

The invention relates to an SRG (sphere rhombus grid) subdivision code and geographic coordinate converting algorithm, which is based on the SRG subdivision method. The SRG subdivision code and geographic coordinate converting algorithm inherits the advantages of the SRG subdivision method, SRG address codes have constant directivity and are favorable for proximity searching, no projection conversion is involved in the SRG subdivision method and no projection is involved during conversion, simple arithmetic operations of addition, subtraction, multiplication and division are involved during computing, and computing speed is high. Besides, rhombus blocks hard to differentiate are differentiated by the aid of the coordinate system, and conversion accuracy is increased.

Description

The transfer algorithm of SRG subdivision coding and geographic coordinate

Technical field

The present invention relates to a kind of based on the subdivision coding of SRG subdivision method and the transfer algorithm between the latitude and longitude coordinates.

Background technology

Present most sphere geodata is to be the basis with the latitude and longitude coordinates; And in the SRG structure; The coordinate of graticule mesh is expressed with address code is recessive, wants effectively to be applied to existing geodata in the SRG structure, or is mapped to traditional latitude and longitude coordinates to the data message among the SRG; To meet people's thinking habit, must realize the mutual conversion between these two kinds of address codes.

The spherical rhombus grid (Sphere Rhombus Grid, SRG) be a kind of based on geographic coordinate combine warp and weft and with regular polygon step by step the thought of recurrence at the subdivision method of the direct subdivision of sphere.

Present most sphere geodata is to be the basis with the latitude and longitude coordinates; And in the SRG structure; The coordinate of graticule mesh is expressed with address code is recessive, wants effectively to be applied to existing geodata in the SRG structure, or is mapped to traditional latitude and longitude coordinates to the data message among the SRG; To meet people's thinking habit, must realize the mutual conversion between these two kinds of address codes.

The spherical rhombus grid (Sphere Rhombus Grid, SRG) be a kind of based on geographic coordinate combine warp and weft and with regular polygon step by step the thought of recurrence at the subdivision method of the direct subdivision of sphere." ranks approximatioss " application in concrete calculating adds, subtracts, takes advantage of and removes simple arithmetical operation, and corresponding slewing rate is very fast, but conversion accuracy is not high enough.

Summary of the invention

To the problems referred to above, the present invention proposes a kind of based on the subdivision coding of SRG subdivision method and the transfer algorithm between the latitude and longitude coordinates.

The SRG subdivision method

SRG combines to have made full use of warp and weft based on the sphere grid of geographic coordinate system with based on two kinds of subdivision methods of sphere mesh generation of regular polygon, connects regular polygon in need not, and need not projection, directly connects with camber line at sphere and carries out recurrence rhombus subdivision.

1, SRG encoding scheme

Through n level subdivision, the whole world can be divided into 4 * 4 ⁿIndividual rhombus sphere.The code length of the rhombus sphere that n level subdivision produces is n+1, and coding all is to be combined by several bit digital in 0,1,2,3, each subdivision level rhombus sphere coding according to from rudimentary subdivision to senior subdivision sequential organization, having levels property between the different stage.Each rhombus sphere all can be divided into four little rhombus spheres, and four little quadrilaterals distinguish corresponding 0,1,2,3 according to order up and down.The first place of coding be several these dough sheets of just representing on which sphere, later each all is on the basis of upper level rhombus sphere coding to compile one more.Suppose a that is encoded to of certain subdivision dough sheet of k layer ₀a ₁a ₂L a _nL a _k, a wherein ₁～a _kBe k layer four demal, value is 0,1,2,3; a ₀Produced by 0 grade of subdivision, value also is 0,1,2,3.Each subdivision dough sheet all has unique encoding corresponding with it, and the length of coding has reflected the level of subdivision, and the subdivision cell encoding has the locus correlativity.For example the coding that produces after through 2 grades of subdivisions of No. 0 sphere is as shown in Figure 2.The process of whole coding is similar with the QTM of DUTTON coding.

2, the transfer algorithm between latitude and longitude coordinates and the SRG subdivision address code

Be convenience of calculation, the position coordinates of other Unit 1～3 (longitude and latitude or address code) at first converts Unit 0 into, and then changes.The first half with No. 0 sphere is the step and the precision of example labor algorithm below, and establishing rhombus subdivision level is that k and address code are a ₀a ₁a ₂L a _nL a _kAnd subdivision is to certain level, and sphere just can be similar to as the plane and handle, and regards spherical approximation as plane in this transfer process and operates.

2.1 latitude and longitude coordinates is to the transformation of SRG coding

" coordinate recurrence method " principle: (row is corresponding with parallel, and the line number that defines the equator is 0, and n level subdivision has 2 to the north of the equator at first to define the row and column of Spherical Surface S RG graticule mesh according to the SRG subdivision method ⁿOK; Row be from longitude 0 beginning along same latitude promptly with the number of the rhombus of delegation, especially, columns is 1 on limit).

Algorithm basic principle is:

(1) for arbitrfary point P if will carry out longitude and latitude and change to address code, just latitude and longitude coordinates (φ, λ) convert into earlier this line number in the SRG graticule mesh and columns (i, j), last according to (i j) carries out recurrence step by step, successively draws SRG and encodes inferiorly.

(2) for the confirming of the n level SRG of a P, as shown in Figure 3, white space confirms easily, is respectively 0,1,2,3 according to up and down order.Middle dash area is difficult to distinguish, and is identical with columns with the Q line number like a P, but is in the different rhombuses, and coding is different.Adopt the auxiliary ownership of distinguishing the point of middle dash area of classification coordinate system in this method; As shown in Figure 4; Adopting the central point of some P in n-1 level rhombus is initial point, and laterally diagonal line is the x axle, and vertically diagonal line is the y axle; The expression formula of separatrix in this coordinate system that n level subdivision produces is respectively y+ax=0 (left side), y-ax=0 (right side).With a p with respect to the coordinate of this coordinate system (α, β) different according to α and β value, substitution y+ax or y-ax, the value that draws and 0 relatively and then confirms which n level rhombus a point P belongs to, and definite n level subdivision coding.

(3) coefficient a value confirms

Behind 0 grade of subdivision; The vertical diagonal line of rhombus that produces is a warp; Laterally diagonal line is 1/4 (supposing that the earth is a spherial body) of equator length, and therefore vertical diagonal line is 2 times of horizontal catercorner length, draws a=2; The rhombus of later subdivisions at different levels is approximate similarity all, so subdivision at different levels all has a=2.

(4) as long as the subdivision sign indicating number of each grade all is on higher level's basis, to confirm, is the process of a recurrence, therefore known initial value, and knows that recursion formula just can obtain whole SRG and encode.

The transformation that latitude and longitude coordinates is encoded to SRG, concrete transfer process:

(1) according to the subdivision level k of graticule mesh, obtain maximum ranks number (I, J): I=2 ^k, J=2 ^k

(2) confirm latitude and longitude coordinates P (φ, λ) the ranks number in graticule mesh (i, j)

$i=\frac{\mathrm{\φ}}{90/2^k}$

$j=\frac{\mathrm{\λ}}{90/[2^k-\mathrm{int}\left(i\right)]}$

Definite method of (3) n+1 level SRG sign indicating numbers

In a n level rhombus at P place, be initial point with the central point, horizontal diagonal line is the x axle, vertically diagonal line is set up coordinate system for the y axle.

X axle upper and lower respectively has 2 ^K-nOK, y axle left and right sides maximum number of column all is 2 ^K-n-1, the line number note at x axle place is I _n, the columns note at y axle place is J _n

Point P is (α in the coordinate note of this coordinate system _N+1, β _N+1)

$\left\{\begin{array}{c}{\mathrm{\β}}_{n+1}=i-I_n\\ {\mathrm{\α}}_{n+1}=j-J_n+{\mathrm{\β}}_{n+1}/2\end{array}\right.$

When $\left\{\begin{array}{c}-2^{k-n-2}\≤{\mathrm{\α}}_{n+1}\≤2^{k-n-2}\\ -2^{k-n-1}\≤{\mathrm{\β}}_{n+1}\≤2^{k-n-1}\end{array}\right.$ The time, adopt coordinate system assist differentiation, as shown in Figure 5, two separatrix of n+1 level subdivision generation are expressed as y+2x=0 (two four-quadrants), y-2x=0 (one or three quadrant) in coordinate system.

When α＞0, β＞0 o'clock, will (α, β) substitution y-2x, then $\left\{\begin{array}{c}\mathrm{\&beta;}-2a>0,a_{n+1}=0\\ \mathrm{\&beta;}-2a<0,a_{n+1}=3\end{array}\right.$

When α＞0, β＜0 o'clock, will (α, β) substitution y+2x, then $\left\{\begin{array}{c}\mathrm{\&beta;}+2a>0,a_{n+1}=3\\ \mathrm{\&beta;}+2a<0,a_{n+1}=1\end{array}\right.$

When α＜0, β＞0 o'clock, will (α, β) substitution y+2x, then $\left\{\begin{array}{c}\mathrm{\&beta;}+2a>0,a_{n+1}=0\\ \mathrm{\&beta;}+2a<0,a_{n+1}=2\end{array}\right.$

When α＜0, β＜0 o'clock, will (α, β) substitution y-2x, then $\left\{\begin{array}{c}\mathrm{\&beta;}-2a>0,a_{n+1}=2\\ \mathrm{\&beta;}-2a<0,a_{n+1}=1\end{array}\right.$

(4) coordinate axis place ranks number confirms

N level coordinate axis is on the basis of n-1 level coordinate axis, according to a _nThe difference of value moves according to certain rule, sums up as follows:

a _n=0 o'clock, $\left\{\begin{array}{c}{I}_n=I_{n-1}+2^{k-n}\\ J_n=J_{n-1}-2^{k-n-1}\end{array}\right.$

a _n=1 o'clock, $\left\{\begin{array}{c}{I}_n=I_{n-1}-2^{k-n}\\ J_n=J_{n-1}+2^{k-n-1}\end{array}\right.$

a _n=2 o'clock, $\left\{\begin{array}{c}{I}_n=I_{n-1}\\ J_n=J_{n-1}-2^{k-n-1}\end{array}\right.$

a _n=3 o'clock, $\left\{\begin{array}{c}{I}_n=I_{n-1}\\ J_n=J_{n-1}+2^{k-n-1}\end{array}\right.$

(5) the complete coding of SRG confirms

Cornerwise ranks number of No. 0 rhombus that produces behind 0 grade of subdivision is respectively I ₀=0, J ₀=2 ^K-1Use the recursion formula in the 3rd step can obtain a ₁With a ₁, I ₀, J ₀The 4th step of substitution just can be obtained I ₁, J ₁, the recursion formula in the 3rd step of substitution can be obtained a ₂, so recurrence can be obtained a ₀a ₁a ₂L a _nL a _k

The conversion of the latter half of No. 0 sphere can all change latitude into north latitude earlier, is transformed into the first half and assigns to calculate, and behind the result who asks the SRG coding is removed a ₀Outward, 0 on other everybody changes 1,1 into and changes 0 into and get final product.Can being transformed on No. 0 sphere of other sphere calculated, with a of result of calculation ₀Change the coding 1～3 of corresponding sphere into.

2.2SRG coding is to the conversion of latitude and longitude coordinates

Transfer algorithm: the longitude and latitude of certain grade of rhombus all is on the basis of upper level; Difference according to encoded radio at the corresponding levels is calculated according to certain rule; Be the process of a recurrence, therefore as long as known initial value and recursion formula can convert the SRG sign indicating number of different stage to latitude and longitude coordinates.

Concrete transfer process

Each tetragonal coding is unique, and its corresponding geographic coordinate is got the coordinate of its central point, is example with No. 0 sphere; Four quadrilateral respective coordinates that the one-level subdivision produces are respectively: 00 quadrilateral (north latitude 45, east longitude 45), 01 quadrilateral (south latitude 45; East longitude 45), 02 quadrilateral (equator, east longitude 22.5); 03 quadrilateral (equator, east longitude 67.5) is as 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

No. 0 sphere one-level of table 1 subdivision coordinate conversion

00 sphere is carried out the secondary subdivision, and coordinate conversion is as 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 secondary subdivision coordinate conversion

00 sphere is carried out three grades of subdivisions, and coordinate conversion is as 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
……	……	……

Three grades of subdivision coordinate conversion of table 3 00 sphere

Draw the transformational relation between coding and the geographic coordinate by subdivision process and above form through analysis and summary.

(1) latitude conversion

Be designated as W to the tetragonal latitude of certain n level, 4 tetragonal latitude computing method of the n+1 level that this quadrilateral is corresponding are following:

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

Know 1 grade of tetragonal latitude of subdivision, w by table 1 ₀₀=45, w ₀₁=-45, (this paper south latitude is represented with negative sign), w ₀₂=0, w ₀₃=0.Formula above the tetragonal latitude that produces of each grade subdivision of No. 0 sphere utilizes on this basis can be obtained a result through recursive calculation step by step.

(2) longitude conversion

For 00 quadrilateral sphere, can get by above form reductive analysis, for certain quadrilateral that n level subdivision produces, its longitude is J=a * (90/x)+45/x, four tetragonal longitudes of the n+1 level that it is corresponding are:

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)

Can know 00 tetragonal longitude j by table 1 ₀₀=0 * (90/1)+45/1 according to top formula, can get:

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

Later each grade can be calculated on 00 basis step by step can draw longitude coordinate.01 is identical with 00 sphere longitude conversion Calculation method, can know j by table 1 ₀₁=0 * (90/1)+45/1 can be at j with the longitude conversion of the quadrilateral sphere of 01 beginning ₀₁On the basis, utilize the formula of 00 sphere to calculate.

02 and 03 quadrilateral sphere is respectively about equator symmetry, advances the quadrilateral that produces behind the subdivision to 02 and 03, has the part quadrilateral symmetrical about the equator; Tetragonal coding about the equator symmetry; Starting two is 02 or 03, and last position is 0,1,2 or 3, and interposition is all formed by 2 and 3.If these quadrilateral tail numbers are 1, be that 0 tetragonal longitude computing method are identical then with their corresponding tail numbers at the same level, tail number is 0,2 or 3, then computing method are identical with above-mentioned formula.Specific as follows:

Certain n level quadrilateral, its longitude are J=a * (90/x)+45/x, and four tetragonal longitudes of the n+1 level that it is corresponding are:

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)

More than be the conversion about the coding and the coordinate of No. 0 sphere, the latitude conversion of 1,2, No. 3 sphere is identical with the corresponding quadrilateral of No. 0 sphere, and just the first place of coding has changed into by 0 and changed 1,2 or 3 into.The quadrilateral longitude conversion that No. 1 sphere subdivision produces with the longitude of No. 0 corresponding quadrilateral of sphere (have only first place different) on add 90 and get final product, in like manner No. 2 spheres add 180 with No. 0 corresponding tetragonal longitude of sphere and get final product, No. 3 sphere adds 270.

For some special quadrilaterals, coordinate conversion also has easy computing method in addition, and for example 000 ... 0x; Tail number is uncertain; Except tail number all the other position encoded all be 0, the coding of n level subdivision transfers the geographic coordinate formula to for (latitude representes that with W longitude is represented with J):

If last position is 0:

W＝45×(2-0.5 ^n-1)，J＝45；

If last position is 1:

W＝45×(2-0.5 ^n-2)-45/2 ^n-1，J＝45；

If last position is 2:

W＝45×(2-0.5 ^n-2)，J＝22.5；

If last position is 3:

W＝45×(2-0.5 ^n-2)，J＝67.5。

This algorithm is to be encoded to the basis with SRG subdivision method and SRG subdivision; Inherited the advantage that the SRG subdivision method is had, itself just has fixing directivity the SRG address code, is beneficial to proximity search; The SRG subdivision method does not relate to any projective transformation; Also do not relate to projection in the transfer process, computation process is only used and is added, subtracts, takes advantage of and remove simple arithmetic operations, and computing velocity is fast.And on the basis of " ranks approximatioss ", made very big improvement, adopted coordinate system to assist and distinguish some diamond blocks that are difficult to distinguish, and then improved the precision of conversion.

Description of drawings

Fig. 1 SRG3 level subdivision

Fig. 2 SRG2 level subdivision coding

The n level SRG of Fig. 3 point P confirms

Fig. 4 coordinate system is auxiliary to be distinguished

Separatrix in the auxiliary coordinate of Fig. 5

Embodiment

Conversion between latitude and longitude coordinates and the SRG subdivision address code for example

The SRG sign indicating number is to the conversion of latitude and longitude coordinates

For example being numbered 0012301 quadrilateral, is that 6 grades of subdivisions produce, and its latitude is designated as w _0112301, longitude is designated as j _0012301, computation process is following:

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

Latitude and longitude coordinates is to the conversion of SRG sign indicating number

Known point P latitude and longitude coordinates (24.25,41.17) is asked its 6 grades of subdivision SRG codings.

At first confirm that according to latitude and longitude coordinates point P is at No. 0 sphere, so a ₀=0;

So K=6 is 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

$\left\{\begin{array}{c}{\mathrm{\&beta;}}_1=i-I_0=17.24-0=17.24\\ {\mathrm{\&alpha;}}_1=j-{\mathrm{<figure-callout\; id="0"\; label="J"\; filenames="HDA0000097186970000012.png,HDA0000097186970000021.png"\; state="\{\{state\}\}">J</figure-callout>}}_0+{\mathrm{\&beta;}}_1/2=21.5-2^5+17.24/2=-1.88\end{array}\right.$

By a ₁Can obtain I ₁, J ₁, obtain β then ₂, α ₂, and then obtain a ₂Deng, so recurrence finally can be tried to achieve a ₀a ₁a ₂a ₃a ₄a ₅a ₆=0012301.

The SRG sign indicating number has only simple arithmetical operation to the transfer process of latitude and longitude coordinates, is the process of a recurrence, and known SRG coding 0012301 can draw latitude w through calculating ₀₁₂₃₀₁=24.25, longitude j _0012301=41.17.And latitude and longitude coordinates is assisted differentiation according to the ranks number and the coordinate system at a place in the transfer process of SRG sign indicating number, known point latitude w ₀₁₂₃₀₁=24.25, longitude j _0012301=41.17, can draw SRG through calculating and be encoded to 0012301, and SRG coding itself just has strict directivity, 0,1,2,3 represent up and down respectively.The algorithm of conversion is different each other, and the conclusion that obtains has but been verified its correctness each other.Can see that from this instance computation process has only simple addition subtraction multiplication and division, process is simple, and speed is fast.

Claims (2)

1.SRG the transfer algorithm of subdivision coding and geographic coordinate is characterized in that, specifically comprises:

(1) SRG encoding scheme

Through n level subdivision, the whole world can be divided into 4 * 4 ⁿIndividual rhombus sphere; The code length of the rhombus sphere that n level subdivision produces is n+1; Coding all is to be combined by several bit digital in 0,1,2,3, each subdivision level rhombus sphere coding according to from rudimentary subdivision to senior subdivision sequential organization, having levels property between the different stage; Each rhombus sphere all can be divided into four little rhombus spheres; Four little quadrilaterals are corresponding respectively 0,1,2,3 according to order up and down, the first place of coding be several these dough sheets of just representing on which sphere, later each all is on the basis of upper level rhombus sphere coding to compile one more;

(2) transfer algorithm between latitude and longitude coordinates and the SRG subdivision address code

(2.1) latitude and longitude coordinates comprises to the transformation of SRG coding:

(2.1.1) for arbitrfary point P if will carry out longitude and latitude and change to address code, just latitude and longitude coordinates (φ, λ) convert into earlier this line number and columns in the SRG graticule mesh (i, j);

(2.1.2) for the confirming of the n level SRG of a P, be respectively 0,1,2,3 according to up and down order, adopting the central point of some P in n-1 level rhombus is initial point; Laterally diagonal is the x axle, and vertically diagonal is the y axle, and the expression formula of line of demarcation in this coordinate system that n level subdivision produces is respectively y+ax=0 (left side); Y-ax=0 (right side), with a p with respect to the coordinate of this coordinate system (α, β) different based on α and β value; Substitution y+ax or y-ax; The value that draws and 0 compares, and then confirms which n level rhombus a point P belongs to, and definite n level subdivision coding;

(2.1.3) coefficient a value confirms

Behind 0 grade of subdivision; The vertical diagonal line of rhombus that produces is a warp, and laterally diagonal line is 1/4 of an equator length, supposes that the earth is a spherial body; Draw vertical diagonal line and be 2 times of horizontal catercorner length; Draw a=2, the rhombus of later subdivisions at different levels is approximate similarity all, so subdivision at different levels all has a=2;

(2.1.4) the subdivision sign indicating number of each grade all is on higher level's basis, to confirm, is the process of a recurrence, as long as known initial value, and knows that recursion formula just can obtain whole SRG and encode;

(2.2) the SRG coding comprises to the conversion of latitude and longitude coordinates:

(2.2.1) latitude conversion

Be designated as W to the tetragonal latitude of certain n level, 4 tetragonal latitude computing method of the n+1 level that this quadrilateral is corresponding are following:

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 certain quadrilateral that n level subdivision produces, its longitude is J=a * (90/x)+45/x, and four tetragonal longitudes of the n+1 level that it is corresponding are:

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 transfer algorithm of SRG subdivision coding according to claim 1 and geographic coordinate is characterized in that latitude and longitude coordinates is to the transformation of SRG coding, and detailed process is:

(1) according to the subdivision level k of graticule mesh, obtain maximum ranks number (I, J): I=2 ^k, J=2 ^k

(2) confirm latitude and longitude coordinates P (φ, λ) the ranks number in graticule mesh (i, j)

$i=\frac{\mathrm{\&phi;}}{90/2^k}$

$j=\frac{\mathrm{\&lambda;}}{90/[2^k-\mathrm{int}\left(i\right)]}$

Definite method of (3) n+1 level SRG sign indicating numbers

In a n level rhombus at P place, be initial point with the central point, horizontal diagonal line is the x axle, vertically diagonal line is set up coordinate system for the y axle,

X axle upper and lower respectively has 2 ^K-nOK, y axle left and right sides maximum number of column all is 2 ^K-n-1, the line number note at x axle place is I _n, the columns note at y axle place is J _n,

Point P is (α in the coordinate note of this coordinate system _N+1, β _N+1)

$\left\{\begin{array}{c}{\mathrm{\&beta;}}_{n+1}=i-I_n\\ {\mathrm{\&alpha;}}_{n+1}=j-J_n+{\mathrm{\&beta;}}_{n+1}/2\end{array}\right.$

(4) coordinate axis place ranks number confirms

N level coordinate axis is on the basis of n-1 level coordinate axis, according to a _nThe difference of value moves according to certain rule, sums up as follows:

a _n=0 o'clock, $\left\{\begin{array}{c}{I}_n=I_{n-1}+2^{k-n}\\ J_n=J_{n-1}-2^{k-n-1}\end{array}\right.$

a _n=1 o'clock, $\left\{\begin{array}{c}{I}_n=I_{n-1}-2^{k-n}\\ J_n=J_{n-1}+2^{k-n-1}\end{array}\right.$

a _n=2 o'clock, $\left\{\begin{array}{c}{I}_n=I_{n-1}\\ J_n=J_{n-1}-2^{k-n-1}\end{array}\right.$

a _n=3 o'clock, $\left\{\begin{array}{c}{I}_n=I_{n-1}\\ J_n=J_{n-1}+2^{k-n-1}\end{array}\right.$

(5) the complete coding of SRG confirms

Cornerwise ranks number of No. 0 rhombus that produces behind 0 grade of subdivision is respectively I ₀=0, J ₀=2 ^K-1Use the recursion formula in the 3rd step can obtain a ₁With a ₁, I ₀, J ₀The 4th step of substitution just can be obtained I ₁, J ₁, the recursion formula in the 3rd step of substitution can be obtained a ₂, so recurrence can be obtained a ₀a ₁a ₂L a _nL a _k

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