CN102567439B - 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 the transfer algorithm between a kind of subdivision based on SRG subdivision method coding and latitude and longitude coordinates.

Background technology

Current most sphere geodata is to take latitude and longitude coordinates as basis, and in SRG structure, the coordinate of graticule mesh address code covert expression, want existing geodata to be effectively applied in SRG structure, or the data message in SRG is mapped to traditional latitude and longitude coordinates, to meet people's thinking habit, must realize the mutual conversion between these two kinds of address codes.

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

Current most sphere geodata is to take latitude and longitude coordinates as basis, and in SRG structure, the coordinate of graticule mesh address code covert expression, want existing geodata to be effectively applied in SRG structure, or the data message in SRG is mapped to traditional latitude and longitude coordinates, to meet people's thinking habit, must realize the mutual conversion between these two kinds of address codes.

Spherical rhombus grid (Sphere Rhombus Grid, SRG) be a kind of based on geographic coordinate in conjunction with warp and weft and with regular polygon step by step the thought of recurrence at the subdivision method of the direct subdivision of sphere." cavalcade approach method " only applied and added, subtracts, takes advantage of and remove simple arithmetical operation in concrete calculating, and corresponding slewing rate is very fast, but conversion accuracy is not high enough.

Summary of the invention

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

SRG subdivision method

SRG, in conjunction with Grid and two kinds of subdivision methods of the Grid subdivision based on regular polygon based on geographic coordinate system, takes full advantage of warp and weft, without the interior regular polygon that connects, without projection, directly at sphere, with camber line, connects 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 is all that several bit digital in 0,1,2,3 combine, and each subdivision level rhombus sphere coding is according to from rudimentary subdivision to senior subdivision sequential organization, having levels property between different stage.Each rhombus sphere 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 is severally just to represent this dough sheet is on which sphere, and later each is all 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 ₀by 0 grade of subdivision, produced, value is also 0,1,2,3.Each subdivision dough sheet has unique coding corresponding with it, and the length of coding has reflected the level of subdivision, and subdivision cell encoding has Space correlation.The coding that for example No. 0 sphere produces after 2 grades of subdivisions as shown in Figure 2.The process of whole coding is similar to the QTM of DUTTON coding.

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

For convenience of calculation, the position coordinates of other Unit 1～3 (longitude and latitude or address code) is first converted to Unit 0, and then changes.Step and precision that the first half of No. 0 sphere of take is below example labor algorithm, establishing rhombus subdivision level is that k and address code are a ₀a ₁a ₂l a _nl a _k.And subdivision is to certain level, and sphere just can be similar to as plane and process, and regards spherical approximation as plane and operate in this transfer process.

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

" coordinate recurrence method " principle: (row is corresponding with parallel, and the line number that defines equator is to have 2 to the north of 0, n level subdivision equator first to define the row and column of Spherical Surface S RG graticule mesh according to SRG subdivision method ⁿoK; Row are to start along Same Latitude with the number of the rhombus of a line from longitude 0, and especially, in limit, columns is 1).

The ultimate principle of algorithm is:

(1), if will carry out longitude and latitude for arbitrfary point P changes to address code, just latitude and longitude coordinates (φ, λ) is first converted to this line number and columns (i in SRG graticule mesh, j), last basis (i, j) is carried out recurrence step by step, successively draws SRG coding inferiorly.

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

(3) coefficient a value determines

After 0 grade of subdivision, the longitudinal diagonal line of rhombus producing is a warp, laterally diagonal line is 1/4 (supposing that the earth is spherial body) of equator length, therefore longitudinal diagonal line is 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 has a=2.

(4) as long as the subdivision code of every one-level is all to determine on higher level's basis, 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) determine the ranks number (i, j) of latitude and longitude coordinates P (φ, λ) in graticule mesh

$i=\frac{\mathrm{\φ}}{90/2^k}$

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

Definite method of (3) n+1 level SRG codes

In the n level rhombus at a P place, take central point as initial point, horizontal diagonal line is x axle, longitudinally diagonal line is that y axle is set up coordinate system.

X axle upper and lower respectively has 2 ^k-noK, y axle left and right maximum number of column is all 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 $\left\{\begin{array}{c}-2^{k-n-2}\≤{\mathrm{\α}}_{n+1}\≤2^{k-n-2}\\ -2^{k-n-1}\≤{\mathrm{\β}}_{n+1}\≤2^{k-n-1}\end{array}\right.$ 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.

As α > 0, during β > 0, by (α, β) substitution y-2x, $\left\{\begin{array}{c}\mathrm{\&beta;}-2a>0,a_{n+1}=0\\ \mathrm{\&beta;}-2a<0,a_{n+1}=3\end{array}\right.$

As α > 0, during β < 0, by (α, β) substitution y+2x, $\left\{\begin{array}{c}\mathrm{\&beta;}+2a>0,a_{n+1}=3\\ \mathrm{\&beta;}+2a<0,a_{n+1}=1\end{array}\right.$

As α < 0, during β > 0, by (α, β) substitution y+2x, $\left\{\begin{array}{c}\mathrm{\&beta;}+2a>0,a_{n+1}=0\\ \mathrm{\&beta;}+2a<0,a_{n+1}=2\end{array}\right.$

As α < 0, during β < 0, by (α, β) substitution y-2x, $\left\{\begin{array}{c}\mathrm{\&beta;}-2a>0,a_{n+1}=2\\ \mathrm{\&beta;}-2a<0,a_{n+1}=1\end{array}\right.$

(4) coordinate axis place ranks number determines

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, is summarized 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 determines

Cornerwise ranks number of No. 0 rhombus producing after 0 grade of subdivision is respectively I ₀=0, J ₀=2 ^k-1use the recursion formula of the 3rd step can obtain a ₁; By a ₁, I ₀, J ₀substitution the 4th step just can be obtained I ₁, J ₁, the recursion formula of substitution the 3rd step 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 first all change north latitude into latitude, is transformed into the first half and assigns to calculate, and after the result of asking, SRG coding is removed to a ₀outward, 0 on other everybody changes 1,1 into and changes 0 into.Can being transformed on No. 0 sphere of other sphere calculated, by 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 is all on the basis of upper level, according to the difference of encoded radio at the corresponding levels, according to certain rule, calculate, the process of a recurrence, therefore as long as known initial value and recursion formula can convert the SRG code of different stage to latitude and longitude coordinates.

Concrete transfer process

Each tetragonal coding is unique, its corresponding geographic coordinate is got the coordinate of its central point, No. 0 sphere of take is example, and four quadrilateral respective coordinates that 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 subdivision coordinate conversion of table 1

00 sphere is carried out to 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 to 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

By subdivision process and above form, through analysis and summary, draw the transformational relation between coding and geographic coordinate.

(1) latitude conversion

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

By table 1, know 1 grade of tetragonal latitude of subdivision, w ₀₀=45, w ₀₁=-45, (south latitude represents with negative sign herein), w ₀₂=0, w ₀₃=0.The tetragonal latitude utilization that every one-level subdivision of No. 0 sphere produces on this basis formula above, can obtain a result through recursive calculation step by step.

(2) longitude conversion

For 00 quadrilateral sphere, by above form reductive analysis, can be obtained, certain quadrilateral producing for n level subdivision, 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)

00 tetragonal longitude j as shown in Table 1 ₀₀=0 * (90/1)+45/1, according to formula above, can obtain:

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 every one-level can draw longitude coordinate by step-by-step calculation on 00 basis.01 is identical with 00 sphere longitude conversion computing method, as shown in Table 1 j ₀₁=0 * (90/1)+45/1, can be at j with the longitude conversion of the quadrilateral sphere of 01 beginning ₀₁on basis, utilize the formula of 00 sphere to calculate.

02 and 03 quadrilateral sphere is symmetrical about equator respectively, enters the quadrilateral producing after subdivision to 02 and 03, has part quadrilateral symmetrical about equator, tetragonal coding about equator symmetry, starting two is 02 or 03, and last position is 0,1,2 or 3, and interposition all forms by 2 and 3.If these quadrilateral tail numbers are 1, the tetragonal longitude computing method that the at the same level tail number corresponding with them is 0 are identical, and tail number is 0,2 or 3, and computing method are identical with above-mentioned formula.Specific as follows:

Certain n level quadrilateral, 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×[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)

Be more than the conversion about 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 adds 90 on the longitude from No. 0 corresponding quadrilateral of sphere (only have first place different), and the tetragonal longitude that in like manner No. 2 spheres are corresponding with No. 0 sphere adds 180, No. 3 spheres and 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 be all that the coding of 0, n level subdivision transfers geographic coordinate formula to for (latitude represent with W, longitude represents 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 basis with SRG subdivision method and SRG subdivision, inherited the advantage that SRG subdivision method has, itself just has fixing directivity SRG address code, be beneficial to proximity search, SRG subdivision method does not relate to any projective transformation, in transfer process, also do not relate to projection, computation process is only applied and is added, subtracts, takes advantage of and remove simple arithmetic operations, and computing velocity is fast.And on the basis of " cavalcade approach method ", made very large improvement, adopted coordinate system to assist and distinguish the diamond block that some are difficult to differentiation, and then improved the precision of conversion.

Accompanying drawing explanation

Fig. 1 SRG3 level subdivision

Fig. 2 SRG2 level subdivision coding

The n level SRG of Fig. 3 point P determines

Fig. 4 coordinate system is auxiliary to be distinguished

Separatrix in Fig. 5 auxiliary coordinate

Embodiment

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

SRG code 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 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

Latitude and longitude coordinates is to the conversion of SRG code

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

First according to latitude and longitude coordinates, determine that some P is at No. 0 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

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

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

SRG code only has simple arithmetical operation to the transfer process of latitude and longitude coordinates, is the process of a recurrence, and known SRG coding 0012301, through can be calculated latitude w ₀₁₂₃₀₁=24.25, longitude j _0012301=41.17.And latitude and longitude coordinates is in the transfer process of SRG code, according to the ranks number at a place and coordinate system, assist differentiation, known point latitude w ₀₁₂₃₀₁=24.25, longitude j _0012301=41.17, through can be calculated SRG, 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 mutually, and the conclusion obtaining has but been verified its correctness mutually.From this example, can see, computation process only has simple addition subtraction multiplication and division, and process is simple, and speed is fast.

Claims (1)

1. The transfer algorithm of 1.SRG 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 individual rhombus sphere, the code length of the rhombus sphere that n level subdivision produces is n+1, coding is all by 0, 1, 2, several bit digital in 3 combine, each subdivision level rhombus sphere coding is according to from rudimentary subdivision to senior subdivision sequential organization, having levels property between different stage, each rhombus sphere can be divided into four little rhombus spheres, four little quadrilaterals distinguish corresponding 0 according to order up and down, 1, 2, 3, the first place of coding is severally just to represent this little quadrilateral is on which sphere, later each is all to compile one on the basis of upper level rhombus sphere coding more,

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

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

   If (2.1.1) will carry out longitude and latitude for arbitrfary point P, to address code, change, just latitude and longitude coordinates (φ, λ) is first converted to this line number and columns (i, j) in SRG graticule mesh;

   (2.1.2) determining for the n level SRG of a P, according to order up and down, be respectively 0, 1, 2, 3, adopting the central point of some P in n-1 level rhombus is initial point, laterally diagonal line is x axle, longitudinally diagonal line is y axle, the expression formula on initial point left side in this coordinate system, separatrix that n level subdivision produces is y+ax=0, expression formula on initial point the right is y-ax=0, coordinate (α by a p with respect to this coordinate system, β) according to the difference of α and β value, substitution y+ax or y-ax, the value drawing and 0 relatively, and then determine which n level rhombus point P belongs to, and definite n level subdivision coding,

   (2.1.3) coefficient a value determines

   After 0 grade of subdivision, the longitudinal diagonal line of rhombus of generation is a warp, and laterally diagonal line is 1/4 of equator length, suppose that the earth is spherial body, show that longitudinal 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 has a=2;

   (2.1.4) the subdivision code of every one-level is all to determine on higher level's basis, 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) SRG coding, to the conversion of latitude and longitude coordinates, comprising:

   (2.2.1) latitude conversion

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

   

   (2.2.2) longitude conversion

   Certain quadrilateral producing for n level subdivision, its longitude is

   

   , four tetragonal longitudes of the n+1 level that it is corresponding are:

   

   

   。

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