CN102589518A - Remote-sensing aerial surveying elevation fitting method - Google Patents

Abstract

The invention relates to the technical field of power engineering survey, in particular to a remote-sensing aerial surveying elevation fitting method. The remote-sensing aerial surveying elevation fitting method comprises the following steps: setting a field surveyed monitoring point, surveying three-dimensional coordinate data of the monitoring point by using a field surveying instrument, and determining a field surveyed elevation surface; surveying a large-scale topographic map, extracting three-dimensional coordinate data of the large-scale topographic map; in combination with a data value of the field surveyed elevation surface, performing elevation fitting on the three-dimensional coordinate data of the large-scale topographic map by using a polynomial fitting model, and working out an elevation correcting value of each point in the large-scale topographic maps; and correcting the elevation data of the large-scale topographic map by a triangular planar fitting method to the field surveyed elevation surface so as to obtain the elevation value of each point in the large-scale topographic map. Through the adoption of the remote-sensing aerial surveying elevation fitting method, the elevation precision of the large-scale topographic map is effectively improved, thus meeting a requirement on the precision of the surveyed elevation of the large-scale topographic map in survey specifications.

Description

Remote sensing aerial survey height fitting method

Technical field

The present invention relates to power engineering prospecting technique field, belong to the Surveying Science and Technology field, specifically is a kind of remote sensing aerial survey height fitting method.

Background technology

The remote sensing aerial survey is mainly used in and obtains high precision landform diagram data in real time.At present; The remote sensing aerial survey stabilized platform; The elevation of measuring through photogrammetric office work is big with the vertical error that adopts field operation surveying instrument actual measurements such as total powerstation, can not satisfy the requirement of large scale topographical map specifications of surveys, especially in each exploration stage of power engineering, uses the remote sensing airborne survey method; The map surveying vertical accuracy is low, does not also have feasible method to address this problem at present.

Summary of the invention

The purpose of this invention is to provide a kind of elevation and handle, satisfy the remote sensing aerial survey height fitting method that large scale topographical map measurement vertical accuracy requires in the specifications of surveys the remote sensing aerial survey.

For realizing above-mentioned purpose, a kind of remote sensing aerial survey height fitting method of the present invention's design comprises following steps:

The first step: field operation actual measurement check point is set, adopts the three-dimensional coordinate data of field operation surveying instrument actual measurement check point, confirm field operation actual measurement elevation face;

Second step: adopt the remote sensing aerial survey stabilized platform, measure large scale topographical map, extract the three-dimensional coordinate data of large scale topographical map;

The 3rd step: combine field operation actual measurement elevation face data value, adopt the height fitting of fitting of a polynomial model, ask for the elevation modified value of each point in the large scale topographical map to the three-dimensional coordinate data in the large scale topographical map;

The 4th step: the elevation modified value that combines each point in the large scale topographical map; Adopt the planar fit method of triangle to revise the altitude figures of large scale topographical map; Be adapted on the field operation actual measurement elevation face, draw the height value of each point in the large scale topographical map.

In the first step of technique scheme, adopt the leg-of-mutton method of De Laonei to confirm field operation actual measurement elevation face.

In the 3rd step of technique scheme, adopt the fitting of a polynomial model to be to the step of the height fitting of the three-dimensional coordinate data in the large scale topographical map:

Any point A in if field operation actual measurement detection is surveyed and distinguished (x, y) elevation modified value ζ and plane coordinate system have following relation:

ζ＝f ₁(x，y)+ε ①，

In the formula: f ₁(x, y) for for elevation modified value ζ trend surface, ε is a residual error, establishes:

f ₁(x，y)＝a ₀+a ₁x+a ₂y+a ₃xy+a ₄x ²+a ₅y ²+a ₆x ²y+a ₇y ²x+a ₈ ^y3+a ₉y ³+------②，

The field operation actual measurement detects to survey in the district has n point, obtains following matrix form:

ζ=AX+ ε 3., formula 3. in:

$\mathrm{\ξ}=\left[\begin{array}{c}{\mathrm{\ξ}}_1\\ {\mathrm{\ξ}}_2\\ {\mathrm{\ξ}}_3\\ \·\·\·\\ {\mathrm{\ξ}}_n\end{array}\right];$ $X=\left[\begin{array}{c}{a}_0\\ a_1\\ a_2\\ \·\·\·\\ a_n\end{array}\right];$ $\mathrm{\ϵ}=\left[\begin{array}{c}{\mathrm{\ϵ}}_1\\ {\mathrm{\ϵ}}_2\\ {\mathrm{\ϵ}}_3\\ \·\·\·\\ {\mathrm{\ϵ}}_n\end{array}\right];$ $A=\left[\begin{array}{ccccc}1& X_1& Y_1& X_1{Y}_1& \·\·\·\\ 1& X_2& Y_2& X_2{Y}_2& \·\·\·\\ 1& X_3& Y_3& X_3{Y}_3& \·\·\·\\ \·\·\·& \·\·\·& \·\·\·& \text{\·\·\·}& \·\·\·\\ 1& X_n& Y_n& X_n{Y}_n& \·\·\·\end{array}\right],$

Under the criterion of least square, try to achieve separating of vectorial X, 2. generation gets back in the formula, interior insert out each point in the large scale topographical map the elevation modified value.

In the 4th step of technique scheme; The concrete steps of the planar fit method of triangle do; Internally the industry spot elevation is constructed the De Laonei network of triangle; Put the field operation check point of the triangulation network for dropping on interior industry, industry is put the interior industry elevation of TIN parsing eyeball position in utilizing, and this elevation and field operation actual measurement elevation are compared and calculate the elevation difference; For the field operation check point outside the interior industry point triangulation network, calculate the elevation difference of the elevation difference on triangulation network summit as the outer field operation check point of the interior industry point triangulation network, guarantee that each field operation eyeball all has the elevation difference; All field operation eyeballs are carried out elevation difference counting statistics, industry point measurement precision in being used for analyzing; The field operation eyeball structure triangulation network is used for match, confirms match triangle elevation difference plane, each three summit that are used for the plane triangle of match all contains match elevation difference, and the elevation difference on three summits constitutes a match elevation difference plane; According to the coordinate and the match elevation difference of each triangular apex, the elevation difference of interior industry each point in the The Fitting Calculation delta-shaped region.

In the 4th step of technique scheme, the mathematical formulae of the planar match of triangle is: establish open-air actual measurement check point three-dimensional coordinate be respectively M1 (X1, Y1, h1), M2 (X2; Y2, h2), M3 (X3, Y3, h3); Arbitrary known point is the P point in the space plane of M1, M2, M3, and h1, h2, h3 are respectively the elevation difference of M1, M2, M3, and M1, M2, M3 triangle be a space plane, and HM1, HM2, HM3 are respectively open-air actual measurement elevation; Corresponding HM1 ', HM2 ', HM3 ' is respectively photogrammetric office work and resolves elevation, h1=HM1-HM1 ', h2=HM2-HM2 '; H3=HM3-HM3 ' is fitted to the P point with interior industry point P ', in the space plane of M1, M2, M3; Elevation is HP, and high difference is h

Then HP=HP '+h 1.,

At first find the solution the vector on two limits in three limits of surveying 3 formations of check point:

The normal vector that can be got plane equation by above-mentioned two vectors is:

②

In the formula:

A＝(Y ₂-Y ₁)(h ₃-h ₁)-(Y ₃-Y ₁)(h ₂-h ₁)

B＝(h ₂-h ₁)(X ₃-X ₁)-(X ₂-X ₁)(h ₃-h ₁)

C＝(X ₂-X ₁)(Y ₃-Y ₁)-(X3-X ₁)(Y ₂-Y ₁)

For plan meaning a bit, then

3.

A(XP-X1)+B(YP-Y1)+C(h-h1)＝0

That is, $h=\frac{{\mathrm{AX}}_1+{\mathrm{BY}}_1+{\mathrm{Ch}}_1-{\mathrm{AX}}_P-{\mathrm{BY}}_P}{C}$ 4.

State the corresponding coordinate Y that measures of X value in the formula,

The corresponding coordinate X that measures of Y value,

Therefore, will be 4. the formula substitution 1. formula promptly try to achieve P point height value.

The present invention adopts a small amount of field operation measurement point of actual measurement that remote sensing photogrammetric office work spot elevation is carried out the altitude figures match; Effectively improved the vertical accuracy of large scale topographical map; Satisfy large scale topographical map measurement vertical accuracy requirement in the specifications of surveys; Can be widely used in the large scale topographical map mapping, be applicable to the survey and design of each design phase of power engineering, widen the range of application of remote sensing greatly.

Description of drawings

Fig. 1 is a method flow diagram of the present invention;

Fig. 2 is that the present invention utilizes computer software to realize the process flow diagram of planar match;

Fig. 3 is the process flow diagram of industry point height corrected value in the present invention calculates;

Embodiment

Below in conjunction with accompanying drawing and specific embodiment the present invention is made further detailed description:

Consult shown in Figure 1ly, remote sensing aerial survey height fitting method comprises following steps:

The first step: field operation actual measurement check point is set, adopts the three-dimensional coordinate data of field operation surveying instrument actual measurement check point, confirm field operation actual measurement elevation face;

Second step: adopt the remote sensing aerial survey stabilized platform, measure large scale topographical map, extract the three-dimensional coordinate data of large scale topographical map;

The 3rd step: combine field operation actual measurement elevation face data value, adopt the height fitting of fitting of a polynomial model, ask for the elevation modified value of each point in the large scale topographical map to the three-dimensional coordinate data in the large scale topographical map;

The 4th step: the elevation modified value that combines each point in the large scale topographical map; Adopt the planar fit method of triangle to revise the altitude figures of large scale topographical map; Be adapted on the field operation actual measurement elevation face, draw the height value of each point in the large scale topographical map.

Particularly, adopt the fitting of a polynomial model to carry out height fitting:

If any point A in the survey district (x, y) elevation modified value ζ and planimetric coordinates have following relation:

ζ＝f ₁(x，y)+ε ①

In the formula: f ₁(x y) is the trend surface of elevation modified value ζ; ε is a residual error.

If: f ₁(x, y)=a ₀+ a ₁X+a ₂Y+a ₃Xy+a ₄x ²+ a ₅y ²+ a ₆x ²Y+a ₇y ²X+a ₈x ³+ a ₉y ³+ ...

②

The field operation actual measurement detects to survey in the district has n point, obtains following matrix form:

ζ=AX+ ε 3., formula 3. in:

$\mathrm{\ξ}=\left[\begin{array}{c}{\mathrm{\ξ}}_1\\ {\mathrm{\ξ}}_2\\ {\mathrm{\ξ}}_3\\ \·\·\·\\ {\mathrm{\ξ}}_n\end{array}\right];$ $X=\left[\begin{array}{c}{a}_0\\ a_1\\ a_2\\ \·\·\·\\ a_n\end{array}\right];$ $\mathrm{\ϵ}=\left[\begin{array}{c}{\mathrm{\ϵ}}_1\\ {\mathrm{\ϵ}}_2\\ {\mathrm{\ϵ}}_3\\ \·\·\·\\ {\mathrm{\ϵ}}_n\end{array}\right];$ $A=\left[\begin{array}{ccccc}1& X_1& Y_1& X_1{Y}_1& \·\·\·\\ 1& X_2& Y_2& X_2{Y}_2& \·\·\·\\ 1& X_3& Y_3& X_3{Y}_3& \·\·\·\\ \·\·\·& \·\·\·& \·\·\·& \text{\·\·\·}& \·\·\·\\ 1& X_n& Y_n& X_n{Y}_n& \·\·\·\end{array}\right],$

Under the criterion of least square, try to achieve separating of vectorial X, 2. generation gets back in the formula, just can in insert out the elevation modified value of unknown point, in 2. formula,, then claim plane fitting if get once item of the unknown; Get quadratic term, claim surface fitting again; Get cubic term, claim the cubic polynomial match, by that analogy.

The altitude figures disposal route:

Utilize field operation actual measurement spot elevation that remote sensing aerial survey altitude figures is carried out the match correction; The altitude figures that the remote sensing aerial survey is obtained adopts the planar fit method of triangle to revise; Correct on the field operation actual measurement elevation face, field operation actual measurement elevation face adopts the De Laonei triangle to confirm.To carry out height fitting the zone need lay the check point of some, the triangulation network that check point constituted (triangulation network that the De Laonei triangle constitutes) will surround the whole measuring district.Concrete approximating method is following:

Internally the industry elevational point structure triangulation network (TIN, De Laonei triangle) is put the field operation test point of the triangulation network for dropping on interior industry, and industry is put the interior industry elevation of TIN parsing eyeball position in utilizing, and this elevation and field operation actual measurement elevation are compared and calculate the elevation difference; For the field operation test point outside the interior industry point triangulation network, calculate the elevation difference of the elevation difference on triangulation network summit as the outer field operation test point of the interior industry point triangulation network, guarantee that each field operation eyeball all has the elevation difference; All eyeballs are carried out difference counting statistics and output; To field operation test point (being used for match point) the structure triangulation network, confirm match triangle elevation difference plane, each three summit that are used for the plane triangle of match all contains match elevation difference, and these three differences have constituted a match elevation difference plane; Based on the coordinate and the match elevation difference of each triangular apex, the elevation difference of interior industry each point in the The Fitting Calculation delta-shaped region.

Computing formula is following:

If open-air actual measurement check point three-dimensional coordinate be respectively M1 (X1, Y1, h1), M2 (X2; Y2, h2), M3 (X3, Y3; H3), h1, h2, h3 are respectively the elevation difference of M1, M2, M3, and M1, M2, M3 triangle are a space plane; HM1, HM2, HM3 are respectively open-air actual measurement elevation, corresponding HM1 ', HM2 ', HM3 '

Be respectively photogrammetric office work and resolve elevation, then,

h1＝HM1-HM1′

h2＝HM2-HM2′

h3＝HM3-HM3′

Be fitted to P point (in the space plane of M1, M2, M3, elevation is HP) with interior industry point P ', high difference is h, then

HP＝HP′+h ①

M1 on the space plane, M2,3 of M3 are known, and P point XP on the plane, YP are known, ask its elevation difference h value.Calculation method is exactly the three-dimensional coordinate by three known some M1, M2, M3, obtains the plane equation that three points constitute, and utilizes the planimetric coordinates that plane equation is ordered according to P to ask its elevation difference.

At first find the solution the vector on two limits in three limits of surveying 3 formations of check point:

The normal vector that can be got plane equation by above-mentioned two vectors is:

②

In the formula:

A＝(Y ₂-Y ₁)(h ₃-h ₁)-(Y ₃-Y ₁)(h ₂-h ₁)

B＝(h ₂-h ₁)(X ₃-X ₁)-(X ₂-X ₁)(h ₃-h ₁)

C＝(X ₂-X ₁)(Y ₃-Y ₁)-(X3-X ₁)(Y ₂-Y ₁)

For plan meaning a bit, then

3.

A(XP-X1)+B(YP-Y1)+C(h-h1)＝0

That is, $h=\frac{{\mathrm{AX}}_1+{\mathrm{BY}}_1+{\mathrm{Ch}}_1-{\mathrm{AX}}_P-{\mathrm{BY}}_P}{C}$ 4.

State the corresponding coordinate Y that measures of X value in the formula,

The corresponding coordinate X that measures of Y value,

Therefore, will be 4. the formula substitution 1. formula promptly try to achieve P point height value.

The planar match step of elevation:

1) makes up the triangulation network according to JX4 photogrammetric office work spot elevation, find the solution the photogrammetric office work height value of corresponding open-air check point.

2) calculate the high difference of each check point according to the photogrammetric office work height value, analyze difference and distribute, carry out accuracy assessment before the match, confirm approximating method.

3) find the solution the height value (high difference) of each photogrammetric office work spot elevation in the match point triangulation network.

4) carry out accuracy assessment after the match, determine whether to lay again match point according to evaluation result and carry out match again.The accuracy assessment result should satisfy code requirement after the match.

The planar match of elevation is designed to computer software programs, and convenient the use consulted shown in Figure 2ly, and the function that program realizes is following:

The input of field operation match spot elevation data;

Utilize the photogrammetric office work data configuration to survey district's digital terrain model (DTM), calculate the elevation of field operation match point position in interior industry DTM, calculate and preserve the difference that this elevation and field operation are measured elevation;

According to field operation measurement point structure field operation measurement point DTM, utilize field operation DTM and field operation point height difference to calculate the elevation modified value of interior industry point.

Program realizes comprising two key algorithms, and the one, already put DTM and field operation match point in utilizing and carry out elevation relatively, calculate the elevation difference of field operation match point; Another is to utilize to calculate the field operation match point elevation difference that obtains, and constructs the difference DTM of field operation match point, and utilizes the elevation difference of industry point in the difference DTM calculating.Industry is put the DTM calculated difference and has been adopted interpolation algorithm in utilizing; For the arbitrary triangle in the interior industry point DTM, arbitrary planimetric position all can be according to inserting its height value in its delta-shaped region in the triangular apex, and program provides the several different methods of calculating the elevation difference; The user can utilize Automatic Program to carry out interpolation calculation; Also can import the elevation difference in a certain zone by hand, the industry point directly matees the calculating height value with the field operation point in can also utilizing, and calculates field operation match point elevation difference.

Calculating field operation match point elevation difference is the key of height fitting program; The elevation correction value of interior industry spot elevation depends on the field operation match point elevation difference of calculating; Difference is calculated and has been adopted Automatic Program to calculate the method that engages with manual input; After difference was calculated completion, the user can check the edlin of going forward side by side to the difference of calculating, if because certain triangle in the interior industry point DTM can not reflect truly that elevation distributes in the delta-shaped region; Then utilize the elevation difference of program interpolation calculation inaccurate; In this case, it is that field operation point calculates the elevation difference that the user can adopt the method for manual input difference and the method that adopts interior field operation point coupling, and the routine data treatment scheme can be consulted Fig. 1.

Industry point height corrected value in calculating: after the elevation difference that obtains the field operation match point, structure match point difference DTM, " difference DTM " is the notion of having used digital terrain model; Promptly utilize the field operation match point structure triangulation network, each triangle in the net is made up of match point, and match point not only has the altitude figures of actual measurement; The difference of elevation value information that also has previous calculations; These three differences have been confirmed triangle difference zone, and the difference in the zone is thought even distribution, utilize insert each equally distributed triangle difference zone in calculate in the elevation correction value of spot elevation already; The elevation of industry measurement point in revising, concrete flow chart of data processing can be consulted shown in Figure 3.

Realization through the height fitting calculation procedure; Alleviated the workload of interior industry point height data fitting correction greatly; Point height match already in the mode that has adopted Automatic Program to calculate and import by hand joint is carried out; Fully take into account the actual conditions of height fitting, obtained good effect in the practical applications in process of the test.

The content of not doing in this instructions to describe in detail belongs to this area professional and technical personnel's known prior art.

Claims (5)

1. remote sensing aerial survey height fitting method is characterized in that comprising following steps:

The first step: field operation actual measurement check point is set, adopts the three-dimensional coordinate data of field operation surveying instrument actual measurement check point, confirm field operation actual measurement elevation face;

Second step: adopt the remote sensing aerial survey stabilized platform, measure large scale topographical map, extract the three-dimensional coordinate data of large scale topographical map;

The 3rd step: combine field operation actual measurement elevation face data value, adopt the carry out height fitting of fitting of a polynomial model, ask for the elevation modified value of each point in the large scale topographical map to the three-dimensional coordinate data in the large scale topographical map;

The 4th step: the elevation modified value that combines each point in the large scale topographical map; Adopt the planar fit method of triangle to revise the altitude figures of large scale topographical map; Be adapted on the field operation actual measurement elevation face, draw the height value of each point in the large scale topographical map.

2. remote sensing aerial survey height fitting method according to claim 1 is characterized in that: in the first step, adopt the leg-of-mutton method of De Laonei to confirm field operation actual measurement elevation face.

3. require 1 described remote sensing aerial survey height fitting method according to patent, it is characterized in that: in the 3rd step, adopt the fitting of a polynomial model to be the step of the height fitting of the three-dimensional coordinate data in the large scale topographical map:

Any point A in if field operation actual measurement detection is surveyed and distinguished (x, y) elevation modified value ζ and plane coordinate system have following relation:

ζ＝f ₁(x，y)+ε ①，

In the formula: f ₁(x, y) for for elevation modified value ζ trend surface, ε is a residual error, establishes:

f ₁(x，y)＝a ₀+a ₁x+a ₂y+a ₃xy+a ₄x ²+a ₅y ²+a ₆x ²y+a ₇y ²x+a ₈x ³+a ₉y ³+------②，

The field operation actual measurement detects to survey in the district has n point, obtains following matrix form:

ζ=AX+ ε 3., formula 3. in:

$\mathrm{\ξ}=\left[\begin{array}{c}{\mathrm{\ξ}}_1\\ {\mathrm{\ξ}}_2\\ {\mathrm{\ξ}}_3\\ \·\·\·\\ {\mathrm{\ξ}}_n\end{array}\right];$ $X=\left[\begin{array}{c}{a}_0\\ a_1\\ a_2\\ \·\·\·\\ a_n\end{array}\right];$ $\mathrm{\ϵ}=\left[\begin{array}{c}{\mathrm{\ϵ}}_1\\ {\mathrm{\ϵ}}_2\\ {\mathrm{\ϵ}}_3\\ \·\·\·\\ {\mathrm{\ϵ}}_n\end{array}\right];$ $A=\left[\begin{array}{ccccc}1& X_1& Y_1& X_1{Y}_1& \·\·\·\\ 1& X_2& Y_2& X_2{Y}_2& \·\·\·\\ 1& X_3& Y_3& X_3{Y}_3& \·\·\·\\ \·\·\·& \·\·\·& \·\·\·& \text{\·\·\·}& \·\·\·\\ 1& X_n& Y_n& X_n{Y}_n& \·\·\·\end{array}\right],$

Under the criterion of least square, try to achieve separating of vectorial X, 2. generation gets back in the formula, interior insert out each point in the large scale topographical map the elevation modified value.

4. remote sensing aerial survey height fitting method according to claim 1; It is characterized in that: in the 4th step; The concrete steps of the planar fit method of triangle are that internally industry spot elevation structure De Laonei network of triangle is put the field operation check point of the triangulation network for dropping on interior industry; Industry is put the interior industry elevation that TIN resolves the eyeball position in utilizing, and this elevation and field operation actual measurement elevation are compared and calculate the elevation difference; For the field operation check point outside the interior industry point triangulation network, calculate the elevation difference of the elevation difference on triangulation network summit as the outer field operation check point of the interior industry point triangulation network, guarantee that each field operation eyeball all has the elevation difference; All field operation eyeballs are carried out elevation difference counting statistics, industry point measurement precision in being used for analyzing; The field operation eyeball structure triangulation network is used for match, confirms match triangle elevation difference plane, each three summit that are used for the plane triangle of match all contains match elevation difference, and the elevation difference on three summits constitutes a match elevation difference plane; According to the coordinate and the match elevation difference of each triangular apex, the elevation difference of interior industry each point in the The Fitting Calculation delta-shaped region.

5. remote sensing aerial survey height fitting method according to claim 4 is characterized in that: in the 4th step, the mathematical formulae of the planar match of triangle is: establish open-air actual measurement check point three-dimensional coordinate and be respectively M1 (X1, Y1; H1), M2 (X2, Y2, h2), M3 (X3, Y3; H3), arbitrary known point is the P point in the space plane of M1, M2, M3, and h1, h2, h3 are respectively the elevation difference of M1, M2, M3, and M1, M2, M3 triangle are a space plane; HM1, HM2, HM3 are respectively open-air actual measurement elevation, and corresponding HM1 ', HM2 ', HM3 ' is respectively photogrammetric office work and resolves elevation, h1=HM1-HM1 ', h2=HM2-HM2 '; H3=HM3-HM3 ' is fitted to the P point with interior industry point P ', in the space plane of M1, M2, M3; Elevation is HP, and high difference is h

Then HP=HP '+h 1.,

At first find the solution the vector on two limits in three limits of surveying 3 formations of check point:

The normal vector that can be got plane equation by above-mentioned two vectors is:

②

In the formula:

A＝(Y ₂-Y ₁)(h ₃-h ₁)-(Y ₃-Y ₁)(h ₂-h ₁)

B＝(h ₂-h ₁)(X ₃-X ₁)-(X ₂-X ₁)(h ₃-h ₁)

C＝(X ₂-X ₁)(Y ₃-Y ₁)-(X3-X ₁)(Y ₂-Y ₁)

For plan meaning a bit, then

3.

A(XP-X1)+B(YP-Y1)+C(h-h1)＝0

That is, $h=\frac{{\mathrm{AX}}_1+{\mathrm{BY}}_1+{\mathrm{Ch}}_1-{\mathrm{AX}}_P-{\mathrm{BY}}_P}{C}$ 4.

State the corresponding coordinate Y that measures of X value in the formula,

The corresponding coordinate X that measures of Y value,

Therefore, will be 4. the formula substitution 1. formula promptly try to achieve P point height value.

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