CN113946982B - Method for obtaining topography profile of dangerous rock mass - Google Patents
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Abstract
The invention relates to the technical field of surface morphology acquisition, and discloses a method for acquiring a dangerous rock body topography profile, which comprises the steps of firstly selecting a starting point coordinate and an ending point coordinate on a three-dimensional oblique photography model of an unmanned aerial vehicle, determining a sectioning line of a dangerous rock body topography in a target area to be acquired, and sequentially selecting a plurality of measuring point coordinates near the sectioning line along the sectioning line; then establishing a plane equation of the section line corresponding to the section plane and calculating to obtain the projection coordinate of the measurement point projected to the section plane; and finally, judging the topographic features of the corresponding areas according to the projection coordinates of the measuring points, acquiring the coordinates of the fitting points according to the judging result, and processing to obtain the topographic profile of the cutting line position. According to the method for acquiring the topographic profile of the dangerous rock mass, disclosed by the invention, the topographic features of the dangerous rock mass can be quickly and accurately acquired by utilizing the measurement data of the three-dimensional oblique photography model of the unmanned aerial vehicle, complicated sectioning operation is not required by professional software, and the method is particularly beneficial to acquiring the topographic features of the steep vertical rock mass and the inverted suspended rock mass.
Description
Technical Field
The invention relates to the technical field of surface morphology acquisition, in particular to a method for acquiring a dangerous rock mass topographic profile.
Background
The area of the mountain area of China accounts for 69.1% of the total area of China, and due to steep topography and landform, dangerous rock mass is formed on high and steep slopes, the safety of buildings and related personnel such as railways, highways and houses is seriously threatened after dangerous rock collapse, and at present, 4 traditional methods for acquiring the topography profile of the high and steep slope dangerous rock mass are available: (1) measuring the dangerous rock profile on site by using measuring equipment such as a total station and the like; (2) obtaining a dangerous rock body section by sectioning a large scale topographic map; (3) acquiring a section of the dangerous rock mass by sectioning three-dimensional point cloud data of an optical image of the unmanned aerial vehicle; (4) and acquiring the section of the dangerous rock mass by sectioning the three-dimensional point cloud data of the laser radar.
The first method is as follows: because dangerous rock is high and steep, measurement staff are difficult to reach, the efficiency is low, the danger is high, the measurement accuracy is low, the micro-landform characteristics of the dangerous rock cannot be accurately obtained on one measurement line, and particularly, actual measurement work cannot be carried out on the inverted suspended dangerous rock; the second method is as follows: the profile form of the topography can be obtained rapidly, but the accuracy is extremely low because the contour line is subjected to fitting treatment on the coordinates of the measuring points during manufacturing, the profile cutting surface can only display macroscopic topographical features, and the microscopic topographical features of the dangling rock mass, which are nearly vertical and inclined, cannot be obtained accurately; the third method is as follows: because the optical image of the unmanned aerial vehicle is often shielded by vegetation, the technical difficulty is high, the operation is not simple and convenient, the sectioning efficiency is low, and the sectioning precision is also influenced by landform vegetation; a fourth method: because unmanned aerial vehicle carries the load and carries the load limitedly, laser radar equipment power that its carried is often less, and the laser of radar shines the dangerous rock mass and returns the measuring point limited, and the raw data who obtains still can contain the morphological data of vegetation, though can have a small amount of laser points to pass through vegetation and obtain the earth's surface form, but acquire with high costs, technical difficulty is big, the operation is not simple and convenient, need later stage go vegetation treatment, and the dissection efficiency is lower.
Disclosure of Invention
The invention aims at: the method for acquiring the dangerous rock body topographic profile in the prior art has the advantages that the manual measurement efficiency is low, the feature accuracy acquired by large-scale topographic map is low, the application cost of unmanned aerial vehicle optical images and laser radars is high, and complex sectioning operation is needed by professional software.
In order to achieve the above purpose, the technical scheme adopted by the invention is as follows:
a method of acquiring a relief profile of a rock mass comprising the steps of:
A. performing three-dimensional oblique photography above a target area by using an unmanned aerial vehicle, and performing three-dimensional modeling on aerial photographs to obtain an unmanned aerial vehicle three-dimensional oblique photography model;
B. selecting a starting point coordinate and an end point coordinate on the three-dimensional oblique photography model of the unmanned aerial vehicle, determining a section line of the dangerous rock mass terrain in a target area to be acquired, and sequentially selecting a plurality of measuring point coordinates near the section line along the section line;
C. establishing a plane equation of a section line corresponding to the section plane;
D. calculating to obtain projection coordinates of the measurement points projected to the section plane;
E. setting a fitting point of a terrain profile, judging the inverted suspension characteristic of the corresponding terrain according to the projection coordinates of the measuring point, and acquiring the coordinates of the fitting point according to the judging result;
F. and sequentially connecting the obtained fitting point coordinates into a line to obtain a terrain profile of the cutting line position.
Determining a straight line serving as a cutting line of a topographic profile of a dangerous rock body to be obtained, generating a cutting plane perpendicular to a three-dimensional coordinate XOY plane along the cutting line, sequentially selecting measuring points near the cutting line along the cutting line on a model according to the topographic trend, sequencing the measuring points in sequence according to the topographic trend on the model, for example, selecting the measuring points along the cutting line, selecting the measuring points along the lower side wall of the pit towards the bottom of the pit from the opening of the pit, selecting the measuring points along the upper side wall of the pit towards the pit opening from the bottom of the pit, ensuring that the sequentially selected measuring points can embody the topographic features of the pit, further, manually selecting the measuring points on the cutting line according to the three-dimensional oblique photographic model of the unmanned plane, projecting the measuring points onto the cutting line to obtain projection after a plurality of measuring point coordinates near the cutting line are selected by the manual force, and then obtaining a projection by calculating the projection of the measuring points, and judging whether the projection coordinates of the adjacent measuring points have the corresponding topographic coordinate of the measuring points in a corresponding outline of the measuring curve in sequence;
according to the method for acquiring the topography profile of the dangerous rock mass, disclosed by the invention, the topography profile of the sectioning surface is obtained through calculation and judgment processing by utilizing the measurement data of the three-dimensional oblique photography model of the unmanned aerial vehicle, so that the topography characteristic of the dangerous rock mass can be quickly and accurately acquired, complex sectioning operation is not required by professional software, the acquisition operation is simple, the technical requirement is low, the practicability in dangerous rock mass control is high, the topography profile characteristics of the steep vertical rock mass and the inverted suspended rock mass are particularly beneficial to acquiring, the type of dangerous rock can be accurately judged, the calculation accuracy of the stability, the square quantity and the movement track of the dangerous rock mass is improved, the design change of dangerous rock mass control is reduced, the construction cost is saved, and the method has high application value.
Preferably, in the step D, the step of determining the overhang feature of the terrain and obtaining the fitting point coordinates includes the steps of:
d1: the starting point coordinate selected in the step A is P 0 (X 0 ，Y 0 ，Z 0 ) Endpoint coordinate is P n (X n ，Y n ，Z n ) (n=1, 2,3 …), the measurement point coordinates are P i (X i ，Y i ，Z i ) (0 < i < n, and i=1, 2,3 …); the projection coordinate of the measurement point obtained in the step C is P i ’(X i ’，Y i ’，Z i ') (0 < i < n, and i=1, 2,3 …);
and judging the projection coordinates of two adjacent measurement points by a judgment formula I, wherein the judgment formula I is as follows:
(X n -X 0 )(X i+1 ’-X i ' s is less than or equal to 0 and (Y) n -Y 0 )(Y i+1 ’-Y i ') is less than or equal to 0, (0 < i < n-1, and i=1, 2,3 …);
the requirement of the first judgment is met, and the topography between two adjacent measuring points has the feature of inverted suspension;
judging the starting point coordinates and the projection coordinates of the first measuring point by a second judgment formula, wherein the second judgment formula is as follows:
(X n -X 0 )(X 1 ’-X 0 ) Is less than or equal to 0 and (Y) n -Y 0 )(Y 1 ’-Y 0 )≤0；
Meeting the requirement of the judgment type II, the terrain between the starting point and the first measuring point has the feature of inverted suspension;
and judging the projection coordinate and the end point coordinate of the last measuring point through a third judgment formula, wherein the third judgment formula is as follows:
(X n -X 0 )(X n -X n-1 ' s is less than or equal to 0 and (Y) n -Y 0 )(Y n -Y n-1 ’)≤0；
The requirement of the third judgment type is met, and then the topography between the last measuring point and the end point has the feature of inverted suspension;
d2: let the fitting point of the topographic profile be DeltaP i The coordinates are set as (L i ，H i ) (0.ltoreq.i.ltoreq.n, and i=1, 2,3 …), H 0 ＝Z 0 Let L be 0 =0, calculating the horizontal increment of the projection coordinates of two adjacent measurement points on the section according to the projection coordinates obtained in the step C:
H i+1 ＝Z i+1 ’ (0 < i < n-1, and i=1, 2,3 …);
if the projection coordinates of two adjacent measurement points do not meet the requirement of the judgment formula one, then: l (L) i+1 ＝L i +△L i+1 ’ (0 < i < n-1, and i=1, 2,3 …);
H i+1 ＝Z i+1 ’ (0 < i < n-1, and i=1, 2,3 …);
horizontal increment of the start point coordinates and the projected coordinates of the first measurement point:
the starting point coordinates and the projection coordinates of the first measurement point meet the requirement of a judgment formula II, and then: l (L) 1 ＝L 0 -△L 1 ；
H 1 ＝Z 1 ’ ；
If the starting point coordinates and the projection coordinates of the first measurement point do not meet the requirement of the judgment formula II, then: l (L) 1 ＝L 0 +△L 1 ；
H 1 ＝Z 1 ’ ；
Horizontal increment of the projection coordinates and the end point coordinates of the last measurement point:
and if the projection coordinate and the end point coordinate of the last measurement point meet the requirement of the judgment formula III, then: l (L) n ＝L n-1 -△L n ；
H n ＝Z n ；
And if the projection coordinate and the end point coordinate of the last measurement point do not meet the requirement of the judgment formula III, then:
L n ＝L n-1 +△L n ；
H n ＝Z n 。
the end point coordinate is P n N-1 selected measuring points are correspondingly arranged, n is the arrangement sequence of a plurality of measuring points along a sectioning line according to the trend of the terrain, and as the terrain section is an XOY plane perpendicular to the three-dimensional model, the coordinate of the fitting point corresponds to the Z-axis coordinate of the projection coordinate, the coordinate of the ordinate of the fitting point corresponds to the Z-axis coordinate of the projection coordinate, the coordinate of the abscissa of the fitting point is the fitting value of the XY-axis coordinate of the projection coordinate, the X-axis initial coordinate of the fitting point is the starting point of the sectioning line, and the initial value can be set arbitrarily without influencing the display of the whole section.
Preferably, in the step D1, the obtaining process of the judgment formula is as follows:
the first judgment formula is to judge the projection coordinates of two adjacent measurement points, and the total of four conditions are the section lines formed by connecting the starting point coordinates and the end point coordinates, and the expression of the straight line is y=kx+b:
and (3) a step of: k (k)>0, then X n -X 0 >0，Y n -Y 0 >0；
When the connecting line of two adjacent measuring points is an inverted suspension feature: x is X i+1 -X i <0 and Y i+1 -Y i <0 (0 < i < n-1, and i=1, 2,3 …);
obtain (X) n -X 0 )(X i+1 ’-X i ’)<0 and (Y) n -Y 0 )(Y i+1 ’-Y i ’)<0；
And II: k (k)<0, then X n -X 0 >0，Y n -Y 0 <0；
When the connecting line of two adjacent measuring points is an inverted suspension feature: x is X i+1 -X i <0 and Y i+1 -Y i >0 (0 < i < n-1, and i=1, 2,3 …);
obtain (X) n -X 0 )(X i+1 ’-X i ’)<0 and (Y) n -Y 0 )(Y i+1 ’-Y i ’)<0；
Thirdly,: x=constant, then X n -X 0 ＝0，Y n -Y 0 >0；
When the connection line of two adjacent measuring points is invertedSuspension feature time: x is X i+1 -X i =0 and Y i+1 -Y i <0 (0 < i < n-1, and i=1, 2,3 …);
obtain (X) n -X 0 )(X i+1 ’-X i ') =0 and (Y) n -Y 0 )(Y i+1 ’-Y i ’)<0；
Fourth, the method comprises the following steps: k=0, then X n -X 0 >0，Y n -Y 0 ＝0；
When the connecting line of two adjacent measuring points is an inverted suspension feature: x is X i+1 -X i <0 and Y i+1 -Y i =0 (0 < i < n-1, and i=1, 2,3 …);
obtain (X) n -X 0 )(X i+1 ’-X i ’)<0 and (Y) n -Y 0 )(Y i+1 ’-Y i ’)＝0；
The judgment formula I for obtaining the feature of the topography that the inverted overhang topography appears on the whole is as follows: (X) n -X 0 )(X i+1 ’-X i ' s is less than or equal to 0 and (Y) n -Y 0 )(Y i+1 ’-Y i ') is less than or equal to 0, (0 < i < n-1, and i=1, 2,3 …); and similarly, calculating to obtain a judgment formula II and a judgment formula III.
In the step of obtaining the first judgment formula, the calculation is performed based on the X-axis coordinate of the starting point coordinate being smaller than or equal to the X-axis coordinate of the ending point coordinate, namely X 0 ≤X n If the X-axis coordinate of the end point coordinate is smaller than or equal to the X-axis coordinate of the start point coordinate when the coordinates are selected, namely X 0 ≥X n In this case, the principle of the first judgment formula is the same, the finally obtained first judgment formula is not changed, and the obtained results of the second judgment formula and the third judgment formula are not changed.
Preferably, the step B includes the steps of:
b1: the corresponding section plane of the section line is an XOY plane perpendicular to the three-dimensional oblique photography model of the unmanned aerial vehicle, and the normal vector of the section plane is (A, B, 0);
b2: c, the starting point coordinates P selected in the step A are processed 0 (X 0 ，Y 0 ，Z 0 ) And endpoint coordinates P n (X n ，Y n ，Z n ) (n=1, 2,3 …) substitution into the point french plane equation yields: a (X) n -X 0 )+B(Y n -Y 0 ) =0, push out: AX n +BY n +(-AX 0 -BY 0 ) =0, substituting the general formula plane equation to obtain: d= -AX 0 -BY 0 Wherein A, B is a coefficient of a point normal plane equation and a coefficient of a general plane equation, and D is a coefficient of a general plane equation;
b3: and (3) setting a non-zero assumed value for one of the coefficient A and the coefficient B, solving the value of the other coefficient and the coefficient D, and establishing a plane equation of the section.
Alternatively, setting a coefficient to a hypothetical value that does not affect the resulting profile curve is a mathematical solution to the equation.
Preferably, in the step C, the calculating includes the steps of:
c1: obtained measuring point P i The coordinates are (X) i ，Y i ，Z i ) (0 < i < n, and i=1, 2,3 …), P i The point projected onto the cutting plane is P i ' the coordinates are (X) i ’，Y i ’，Z i ') (0 < i < n, and i=1, 2,3 …);
C2：P i and P i The' connecting line is parallel to the normal vector of the section, and the slopes of the two lines are equal to obtain:
setting an intermediate value t i (0 < i < n, and i=1, 2,3 …), and the conversion results in: x is X i -X i ’＝At i ，Y i -Y i ’＝Bt i And Z is i ＝Z i ' further push out X i ’＝X i –At i ，Y i ’＝Y i –Bt i Combined with the coordinates P i ' in the section, AX i +BY i +d=0, giving
Let t i Substitution into X i ’＝X i –At，Y i ’＝Y i Bt, finding the measurement point P i Projection coordinates P on a cutting plane i ’(X i ’，Y i ’，Z i ’)。
Preferably, in the step a, at the position of the change or turning of the topography, the selected distance between the two adjacent measurement points is reduced.
The distance between two adjacent measuring points refers to the actual space distance in the three-dimensional coordinate system of the model, the area on the model, which is difficult to judge clearly or obviously has the topographic change, is reduced, the selected distance between the two adjacent measuring points is reduced, the measuring data for calculation processing is increased, and the accuracy of displaying the topographic section of the area can be increased.
Preferably, when the selection density of the measurement points is increased, the distance between two adjacent measurement points is selected to be not more than 0.1m along the direction of the section line according to the trend of the topography on the model.
In the design of dangerous rock falling prevention and control, the volume of rock blocks with the diameter of less than 0.1m of dangerous rock blocks is about 7.85dm 3 (about fist size), the probability of a disaster-bearing body in smashing is extremely small, the energy is low when the disaster-bearing body rolls down to the toe, the disaster-bearing body is easy to prevent and treat, the threat to the disaster-bearing body is small, and then the dangerous rock body with the diameter smaller than 0.1m does not play a decisive role in dangerous rock body engineering prevention and treatment measures, and the difficulty in acquiring the microtopography of the dangerous rock body is increased by combining the measurement accuracy of the three-dimensional oblique photographic model, so that the distance between two adjacent measurement points is controlled and selected at a suspected dangerous rock area, and calculation of dangerous rock with the dangerous rock body block diameter larger than 0.1m can be effectively reduced or avoided.
Preferably, after the step B is completed, before the step C is performed, checking the selected measurement points, and screening out the measurement points deviating from the cutting plane by a defined distance.
The measurement points selected manually inevitably have errors, if the distance between the selected measurement points and the cutting plane is too large, the obtained topographic profile is distorted, the limiting distance is an accuracy parameter for controlling the topographic profile, the step of checking the measurement points is added, the distortion degree of the topographic profile can be effectively controlled, and the utilization value of the topographic profile is ensured.
Preferably, the defined distance is set to 0.2m.
Because the measurement accuracy of the unmanned aerial vehicle three-dimensional oblique photography model is generally 3 cm-5 cm, the accuracy of displaying the acquired dangerous rock body terrain profile is ensured on the basis of not influencing the distortion or the overlarge error of the profile cut-off surface, and the terrain features of dangerous rock with the missing dangerous rock mass diameter larger than 0.2m are reduced or avoided.
Preferably, the checking of the measurement points is to calculate the vertical distance from the measurement points to the section, wherein the calculated vertical distance is larger than the limiting distance, screen out the corresponding measurement points and reselect the measurement points for replacement, and the formula for calculating the vertical distance is as follows:
Wherein: d, d i Is a vertical distance X i 、Y i The three-dimensional coordinates of the measurement points X and Y axes, respectively, A, B, D are coefficients of general equations of the cut plane.
When the measuring points are selected again for replacement, attention is paid to the topographic positions of the screened measuring points on the model, and the replacement measuring points are ensured to conform to the position sequence of the screened measuring points, namely, the topographic positions of the newly selected measuring points are required to be between the topographic positions of two adjacent measuring points before and after the screened measuring points.
In summary, due to the adoption of the technical scheme, the beneficial effects of the invention are as follows:
1. according to the method for acquiring the topography profile of the dangerous rock mass, disclosed by the invention, the topography profile of the sectioning surface is obtained through processing and calculation by utilizing the measurement data of the three-dimensional oblique photography model of the unmanned aerial vehicle, so that the topography characteristic of the dangerous rock mass can be quickly and accurately acquired, complex sectioning operation is not required by professional software, the acquisition operation is simple, the technical requirement is low, the practicability in dangerous rock falling prevention is high, the topography profile characteristics of the steep vertical rock mass and the inverted suspended rock mass are particularly beneficial to acquisition, the type of the dangerous rock can be accurately judged, the calculation accuracy of the stability, the square quantity and the falling movement track of the dangerous rock mass is improved, the design change of dangerous rock falling prevention is reduced, the construction cost is saved, and the method has high application value;
2. the accuracy of displaying the topographic profile of the area can be increased by reducing the selection interval between two adjacent measurement points in the area where the topographic change is difficult to judge clearly or obviously on the model and increasing the measurement data for calculation processing;
3. by adding a checking step of selecting the measuring points, the distortion degree of the terrain profile can be effectively controlled, and the utilization value of the acquired terrain profile is ensured.
Drawings
FIG. 1 is a flow chart of a method of acquiring a relief profile of a rock mass in accordance with the present invention;
FIG. 2 is a three-dimensional model of the entrance of a high-speed railway tunnel according to example 1;
FIG. 3 is a schematic view showing the selection of the coordinates of the starting point in example 1;
FIG. 4 is a schematic view of the cut line of example 1;
FIG. 5 is a topographical profile taken by one method of obtaining a topographical profile of a body of dangerous rock as described in example 1;
FIG. 6 is a topographical cross-sectional view of example 1 obtained by sectioning a large scale topographical map;
FIG. 7 is a cross-sectional view of the terrain of example 1 obtained by sectioning three-dimensional point cloud data of an optical image of a drone;
FIG. 8 is a topographical profile taken by one method of obtaining a topographical profile of a body of dangerous rock as described in example 2;
fig. 9 is a topographical cross-sectional view of example 2 obtained by sectioning a large scale topographical map.
Detailed Description
The present invention will be described in detail with reference to the accompanying drawings.
For the purpose of making apparent the objects, technical solutions and advantages of the present invention, the present invention will be further described in detail with reference to the accompanying drawings and examples, it being understood that the specific examples described herein are for the purpose of illustration only and are not intended to limit the present invention.
Example 1
As shown in fig. 1, the method for acquiring the topographic profile of the dangerous rock mass comprises the following steps:
A. performing three-dimensional oblique photography above a target area by using an unmanned aerial vehicle, and performing three-dimensional modeling on aerial photographs to obtain an unmanned aerial vehicle three-dimensional oblique photography model;
B. selecting a starting point coordinate and an end point coordinate on the three-dimensional oblique photography model of the unmanned aerial vehicle, determining a section line of the dangerous rock mass terrain in a target area to be acquired, and sequentially selecting a plurality of measuring point coordinates near the section line along the section line;
C. establishing a plane equation of a section line corresponding to the section plane;
D. calculating to obtain projection coordinates of the measurement points projected to the section plane;
E. setting a fitting point of a terrain profile, judging the inverted suspension characteristic of the corresponding terrain according to the projection coordinates of the measuring point, and acquiring the coordinates of the fitting point according to the judging result;
F. and sequentially connecting the obtained fitting point coordinates into a line to obtain a terrain profile of the cutting line position.
In the embodiment, taking a dangerous rock mass at the entrance of a high-speed railway tunnel as an example, the typical section and micro-topography of the dangerous rock mass are obtained by the method;
step A is carried out: performing three-dimensional oblique photography above the tunnel entrance by using an unmanned aerial vehicle, acquiring a sufficient amount of aerial photographs, performing three-dimensional modeling on the aerial photographs to obtain a three-dimensional oblique photography model of the unmanned aerial vehicle, and obtaining a three-dimensional model corresponding to the tunnel entrance area as shown in fig. 2;
and (C) performing the step B: as shown in fig. 3 to 4, a typical section of a dangerous rock mass to be sectioned is determined, and two points are manually clicked on a three-dimensional oblique photography model of an unmanned aerial vehicle to serve as starting point coordinates P of a section line 0 (513528.31, 4028116.81, 350.38) and end point coordinates P n (513586.65，4028138.93，346.12)；
Then, the measurement is selected on the unmanned aerial vehicle three-dimensional oblique photography model manuallyPoint P i When the unmanned aerial vehicle three-dimensional oblique photography model is manually selected, selecting the areas with small or clear change of the landform and the landform which can be identified by naked eyes on the unmanned aerial vehicle three-dimensional oblique photography model from the starting point coordinates to the ending point coordinates at certain intervals, wherein the interval distance between the selected measuring points can be large, and the selecting interval between two adjacent measuring points needs to be reduced at the area with the change or turning of the landform and the area which is difficult to identify by naked eyes, wherein the selecting interval is the actual space distance between the two adjacent measuring points, and the selecting interval is controlled to be within 0.1m as much as possible;
when the measuring points are selected, the ordering of the measuring points is determined according to the specific terrain on the model, namely, when the measuring points are selected from the selected starting point coordinates to the end point coordinates, the measuring points are sequentially selected along the trend of the actual terrain, particularly the concave part and the inverted suspension part of the terrain are noted, the ordering of the measuring points can be ensured to correspond to the trend of the terrain,
when the measuring points are selected, the measuring points need to be selected close to the section line or on the section line, but the error exists in naked eye judgment and the model, so that the measuring points obtained by clicking on the model are all considered to be near the section line;
finally, 26 measuring points P are selected in total i I.e. 0 < i < 27 and i=1, 2,3 …), respectively, having P 1 (513531.68，4028117.91，349.88)、P 2 (513538.80，4028120.85，349.78)……P 19 (513559.65，4028128.47，365.98)、P 20 (513559.17，4028127.93，359.4)……P 26 (513579.40, 4028135.91, 347.18), then the end point coordinate is P 27 I.e. n=27.
And (C) performing the step B: coordinates of origin P 0 And endpoint coordinates P 27 Is substituted into the point french plane equation: a (X) n -X 0 )+B(Y n -Y 0 ) =0, can be obtained:
assuming b=1, a= -0.379156668, so d= -AX 0 -BY 0 ＝-3833409.127；
The general plane equation for obtaining the cut plane is: 0.379156668X n +Y n 3833409.127 =0, the normal vector of the plane is (-0.379156668,1,0).
After the step C is completed, checking the selected measurement point, calculating the vertical distance from the measurement point to the cutting plane, if the calculated vertical distance is greater than 0.2m, screening out the corresponding measurement point and reselecting the measurement point for replacement, if the calculated vertical distance is less than or equal to 0.2m, the measurement point meets the requirement, and continuing the subsequent calculation, for example:
will P 1 (513531.68, 4028117.91, 349.88) into the formula:
Obtaining a measuring point P 1 Perpendicular distance d to the section 1 ＝0.166211729<0.2, then measuring point P 1 Is selected to meet the requirement, and the measurement point P is obtained by such a check 2 ～P 26 All meet the requirements and the next step is continued.
And D, performing the step: set a measuring point P i The point projected onto the cutting plane is P i ' the coordinates are (X) i ’，Y i ’，Z i ') (0 < i < 27, and i=1, 2,3 …); p (P) i And P i The' connecting line is parallel to the normal vector of the section, and the slopes of the two lines are equal to obtain:
setting an intermediate value t i (0 < i < 27, and i=1, 2,3 …), and the conversion results in: x is X i -X i ’＝At i ，Y i -Y i ’＝Bt i And Z is i ＝Z i ' further push out X i ’＝X i –At i ，Y i ’＝Y i –Bt i Combined with the coordinates P i ' in the section, AX i +BY i +d=0, giving +.>
Then
X 1 ’＝X 1 –At 1 ＝513531.62，Y 1 ’＝Y 1 –Bt 1 = 4028118.07, give P 1 ' has the coordinates (513531.62, 4028118.07, 349.88);
and so on to obtain P 2 ’(513538.82，4028120.80，349.78)……P 19 ’(513559.58，4028128.66，365.98)、P 20 ’(513558.98，4028128.44，359.4)……P 26 ’(513579.31，4028136.15，347.18)。
And E, performing the step: let the fitting point of the topographic profile be DeltaP i The coordinates are set as (L i ，H i ) (0.ltoreq.i.ltoreq.27, and i=1, 2,3 …), H 0 = 350.38, let L 0 =0, calculating the horizontal increment of the projection coordinates of two adjacent measurement points on the section according to the projection coordinates calculated in the step C:
horizontal increment of the start point coordinates and the projected coordinates of the first measurement point:
the starting point coordinates and the projection coordinates P of the first measuring point 1 ' judge through the second judgement formula, the second judgement formula is:
(X 27 -X 0 )(X 1 ’-X 0 ) Is less than or equal to 0 and (Y) 27 -Y 0 )(Y 1 ’-Y 0 )≤0；
Does not meet the requirement of the second judgment formula to obtain the fitting point delta P 1 The coordinates of (2) are:
L 1 ＝L 0 +△L 1 ＝3.54；
H 1 ＝Z 1 ’ ＝349.88；
projection coordinates P of first measuring point 1 The projection coordinates P of' and the adjacent second measuring point 2 ' horizontal increment:
the projection coordinate P of the first measuring point 1 The projection coordinates P of' and the adjacent second measuring point 2 ' judge through judgment formula one, judge formula one is:
(X 27 -X 0 )(X 2 ’-X 1 ' s is less than or equal to 0 and (Y) 27 -Y 0 )(Y 2 ’-Y 1 ’)≤0；
Does not meet the requirement of the first judgment formula to obtain the fitting point delta P 2 The coordinates of (2) are:
L 2 ＝L 1 +△L 2 ＝11.24；
H 2 ＝Z 2 ’ ＝349.78；
similarly, ΔP is calculated 3 ～△P 26 Wherein the projection coordinates P of the nineteenth measurement point 19 Projection coordinates P of' and the adjacent twentieth measuring point 20 ' horizontal increment:
the projection coordinate P of the first measuring point 19 The projection coordinates P of' and the adjacent second measuring point 20 ' judge through judgment formula one, judge formula one is:
(X 27 -X 0 )(X 20 ’-X 19 ' s is less than or equal to 0 and (Y) 27 -Y 0 )(Y 20 ’-Y 19 ’)≤0；
Meets the requirement of the judgment formula I to obtain the fitting point delta P 20 The coordinates of (2) are:
L 20 ＝L 19 -△L 20 ＝32.80；
H 20 ＝Z 20 ’ ＝359.40；
projection coordinates P of last measurement point 26 ' and endpoint coordinates P 27 Is a horizontal increment of (2):
the projection coordinate P of the last measuring point 26 ' and endpoint coordinates P 27 Judging by a judgment formula III, wherein the judgment formula III is as follows:
(X 27 -X 0 )(X 27 -X 26 ' s is less than or equal to 0 and (Y) 27 -Y 0 )(Y 27 -Y 26 ’)≤0；
Does not meet the requirement of the judgment formula III, and obtains the fitting point delta P 27 The coordinates of (2) are:
L 27 ＝L 26 +△L 27 ＝62.39；
H 27 ＝Z 27 ＝346.12；
obtaining coordinates of fitting points: deltaP 0 (0，350.38)、△P 1 (3.54，349.88)、△P 2 (11.24，349.78)……△P 19 (33.44，365.98)、△P 20 (32.80，359.40)……△P 26 (54.54，347.18)、△P 27 (62.39，346.12)；
And F, performing the step: the obtained fitting point delta P 0 ～△P 27 The coordinates of (c) are connected by a straight line in the XOY plane, as shown in fig. 5, to obtain a topographical profile of the position of the section line.
As can be obtained from fig. 5, the dangerous rock body has a slightly oversuspension topographic feature, and according to the judgment result, the subsequent stability calculation is facilitated, if the dangerous rock body section is obtained by sectioning a large scale topographic map according to the prior art, the topographic section shown in fig. 6 is obtained, the topography of the dangerous rock body cannot be accurately known, and the oversuspension and steep-inclination nearly upright topographic features cannot be reflected, so that the subsequent calculation error is larger;
when the three-dimensional point cloud data of the optical image of the unmanned aerial vehicle is cut to obtain the section of the dangerous rock body, the data is required to be manually preprocessed to remove vegetation, the workload is high, special software special for foreign countries is required to be used, the requirement is high, the cut CAD section is a space three-dimensional diagram, projection is required to be carried out again to form a two-dimensional plane, the operation is troublesome, when the acquisition density of the three-dimensional point cloud data of the optical image of the unmanned aerial vehicle is insufficient, the obtained topographic section is a discontinuous line, and the obtained section is severely distorted and difficult to apply; the cost of data acquisition by the laser radar is high, and the technical difficulty is high.
In this embodiment, the topographic profile may be obtained from the section line segment between the start point coordinate and the end point coordinate, or the extension line region of the section line segment, and the extension line region of the start point coordinate and the extension line region of the end point coordinate may be obtained, and only when the measurement points near the extension line are selected, the arrangement order of the measurement points may be noted.
The method can avoid the area covered by vegetation as much as possible when the measuring points are manually selected on the unmanned aerial vehicle three-dimensional oblique photography model, reduces the interference of vegetation form data, reduces the error of the obtained landform section display, and has negligible influence on operation when the method is used for operating the movement track of the falling rocks for the vegetation development section, which is usually only the area of the dangerous rock body movement path and the development area of the dangerous rock body is usually the bare terrain.
Example 2
The invention discloses a method for acquiring a topographic profile of a dangerous rock mass, which comprises the following steps:
A. performing three-dimensional oblique photography above a target area by using an unmanned aerial vehicle, and performing three-dimensional modeling on aerial photographs;
B. selecting a starting point coordinate and an end point coordinate on the three-dimensional oblique photography model of the unmanned aerial vehicle, determining a section line of the dangerous rock mass terrain in a target area to be acquired, and sequentially selecting a plurality of measuring point coordinates near the section line along the section line;
C. establishing a plane equation of a section line corresponding to the section plane;
D. calculating to obtain projection coordinates of the measurement points projected to the section plane;
E. setting a fitting point of a terrain profile, judging the inverted suspension characteristic of the corresponding terrain according to the projection coordinates of the measuring point, and acquiring the coordinates of the fitting point according to the judging result;
F. and sequentially connecting the obtained fitting point coordinates into a line to obtain a terrain profile of the cutting line position.
In the embodiment, taking a dangerous rock body at an outlet of a certain tunnel as an example, the method is used for acquiring a typical section and a micro-landform of the dangerous rock body;
step A is carried out: performing three-dimensional oblique photography above the tunnel outlet by using an unmanned aerial vehicle, acquiring a sufficient quantity of aerial photographs, performing three-dimensional modeling on the aerial photographs, and obtaining a three-dimensional oblique photography model of the unmanned aerial vehicle, namely obtaining a three-dimensional model corresponding to the tunnel outlet area;
and (C) performing the step B: determining a typical section of a dangerous rock mass to be cut, and manually clicking two points on a three-dimensional oblique photography model of the unmanned aerial vehicle to serve as starting point coordinates P of a cutting line 0 (412801.81, 3453992.14, 547.75) and end point coordinates P n (412743.08，3453993.87，503.5)；
Then, a measuring point P is manually selected on the three-dimensional oblique photography model of the unmanned aerial vehicle i Totally select 16 measuring points P i I.e. 0 < i < 16, and i=1, 2,3 …), respectively, having P 1 (412798.55，3453991.96，549.18)、P 2 (412796.76，3453992.01，549.95)……P 6 (412787.74，3453992.58，550.87)、P 7 (412788.92，3453992.57，549)、P 8 (412790.68，3453992.63，547.27)、P 9 (412793.48，3453992.52，544.46)……P 16 (412744.67, 3453996.2, 505.42), then the end point coordinate is P 17 I.e. n=17.
And C, performing the step: coordinates of origin P 0 And endpoint coordinates P 17 Is substituted into the point french plane equation: a (X) n -X 0 )+B(Y n -Y 0 ) =0, can be obtained:
assuming b=1, a= 0.029456836, so that d= -AX 0 -BY 0 ＝-3466151.975；
The general plane equation for obtaining the cut plane is: 0.379156668X n +Y n 3833409.127 =0, the normal vector of the plane is (0.029456836,1,0).
And D, performing the step: set a measuring point P i The point projected onto the cutting plane is P i ' the coordinates are (X) i ’，Y i ’，Z i ') (0 < i < 17, and i=1, 2,3 …); p (P) i And P i The' connecting line is parallel to the normal vector of the section, and the slopes of the two lines are equal to obtain:
setting an intermediate value t i (0 < i < 17, and i=1, 2,3 …), and the conversion results in: x is X i -X i ’＝At i ，Y i -Y i ’＝Bt i And Z is i ＝Z i ' further push out X i ’＝X i –At i ，Y i ’＝Y i –Bt i Combined with the coordinates P i ' in the section, AX i +BY i +d=0, giving +.>
Then
X 1 ’＝X 1 –At 1 ＝412798.56，Y 1 ’＝Y 1 –Bt 1 = 3453992.24, give P 1 ' has the coordinates (412798.56, 3453992.24, 549.18);
and so on to obtain P 2 ’(412796.77，3453992.29，549.95)……P 6 ’(412787.74，3453992.55，550.87)、P 7 ’(412788.92，3453992.52，549)、P 8 ’(412790.68，3453992.47，547.27)、P 9 ’(412793.48，3453992.39，544.46)……P 16 ’(412744.6，3453993.83，505.42)。
And E, performing the step: let the fitting point of the topographic profile be DeltaP i The coordinates are set as (L i ，H i ) (0.ltoreq.i.ltoreq.17, and i=1, 2,3 …), H 0 = 547.75, let L 0 =0, calculating the horizontal increment of the projection coordinates of two adjacent measurement points on the section according to the projection coordinates calculated in the step C:
horizontal increment of the start point coordinates and the projected coordinates of the first measurement point:
the starting point coordinates and the projection coordinates P of the first measuring point 1 ' judge through the second judgement formula, the second judgement formula is:
(X 17 -X 0 )(X 1 ’-X 0 ) Is less than or equal to 0 and (Y) 17 -Y 0 )(Y 1 ’-Y 0 )≤0；
Does not meet the requirement of the second judgment formula to obtain the fitting point delta P 1 The coordinates of (2) are:
L 1 ＝L 0 +△L 1 ＝3.25；
H 1 ＝Z 1 ’ ＝549.18；
projection coordinates P of first measuring point 1 The projection coordinates P of' and the adjacent second measuring point 2 ' horizontal increment:
the projection coordinate P of the first measuring point 1 The projection coordinates P of' and the adjacent second measuring point 2 ' judge through judgment formula one, judge formula one is:
(X 17 -X 0 )(X 2 ’-X 1 ’)≤0 and (Y) 17 -Y 0 )(Y 2 ’-Y 1 ’)≤0；
Does not meet the requirement of the first judgment formula to obtain the fitting point delta P 2 The coordinates of (2) are:
L 2 ＝L 1 +△L 2 ＝5.04；
H 2 ＝Z 2 ’ ＝549.95；
similarly, ΔP is calculated 3 ～△P 16 Wherein the projection coordinates P of the sixth measurement point 6 ' projection coordinates P with the seventh measurement point adjacent thereto 7 ' horizontal increment:
the projection coordinate P of the sixth measuring point 6 ' projection coordinates P with the seventh measurement point adjacent thereto 7 ' judge through judgment formula one, judge formula one is:
(X 17 -X 0 )(X 7 ’-X 6 ' s is less than or equal to 0 and (Y) 17 -Y 0 )(Y 7 ’-Y 6 ’)≤0；
Meets the requirement of the judgment formula I to obtain the fitting point delta P 7 The coordinates of (2) are:
L 7 ＝L 6 -△L 7 ＝12.9；
H 7 ＝Z 7 ’ ＝549；
projection coordinates P of seventh measurement point 7 The projection coordinates P of' and the adjacent eighth measuring point 8 ' horizontal increment:
projection coordinate P of seventh measuring point 7 The projection coordinates P of' and the adjacent eighth measuring point 8 ' judge through judgment formula one, judge formula one is:
(X 17 -X 0 )(X 8 ’-X 7 ' s is less than or equal to 0 and (Y) 17 -Y 0 )(Y 8 ’-Y 7 ’)≤0；
Meets the requirement of the judgment formula I to obtain the fitting point delta P 8 The coordinates of (2) are:
L 8 ＝L 7 -△L 8 ＝11.14；
H 8 ＝Z 8 ’ ＝547.27；
projection coordinates P of eighth measurement point 8 Projection coordinates P of' and adjacent ninth measurement point 9 ' horizontal increment:
the projection coordinate P of the sixth measuring point 6 ' projection coordinates P with the seventh measurement point adjacent thereto 7 ' judge through judgment formula one, judge formula one is:
(X 17 -X 0 )(X 7 ’-X 6 ' s is less than or equal to 0 and (Y) 17 -Y 0 )(Y 7 ’-Y 6 ’)≤0；
Meets the requirement of the judgment formula I to obtain the fitting point delta P 9 The coordinates of (2) are:
L 9 ＝L 8 -△L 9 ＝8.34；
H 9 ＝Z 9 ’ ＝544.46；
projection coordinates P of last measurement point 16 ' and endpoint coordinates P 17 Is a horizontal increment of (2):
the projection coordinate P of the last measuring point 16 ' and endpoint coordinates P 17 Judging by a judgment formula III, wherein the judgment formula III is as follows:
(X 17 -X 0 )(X 17 -X 16 ' s is less than or equal to 0 and (Y) 17 -Y 0 )(Y 17 -Y 16 ’)≤0；
Does not meet the requirement of the judgment formula III, and obtains the fitting point delta P 17 The coordinates of (2) are:
L 17 ＝L 16 +△L 17 ＝58.75；
H 17 ＝Z 17 ＝503.5；
obtaining coordinates of fitting points: deltaP 0 (0，547.75)、△P 1 (3.25，549.18)、△P 2 (5.04，549.95)……△P 6 (14.08，550.87)、△P 7 (12.90，549)、△P 8 (11.14，547.27)、△P 9 (8.34，544.46)……△P 16 (57.23，505.42)、△P 17 (58.75，503.5)；
And F, performing the step: the obtained fitting point delta P 0 ～△P 17 The coordinates of (2) are connected by a straight line in the XOY plane to obtain the topographic profile of the position of the section line.
As shown in fig. 8, due to the P of the projection coordinates of the measurement point 6 ' to P 9 The condition of the first judgment formula is met, so that the dangerous rock body has obvious inverted topography characteristics, the type of the dangerous rock body is clearly determined, subsequent stability calculation is facilitated, if the dangerous rock body section is obtained by cutting a large-scale topographic map according to the prior art, the topographic section shown in fig. 9 is obtained, the topography of the dangerous rock body cannot be accurately known, obvious inverted topography characteristics cannot be reflected, and subsequent calculation errors are large.
The foregoing description of the preferred embodiments of the invention is not intended to be limiting, but rather is intended to cover all modifications, equivalents, and alternatives falling within the spirit and principles of the invention.
Claims (9)
1. A method of acquiring a topographic profile of a hazardous rock mass comprising the steps of:
A. performing three-dimensional oblique photography above a target area by using an unmanned aerial vehicle, and performing three-dimensional modeling on aerial photographs to obtain an unmanned aerial vehicle three-dimensional oblique photography model;
B. selecting a starting point coordinate and an end point coordinate on the three-dimensional oblique photography model of the unmanned aerial vehicle, determining a section line of the dangerous rock mass terrain in a target area to be acquired, and sequentially selecting a plurality of measuring point coordinates near the section line along the section line;
C. establishing a plane equation of a section line corresponding to the section plane;
D. calculating to obtain projection coordinates of the measurement points projected to the section plane;
E. setting a fitting point of a terrain profile, judging the inverted suspension characteristic of the corresponding terrain according to the projection coordinates of the measuring point, and acquiring the coordinates of the fitting point according to the judging result;
F. sequentially connecting the obtained fitting point coordinates into a line to obtain a terrain profile of a section line position;
in the step D, the step of judging the overhang feature of the terrain and obtaining the coordinate of the fitting point includes the following steps:
d1: the starting point coordinate selected in the step A is P 0 (X 0 ，Y 0 ，Z 0 ) Endpoint coordinate is P n (X n ，Y n ，Z n ) N=1, 2,3 …, the measurement point coordinates are P i (X i ，Y i ，Z i ) 0 < i < n, and i=1, 2,3 …; the projection coordinate of the measurement point obtained in the step C is P i ’(X i ’，Y i ’，Z i '), 0 < i < n, and i=1, 2,3 …;
and judging the projection coordinates of two adjacent measurement points by a judgment formula I, wherein the judgment formula I is as follows:
(X n -X 0 )(X i+1 ’-X i ' s is less than or equal to 0 and (Y) n -Y 0 )(Y i+1 ’-Y i ') is less than or equal to 0,0 < i < n-1, and i=1, 2,3 …;
the requirement of the first judgment is met, and the topography between two adjacent measuring points has the feature of inverted suspension;
judging the starting point coordinates and the projection coordinates of the first measuring point by a second judgment formula, wherein the second judgment formula is as follows:
(X n -X 0 )(X 1 ’-X 0 ) Is less than or equal to 0 and (Y) n -Y 0 )(Y 1 ’-Y 0 )≤0；
Meeting the requirement of the judgment type II, the terrain between the starting point and the first measuring point has the feature of inverted suspension;
and judging the projection coordinate and the end point coordinate of the last measuring point through a third judgment formula, wherein the third judgment formula is as follows:
(X n -X 0 )(X n -X n-1 ' s is less than or equal to 0 and (Y) n -Y 0 )(Y n -Y n-1 ’)≤0；
The requirement of the third judgment type is met, and then the topography between the last measuring point and the end point has the feature of inverted suspension;
d2: let the fitting point of the topographic profile be DeltaP i The coordinates are set as (L i ，H i ) I is more than or equal to 0 and less than or equal to n, and i=1, 2,3 … and H 0 ＝Z 0 Let L be 0 =0, calculating the horizontal increment of the projection coordinates of two adjacent measurement points on the section according to the projection coordinates obtained in the step C:
the projection coordinates of two adjacent measurement points meet the requirement of the judgment formula I, and then:
L i+1 ＝L i -△L i+1 0 < i < n-1, and i=1, 2,3 …;
H i+1 ＝Z i+1 ' 0 < i < n-1, and i=1, 2,3 …;
if the projection coordinates of two adjacent measurement points do not meet the requirement of the judgment formula one, then:
L i+1 ＝L i +△L i+1 ' 0 < i < n-1, and i=1, 2,3 …;
H i+1 ＝Z i+1 ' 0 < i < n-1, and i=1, 2,3 …;
horizontal increment of the start point coordinates and the projected coordinates of the first measurement point:
the starting point coordinates and the projection coordinates of the first measurement point meet the requirement of a judgment formula II, and then:
L 1 ＝L 0 -△L 1 ；
H 1 ＝Z 1 ’ ；
if the starting point coordinates and the projection coordinates of the first measurement point do not meet the requirement of the judgment formula II, then:
L 1 ＝L 0 +△L 1 ；
H 1 ＝Z 1 ’ ；
horizontal increment of the projection coordinates and the end point coordinates of the last measurement point:
and if the projection coordinate and the end point coordinate of the last measurement point meet the requirement of the judgment formula III, then:
L n ＝L n-1 -△L n ；
H n ＝Z n ；
and if the projection coordinate and the end point coordinate of the last measurement point do not meet the requirement of the judgment formula III, then:
L n ＝L n-1 +△L n ；
H n ＝Z n 。
2. the method for obtaining a topographic profile of a dangerous rock mass according to claim 1, wherein in the step D1, the obtaining process of the judgment formula is as follows:
the first judgment formula is to judge the projection coordinates of two adjacent measurement points, and the total of four conditions are the section lines formed by connecting the starting point coordinates and the end point coordinates, and the expression of the straight line is y=kx+b:
and (3) a step of: k (k)>0, then X n -X 0 >0，Y n -Y 0 >0；
When the connecting line of two adjacent measuring points is an inverted suspension feature: x is X i+1 -X i <0 and Y i+1 -Y i <0,0 < i < n-1, and i=1, 2,3, …;
obtain (X) n -X 0 )(X i+1 ’-X i ’)<0 and (Y) n -Y 0 )(Y i+1 ’-Y i ’)<0；
And II: k (k)<0, then X n -X 0 >0，Y n -Y 0 <0；
When the connecting line of two adjacent measuring points is an inverted suspension feature: x is X i+1 -X i <0 and Y i+1 -Y i >0,0 < i < n-1, and i=1, 2,3, …;
obtain (X) n -X 0 )(X i+1 ’-X i ’)<0 and (Y) n -Y 0 )(Y i+1 ’-Y i ’)<0；
Thirdly,: x=constant, then X n -X 0 ＝0，Y n -Y 0 >0；
When the connecting line of two adjacent measuring points is an inverted suspension feature: x is X i+1 -X i =0 and Y i+1 -Y i <0,0 < i < n-1, and i=1, 2,3, …;
obtain (X) n -X 0 )(X i+1 ’-X i ') =0 and (Y) n -Y 0 )(Y i+1 ’-Y i ’)<0；
Fourth, the method comprises the following steps: k=0, then X n -X 0 >0，Y n -Y 0 ＝0；
When the connecting line of two adjacent measuring points is an inverted suspension feature: x is X i+1 -X i <0 and Y i+1 -Y i =0, 0 < i < n-1, and i=1, 2,3, …;
obtain (X) n -X 0 )(X i+1 ’-X i ’)<0 and (Y) n -Y 0 )(Y i+1 ’-Y i ’)＝0；
The judgment formula I for obtaining the feature of the topography that the inverted overhang topography appears on the whole is as follows: (X) n -X 0 )(X i+1 ’-X i ' s is less than or equal to 0 and (Y) n -Y 0 )(Y i+1 ’-Y i ') is less than or equal to 0,0 < i < n-1, and i=1, 2,3 …; and similarly, calculating to obtain a judgment formula II and a judgment formula III.
3. A method of acquiring a topographic profile of a rock mass as set forth in claim 1, wherein said step B includes the steps of:
b1: the corresponding section plane of the section line is an XOY plane perpendicular to the three-dimensional oblique photography model of the unmanned aerial vehicle, and the normal vector of the section plane is (A, B, 0);
b2: c, the starting point coordinates P selected in the step A are processed 0 (X 0 ，Y 0 ，Z 0 ) And endpoint coordinates P n (X n ，Y n ，Z n ) N=1, 2,3 … is substituted into the point french plane equation to obtain: a (X) n -X 0 )+B(Y n -Y 0 ) =0, push out: AX n +BY n +(-AX 0 -BY 0 ) =0, substituting the general formula plane equation to obtain: d= -AX 0 -BY 0 Wherein A, B is a coefficient of a point normal plane equation and a coefficient of a general plane equation, and D is a coefficient of a general plane equation;
b3: and (3) setting a non-zero assumed value for one of the coefficient A and the coefficient B, solving the value of the other coefficient and the coefficient D, and establishing a plane equation of the section.
4. A method of obtaining a topographic profile of a rock mass as set forth in claim 3, wherein in step C, the calculating includes the steps of:
c1: obtained measuring point P i The coordinates are (X) i ，Y i ，Z i ) 0 < i < n, and i=1, 2,3 …, P i The point projected onto the cutting plane is P i ' the coordinates are (X) i ’，Y i ’，Z i '), 0 < i < n, and i=1, 2,3 …;
C2：P i and P i The' connecting line is parallel to the normal vector of the section, and the slopes of the two lines are equal to obtain
Setting an intermediate value t i 0 < i < n, and i=1, 2,3 …, converted to: x is X i -X i ’＝At i ，Y i -Y i ’＝Bt i And Z is i ＝Z i ' further push out X i ’＝X i –At i ，Y i ’＝Y i –Bt i Combined with the coordinates P i ' in the section, AX i +BY i +d=0, giving
Let t i Substitution into X i ’＝X i –At，Y i ’＝Y i Bt, finding the measurement point P i Projection coordinates P on a cutting plane i ’(X i ’，Y i ’，Z i ’)。
5. The method of claim 1, wherein in the step a, the selected distance between two adjacent measurement points is narrowed at a change or turn of the topography.
6. The method for obtaining a topographic profile of a dangerous rock mass according to claim 5, wherein when the selected density of the measurement points is increased, the distance between two adjacent measurement points is selected to be not more than 0.1m according to the topographic trend on the model along the direction of the section line.
7. A method of obtaining a topographic profile of a dangerous rock mass according to any one of claims 1-6, wherein after said step B is completed, selected measurement points are checked and screened out for measurement points that deviate from the defined distance of the cut surface prior to said step C.
8. A method of acquiring a topographic profile of a rock mass as set forth in claim 7, wherein the defined distance is set to 0.2m.
9. The method for obtaining a topographic profile of a dangerous rock mass according to claim 7, wherein the checking of the measurement points is to calculate a vertical distance from the measurement points to the section plane, wherein the calculated vertical distance is greater than a defined distance, screen out the corresponding measurement points and reselect the measurement points for replacement, and the formula for calculating the vertical distance is as follows:
wherein: d, d i Is a vertical distance X i 、Y i The three-dimensional coordinates of the measurement points X and Y axes, respectively, A, B, D are coefficients of general equations of the cut plane.
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