CN104392491B - Rotating surface based goaf laser scanning point cloud triangulation method - Google Patents

Abstract

The invention discloses a laser scanning point cloud triangulation method for gobs based on a rotating surface, which comprises the following steps: ① Converting the irregular measured scanning point cloud into a circle-by-circle spherical projection point cloud through spherical projection , to interpolate the spherical projection point cloud, restore the original spatial topological relationship, and simultaneously interpolate the measured scanning point cloud. ② Generate a rotation surface from the points on the circle on the spherical surface and the central rotation axis, search for the point closest to the rotation surface on the adjacent circle, and construct the optimal grid. ③ The optimal grid is triangulated by the intermediate position judgment method, and the in-situ point cloud of the goaf is simultaneously triangulated to obtain the triangular mesh model of the goaf. The method of the invention has high efficiency and high accuracy.

Description

Triangulation method of laser scanning point cloud in goaf based on rotating surface

technical field

The invention relates to a laser scanning point cloud triangulation method of a goaf based on a rotating surface.

Background technique

The goaf formed by underground metal mining [goaf refers to the empty area formed by mining] often leads to the deterioration of mining conditions, difficulties in the maintenance of stopes and roadways in adjacent operating areas, and even causes large-scale underground caving and rock movement Disasters such as land subsidence and surface subsidence pose a serious threat to mine safety production. At present, the detection technologies of gobs at home and abroad mainly include engineering drilling, geophysical exploration, laser scanning detection and other technologies. In terms of accurately obtaining the three-dimensional shape of gobs, laser scanning detection technology has certain advantages. [Point cloud refers to the collection of points obtained after obtaining the spatial coordinates of each sampling point on the surface of the object, which is called "point cloud". Point Cloud is a collection of massive points expressing the spatial distribution of the target and the surface characteristics of the target under the same spatial reference system. The point cloud obtained according to the principle of laser measurement, including three-dimensional coordinates (XYZ). 】Can establish a triangulation solid model of the goaf [Tangulation solid model refers to the solid model composed of triangle mesh patches used to simulate the three-dimensional shape of the solid], the triangulation solid model can be used for mining design, stope recovery index Calculation, numerical simulation analysis, visual safety supervision, etc. The widely used airspace laser scanning detection equipment includes the Canadian airspace monitoring system CMS and the British airspace automatic scanning laser system C-ALS.

The goaf is detected with the help of laser scanning detection equipment, and its working principle is as follows: the laser scanning head is extended into the gob through the connecting rod. After completing a circle, the scanning head will automatically raise the preset angle and scan a new circle until all the detection work is completed. The principle of CMS detection is shown in Figure 1.

The ideal airspace laser detection data is a very regular and ordered point cloud, and the angle between the points is certain, arranged in circles one after another. In the actual detection, due to the influence of unfavorable factors such as large water vapor, dust, accumulated water, and local obstacles in the goaf, the point cloud information may generate noise points or local data loss, which destroys the proper function of the scanning point cloud. Topological law, which has a very negative impact on the ordered point cloud triangulation [Point cloud triangulation refers to the construction of a series of triangles with the point cloud as the vertex according to certain rules, all triangles do not overlap, do not cross, and have no gaps form a triangulation surface. 】.

Existing algorithms for triangulation of ordered point clouds in gobs include grid-based triangulation methods and maximum opening angle triangulation methods. The idea of the grid-based triangulation method is to first connect the points between the circles into a square grid in order, and then divide each grid into two triangular grids. The schematic diagram of the method is shown in Figure 2 shown. The maximum opening angle triangulation method is to refer to the connecting line between the circles (the two vertices of the new triangle), and select the adjacent point with the larger opening angle in the two circles according to the principle of the maximum opening angle as the third vertex of the new triangle. Continuously update and finally complete all triangulation, the schematic diagram of the method is shown in Figure 3.

The grid-based triangulation method and the maximum angle triangulation method, which consider the ordered topological relationship of the point cloud, can construct a better triangulation network when the laser detection point cloud data is relatively complete and the spatial topological relationship is well preserved. grid model. However, in actual situations, when the point cloud data is missing and the spatial topological relationship is destroyed, the constructed triangulation model will appear local narrow and long triangles or the model will be locally deformed.

If the regularity of the point cloud is not considered, that is, it is studied as a scattered point cloud, the main methods that can be referred to at present are the three-dimensional Delaunay triangulation method, the front (frontier) advancement method (Advancing Front Method) and the octree (Octree) law etc. The above methods have little research and application on the triangulation of laser scanning point clouds in complex shapes of gobs. Since the existing topological laws of laser scanning point clouds are not considered, the algorithm complexity is high, the efficiency is low, and the effect has not been verified; The applicability of gobs with complex shapes is not strong. At present, there is no very effective accurate modeling method for scattered point clouds at the boundaries of gobs.

Contents of the invention

The technical problem solved by the present invention is to provide a method for triangulation of goaf laser scanning point cloud based on rotating surface, and to make full use of the spatial topological law of gob laser scanning point cloud. Scattered point cloud triangulation efficiency is high; at the same time, for unfavorable environmental factors that lead to incomplete acquisition and topological relationship damage scanning point cloud data, the method of topology law repair and triangulation is better than the existing orderly point cloud triangulation The method has high accuracy.

Technical scheme of the present invention is:

A method of triangulation of gob laser scanning point cloud based on rotating surface,

Use laser scanning detection equipment to detect gobs, extend the laser scanning head into the goaf through the connecting rod, rotate the scanning head 360° and continuously detect the boundary point information of the goaf through the laser, and scan the points obtained by the scanning head Connected in sequence to form a scanning circle; after scanning a circle, the scanning head automatically raises the preset angle and scans a new circle until all the detection work is completed; finally, Y scanning circles are obtained;

The laser scan point cloud triangulation is then performed as follows:

Step 1: Set the projection sphere and calculate the projection point cloud data: set the position of the scanning head as the center of the sphere, and set the radius of the sphere to 0.5 to 2 times the length of the stope design; The points above are projected onto the spherical surface to form Y projection circles corresponding to Y scan circles, which are sequentially recorded as Q ₁ circle, Q ₂ circle, ..., Q _y circle, ..., Q _Y circle; where y is the projection circle number ;

Step 2: Perform interpolation processing:

In order to determine whether there is a point missing on each projection circle, the method is: if the points on a certain projection circle are a series of equally spaced points, there is no point data missing, and no interpolation processing is performed; if the local adjacent points on the projection circle If the distance between two points is greater than 1.5 times the average distance between the circle points, it is considered that the distance is too large, indicating that there is a point missing, and interpolation processing is required; perform interpolation on all projection circles and the scanning circle corresponding to the projection circle;

Step 3: Extract the optimal grid based on the rotating surface:

Take the line connecting the center points of all projection circles on the projection sphere as the axis of rotation, and extract points Q _{y, i} from the circle Q _y in order to form a plane with the rotation axis [the so-called rotation plane means that because the midpoints of the circles are sorted clockwise Or counterclockwise, so points are extracted from the circle in order and the plane plane composed of the rotation axis is continuously pushed forward and rotated, so it is defined as a rotation surface. The schematic diagram of the rotating surface is shown in Figure 7. ], search for the nearest point on the adjacent circle Q _y+1 to this plane; extract the point Q y from the Q _y circle _{, i+1} forms a plane with the rotation axis, and search for the nearest point on the adjacent circle Q _y+1 to this plane , then the closed circle formed by point Q _{y, i} , point Q _{y, i+1} and the points closest to the two adjacent planes searched on the adjacent circle Q _y+1 is approximately a grid , defined as the optimal grid;

Wherein the subscript y of Q is the sequence number of the projection circle, y=[1, Y]; i is the sequence number of the point on the projection circle, i=[1, I], and I is the number of points on the projection circle;

Let the initial value of y be 1, and the initial value of i be 1, and search and extract all the optimal grids on the sphere in turn;

Step 4: Triangulate the projection circle on the sphere based on the optimal grid:

Assume that the two nearest points from the two adjacent planes searched on the adjacent circle Q _y+1 are point Q _y+1,n and point Q _y+1,m ;

If Q _{y+1, n} and Q _{y+1, m} are two adjacent points on the circle of Q _y+1 , then (Q _{y+1, n} , Q _{y+1, m} , Q _{y, i} ) constitute A triangle, (Q _{y+1, m} , Q _{y, i} , Q _{y, i+1} ) constitutes a triangle;

If Q _{y+1, n} and Q _{y+1, m} are the same point on the circle of Q _y+1 , then (Q _{y, i} , Q _{y, i+1} , Q _{y+1, n} ) form a triangle ;

If Q _{y+1, n} and Q _{y+1, m} are two points of two non-adjacent points on the circle of Q _y+1 , the optimal grid is triangulated using the intermediate position judgment method, specifically :

Take p as the integer part of the value of (n+m)/2, point Q _{y+1, p} is the middle position point of point Q _{y+1, n} and point Q _{y+1, m} ; for point Q _{y+ 1, x} , when n≤x<p, (Q _{y+1, x} , Q _{y+1, x+1} , Q _{y, i} ) form a triangle; when x=p, (Q _{y, i} , Q _{y, i+1} , Q _{y+1, x} ) form a triangle; when p<x≤m, (Q _{y+1, x} , Q _{y+1, x-1} , Q _{y, i+1} ) form a triangle ; Wherein the subscripts n, m, p, x are points Q y+ ₁ on the circle of Q _{y+1, n} , Q _{y+1, m} , Q _{y+1, x} , Q _{y+1, the sequence number of p} ;

According to this method, a triangular mesh model of the spherical projection point cloud is generated;

Step 5: According to the projection corresponding relationship between the projected point cloud and the measured scanned point cloud, correspondingly generate a triangular mesh model of the measured scanned point cloud.

Further, in the second step, interpolation is performed on all the projection circles and the scan circles corresponding to the projection circles in the following way:

(1) Calculate the distance between two adjacent points on the projection circle. If the distance is greater than 1.5 times the average distance between the circle points, it is considered that there is a point missing, and a new point P _N needs to be inserted;

(2) Calculate the distance between two adjacent points on the projection circle. If the distance between two adjacent points P ₂ and P ₃ on a certain projection circle is greater than 1.5 times the average distance between the circle points, then the line segment P ₂ The distance from point P ₂ on P ₃ is the insertion point P _N at d ₁ , where d ₁ is the average distance between the circle points, and the line segment corresponding to line segment P ₂ P ₃ is on the scanning circle corresponding to the projection circle according to the linear ratio Insert a new point A _N on A ₂ A ₃ , and the position of the inserted point A _N satisfies the linear proportional relationship d ₁ : d ₂ = d ₃ : d ₄ , where d ₂ is the length of the line segment P _N P ₃ , and d ₃ is the line segment A ₂ The length of A _N , d ₄ is the length of the line segment A _N A ₃ ;

Further, the scanning head scans a circle to obtain 320-340 points; after scanning a circle, the scanning head automatically raises the preset angle by 5 degrees; until the scanning head is raised to 140 degrees to complete all the detection work [that is, the inclination angle of the scanning head The range is 0°—140°].

Beneficial effect:

The present invention is based on the laser scanning ordered point cloud triangulation method of the goaf on the rotating surface. The method first performs interpolation through the ordered point interpolation method based on spherical projection, restores the spatial topological law of the scanning point cloud rules, and then uses the spherical projection The line connecting the center points of the scanning circle is the axis of rotation. Points are extracted from one circle in turn to generate a rotating surface, and the points that can generate the optimal grid are searched for in the next circle based on the rotating plane, and the triangulation is completed on the basis of the optimal grid. point. The present invention starts from practical engineering applications, on the basis of fully understanding and applying the spatial topological relationship of laser scanning point cloud data in gobs, and considering the incompleteness of scanning point cloud data and the destruction of topological relationship due to the influence of unfavorable environmental factors, a new method is proposed. Set of effective solutions.

On the one hand, the present invention performs ordered point interpolation based on spherical projection for the point cloud data obtained by the laser detection technology similar to the empty area, so as to repair the spatial topological relationship of the ordered point cloud and restore the proper topological law. This method is more practical. It is relatively easy to implement; the spatial topological relationship of the gob laser scanning point cloud is fully utilized to ensure the efficiency of triangulation. At the same time, the topological relationship is repaired through spherical projection interpolation, and the optimal grid is generated by combining the rotation axis and rotation surface search. On this basis, the triangulation is completed to ensure the accuracy of the constructed triangulation model.

For the ordered point cloud, a new search method based on the rotating surface is proposed to obtain the optimal grid; the grid triangulation method based on the rotating surface is studied, which can well realize the laser detection point cloud of the goaf Triangulation, through ordered point interpolation based on spherical projection, makes up for the lack of local point data caused by environmental factors (dust, water vapor, water, etc.), compared with grid triangulation methods and maximum angle triangulation method has better performance.

Description of drawings

Fig. 1 Schematic diagram of laser scanning detection in goaf;

Fig. 2 is a schematic diagram of a grid-based triangulation algorithm in the prior art;

Fig. 3 is a schematic diagram of the maximum opening angle triangulation algorithm in the prior art;

Fig. 4 is a flow chart of the method of the present invention;

Fig. 5 is a schematic diagram of spherical projection of the present invention;

Fig. 6 is the principle diagram of the equal ratio interpolation of the scanning circle and the projection circle of the present invention;

Fig. 7 is a schematic diagram of the rotating surface of the present invention;

Fig. 8 is a schematic diagram of the optimal grid of the present invention;

Fig. 9 is a special case of the optimal grid of the present invention;

Fig. 10 is the optimal grid triangulation method of the present invention;

Fig. 11 is based on the grid triangulation algorithm effect analysis of the surface of rotation, wherein 11 (a) is based on the grid triangulation 11 (b), is based on the maximum opening angle triangulation 11 (c), is based on the present invention method of triangulation.

detailed description

The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

The present invention realizes steps as follows, method flowchart is shown in Fig. 4:

Use the laser scanning detection equipment to detect the goaf, and extend the laser scanning head into the gob through the connecting rod. During the detection, the scanning head rotates 360° and continuously measures the boundary point information of the goaf through the laser, and scans after each scan The head will automatically raise the preset angle and scan a new circle until all the detection work is completed.

①Through spherical projection, the in-situ point cloud with no obvious rules is converted into a circle-by-circle spherical point cloud, and the spherical point cloud is interpolated to restore the original spatial topological relationship, and the in-situ point cloud is interpolated synchronously.

② Generate a rotation surface from the points on the circle on the spherical surface and the central rotation axis, search for the point closest to the rotation surface on the adjacent circle, and construct the optimal grid.

③ The optimal grid is triangulated by the intermediate position judgment method, and the in-situ point cloud of the goaf is simultaneously triangulated to obtain the triangular mesh model of the goaf.

The main steps are further described in detail below:

Ordered Point Interpolation Method Based on Spherical Projection

Determine the projection sphere: set the scanning center as the center of the projection sphere, and set the radius of the projection sphere to 0.5 to 2 times the length of the stope design. Through spherical projection, the goaf boundary data detected by the laser scanning detection equipment scanning a circle is projected onto the spherical surface to form a projection circle;

Perform interpolation. As shown in Figure 5

Judging whether there is missing point data: If the data on the projection circle is a series of points at equal intervals, there is no point data missing, and interpolation processing will not be performed; if the distance between local adjacent points on the projection circle is too large, then It shows that there is a lack of point data, and the interpolation process is performed on the projection circle; the actual scanning circle points are synchronously interpolated according to the linear proportional relationship. Specifically: the schematic diagram of the interpolation method is shown in Figure 6, and the description of the interpolation method is as follows:

(1) Calculate the distance between two adjacent points on the projection circle. If the distance is greater than 1.5 times the average distance between the circle points, it is considered that there is a point missing, and a new point P _N needs to be inserted.

(2) Insert point P _N at a distance of d ₁ from point P ₂ on line segment P ₂ P ₃ , where d ₁ is the average distance between the points in the circle, and the length of P _N P ₃ is d ₂ , and find d ₁ and The linear ratio of d ₂ , inserting a new point A _N on the line segment A ₂ A ₃ on the scanning circle according to the linear ratio, the insertion point satisfies the linear proportional relationship d ₁ :d ₂ =d ₃ :d ₄ ;

(3) Perform interpolation on all scanning circles in turn to restore the spatial topology law that the scanning circles should have.

The ordered point interpolation based on the spherical projection lays the foundation for the grid triangulation algorithm based on the rotating surface.

Extracting Optimal Grid Based on Rotated Surface

The so-called rotating surface is to take the line connecting the center points of the projection circle on the projection sphere as the rotation axis, and extract points from a certain circle (Q _y circle) in order to form a plane with the rotation axis; The hour hand, so the plane is continuously pushed forward and rotated, so it is defined as a rotating surface. The schematic diagram of the rotating surface is shown in Figure 7. In order to show more clearly, Figure 7 only draws the rotating surface corresponding to 5 projection circles and 6 points. In practical applications, more projection circles and rotating surfaces are included. 】

Construct the rotation plane through the points on the Q _y circle and the rotation axis to search for the nearest point on the adjacent circle Q _y+1 circle to the rotation plane: the rotation plane is formed by the point Q _{y, i} and the rotation axis, and the point Q _{y, i+1} and The rotation axis constitutes the rotation plane, respectively search for the nearest point on the adjacent circle Q _y+1 to the rotation plane, let the searched points be Q _{y+1, n} and Q _{y+1, m} respectively, points Q _{y, i} , The closed circle composed of Q _y,i+1 , Q _y+1,n and Q _y+1,m is approximately a grid, which is defined as the optimal grid, as shown in Figure 8.

Triangulation based on an optimal grid

In general, the optimal grid is to take two adjacent points in the Q _y circle and Q _y+1 circle respectively, that is, the 2:2 optimal grid.

Special case 1: Take 2 points in the Q _y circle, and the closest points of the two rotating surfaces in the Q _y+1 circle are the same point, that is, the 2:1 optimal grid;

Special case 2: Take 2 points in the Q _y circle, and the nearest points of the two rotating planes in the Q _y+1 circle are non-adjacent points, that is, the optimal grid is 2:n. The special case of the optimal grid is shown in Fig. 9.

Assume that the two nearest points searched by two adjacent planes on the adjacent circle Q _y+1 are respectively point Q _y+1,n and point Q _y+1,m on the Q _y+1 circle;

If Q _{y+1, n} and Q _{y+1, m} are two adjacent points on the circle of Q _y+1 , then (Q _{y+1, n} , Q _{y+1, m} , Q _{y, i} ) constitute A triangle, (Q _{y+1, m} , Q _{y, i} , Q _{y, i+1} ) constitutes a triangle;

If Q _{y+1, n} and Q _{y+1, m} are the same point on the circle of Q _y+1 , then (Q _{y, i} , Q _{y, i+1} , Q _{y+1, n} ) form a triangle ;

If Q _{y+1, n} and Q _{y+1, m} are two points of two non-adjacent points on the circle of Q _y+1 , the optimal grid is triangulated by the middle position judgment method, the method is shown As shown in Figure 10; specifically:

Take p as the integer part of the value of (n+m)/2, point Q _{y+1, p} is the middle position point of point Q _{y+1, n} and point Q _{y+1, m} ; for point Q _{y+ 1, x} , when n≤x<p, (Q _{y+1, x} , Q _{y+1, x+1} , Q _{y, i} ) form a triangle; when x=p, (Q _{y, i} , Q _{y, i+1} , Q _{y+1, x} ) form a triangle; when the judgment position p<x≤m, (Q _{y+1, x} , Q _{y+1, x-1} , Q _{y, i+1} ) form a triangle; where the subscripts n, m, p, x are points Q _{y +1, n} , Q _{y+1, m} , Q _{y+1, x} , Q _{y+1, p} on the circle of Q y+1 serial number;

According to this method, the triangular mesh model of the spherical projection point cloud is generated; through the optimal grid triangulation, the triangular mesh model of the spherical projection point cloud can be generated, because the projected point cloud and the measured point cloud are stored in the storage container The order is consistent, and the location of the triangle vertices in the storage container is applied to the measured point cloud container, and the measured point cloud triangle mesh model can be generated synchronously.

Fig. 11 is based on the effect analysis of the grid triangulation algorithm of rotating surface, wherein 11 (a) is based on the grid triangulation, 11 (b) is the triangulation based on the maximum opening angle, and 11 (c) is based on the present invention method of triangulation. The simulation results show that the grid triangulation method based on 11(a) is prone to produce narrow and long deformed triangles when the point data is missing, while the triangulation method based on the maximum opening angle in 11(b) is prone to excessive concentration of triangle vertices. The inventive method makes up for the local defects in the first two algorithms, and can well realize the triangulation of laser detection point clouds in gobs. , stagnant water, etc.), the local point data is missing, and it has better performance than 11(a) based on the grid triangulation method and 11(b) based on the maximum angle triangulation method.

Claims (3)

1. a kind of goaf laser scanning point cloud triangulation methodology based on the surfaces of revolution it is characterised in that:

Using laser scanning, detecting equipment, goaf is detected, laser scanning head is stretched into by goaf by connecting rod, sweep Retouch 360 ° and rotate and pass through laser continuous probe gob edge point information, the point phase successively that probe scanning one circle obtains Even, form a surface sweeping circle；After scanning through a circle, probe is automatically raised predetermined angle and is carried out the scanning of a new circle, until complete Become whole detection operations；Finally give Y scanning circle；

Then carry out laser scanning point cloud triangulation according to the following steps：

Step one：Set projection sphere, be calculated point cloud projection data：Probe position is set as the centre of sphere of sphere, ball The radius in face is set as 0.5～2 times of stope design length；By spherical projection method the spot projection on scanning circle to sphere On, formed and enclose corresponding Y projection circle with Y scanning, be designated as Q successively₁Circle, Q₂Circle ..., Q_yCircle ..., Q_YCircle；Wherein y is to throw Cinema-circle's sequence number；

Step 2：Carry out interpolation processing:

Judge that, with the presence or absence of point disappearance on each projection circle, method is successively：If the point on certain projection circle is a series of etc. , then there is not point data disappearance, do not carry out interpolation processing in the point of spacing；If the adjacent distance between two points of the upper local of projection circle Between punctuating more than this, 1.5 times of average distance are then it is assumed that apart from excessive, then illustrating there is point disappearance, needing to carry out interpolation processing； All of projection circle and this corresponding scanning of projection circle are enclosed into row interpolation；

Step 3：Optimum grid is extracted based on the surfaces of revolution:

To project the central point line that on sphere, all projections are enclosed as rotary shaft, successively from Q_yPoint Q is extracted in order in circle_{Y, i}With Rotary shaft forms plane, search adjacent circle Q_y+1Apart from the point that this plane is nearest on circle；From Q_yPoint Q is extracted in circle_{Y, i+1}With rotary shaft group Become plane, search adjacent circle Q_y+1Apart from the point that this plane is nearest on circle, then point Q_{Y, i}, point Q_{Y, i+1}Enclose Q with adjacent_y+1Search on circle The closure circle away from the nearest point composition of two adjacent planes respectively, be approximately a grid, be defined as optimum grid；

Wherein subscript y of Q is the sequence number of projection circle, y ∈ [1, Y]；I is the sequence number of the point on projection circle, and i ∈ [1, I], I are to throw Points in cinema-circle；

Make y initial value be 1, i initial value be 1, successively search extract on sphere all of optimum grid；

Step 4：Carry out the triangulation of sphere upslide cinema-circle based on optimum grid:

It is located at adjacent circle Q_y+1Search on circle respectively away from two nearest points of two adjacent planes be point Q_{Y+1, n}With point Q_{Y+1, m}；

If Q_{Y+1, n}And Q_{Y+1, m}For Q_y+1Adjacent two points on circle, then (Q_{Y+1, n}, Q_{Y+1, m}, Q_{Y, i}) constitute a triangle, (Q_{Y+1, m}, Q_{Y, i}, Q_{Y, i+1}) constitute a triangle；

If Q_{Y+1, n}And Q_{Y+1, m}For Q_y+1Same point on circle, then (Q_{Y, i}, Q_{Y, i+1}, Q_{Y+1, n}) constitute a triangle；

If Q_{Y+1, n}And Q_{Y+1, m}For Q_y+1Enclose two points of two non-conterminous points, then adopt centre position determining method to optimum grid Carry out triangulation, specifically：

Take the integer part of the value that p is (n+m)/2, point Q_{Y+1, p}It is point Q_{Y+1, n}With point Q_{Y+1, m}Intermediate position points；For point Q_{Y+1, x}, as n≤x<During p, (Q_{Y+1, x}, Q_{Y+1, x+1}, Q_{Y, i}) group triangularity；As x=p, (Q_{Y, i}, Q_{Y, i+1}, Q_{Y+1, x}) composition triangle Shape；Work as p<During x≤m, (Q_{Y+1, x}, Q_{Y+1, x-1}, Q_{Y, i+1}) group triangularity；Wherein subscript n, m, p, x are Q_y+1Point Q on circle_{Y+1, n}, Q_{Y+1, m}, Q_{Y+1, x}, Q_{Y+1, p}Sequence number；

In this manner, generate the triangle grid model of spherical projection point cloud；

Step 5：According to the projection corresponding relation of point cloud projection and actual measurement scanning element cloud, corresponding generation surveys scanning element cloud triangle Grid model.

2. the goaf laser scanning point cloud triangulation methodology based on the surfaces of revolution according to claim 1, its feature exists In, in described step 2, scan circle corresponding to all of projection circle and this projection circle enters row interpolation by the following method：

(1) calculate projection circle the distance between upper adjacent 2 points, if distance more than this punctuate between 1.5 times of average distance; recognize For there is point disappearance, need the new point P of insertion_N；

(2) calculate the distance between upper adjacent 2 points of projection circle, if on certain projection circle, adjacent 2 points of P₂And P₃The distance between big In 1.5 times of this average distance of punctuating, then in line segment P₂P₃On away from point P₂Distance be d₁Place insertion point P_N, wherein d₁For this circle Average distance between point, according to linear scale on this projection circle corresponding scanning circle, with line segment P₂P₃Corresponding line segment A₂A₃Upper slotting Enter new point A_N, insertion point A_NPosition meet linear ratio relation d₁：d₂=d₃：d₄, wherein d₂For line segment P_NP₃Length, d₃For Line segment A₂A_NLength, d₄For line segment A_NA₃Length.

3. the goaf laser scanning point cloud triangulation methodology based on the surfaces of revolution according to claim 1, its feature exists In probe scanning one circle obtains 320 340 points；After scanning through a circle, 5 degree of predetermined angle raised automatically by probe；Until Probe is lifted to 140 degree and completes whole detection operations.