Cavern Capacity Calculation Using Terrestrial Lidar

Fig. 1. Schematic of reconstructing convex hull by Graham scan algorithm. (a) Search for pole; (b) polar-angle based ordering; (c) elimination of internal points; (d)(e)(f) three sequential points form anticlockwise direction; (g) three sequential points form clockwise direction; (h) reconstructed convex hull

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Fig. 2. Distance from candidate point to edge of polygon. (a) ρ∈(-￥,0]; (b) ρ∈(0,1); (c) ρ∈[1,+￥)

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Fig. 3. Effect pictures of experimental data. (a) Size of cross section of cavern; (b) line-shaped point cloud fragment; (c)(d)(e) sizes of line-shaped, turning-shaped, and intersection-shaped point cloud fragments

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Fig. 4. Experimental results of contour point extraction. (a) Schematic of hierarchical projection; (b) detailed image of contour points

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Fig. 5. Experimental results of section contour point ordering (data are down-sampled for better visualization). (a)(b)(c) Polar-angle based ordering method; (d)(e)(f) our method

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Table 1. Parameter information of experimental data
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Table 1. Parameter information of experimental data
Data Number of points Average pointdensity /mm
Line-shape 981,837
Turning-shape 1,042,796 8
Intersection-shape 1,836,865

Table 2. Experimental parameters
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Table 2. Experimental parameters
Stage Parameter Value
Point cloud slicing h_U/cm 4
h_L/cm 10
Contour point extraction ε /mm 1
r/mm 8

Table 3. Comparison between polar-angle based ordering method and our method
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Table 3. Comparison between polar-angle based ordering method and our method
Data Numberof points Number of pointswith wrong order
Polar-anglebased ordering Ours
Line-shape 1,345 20
Turning-shape 1,148 213 0
Intersection-shape 2,610 1,039

Table 4. Area table of line-shaped data

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Table 4. Area table of line-shaped data

Height /m	Area of cross sections /m²			Relative error /%
Height /m	Ground truth	Trigonometric method	Ours	Trigonometric method	Ours
0.5	36.105	36.103	36.105	0.006	0
1.0	36.208	36.204	36.205	0.011	0.008
1.5	36.030	36.040	36.035	0.028	0.014
2.0	35.466	35.472	35.469	0.017	0.008
2.5	28.746	28.750	28.749	0.014	0.010

Table 5. Area table of turning-shaped data

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Table 5. Area table of turning-shaped data

Height /m	Area of cross sections /m²			Relative error /%
Height /m	Ground truth	Trigonometric method	Ours	Trigonometric method	Ours
0.5	43.839	43.950	43.846	0.253	0.016
1.0	43.874	43.994	43.874	0.274	0
1.5	43.881	43.914	43.867	0.075	0.032
2.0	43.065	44.127	43.068	2.466	0.007
2.5	34.114	35.117	34.109	2.940	0.015

Table 6. Area table of intersection-shaped data

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Table 6. Area table of intersection-shaped data

Height /m	Area of cross sections /m²			Relative error /%
Height /m	Ground truth	Trigonometric method	Ours	Trigonometric method	Ours
0.5	67.061	79.039	67.073	17.861	0.018
1.0	66.966	79.055	66.975	18.052	0.013
1.5	66.791	79.196	66.785	18.573	0.009
2.0	66.902	79.047	66.906	18.153	0.006
2.5	53.924	67.249	53.920	24.711	0.007

Table 7. Capacity table of three experimental data

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Table 7. Capacity table of three experimental data

Height /m	Line-shaped data			Turning-shaped data			Intersection-shaped data
Height /m	Ours /m³	Groundtruth /m³	Relativeerror /%	Ours /m³	Groundtruth / m³	Relativeerror /%	Ours /m³	Groundtruth /m³	Relativeerror /%
0.50	18.019	18.019	0	21.879	21.878	0.005	33.532	33.530	0.006
0.75	27.055	27.054	0.004	32.840	32.840	0	50.286	50.284	0.004
1.00	36.107	36.105	0.006	43.804	43.805	0.002	67.038	67.035	0.004
1.25	45.146	45.144	0.004	54.771	54.772	0.002	83.771	83.766	0.006
1.50	54.165	54.163	0.004	65.742	65.743	0.002	100.482	100.477	0.005
1.75	63.169	63.166	0.005	76.705	76.707	0.003	117.169	117.163	0.005
2.00	72.124	72.122	0.003	87.625	87.629	0.005	133.958	133.953	0.004
2.25	80.729	80.728	0.001	97.992	97.999	0.007	150.186	150.184	0.001
2.50	88.480	88.480	0	107.257	107.268	0.010	164.773	164.773	0

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Xiaojun Cheng, Xinxin Xiong, Zexin Yang, Rongqi Yang. Cavern Capacity Calculation Using Terrestrial Lidar[J]. Laser & Optoelectronics Progress, 2019, 56(23): 231201

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