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

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

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

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

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

Table 1. Parameter information of experimental data

Table 2. Experimental parameters

Table 3. Comparison between polar-angle based ordering method and our method

Table 4. Area table of line-shaped data

Table 5. Area table of turning-shaped data

Table 6. Area table of intersection-shaped data

Table 7. Capacity table of three experimental data