Algorithm 1 The algorithm to find edge lines at orthogonal plane intersections within the point cloud.
EdgeExtraction(M)
	Input:
	M : Point cloud.
	Output:
	E: 3D lines.
1:	D ← ø
2:	for each pi ∈ M do
3:	Ni ← FindNeighbors(pi, M)
4:	ni ← ComputeNormal(pi, Ni)
5:	Label(pi) ← i
6:	D ← D ⋃ FindDistances(pi, Ni)
7:	end for
8:	D ← SortDistances(D)
9:	for each dk ∈ D do
10:	ci ← Start(dk)
11:	cj ← End(dk)
12:	if Label(ci) ≠ Label(cj) then
13:	if $|{cos}^{-1}({\mathbf{\text{n}}}_i^T{\mathbf{\text{n}}}_j)|<t_c$ then
14:	if $\frac{k_i\left|{(c_i-c_j)}^T{\mathbf{\text{n}}}_j\right|+k_j\left|{({\mathbf{\text{c}}}_j-{\mathbf{\text{c}}}_i)}^T{\mathbf{\text{n}}}_i\right|}{k_i+k_j}<t_d$ then
15:	MergeTrees(ci, cj)
16:	end if
17:	end if
18:	end if
19:	end for
20:	E ← ø
21:	L ← Labels(M)
22:	for each pair of segments (si, sj) ∈ L with respective (ni, nj) do
23:	if Orthogonal(ni, nj) then
24:	E ← E ⋃ PlaneIntersection(ni, nj)
25:	end if
26:	end for