Algorithm 1 Last Resort Flowchart
1:	Last_Resort_Algorithm(Ψi,ηe)
2:	Ψi ← Boundary surface
3:	ηe ← Minimum desired element quality
4:	Output: PotentialMeshj
5:	if Ψi has only 4 remaining faces then
6:	Form the tetrahedral element e
7:	PotentialMeshj ← e
8:	return PotentialMeshj
9:	end if
10:	for all Faces, Fi, in current boundary surface Ψi do
11:	if Fi can produce at least one acceptable tetrahedron whose quality q > ηe then
12:	Ni ← number of possible tetrahedrons
13:	if Ni < Nmin then
14:	Nmin← Ni
15:	Insert Fi to the top of Listfaces stack and push all the current faces down
16:	end if
17:	else
18:	return NULL
19:	end if
20:	end for
21:	while Listfaces ≠ ∅ do
22:	Pick the face from top of the Listfaces stack andform its best tetrahedron e
23:	Update Ψi boundary surface based on insertion of element e
24:	Assign the new boundary to ψi
25:	Call M ← Last_Resort_Algorithm(ψi,ηe)
26:	if M is not NULL then
27:	PotentialMeshj = PotentialMeshj ∪ M
28:	return PotentialMeshj
29:	else
30:	Remove the top enitity in Listfaces stack and continue
31:	end if
32:	end while
33:	return NULL