Table 1.

Definition of geometric constraints parameters

Equation	Symbol	Definition
9	ϕ i	Propagation direction of fragment i.
9	ϕ j	Propagation direction of fragment j.
9	D	The function that calculates the orientation difference between ϕi and the reverse direction of ϕj.
9	ϕ max	The maximum allowable difference between ϕi and the reverse direction of ϕj.
10	d i,j	The magnitude of the distance vector between i and j.
10	d max	The maximum allowable gap length.
11	φ i,j	The direction of the distance vector pointing from i to j.
11	ψ max	The maximum allowed direction mismatch between the fragment i and distance vector.
12	ϕ am	The propagation direction of the tip of bridging fragment m close to fragment i.
13	φ ai,m	The distance vector between fragment i and the its closest tip of fragment m.
14	ϕ bm	The propagation direction of the tip of bridging fragment m close to fragment j.
15	φ bj,m	The distance vector between fragment j and the its closest tip of fragment m.
16	C i	Eligibility cost for connecting the base terminus and its ith partner tips.
16	C angle_weight	Weight for similarity criterion.
16	C gap_weight	Weight for continuity criterion.
16	Δ θ i	Difference for similarity.
16	Δ θ gapi	Difference for continuity.