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HandleEndVertex(<tex>v_{i}</tex>)
if (Type_of_vertex(<tex>helper(e_{i-1})</tex> = 'merge') Insert edge(<tex>v_{i}</tex>, <tex>helper(e_{i-1})</tex>) in <tex>D</tex>
Delete <tex>e_{i-1}</tex> from <tex>T</tex>
HandleMergeVertex(<tex>v_{i}</tex>)
if (Type_of_vertex(<tex>helper(e_{i-1})</tex> = 'merge') Insert edge(<tex>v_{i}</tex>, <tex>helper(e_{i-1})</tex>) in <tex>D</tex>
Delete <tex>e_{i-1}</tex> from <tex>T</tex>
edge <tex>e_j</tex> = <tex>l \cap P</tex>
if (interior of <tex>P</tex> lies to the right of <tex>v_{i}</tex>)
then
if (Type_of_vertex(<tex>helper(e_{i-1})</tex> = 'merge') Insert edge(<tex>v_{i}</tex>, <tex>helper(e_{i-1})</tex>) in <tex>D</tex>
Delete <tex>e_{i-1}</tex> from <tex>T</tex>
Insert <tex>e_{i}</tex> in <tex>T</tex>
