## Collapse Edge

The Collapse Edge tool looks like this and is located on the Modify Tab of the Toolbar. The Collapse Edge tool operates on the end points of an edge. The direction of collapse is toward the second clicked point. Click the Collapse Edge button. Geodesica prompts you to pick the first point. Geodesica prompts you to pick the second point. The first point and the intervening edge are removed from the lattice. All edges leaving the first point now leave the second point. Fig. 1 Fig. 2

Fig 1: e is the edge to collapse, the direction of collapse being from 1 to 2.

Fig 2: edges q, r and s now leave the second point.

Note, fig 1: edges p and t, and the faces left and right of e are automatically removed from the lattice – otherwise there will be sliver faces and coincident edges at x and y. The rules governing removal are as follows: if the number of edges in face Left of e = 3, then edge p is removed. If the number of edges in face Right of e = 3, then edge t is removed. If removal of these edges violates the topology, 'Collapse Edge' will treat them the same as edges q, r and s. In which case the user is informed that coincident edges exist when the operation completes.

### Coincident Edges

When 'Collapse Edge' removes an edge, the test for coincident edges can fail in certain circumstances. Consider the following: Fig. 3 Fig. 4

Fig 3: e is the edge to collapse, the direction of collapse being from 1 to 2. However, the 'Divide Edge' tool has created new edges h, i, j and k. This means the faces left and right of e have four edges, not three. So 'Collapse Edge' will treat edges p and t as it did edges q, r, s in fig 2. This means edge p is now superimposed on edges h and i; and edge t is superimposed on j and k.

Fig 4: if you now try to use 'Make Edge' between v and w an error dialog informs you that point v does not belong to the same face as point w. This is because there is a sliver face which you cannot see. However, switching to the 'Select' tool and highlighting an edge can sometimes reveal the problem. Here the highlit edge is in fact p which can be deleted with the 'Kill Edge' tool. It is now safe to use 'Make Edge' between v and w.