Add Vertex 
Add a Vertex
Use the Add Vertex option to insert a vertex into a triangulation. The triangles created by adding a point inside an existing triangle will automatically be added to the triangulation.
Figure 1: The Original Triangulation
Figure 2: After a Vertex has been Added
Note: This option cannot be used to add new points outside the triangulation boundary. Use the Insert Triangle option to insert points outside the triangulation.
Instructions
On the Model menu, point to Triangle Surface, and then click Add Vertex.
Select the triangulation. The triangulation model will be selected automatically if there is only one loaded onscreen.
Select the point to add as a vertex. Use the Snap to Objects,
Snap to Points or
Keyboard Input modes to ensure accurate placement.
The triangles created by the addition of the vertex are then displayed. You will then be asked to confirm the change.
Select another point to add as a vertex. Cancel when you have finished adding vertices.