"Ensure integrity of the mesh" in the Points + Triangles representation means that, because all vertices are stored in a single data structure, if we change the position of a vertex, we only need to update it in that data structure (as opposed to the Triangles representation, where we will have to search for and edit all triangles which share that vertex).
Michael-hsiu
It seems that updating a vertex with Triangle representation is O(N), where N is the # of triangles in the mesh, while updating a vertex with Points+Triangle representation is O(1), since we are just editing a single entry in the vertex table.
"Ensure integrity of the mesh" in the Points + Triangles representation means that, because all vertices are stored in a single data structure, if we change the position of a vertex, we only need to update it in that data structure (as opposed to the Triangles representation, where we will have to search for and edit all triangles which share that vertex).
It seems that updating a vertex with Triangle representation is O(N), where N is the # of triangles in the mesh, while updating a vertex with Points+Triangle representation is O(1), since we are just editing a single entry in the vertex table.