I have a triangular mesh that has 1038458 polygons, 517817 points, 1557687 edges. During the simplification process, I am getting the message that there are 1092 disconnected vertices, 516725 connected vertices. Because of disconnected components, the simplification is not improving as expected Using VTK how can I check which vertices are disconnected and color them so I can visualize them clearly and can dig into them.

When I applied the feature edges. It shows a lot of coloring of feature edges. Which feature should I use to see the disconnected vertices? And how to resolve that problem?

Boundary edges are used by exactly one polygon, or defined by a line cell.

Feature edges are shared by two polygons and whose dihedral angle > featureAngle.

Manifold edges are shared by exactly two polygons.

Non-manifold edges are shared by three or more polygons.

If the sum of boundary edges (1) and non-manifold edges (4) is greater than zero, then the geometry does not define a closed surface.

So for a “pure surface” with no expected internal geometry, to find extraneous junk I turn on only boundary edges; to find pathological connections, I turn on only non-manifold edges. From the edges you can chase back into the points or whatever and diagnose the appropriate bits.