3D Painting

is it possible to paint each single vertex of a 3d mesh (consisting of triangles).
does a method exit for finding a vertex, when i touch the mesh with the mouse.
i want to create a 3d painting application for a virtual environment.

It sounds like you want to do “picking” - convert screen coords (from mouse clicks) to object space coords. You’ll find lots of info here and elsewhere if you do a search.