Colored coincident surface display problem

As shown in the figure, the three colored surfaces partially overlap. It appears weird.
How can i avoid this?

This may help:

Hello,Andras lasso.This link seems to have failed.

The archive on nabble seems to be gone, but you can use this page instead: [vtkusers] Coincident topology questions

Hello,Andras lasso.Is there a similar package in VTK? Just like the content in the link.OpenGL Tessellation

Check out vrkTriangleFilter, it probably does what you need.