Hi Tom, make sure that your surfaces are joined so that there is a shared edge between them.
When there are joined edges MoI will do some extra work to ensure that the generated mesh is "watertight" and has no gaps or holes between the meshes created for different surfaces.
If you don't want any triangles in the generated mesh, you can make that happen by using the "Output: N-gons" option at mesh export time, that will create multi-sided polygons at trimming boundaries instead of any triangles. But be aware that some polygon mesh programs cannot deal with n-gons very well. Modo, Lightwave, Cinema4D, Softimage, and 3DS Max (with FBX format) can typically handle them well though. So if having no triangles is important to you, you might try using one of these programs that can handle n-gons well.
Since you didn't post an example image, I can't be exactly 100% sure what you are asking specifically about, but maybe you are also asking about having the underlying UV grid of each surface be completely aligned with one another - that can only happen in certain cases where the surfaces have the same size and share a natural trim edge.
If the surfaces have completely different UV spaces, then there isn't really any way for the mesh to have the exact same UV quad grid on each one, in those cases you will get n-gons at trimming edges and not simple quads.
In order to avoid that you would need to alter the way the model has been created, to make surfaces the same size along those areas and have the same UV layout.
Here are some previous discussions which may help to explain:
http://moi3d.com/forum/index.php?webtag=MOI&msg=1536.30
http://moi3d.com/forum/index.php?webtag=MOI&msg=1016.2
http://moi3d.com/forum/index.php?webtag=MOI&msg=2451.42
http://moi3d.com/forum/index.php?webtag=MOI&msg=1536.33
In the future I do want to experiment with some different meshing strategies, but it is a very difficult and time consuming area to work on so it may take a while.
In the meantime, just be aware that the mesher is not able to use things like human judgment or artificial intelligence, so it may not always produce the same kind of a thing that a human would. It tends to produce the cleanest output and UV quad alignment with mechanical type shapes, things like cylinders and spheres that have straight cuts on them.
Another possibility which can be effective if you want to have a particular mesh topology is to use a retopology tool like TopoGun (
http://www.topogun.com/). Also 3D-Coat (
http://www.3d-coat.com/) has a good set of retopology tools.
- Michael