I want to join two meshes in a way that creates one continuous suface, eliminating all parts of the meshes where they intersect, and cutting new faces along their intersection lines to manage the intersection.
Here is a simplified version of the concept:
You have Mesh A, and Mesh B, and I would like to create a continuous mesh as you can see under the 'Yes'. I do not want to join them so they are still intersecting, as you would do with the standard 'join' feature.
This mockup was created manually, however just doing it by hand is not an option for me since the actual meshes I want to work on are very complex.
It should be a simple concept to automate though, just create new vertices where the edges of the other mesh intersect the faces of the mesh and connect these to existing parts of the mesh, delete parts of the mesh that are inside the other, do this for both/all meshes and then join the vertices of the newly cut meshes into one continuous surface.
Is there a way to join meshes like this in blender?
What you are discussing is called Constructive Solid Geometry (CSG) and is a common feature in CAD programs. Blender is not a CAD program and CSG or boolean operations is not its strongest feature.
Often times, you are better off creating the necessary edges and faces by hand using Blender's mesh operations.
I was looking for this for a while too. It's the Boolean modifier.
Have the cylinder and cube as separate objects.
It'll probably be set to intersection by default. You want union.
In "object" select the other object from the list.