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How do I cut a hole in the plane using the hollow line loop in the middle they're part of the same mesh and both 2d.

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You could convert your objects to curves and select 2D under the curve options. Doing this gives you a bit more flexibility as you can tweak the loop and see the changes as you do so. Use AltC > Curve from Mesh/Text to do this.

enter image description here

Once you are finished tweaking, convert back to a mesh with AltC > Mesh from Curve/Meta/... You will notice that the plane is triangulated. To clean this up, run a Limited Dissolve on the mesh.

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Done

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  • $\begingroup$ Can you explain why we always need this two edges from outer border to inner one? Is it blender specific? And why two not one? $\endgroup$ – Sukhanov Niсkolay Feb 25 '15 at 23:04
  • $\begingroup$ Thank you for limited dissolve. Thing is beautiful. $\endgroup$ – Qix - MONICA WAS MISTREATED Oct 5 '15 at 4:53
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This can be done using Knife Project, however for the case you show to work, you will have to use a recent Blender build, since improved knife support was added after 2.69 release.

To use Knife Project, in Object mode select the object you want to project (use and cut the other) first then Shift select the "object to be cut". Now Tab into Edit mode and press Knife project.

enter image description here enter image description here

Before projecting from a text object and Resulting knife projection.

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Another option is the Bridge tool.

  1. Delete the face of the plane (Delete> Only Faces)

  2. Select all and press W> Bridge Edge loops:

    enter image description here

Result:

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If you want to use ngons instead of tris, press Delete> Limited Dissolve:

enter image description here

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