A technique for conforming an interface between a first mesh and a second mesh is disclosed. A first interface surface in the first mesh and a second interface surface in the second mesh residing along the interface are identified. The first and second interface surfaces are initially non-conforming along the interface. Chords within the first and second interface surfaces that fall within a threshold separation distance of each other are paired. Sheets having chords that reside within the first or second interface surfaces are recursively inserted into or extracted from one or both of the first and second meshes until all remaining chords within the first interface surface are paired with corresponding chords in the second interface surface and all remaining chords within the second interface surface are paired with corresponding chords in the first interface surface.