Surface
Mesh Overlay
The objective of this project is to develop efficient and reliable
algorithms
for constructing a common refinement (a.k.a. common tesselation) of two
nonmatching surface meshes that discretize the same 2-manifold with or
without boundary. The construction of a common refinement defines a
continuous and one-to-one mapping between the surfaces defined by two
meshes and then allow transferring data between the meshes accurately
and
conservatively. Two nonmatching meshes in general have different
topological
structures and potentially different geometric realizations. Further
complications arise for surfaces with boundary where the boundary of
the two meshes may mismatch and for surfaces that have sharp edges and
corners.
We construct the common refinement by overlaying them on top of each
other.
In a nutshell, the overlay algorithm takes two
surface meshes as input, computes intersections of edges from the two
meshes.
These edge intersections are sorted in their parent edges and connected
to
form the polygons of the overlay mesh. To define the intersection of
two
edges from different surfaces, we introduce a conforming homeomorphism
concept. The algorithm outputs a polygonal mesh which subdivides both
input meshes.
The following examples illustrate the objective and the capabilities
of our algorithm. We color the input meshes in blue and green. Due to
discretization and/or round-off errors, the meshes may have gaps in
between or interpenetrate each other.
Example 0. Overlay of surfaces of a tetrahedron and a cube.
(1) Realization of overlay in the tetrahedron.
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(2) Realization of overlay in the cube.
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Example 1. Overlay of two triangulations of a cuboctohedron.
Example 2. Overlay of two triangulations of a star grain.
Example 3. Overlay of on an engine nacelle of falcon aircraft.
(1) Realization of overlay in the coarse mesh.
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(2) Realization of overlay in the fine mesh.
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Publications