**
Generation of Semi-Structured Meshes**

over Generalized Extruded Volumes

**
Daniel Rypl
**

Department of Mechanics

Faculty of Civil Engineering

Czech Technical University in Prague

Thákurova 7, 166 29 Prague, Czech Republic

### Abstract:

Sweeping is a common method for the generation of structured and semi-structured
meshes over extrusion volumes. Traditional sweeping techniques are
based on propagating a surface mesh layer by layer along a particular control curve.
Each layer of the extruded mesh is thus bounded by the same
surface mesh, possibly subjected to rigid body motion.
The present work enhances the traditional method by
considering geometrical evolution of the extruded surface mesh during
the sweeping. Thus each layer of the resulting mesh is bounded by
meshes that are still topologically identical but geometrically only
similar. This enables to generate semi-structured meshes over
generalized extrusion volumes formed by two opposite geometrically
similar and topologically identical cap surfaces and set of lateral
quad-mappable surfaces. The source cap surface is discretized by an
appropriate unstructured surface mesh which is projected onto the target cap surface using
an affine mapping defined between the parametric spaces of the cap
surfaces. This mapping is established by a least-squares fit of
boundary nodes on the target surface. The structured quad meshes on
lateral surfaces are obtained by transfinite interpolation. The volume
interior nodes used to form inner layer of elements are defined by the mapping
derived from a least-squares approximation of all boundary
nodes. The obtained mesh is then subjected to a specific two-phase
smoothing.