for Triangulation of 3D Surfaces

** Daniel Rypl, Zdenek Bittnar
Department of Structural Mechanics
Faculty of Civil Engineering
Czech Technical University in Prague
Thákurova 7, 166 29 Prague, Czech Republic**

The present paper deals with the generation of computational meshes over 3D
surfaces described by discrete data in the form of a triangular grid of
arbitrary topology. This may be a deformed finite element mesh from
the previous step of an analysis, grid obtained from computer
tomography, digital representation of terrain, grid representing
a surface in stereolithography (STL) format etc. The new computational mesh is
generated over a smooth surface that is topologically and geometrically
similar to the underlying piecewise planar control grid. The
recovery of the smooth surface is performed using a recursive
subdivision technique based on hierarchical refinement of
triangular simplices forming the control grid. In the present
approach, the interpolating subdivision based on the modified
Butterfly scheme, yielding continuous surface even in the topologically
irregular setting of the control grid, is adopted. With respect to the
application to STL meshes, the modified Butterfly scheme was subjected
to slight amendments in order to make the recovered surface
more regular in situations where the original strategy seemed to be not
enough flexible. The actual discretization is accomplished using the
advancing front technique operating directly on the surface. This
avoids difficulties with construction of smooth parameterization of
the whole surface. The crucial aspect of the discretization is the
projection algorithm, required to comply with the surface constraint,
which must be reliable, efficient, and accurate. The adopted
projection technique is based on local progressive refinement
(subdivision) of the control grid. To overcome its high computational
demands, an approximate but computationally more efficient projection, based on
projection to a parametric triangular patch used to approximate the
recovered smooth surface over individual elements of the control grid,
is applied during the some stages of the mesh generation process. The
capability of the proposed methodology is demonstrated
on a few examples.

- Introduction
- Smooth Surface Recovery
- Limit Surface Triangulation
- Implementation Issues
- Examples
- Conclusions
- Acknowledgments
- Bibliography
- Figures

*Daniel Rypl
2005-12-08*