### Boundary recognition

#### by Yi Zhang

Based on the idea of alpha shape, one can devise a boundary recognition scheme by eliminating the elements whose circumsphere contains no nodes which are within the boundary. This means, first one must have those nodes identified, then those nodes and the coefficient (defines the extended version of circumsphere) are used for boundary recognition. Here is a example of identifying the boundary of those nodes lying inside a cube but outside its inscribed sphere.

The first four plots show original meshed cube with inside view, the next six plots are when elements inside the sphere are eliminated. The rest is what we have when we change , i.e. the coefficient determining whether one tetrahedron should be eliminated because its extended circumsphere, whose radius depends on , contains nodes within the boundary. Here is reduces, resulting in more elements erased from the picture.

Great Blog!……There’s always something here to make me laugh…Keep doing what ya do 🙂

These figures are very beautiful! May I know what software you used to generate these figures?

They are from the mesh viewer with tetgen, a free 3D tetrahedron mesh generator.