A second method of mesh generation is the Delaunay triangulation strategy.
Given a two- or three-dimensional set of points which define the boundaries
and interior regions of the domain to be modeled, one tessellates the point
cloud into an optimal mesh of triangles or tetrahedra. For bioelectric
field problems, the advantages and disadvantages tend to be exactly
contrary to those arising from the divide and conquer strategy. The
primary advantage is that the mesh can be developed to fit any predefined
geometry, including subsurfaces, by starting with points which define all
the necessary surfaces and subsurfaces and then adding additional interior
points to minimize the aspect ratio. For triangles, the aspect ratio is
defined to be either the ratio of the maximum horizontal length of the
element to the maximum vertical length of the element, or the ratio of the
diameter of a circumscribed circle to the maximal distance between
vertices. For tetrahedra, the aspect ratio can be defined as
where 
denotes the
diameter of the sphere circumscribed about the tetrahedron and 
is
the maximum distance between two vertices. These formulations yield a
value of 1 for an ``isosceles'' tetrahedron (triangle) and a value of 0 for
a degenerate (flat) element [22]. The closer to the value of
1, the better (it should be noted that this is not a general rule for all
problems: in certain problems where there are very high gradients in a
uniform direction, as in high speed fluid flow, for example, it is often
better to distort the aspect ratio of the element to take into account this
phenomena).
