Possible to speed up _parametric(::Tetrahedron) #145
Description
Background
I found in #139 that the performance of _parametric(::Triangle) improved by an order-of-magnitude by re-formulating the calculation to use fewer calls to Meshes.jl parametric functions. The original version used t2 to locate points along two edges of the triangle, generated a Segment between them, and then returns segment(t1) as the desired Point. The replacement version simply calculates the equivalent barycentric coordinates (u, v) for the same Point and then calls triangle(u, v).
The current formulation for _parametric(::Tetrahedron) similarly uses t3 to locate three points on the edges of the tetrahedron to form a triangular cross_section, then calls _parametric(cross_section::Triangle)(t1, t2) on it.
Idea
If we can implement something similar for Tetrahedron where the barycentric coordinates (u, v, w) are calculate directly and tetrahedron(u, v, w) is returned, we can expect to see a similarly impressive performance boost for integrals of tetrahedra.