Actually, is keeping track of how all the four vertices form the triangles of the tetrahedron (the matrix with header i,j,k) necessary here? Is there another way to form a tetrahedron in a 3D space if all the vertices are given?
To make sure I understand, the purpose of barycentric coordinates here is to provide an explicit formula for generating all the points within a given triangle, in terms of the basis formed by the three points of that triangle.
Does using this much space for storage slow down the computations we perform?
If we're just drawing the outline of a surface with a mesh why is keeping track of the bayrcentric coordinates important?