Stefan Röttger MedicalVisualization/Marching Tetrahedra Cases

Marching Tetrahedra Cases

Classification of corner points into greater than (+) or smaller as (-) the iso value $c_{iso}$ .

A edge with changing (+ -) classification intersects the iso surface.
For a tetrahedron exist only 2 non-symmetrical cases (compared to 16 for hexahedra):

The intersection point $\vec{p}$ on an edge with the two end points $\vec{a}$ and $\vec{b}$ and the scalar values $s_a$ und $s_b$ is

$\vec{p}= \frac{s_b-c_{iso}}{s_b-s_a}\vec{ a } + \frac{c_{iso}-s_a}{s_b-s_a}\vec{ b }$