Barycentric coordinates of a tetrahedron

Question

I would like to ask for help regarding barycentric coordinates of a tetrahedron:

Following an approach I found here: http://www.cdsimpson.net/2014/10/barycentric-co

Answer 1

Blind guess:

Vec4f bary_tet(const Vec3f & a, const Vec3f & b, const Vec3f & c, const Vec3f & d, const Vec3f & p)
{
    Vec3f vap = p - a;
    Vec3f vbp = p - b;

    Vec3f vab = b - a;
    Vec3f vac = c - a;
    Vec3f vad = d - a;

    Vec3f vbc = c - b;
    Vec3f vbd = d - b;
    // ScTP computes the scalar triple product
    float va6 = ScTP(vbp, vbd, vbc);
    float vb6 = ScTP(vap, vac, vad);
    float vc6 = ScTP(vap, vad, vab);
    float vd6 = ScTP(vap, vab, vac);
    float v6 = 1 / ScTP(vab, vac, vad);
    return Vec4f(va6*v6, vb6*v6, vc6*v6, vd6*v6);
}