projectionOnSegment.h

    // https://github.com/libigl/libigl/blob/master/include/igl/project_to_line.cpp
    auto projectionOnSegment = [&](const Vector3 & p, const Vector3 & s, const Vector3 & d){
        Real px = p[0], py = p[1], pz = p[2];
        Real sx = s[0], sy = s[1], sz = s[2];
        Real dx = d[0], dy = d[1], dz = d[2];
        Real dms[3], smp[3];
        dms[0] = dx-sx; dms[1] = dy-sy; dms[2] = dz-sz;
        Real v_sqrlen = dms[0]*dms[0] + dms[1]*dms[1] + dms[2]*dms[2]; assert(v_sqrlen != 0);
        smp[0] = sx-px; smp[1] = sy-py; smp[2] = sz-pz;
        t = -(dms[0]*smp[0]+dms[1]*smp[1]+dms[2]*smp[2])/v_sqrlen;
        return t;
    };