void JacobianCalculator::get_Jacobian_3D( const MappingFunction3D* mf,
NodeSet ho_bits,
Sample location,
const Vector3D* verts,
size_t num_type_vert,
MsqMatrix<3,3>& J_out,
MsqError& err )
{
size_t num_vtx = 0;
mf->derivatives( location, ho_bits, mIndices, mDerivs3D, num_vtx, err ); MSQ_ERRRTN(err);
mf->convert_connectivity_indices( num_type_vert, mIndices, num_vtx, err ); MSQ_ERRRTN(err);
const MsqVector<3>* d = mDerivs3D;
const size_t* const e = mIndices + num_vtx;
Vector3D c[3] = {Vector3D(0,0,0), Vector3D(0,0,0), Vector3D(0,0,0)};
for (const size_t* i = mIndices; i != e; ++i, ++d) {
c[0] += (*d)[0] * verts[*i];;
c[1] += (*d)[1] * verts[*i];;
c[2] += (*d)[2] * verts[*i];;
}
J_out.set_column( 0, MsqMatrix<3,1>(c[0].to_array()) );
J_out.set_column( 1, MsqMatrix<3,1>(c[1].to_array()) );
J_out.set_column( 2, MsqMatrix<3,1>(c[2].to_array()) );
}
/* Do transform M_hat = S_a M_{3x2}, M_{2x2} Theta^-1 M_hat
* where the plane into which we are projecting is orthogonal
* to the passed u vector.
*/
static inline bool
project_to_perp_plane( MsqMatrix<3,2> J,
const MsqVector<3>& u,
const MsqVector<3>& u_perp,
MsqMatrix<2,2>& A,
MsqMatrix<3,2>& S_a_transpose_Theta )
{
MsqVector<3> n_a = J.column(0) * J.column(1);
double sc, len = length(n_a);
if (!divide(1.0, len, sc))
return false;
n_a *= sc;
double ndot = n_a % u;
double sigma = (ndot < 0.0) ? -1 : 1;
double cosphi = sigma * ndot;
MsqVector<3> cross = n_a * u;
double sinphi = length(cross);
MsqMatrix<3,2> Theta;
Theta.set_column(0, u_perp);
Theta.set_column(1, u*u_perp);
// If columns of J are not in plane orthogonal to u, then
// rotate J such that they are.
if (sinphi > 1e-12) {
MsqVector<3> m = sigma * cross;
MsqVector<3> n = (1/sinphi) * m;
MsqVector<3> p = (1-cosphi) * n;
double s_a[] =
{ p[0]*n[0] + cosphi, p[0]*n[1] - m[2], p[0]*n[2] + m[1],
p[1]*n[0] + m[2], p[1]*n[1] + cosphi, p[1]*n[2] - m[0],
p[2]*n[0] - m[1], p[2]*n[1] + m[0], p[2]*n[2] + cosphi
};
MsqMatrix<3,3> S_a(s_a);
J = S_a * J;
S_a_transpose_Theta = transpose(S_a) * Theta;
}
else {
S_a_transpose_Theta = Theta;
// J *= sigma;
}
// Project to get 2x2 A from A_hat (which might be equal to J)
A = transpose(Theta) * J;
return true;
}
bool AffineMapMetric::evaluate( PatchData& pd, size_t handle, double& value, MsqError& err )
{
Sample s = ElemSampleQM::sample( handle );
size_t e = ElemSampleQM:: elem( handle );
MsqMeshEntity& elem = pd.element_by_index( e );
EntityTopology type = elem.get_element_type();
unsigned edim = TopologyInfo::dimension( type );
const size_t* conn = elem.get_vertex_index_array();
// This metric only supports sampling at corners, except for simplices.
// If element is a simpex, then the Jacobian is constant over a linear
// element. In this case, always evaluate at any vertex.
//unsigned corner = s.number;
if (s.dimension != 0) {
if (type == TRIANGLE || type == TETRAHEDRON)
/*corner = 0*/;
else {
MSQ_SETERR(err)("Invalid sample point for AffineMapMetric", MsqError::UNSUPPORTED_ELEMENT );
return false;
}
}
bool rval;
if (edim == 3) { // 3x3 or 3x2 targets ?
Vector3D c[3] = { Vector3D(0,0,0), Vector3D(0,0,0), Vector3D(0,0,0) };
unsigned n;
const unsigned* adj = TopologyInfo::adjacent_vertices( type, s.number, n );
c[0] = pd.vertex_by_index( conn[adj[0]] ) - pd.vertex_by_index( conn[s.number] );
c[1] = pd.vertex_by_index( conn[adj[1]] ) - pd.vertex_by_index( conn[s.number] );
c[2] = pd.vertex_by_index( conn[adj[2]] ) - pd.vertex_by_index( conn[s.number] );
MsqMatrix<3,3> A;
A.set_column( 0, MsqMatrix<3,1>(c[0].to_array()) );
A.set_column( 1, MsqMatrix<3,1>(c[1].to_array()) );
A.set_column( 2, MsqMatrix<3,1>(c[2].to_array()) );
if (type == TETRAHEDRON)
A = A * TET_XFORM;
MsqMatrix<3,3> W;
targetCalc->get_3D_target( pd, e, s, W, err ); MSQ_ERRZERO(err);
rval = targetMetric->evaluate( A * inverse(W), value, err ); MSQ_ERRZERO(err);
}
else {
Vector3D c[2] = { Vector3D(0,0,0), Vector3D(0,0,0) };
unsigned n;
const unsigned* adj = TopologyInfo::adjacent_vertices( type, s.number, n );
c[0] = pd.vertex_by_index( conn[adj[0]] ) - pd.vertex_by_index( conn[s.number] );
c[1] = pd.vertex_by_index( conn[adj[1]] ) - pd.vertex_by_index( conn[s.number] );
MsqMatrix<3,2> App;
App.set_column( 0, MsqMatrix<3,1>(c[0].to_array()) );
App.set_column( 1, MsqMatrix<3,1>(c[1].to_array()) );
MsqMatrix<3,2> Wp;
targetCalc->get_surface_target( pd, e, s, Wp, err ); MSQ_ERRZERO(err);
MsqMatrix<2,2> A, W;
MsqMatrix<3,2> RZ;
surface_to_2d( App, Wp, W, RZ );
A = transpose(RZ) * App;
if (type == TRIANGLE)
A = A * TRI_XFORM;
rval = targetMetric->evaluate( A*inverse(W), value, err ); MSQ_ERRZERO(err);
}
// apply target weight to value
if (weightCalc) {
double ck = weightCalc->get_weight( pd, e, s, err ); MSQ_ERRZERO(err);
value *= ck;
}
return rval;
}
