/* 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;
}
template <class QMType> inline
void TMPQualityMetricTest<QMType>::test_evaluate_3D()
{
MsqPrintError err(cout);
PatchData pd;
bool rval;
double value;
QMType m( &ideal, &faux_two );
// test with aligned elements
faux_two.count = 0;
tester.get_ideal_element( HEXAHEDRON, true, pd );
rval = m.evaluate( pd, 0, value, err );
CPPUNIT_ASSERT(!MSQ_CHKERR(err));
CPPUNIT_ASSERT(rval);
CPPUNIT_ASSERT_DOUBLES_EQUAL( faux_two.value, value, DBL_EPSILON );
CPPUNIT_ASSERT_EQUAL( 1, faux_two.count );
// test that columns are orthogonal for ideal hex element
MsqMatrix<3,3> A = faux_two.last_A_3D;
CPPUNIT_ASSERT_DOUBLES_EQUAL( 0.0, A.column(0) % A.column(1), 1e-6 );
CPPUNIT_ASSERT_DOUBLES_EQUAL( 0.0, A.column(0) % A.column(2), 1e-6 );
CPPUNIT_ASSERT_DOUBLES_EQUAL( 0.0, A.column(1) % A.column(2), 1e-6 );
// test with rotated element
faux_two.count = 0;
tester.get_ideal_element( TETRAHEDRON, true, pd );
// rotate by 90-degrees about X axis
for (size_t i = 0; i < pd.num_nodes(); ++i) {
Vector3D orig = pd.vertex_by_index(i);
Vector3D newp( orig[0], -orig[2], orig[1] );
pd.set_vertex_coordinates( newp, i, err );
}
rval = m.evaluate( pd, 0, value, err );
CPPUNIT_ASSERT(!MSQ_CHKERR(err));
CPPUNIT_ASSERT(rval);
CPPUNIT_ASSERT_DOUBLES_EQUAL( faux_two.value, value, DBL_EPSILON );
CPPUNIT_ASSERT_EQUAL( 1, faux_two.count );
}
void test_3d_eval_ortho_hex()
{
MsqPrintError err(cout);
PatchData pd;
bool rval;
double value;
QMType m( &ideal, &faux_zero );
faux_zero.count = 0;
tester.get_ideal_element( HEXAHEDRON, true, pd );
rval = m.evaluate( pd, 0, value, err );
CPPUNIT_ASSERT(!MSQ_CHKERR(err));
CPPUNIT_ASSERT(rval);
CPPUNIT_ASSERT_EQUAL( 1, faux_zero.count );
// test that columns are orthogonal for ideal hex element
MsqMatrix<3,3> A = faux_zero.last_A_3D;
CPPUNIT_ASSERT_DOUBLES_EQUAL( 0.0, A.column(0) % A.column(1), 1e-6 );
CPPUNIT_ASSERT_DOUBLES_EQUAL( 0.0, A.column(0) % A.column(2), 1e-6 );
CPPUNIT_ASSERT_DOUBLES_EQUAL( 0.0, A.column(1) % A.column(2), 1e-6 );
}
bool LambdaTarget::get_surface_target( PatchData& pd,
size_t element,
Sample sample,
MsqMatrix<3,2>& W_out,
MsqError& err )
{
bool valid = lambdaSource->get_surface_target( pd, element, sample, W_out, err );
if (MSQ_CHKERR(err) && !valid)
return false;
MsqVector<3> cross = W_out.column(0) * W_out.column(1);
double det1 = cross % cross; // length squared
valid = compositeSource->get_surface_target( pd, element, sample, W_out, err );
if (MSQ_CHKERR(err) && !valid)
return false;
cross = W_out.column(0) * W_out.column(1);
double det2 = cross % cross; // length squared
if (det2 < 1e-15)
return false;
W_out *= sqrt( sqrt( det1/det2 ) );
return true;
}
