double
FEI3dTetQuad :: surfaceEvalNormal(FloatArray &answer, int isurf, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
{
IntArray snodes(3);
FloatArray a,b;
this->computeLocalSurfaceMapping(snodes, isurf);
double l1, l2, l3;
l1 = lcoords.at(1);
l2 = lcoords.at(2);
l3 = 1.0 - l1 - l2;
FloatArray dNdxi(6), dNdeta(6);
dNdxi(0) = 4.0 * l1 - 1.0;
dNdxi(1) = 0.0;
dNdxi(2) = -1.0 * ( 4.0 * l3 - 1.0 );
dNdxi(3) = 4.0 * l2;
dNdxi(4) = -4.0 * l2;
dNdxi(5) = 4.0 * l3 - 4.0 * l1;
dNdeta(0) = 0.0;
dNdeta(1) = 4.0 * l2 - 1.0;
dNdeta(2) = -1.0 * ( 4.0 * l3 - 1.0 );
dNdeta(3) = 4.0 * l1;
dNdeta(4) = 4.0 * l3 - 4.0 * l2;
dNdeta(5) = -4.0 * l1;
for (int i = 0; i < 6; ++i) {
a.add(dNdxi(i), *cellgeo.giveVertexCoordinates(snodes(i)));
b.add(dNdeta(i), *cellgeo.giveVertexCoordinates(snodes(i)));
}
answer.beVectorProductOf(a, b);
double J = answer.computeNorm();
answer.times(1/J);
return J;
}
int
LSpace :: computeLoadLSToLRotationMatrix(FloatMatrix &answer, int isurf, GaussPoint *gp)
{
// returns transformation matrix from
// surface local coordinate system
// to element local c.s
// (same as global c.s in this case)
//
// i.e. f(element local) = T * f(edge local)
// definition of local c.s on surface:
// local z axis - perpendicular to surface, pointing outwards from element
// local x axis - is in global xy plane (perpendicular to global z axis)
// local y axis - completes the righ hand side cs.
/*
* OOFEM_ERROR("surface local coordinate system not supported");
* return 1;
*/
FloatArray gc(3);
FloatArray h1(3), h2(3), nn(3), n(3);
IntArray snodes(4);
answer.resize(3, 3);
this->interpolation.computeSurfaceMapping(snodes, dofManArray, isurf);
for ( int i = 1; i <= 4; i++ ) {
gc.add( * domain->giveNode( snodes.at(i) )->giveCoordinates() );
}
gc.times(1. / 4.);
// determine "average normal"
for ( int i = 1; i <= 4; i++ ) {
int j = ( i ) % 4 + 1;
h1 = * domain->giveNode( snodes.at(i) )->giveCoordinates();
h1.subtract(gc);
h2 = * domain->giveNode( snodes.at(j) )->giveCoordinates();
h2.subtract(gc);
n.beVectorProductOf(h1, h2);
if ( n.computeSquaredNorm() > 1.e-6 ) {
n.normalize();
}
nn.add(n);
}
nn.times(1. / 4.);
if ( nn.computeSquaredNorm() < 1.e-6 ) {
answer.zero();
return 1;
}
nn.normalize();
for ( int i = 1; i <= 3; i++ ) {
answer.at(i, 3) = nn.at(i);
}
// determine lcs of surface
// local x axis in xy plane
double test = fabs(fabs( nn.at(3) ) - 1.0);
if ( test < 1.e-5 ) {
h1.at(1) = answer.at(1, 1) = 1.0;
h1.at(2) = answer.at(2, 1) = 0.0;
} else {
h1.at(1) = answer.at(1, 1) = answer.at(2, 3);
h1.at(2) = answer.at(2, 1) = -answer.at(1, 3);
}
h1.at(3) = answer.at(3, 1) = 0.0;
// local y axis perpendicular to local x,z axes
h2.beVectorProductOf(nn, h1);
for ( int i = 1; i <= 3; i++ ) {
answer.at(i, 2) = h2.at(i);
}
return 1;
}
void LSpace :: drawTriad(FloatArray &coords, int isurf)
{
FloatMatrix jm(3, 3);
FloatArray gc(3);
GraphicObj *go;
WCRec p [ 2 ]; // point
double coeff = 1.0;
int i, succ;
/*
* // version I
* this->interpolation.giveJacobianMatrixAt (jm, domain, nodeArray, coords);
* // determine origin
* this->interpolation.local2global (gc, domain, nodeArray, coords, 0.0);
* // draw triad
*
*/
// version II
// determine surface center
IntArray snodes(4);
FloatArray h1(3), h2(3), nn(3), n(3);
int j;
const char *colors[] = {
"red", "green", "blue"
};
this->interpolation.computeSurfaceMapping(snodes, dofManArray, isurf);
for ( i = 1; i <= 4; i++ ) {
gc.add( * ( domain->giveNode( snodes.at(i) )->giveCoordinates() ) );
}
gc.times(1. / 4.);
// determine "average normal"
nn.zero();
for ( i = 1; i <= 4; i++ ) {
j = ( i ) % 4 + 1;
h1 = * domain->giveNode( snodes.at(i) )->giveCoordinates();
h1.subtract(gc);
h2 = * domain->giveNode( snodes.at(j) )->giveCoordinates();
h2.subtract(gc);
n.beVectorProductOf(h1, h2);
if ( n.dotProduct(n, 3) > 1.e-6 ) {
n.normalize();
}
nn.add(n);
}
nn.times(1. / 4.);
if ( nn.dotProduct(nn, 3) < 1.e-6 ) {
return;
}
nn.normalize();
for ( i = 1; i <= 3; i++ ) {
jm.at(i, 3) = nn.at(i);
}
// determine lcs of surface
// local x axis in xy plane
double test = fabs(fabs( nn.at(3) ) - 1.0);
if ( test < 1.e-5 ) {
h1.at(1) = jm.at(1, 1) = 1.0;
h1.at(2) = jm.at(2, 1) = 0.0;
} else {
h1.at(1) = jm.at(1, 1) = jm.at(2, 3);
h1.at(2) = jm.at(2, 1) = -jm.at(1, 3);
}
h1.at(3) = jm.at(3, 1) = 0.0;
// local y axis perpendicular to local x,z axes
h2.beVectorProductOf(nn, h1);
for ( i = 1; i <= 3; i++ ) {
jm.at(i, 2) = h2.at(i);
}
p [ 0 ].x = gc.at(1);
p [ 0 ].y = gc.at(2);
p [ 0 ].z = gc.at(3);
for ( i = 1; i <= 3; i++ ) {
p [ 1 ].x = p [ 0 ].x + coeff *jm.at(1, i);
p [ 1 ].y = p [ 0 ].y + coeff *jm.at(2, i);
p [ 1 ].z = p [ 0 ].z + coeff *jm.at(3, i);
EASValsSetColor( ColorGetPixelFromString(const_cast< char * >(colors [ i - 1 ]), & succ) );
go = CreateLine3D(p);
EGWithMaskChangeAttributes(WIDTH_MASK | COLOR_MASK | LAYER_MASK, go);
EMAddGraphicsToModel(ESIModel(), go);
}
}
