void PlaneGeometry::EnsurePerpendicularNormal( mitk::AffineTransform3D *transform )
{
/** \brief ensure column(2) of indexToWorldTransform-matrix to be perpendicular to plane, keep length and handedness. */
VnlVector normal = vnl_cross_3d( transform->GetMatrix().GetVnlMatrix().get_column(0),
transform->GetMatrix().GetVnlMatrix().get_column(1) );
normal.normalize(); // Now normal is a righthand normal unit vector, perpendicular to the plane.
ScalarType len = transform->GetMatrix().GetVnlMatrix().get_column(2).two_norm();
if (len==0) { len = 1; }
normal *= len;
// Get the existing normal vector zed:
vnl_vector_fixed<double, 3> zed = transform->GetMatrix().GetVnlMatrix().get_column(2);
/** If det(matrix)<0, multiply normal vector by (-1) to keep geometry lefthanded. */
if( vnl_determinant( transform->GetMatrix().GetVnlMatrix()) < 0 )
{
MITK_DEBUG << "EnsurePerpendicularNormal(): Lefthanded geometry preserved, rh-normal: [ " << normal << " ],";
normal *= (-1.0);
MITK_DEBUG << "lh-normal: [ " << normal << " ], original vector zed is: [ " << zed << " ]";
}
// Now lets compare and only replace if necessary and only then warn the user:
// float epsilon is precise enough here, but we need to respect numerical condition:
// Higham, N., 2002, Accuracy and Stability of Numerical Algorithms,
// SIAM, page 37, 2nd edition:
double feps = std::numeric_limits<float>::epsilon();
double zedsMagnitude = zed.two_norm();
feps = feps * zedsMagnitude * 2;
/** Check if normal (3. column) was perpendicular: If not, replace with calculated normal vector: */
if( normal != zed )
{
vnl_vector_fixed<double, 3> parallel;
for ( unsigned int i = 0; i<3 ; ++i )
{
parallel[i] = normal[i] / zed[i]; // Remember linear algebra: checking for parallelity.
}
// Checking if really not paralell i.e. non-colinear vectors by comparing these floating point numbers:
if( (parallel[0]+feps < parallel[1] || feps+parallel[1] < parallel[0])
&& (parallel[0]+feps < parallel[2] || feps+parallel[2] < parallel[0]) )
{
MITK_WARN << "EnsurePerpendicularNormal(): Plane geometry was _/askew/_, so here it gets rectified by substituting"
<< " the 3rd column of the indexToWorldMatrix with an appropriate normal vector: [ " << normal
<< " ], original vector zed was: [ " << zed << " ].";
Matrix3D matrix = transform->GetMatrix();
matrix.GetVnlMatrix().set_column( 2, normal );
transform->SetMatrix( matrix );
}
}
else
{
// Nothing to do, 3rd column of indexToWorldTransformMatrix already was perfectly perpendicular.
}
}
void
PlaneGeometry::InitializeStandardPlane( const VnlVector& rightVector,
const VnlVector &downVector, const Vector3D *spacing )
{
ScalarType width = rightVector.magnitude();
ScalarType height = downVector.magnitude();
InitializeStandardPlane( width, height, rightVector, downVector, spacing );
}
void
PlaneGeometry::SetMatrixByVectors( const VnlVector &rightVector,
const VnlVector &downVector, ScalarType thickness )
{
VnlVector normal = vnl_cross_3d(rightVector, downVector);
normal.normalize();
normal *= thickness;
AffineTransform3D::Pointer transform = AffineTransform3D::New();
Matrix3D matrix;
matrix.GetVnlMatrix().set_column(0, rightVector);
matrix.GetVnlMatrix().set_column(1, downVector);
matrix.GetVnlMatrix().set_column(2, normal);
transform->SetMatrix(matrix);
transform->SetOffset(m_IndexToWorldTransform->GetOffset());
SetIndexToWorldTransform(transform);
}
void
PlaneGeometry::EnsurePerpendicularNormal(mitk::AffineTransform3D *transform)
{
//ensure row(2) of transform to be perpendicular to plane, keep length.
VnlVector normal = vnl_cross_3d(
transform->GetMatrix().GetVnlMatrix().get_column(0),
transform->GetMatrix().GetVnlMatrix().get_column(1) );
normal.normalize();
ScalarType len = transform->GetMatrix()
.GetVnlMatrix().get_column(2).two_norm();
if (len==0) len = 1;
normal*=len;
Matrix3D matrix = transform->GetMatrix();
matrix.GetVnlMatrix().set_column(2, normal);
transform->SetMatrix(matrix);
}
void
PlaneGeometry::SetMatrixByVectors( const VnlVector &rightVector,
const VnlVector &downVector, ScalarType thickness /* = 1.0 */ )
{
VnlVector normal = vnl_cross_3d(rightVector, downVector);
normal.normalize();
normal *= thickness;
// Crossproduct vnl_cross_3d is always righthanded, but that is okay here
// because in this method we create a new IndexToWorldTransform and
// a negative thickness could still make it lefthanded.
AffineTransform3D::Pointer transform = AffineTransform3D::New();
Matrix3D matrix;
matrix.GetVnlMatrix().set_column(0, rightVector);
matrix.GetVnlMatrix().set_column(1, downVector);
matrix.GetVnlMatrix().set_column(2, normal);
transform->SetMatrix(matrix);
transform->SetOffset(this->GetIndexToWorldTransform()->GetOffset());
SetIndexToWorldTransform(transform);
}
void
PlaneGeometry::InitializeStandardPlane(
mitk::ScalarType width, ScalarType height,
const VnlVector &rightVector, const VnlVector &downVector,
const Vector3D *spacing )
{
assert(width > 0);
assert(height > 0);
VnlVector rightDV = rightVector; rightDV.normalize();
VnlVector downDV = downVector; downDV.normalize();
VnlVector normal = vnl_cross_3d(rightVector, downVector);
normal.normalize();
if(spacing!=NULL)
{
rightDV *= (*spacing)[0];
downDV *= (*spacing)[1];
normal *= (*spacing)[2];
}
AffineTransform3D::Pointer transform = AffineTransform3D::New();
Matrix3D matrix;
matrix.GetVnlMatrix().set_column(0, rightDV);
matrix.GetVnlMatrix().set_column(1, downDV);
matrix.GetVnlMatrix().set_column(2, normal);
transform->SetMatrix(matrix);
transform->SetOffset(m_IndexToWorldTransform->GetOffset());
ScalarType bounds[6] = { 0, width, 0, height, 0, 1 };
this->SetBounds( bounds );
this->SetIndexToWorldTransform( transform );
}
void
PlaneGeometry::InitializeStandardPlane( mitk::ScalarType width, ScalarType height,
const VnlVector &rightVector, const VnlVector &downVector,
const Vector3D *spacing )
{
assert(width > 0);
assert(height > 0);
VnlVector rightDV = rightVector; rightDV.normalize();
VnlVector downDV = downVector; downDV.normalize();
VnlVector normal = vnl_cross_3d(rightVector, downVector);
normal.normalize();
// Crossproduct vnl_cross_3d is always righthanded, but that is okay here
// because in this method we create a new IndexToWorldTransform and
// spacing with 1 or 3 negative components could still make it lefthanded.
if(spacing!=nullptr)
{
rightDV *= (*spacing)[0];
downDV *= (*spacing)[1];
normal *= (*spacing)[2];
}
AffineTransform3D::Pointer transform = AffineTransform3D::New();
Matrix3D matrix;
matrix.GetVnlMatrix().set_column(0, rightDV);
matrix.GetVnlMatrix().set_column(1, downDV);
matrix.GetVnlMatrix().set_column(2, normal);
transform->SetMatrix(matrix);
transform->SetOffset(this->GetIndexToWorldTransform()->GetOffset());
ScalarType bounds[6] = { 0, width, 0, height, 0, 1 };
this->SetBounds( bounds );
this->SetIndexToWorldTransform( transform );
}
void mitk::ExtrudedContour::BuildGeometry()
{
if(m_Contour.IsNull())
return;
// Initialize(1);
Vector3D nullvector; nullvector.Fill(0.0);
float xProj[3];
unsigned int i;
unsigned int numPts = 20; //m_Contour->GetNumberOfPoints();
mitk::Contour::PathPointer path = m_Contour->GetContourPath();
mitk::Contour::PathType::InputType cstart = path->StartOfInput();
mitk::Contour::PathType::InputType cend = path->EndOfInput();
mitk::Contour::PathType::InputType cstep = (cend-cstart)/numPts;
mitk::Contour::PathType::InputType ccur;
// Part I: guarantee/calculate legal vectors
m_Vector.Normalize();
itk2vtk(m_Vector, m_Normal);
// check m_Vector
if(mitk::Equal(m_Vector, nullvector) || m_AutomaticVectorGeneration)
{
if ( m_AutomaticVectorGeneration == false)
itkWarningMacro("Extrusion vector is 0 ("<< m_Vector << "); trying to use normal of polygon");
vtkPoints *loopPoints = vtkPoints::New();
//mitk::Contour::PointsContainerIterator pointsIt = m_Contour->GetPoints()->Begin();
double vtkpoint[3];
unsigned int i=0;
for(i=0, ccur=cstart; i<numPts; ++i, ccur+=cstep)
{
itk2vtk(path->Evaluate(ccur), vtkpoint);
loopPoints->InsertNextPoint(vtkpoint);
}
// Make sure points define a loop with a m_Normal
vtkPolygon::ComputeNormal(loopPoints, m_Normal);
loopPoints->Delete();
vtk2itk(m_Normal, m_Vector);
if(mitk::Equal(m_Vector, nullvector))
{
itkExceptionMacro("Cannot calculate normal of polygon");
}
}
// check m_RightVector
if((mitk::Equal(m_RightVector, nullvector)) || (mitk::Equal(m_RightVector*m_Vector, 0.0)==false))
{
if(mitk::Equal(m_RightVector, nullvector))
{
itkDebugMacro("Right vector is 0. Calculating.");
}
else
{
itkWarningMacro("Right vector ("<<m_RightVector<<") not perpendicular to extrusion vector "<<m_Vector<<": "<<m_RightVector*m_Vector);
}
// calculate a legal m_RightVector
if( mitk::Equal( m_Vector[1], 0.0f ) == false )
{
FillVector3D( m_RightVector, 1.0f, -m_Vector[0]/m_Vector[1], 0.0f );
m_RightVector.Normalize();
}
else
{
FillVector3D( m_RightVector, 0.0f, 1.0f, 0.0f );
}
}
// calculate down-vector
VnlVector rightDV = m_RightVector.GetVnlVector(); rightDV.normalize(); vnl2vtk(rightDV, m_Right);
VnlVector downDV = vnl_cross_3d( m_Vector.GetVnlVector(), rightDV ); downDV.normalize(); vnl2vtk(downDV, m_Down);
// Part II: calculate plane as base for extrusion, project the contour
// on this plane and store as polygon for IsInside test and BoundingBox calculation
// initialize m_ProjectionPlane, yet with origin at 0
m_ProjectionPlane->InitializeStandardPlane(rightDV, downDV);
// create vtkPolygon from contour and simultaneously determine 2D bounds of
// contour projected on m_ProjectionPlane
//mitk::Contour::PointsContainerIterator pointsIt = m_Contour->GetPoints()->Begin();
m_Polygon->Points->Reset();
m_Polygon->Points->SetNumberOfPoints(numPts);
m_Polygon->PointIds->Reset();
m_Polygon->PointIds->SetNumberOfIds(numPts);
mitk::Point2D pt2d;
mitk::Point3D pt3d;
mitk::Point2D min, max;
min.Fill(ScalarTypeNumericTraits::max());
max.Fill(ScalarTypeNumericTraits::min());
xProj[2]=0.0;
for(i=0, ccur=cstart; i<numPts; ++i, ccur+=cstep)
{
pt3d.CastFrom(path->Evaluate(ccur));
m_ProjectionPlane->Map(pt3d, pt2d);
xProj[0]=pt2d[0];
if(pt2d[0]<min[0]) min[0]=pt2d[0];
if(pt2d[0]>max[0]) max[0]=pt2d[0];
xProj[1]=pt2d[1];
if(pt2d[1]<min[1]) min[1]=pt2d[1];
if(pt2d[1]>max[1]) max[1]=pt2d[1];
m_Polygon->Points->SetPoint(i, xProj);
m_Polygon->PointIds->SetId(i, i);
}
// shift parametric origin to (0,0)
for(i=0; i<numPts; ++i)
{
double * pt = this->m_Polygon->Points->GetPoint(i);
pt[0]-=min[0]; pt[1]-=min[1];
itkDebugMacro( << i << ": (" << pt[0] << "," << pt[1] << "," << pt[2] << ")" );
}
this->m_Polygon->GetBounds(m_ProjectedContourBounds);
//m_ProjectedContourBounds[4]=-1.0; m_ProjectedContourBounds[5]=1.0;
// calculate origin (except translation along the normal) and bounds
// of m_ProjectionPlane:
// origin is composed of the minimum x-/y-coordinates of the polygon,
// bounds from the extent of the polygon, both after projecting on the plane
mitk::Point3D origin;
m_ProjectionPlane->Map(min, origin);
ScalarType bounds[6]={0, max[0]-min[0], 0, max[1]-min[1], 0, 1};
m_ProjectionPlane->SetBounds(bounds);
m_ProjectionPlane->SetOrigin(origin);
// Part III: initialize geometry
if(m_ClippingGeometry.IsNotNull())
{
ScalarType min_dist=ScalarTypeNumericTraits::max(), max_dist=ScalarTypeNumericTraits::min(), dist;
unsigned char i;
for(i=0; i<8; ++i)
{
dist = m_ProjectionPlane->SignedDistance( m_ClippingGeometry->GetCornerPoint(i) );
if(dist<min_dist) min_dist=dist;
if(dist>max_dist) max_dist=dist;
}
//incorporate translation along the normal into origin
origin = origin+m_Vector*min_dist;
m_ProjectionPlane->SetOrigin(origin);
bounds[5]=max_dist-min_dist;
}
else
bounds[5]=20;
itk2vtk(origin, m_Origin);
mitk::Geometry3D::Pointer g3d = GetGeometry( 0 );
assert( g3d.IsNotNull() );
g3d->SetBounds(bounds);
g3d->SetIndexToWorldTransform(m_ProjectionPlane->GetIndexToWorldTransform());
g3d->TransferItkToVtkTransform();
ProportionalTimeGeometry::Pointer timeGeometry = ProportionalTimeGeometry::New();
timeGeometry->Initialize(g3d,1);
SetTimeGeometry(timeGeometry);
}
