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<h1>DataRepresentation/Mesh/PointSetWithCovariantVectors.cxx</h1><div class="fragment"><pre class="fragment"><span class="comment">/*=========================================================================</span>
<span class="comment"></span>
<span class="comment"> Program: Insight Segmentation & Registration Toolkit</span>
<span class="comment"> Module: $RCSfile: PointSetWithCovariantVectors.cxx,v $</span>
<span class="comment"> Language: C++</span>
<span class="comment"> Date: $Date: 2008-01-20 21:19:51 $</span>
<span class="comment"> Version: $Revision: 1.15 $</span>
<span class="comment"></span>
<span class="comment"> Copyright (c) Insight Software Consortium. All rights reserved.</span>
<span class="comment"> See ITKCopyright.txt or http://www.itk.org/HTML/Copyright.htm for details.</span>
<span class="comment"></span>
<span class="comment"> This software is distributed WITHOUT ANY WARRANTY; without even </span>
<span class="comment"> the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR </span>
<span class="comment"> PURPOSE. See the above copyright notices for more information.</span>
<span class="comment"></span>
<span class="comment">=========================================================================*/</span>
<span class="preprocessor">#if defined(_MSC_VER)</span>
<span class="preprocessor"></span><span class="preprocessor">#pragma warning ( disable : 4786 )</span>
<span class="preprocessor"></span><span class="preprocessor">#endif</span>
<span class="preprocessor"></span>
<span class="comment">// Software Guide : BeginLatex</span>
<span class="comment">//</span>
<span class="comment">// It is common to represent geometric object by using points on their surfaces</span>
<span class="comment">// and normals associated with those points. This structure can be easily </span>
<span class="comment">// instantiated with the \doxygen{PointSet} class.</span>
<span class="comment">//</span>
<span class="comment">// The natural class for representing normals to surfaces and</span>
<span class="comment">// gradients of functions is the \doxygen{CovariantVector}. A</span>
<span class="comment">// covariant vector differs from a vector in the way they behave</span>
<span class="comment">// under affine transforms, in particular under anisotropic</span>
<span class="comment">// scaling. If a covariant vector represents the gradient of a</span>
<span class="comment">// function, the transformed covariant vector will still be the valid</span>
<span class="comment">// gradient of the transformed function, a property which would not</span>
<span class="comment">// hold with a regular vector.</span>
<span class="comment">// </span>
<span class="comment">// \index{itk::PointSet!itk::CovariantVector}</span>
<span class="comment">// \index{itk::CovariantVector!itk::PointSet}</span>
<span class="comment">//</span>
<span class="comment">// The following code shows how vector values can be used as pixel type on the</span>
<span class="comment">// PointSet class. The CovariantVector class is used here as the</span>
<span class="comment">// pixel type. The example illustrates how a deformable model could move under</span>
<span class="comment">// the influence of the gradient of potential function.</span>
<span class="comment">// </span>
<span class="comment">// In order to use the CovariantVector class it is necessary to</span>
<span class="comment">// include its header file along with the header of the point set.</span>
<span class="comment">//</span>
<span class="comment">// \index{itk::CovariantVector!Header}</span>
<span class="comment">//</span>
<span class="comment">// Software Guide : EndLatex </span>
<span class="comment">// Software Guide : BeginCodeSnippet</span>
<span class="preprocessor">#include "<a class="code" href="itkCovariantVector_8h.html">itkCovariantVector.h</a>"</span>
<span class="preprocessor">#include "<a class="code" href="itkPointSet_8h.html">itkPointSet.h</a>"</span>
<span class="comment">// Software Guide : EndCodeSnippet</span>
<span class="keywordtype">int</span> <a name="a0"></a><a class="code" href="itkTestMain_8h.html#dacbe0175a79dff748855d8c9839f82b">main</a>(<span class="keywordtype">int</span>, <span class="keywordtype">char</span> *[])
{
<span class="comment">// Software Guide : BeginLatex</span>
<span class="comment">//</span>
<span class="comment">// The CovariantVector class is templated over the type used to</span>
<span class="comment">// represent the spatial coordinates and over the space dimension. Since</span>
<span class="comment">// the PixelType is independent of the PointType, we are free to select any</span>
<span class="comment">// dimension for the covariant vectors to be used as pixel type. However, we</span>
<span class="comment">// want to illustrate here the spirit of a deformable model. It is then</span>
<span class="comment">// required for the vectors representing gradients to be of the same</span>
<span class="comment">// dimension as the points in space.</span>
<span class="comment">//</span>
<span class="comment">// \index{itk::CovariantVector!Instantiation}</span>
<span class="comment">//</span>
<span class="comment">// Software Guide : EndLatex </span>
<span class="comment">// Software Guide : BeginCodeSnippet</span>
<span class="keyword">const</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> Dimension = 3;
<span class="keyword">typedef</span> <a name="_a1"></a><a class="code" href="classitk_1_1CovariantVector.html" title="A templated class holding a n-Dimensional covariant vector.">itk::CovariantVector< float, Dimension ></a> PixelType;
<span class="comment">// Software Guide : EndCodeSnippet</span>
<span class="comment">// Software Guide : BeginLatex</span>
<span class="comment">//</span>
<span class="comment">// Then we use the PixelType (which are actually CovariantVectors) to</span>
<span class="comment">// instantiate the PointSet type and subsequently create a PointSet object.</span>
<span class="comment">//</span>
<span class="comment">// Software Guide : EndLatex </span>
<span class="comment">// Software Guide : BeginCodeSnippet</span>
<span class="keyword">typedef</span> <a name="_a2"></a><a class="code" href="classitk_1_1PointSet.html" title="A superclass of the N-dimensional mesh structure; supports point (geometric coordinate...">itk::PointSet< PixelType, Dimension ></a> PointSetType;
<a name="a3"></a><a class="code" href="itkFEMMacro_8h.html#539cce1a3282ba59952dedcbf9cdb23f">PointSetType::Pointer</a> pointSet = <a name="a4"></a><a class="code" href="namespaceHardConnectedComponentImageFilter.html#870262f145e0b45206db74df8053b59c">PointSetType::New</a>();
<span class="comment">// Software Guide : EndCodeSnippet</span>
<span class="comment">// Software Guide : BeginLatex</span>
<span class="comment">//</span>
<span class="comment">// The following code generates a sphere and assigns gradient values to</span>
<span class="comment">// the points. The components of the CovariantVectors in this example are</span>
<span class="comment">// computed to represent the normals to the circle.</span>
<span class="comment">//</span>
<span class="comment">// \index{itk::PointSet!SetPoint()}</span>
<span class="comment">// \index{itk::PointSet!SetPointData()}</span>
<span class="comment">//</span>
<span class="comment">// Software Guide : EndLatex </span>
<span class="comment">// Software Guide : BeginCodeSnippet</span>
PointSetType::PixelType gradient;
PointSetType::PointType point;
<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> pointId = 0;
<span class="keyword">const</span> <span class="keywordtype">double</span> radius = 300.0;
<span class="keywordflow">for</span>(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i=0; i<360; i++)
{
<span class="keyword">const</span> <span class="keywordtype">double</span> angle = i * atan(1.0) / 45.0;
point[0] = radius * sin( angle );
point[1] = radius * cos( angle );
point[2] = 1.0; <span class="comment">// flat on the Z plane</span>
gradient[0] = sin(angle);
gradient[1] = cos(angle);
gradient[2] = 0.0; <span class="comment">// flat on the Z plane</span>
pointSet->SetPoint( pointId, point );
pointSet->SetPointData( pointId, gradient );
pointId++;
}
<span class="comment">// Software Guide : EndCodeSnippet</span>
<span class="comment">// Software Guide : BeginLatex</span>
<span class="comment">//</span>
<span class="comment">// We can now visit all the points and use the vector on the pixel values</span>
<span class="comment">// to apply a deformation on the points by following the gradient of the</span>
<span class="comment">// function. This is along the spirit of what a deformable model could do</span>
<span class="comment">// at each one of its iterations. To be more formal we should use the</span>
<span class="comment">// function gradients as forces and multiply them by local stress tensors</span>
<span class="comment">// in order to obtain local deformations. The resulting deformations</span>
<span class="comment">// would finally be used to apply displacements on the points. However,</span>
<span class="comment">// to shorten the example, we will ignore this complexity for the moment.</span>
<span class="comment">//</span>
<span class="comment">// \index{itk::PointSet!PointDataIterator}</span>
<span class="comment">//</span>
<span class="comment">// Software Guide : EndLatex </span>
<span class="comment">// Software Guide : BeginCodeSnippet</span>
<span class="keyword">typedef</span> PointSetType::PointDataContainer::ConstIterator PointDataIterator;
PointDataIterator pixelIterator = pointSet->GetPointData()->Begin();
PointDataIterator pixelEnd = pointSet->GetPointData()->End();
<span class="keyword">typedef</span> PointSetType::PointsContainer::Iterator PointIterator;
PointIterator pointIterator = pointSet->GetPoints()->Begin();
PointIterator pointEnd = pointSet->GetPoints()->End();
<span class="keywordflow">while</span>( pixelIterator != pixelEnd && pointIterator != pointEnd )
{
point = pointIterator.Value();
gradient = pixelIterator.Value();
<span class="keywordflow">for</span>(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i=0; i<Dimension; i++)
{
point[i] += gradient[i];
}
pointIterator.Value() = point;
++pixelIterator;
++pointIterator;
}
<span class="comment">// Software Guide : EndCodeSnippet</span>
<span class="comment">// Software Guide : BeginLatex</span>
<span class="comment">//</span>
<span class="comment">// The CovariantVector class does not overload the \code{+}</span>
<span class="comment">// operator with the \doxygen{Point}. In other words, CovariantVectors can</span>
<span class="comment">// not be added to points in order to get new points. Further, since we</span>
<span class="comment">// are ignoring physics in the example, we are also forced to do the</span>
<span class="comment">// illegal addition manually between the components of the gradient and</span>
<span class="comment">// the coordinates of the points.</span>
<span class="comment">//</span>
<span class="comment">// Note that the absence of some basic operators on the ITK geometry classes</span>
<span class="comment">// is completely intentional with the aim of preventing the incorrect use</span>
<span class="comment">// of the mathematical concepts they represent.</span>
<span class="comment">//</span>
<span class="comment">// \index{itk::CovariantVector}</span>
<span class="comment">//</span>
<span class="comment">// Software Guide : EndLatex </span>
<span class="comment">//</span>
<span class="comment">// We can finally visit all the points and print out the new values.</span>
<span class="comment">//</span>
pointIterator = pointSet->GetPoints()->Begin();
pointEnd = pointSet->GetPoints()->End();
<span class="keywordflow">while</span>( pointIterator != pointEnd )
{
std::cout << pointIterator.Value() << std::endl;
++pointIterator;
}
<span class="keywordflow">return</span> 0;
}
</pre></div> </div>
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