# Difference between revisions of "ITK/Examples/Meshes/AreaAndVolume"

< ITK‎ | Examples

This example demonstrates how to calculate the area and volume of an itk::Mesh by (a) ensuring that it is triangular and (b) converting it to an itk::SimplexMesh.

Contributed by: Davis Vigneault

## AreaAndVolume.cxx

```#define _USE_MATH_DEFINES //needed for Visual Studio (before #include <cmath>)
#include <itkSimplexMesh.h>
#include <itkRegularSphereMeshSource.h>
#include <itkTriangleMeshToSimplexMeshFilter.h>
#include <itkSimplexMeshVolumeCalculator.h>

typedef itk::Mesh< float, 3 >        TMesh;
typedef itk::SimplexMesh< float, 3 > TSimplex;
typedef itk::RegularSphereMeshSource< TMesh >                   TSphere;
typedef itk::TriangleMeshToSimplexMeshFilter< TMesh, TSimplex > TConvert;
typedef itk::SimplexMeshVolumeCalculator< TSimplex >            TVolume;

int main(int, char *[])
{

// Create a spherical mesh with known radius and resolution.
TSphere::Pointer source = TSphere::New();
TSphere::VectorType scale;
scale.Fill( 5.0 );
source->SetScale( scale );
source->SetResolution( 5 );
source->Update();

// Ensure that all cells of the mesh are triangles.
for (TMesh::CellsContainerIterator it = source->GetOutput()->GetCells()->Begin();
it != source->GetOutput()->GetCells()->End();
++it)
{
TMesh::CellAutoPointer cell;
source->GetOutput()->GetCell(it->Index(), cell);
if (3 != cell->GetNumberOfPoints())
{
std::cerr << "ERROR: All cells must be trianglar." << std::endl;
return EXIT_FAILURE;
}
}

// Convert the triangle mesh to a simplex mesh.
TConvert::Pointer convert = TConvert::New();
convert->SetInput( source->GetOutput() );
convert->Update();

// Calculate the volume and area of the simplex mesh.
TVolume::Pointer volume = TVolume::New();
volume->SetSimplexMesh( convert->GetOutput() );
volume->Compute();

// Compare with the volume and area of an ideal sphere.
std::cout << "Ideal Volume: "       << 4.0/3.0*M_PI*pow(5.0,3) << std::endl;
std::cout << "Mesh Volume: "        << volume->GetVolume()     << std::endl;
std::cout << "Ideal Surface Area: " << 4.0*M_PI*pow(5.0,2)     << std::endl;
std::cout << "Mesh Surface Area: "  << volume->GetArea()       << std::endl;

return EXIT_SUCCESS;

}
```

## CMakeLists.txt

```cmake_minimum_required(VERSION 3.9.5)

project(AreaAndVolume)

find_package(ITK REQUIRED)
include(\${ITK_USE_FILE})
find_package(VTK REQUIRED)
include(\${VTK_USE_FILE})
endif()

if( "\${ITK_VERSION_MAJOR}" LESS 4 )
else( "\${ITK_VERSION_MAJOR}" LESS 4 )
endif( "\${ITK_VERSION_MAJOR}" LESS 4 )
```

```cd AreaAndVolume/build
```
• If ITK is installed:
```cmake ..
```
• If ITK is not installed but compiled on your system, you will need to specify the path to your ITK build:
```cmake -DITK_DIR:PATH=/home/me/itk_build ..
```

Build the project:

```make
```

and run it:

```./AreaAndVolume
```

WINDOWS USERS PLEASE NOTE: Be sure to add the ITK bin directory to your path. This will resolve the ITK dll's at run time.

## Building All of the Examples

Many of the examples in the ITK Wiki Examples Collection require VTK. You can build all of the the examples by following these instructions. If you are a new VTK user, you may want to try the Superbuild which will build a proper ITK and VTK.

## ItkVtkGlue

### ITK >= 4

For examples that use QuickView (which depends on VTK), you must have built ITK with Module_ITKVtkGlue=ON.

### ITK < 4

Some of the ITK Examples require VTK to display the images. If you download the entire ITK Wiki Examples Collection, the ItkVtkGlue directory will be included and configured. If you wish to just build a few examples, then you will need to download ItkVtkGlue and build it. When you run cmake it will ask you to specify the location of the ItkVtkGlue binary directory.