```{index} single: Filters; Compute Feature Volumes from Triangle Geometry
```
# Compute Feature Volumes from Triangle Geometry

## Group (Subgroup)

Statistics (Morphological)

## Description

This **Filter** computes the enclosed volume of each **Feature** in a **Triangle Geometry**. The result is the volume of
each surface meshed **Feature**, or alternatively the volume of each unique polyhedron defined by the given _Face
Labels_ array. The volume of any generic polyhedron can be computed using the following algorithm:

1. Triangulate each face of the polyhedron (in this case, each face is already a triangle within the **Triangle
   Geometry**)
2. For each triangular face, ensure the normals are all consistent (this **Filter** uses the convention where normals
   point inwards; note that the actual winding of the **Triangle Geometry** is not modified)
3. For each triangular face, create a tetrahedron where the fourth vertex is the origin
4. Compute the signed volume of each tetrahedron
5. Sum the signed tetrahedra volumes to obtain the volume of the enclosing polyhedron

### Filter Parameters

| Parameter Name | Parameter Type | Parameter Notes | Description |
|----------------|----------------|-----------------|-------------|
| Triangle Geometry | Geometry Selection | Triangle | The complete path to the Geometry for which to calculate the normals |

### Input Triangle Face Data

| Parameter Name | Parameter Type | Parameter Notes | Description |
|----------------|----------------|-----------------|-------------|
| Face Labels | Array Selection | Allowed Types: int32 Comp. Shape: 2 | The DataPath to the FaceLabels values. |

### Input Face Feature Data

| Parameter Name | Parameter Type | Parameter Notes | Description |
|----------------|----------------|-----------------|-------------|
| Face Feature Attribute Matrix | AttributeMatrixSelection |  | The DataPath to the AttributeMatrix that holds feature data for the faces |

### Output Face Feature Data

| Parameter Name | Parameter Type | Parameter Notes | Description |
|----------------|----------------|-----------------|-------------|
| Calculated Volumes | DataObjectName |  | Calculated volumes data created in the Face Feature Data Attribute Matrix |

## Example Pipelines

## License & Copyright

Please see the description file distributed with this plugin.

## DREAM3D-NX Help

If you need help, need to file a bug report or want to request a new feature, please head over to the [DREAM3DNX-Issues](https://github.com/BlueQuartzSoftware/DREAM3DNX-Issues/discussions) GitHub site where the community of DREAM3D-NX users can help answer your questions.
