Find 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 convetion 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

This computation is not the same as the Find Feature Sizes for Triangle Geometries, which computes the sum of the unit element sizes for a set of Features (thus, the Find Feature Sizes would compute the area of Features in a Triangle Geometry, whereas this Filter is specialized to compute the enclosed volumes of Features in a surface mesh).

Parameters

None

Required Geometry

Triangle

Required Objects

Kind	Default Name	Type	Component Dimensions	Description
Face Attribute Array	FaceLabels	int32_t	(2)	Specifies which Features are on either side of each Face

Created Objects

Kind	Default Name	Type	Component Dimensions	Description
Attribute Matrix	FaceFeatureData	Face Feature	N/A	Created Feature Attribute Matrix name
Feature Attribute Array	Volumes	float	(1)	Volume of the enclosed Feature

Example Pipelines

License & Copyright

Please see the description file distributed with this plugin.

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