10.30. Compute Feature Face Curvature

Group (Subgroup)

Surface Meshing (Curvature)

Description

This filter calculates principal direction vectors and the principal curvatures, and optionally the mean and Gaussian curvature, for each Triangle in a Triangle Geometry (a surface mesh built from triangles) using the technique in [1]. The groups of Triangles over which to compute the curvatures are determined by the Features they belong to, as denoted by their Face Labels (the pair of Feature Ids on either side of each triangle). The curvature information is stored in a Face Attribute Matrix.

Curvature measures how sharply the surface bends at a point: a flat region has zero curvature, while a tightly rounded region has high curvature. The principal curvatures are the maximum and minimum bending values at a point, and the principal directions are the (unit) directions along the surface in which those extreme bends occur.

Principal Curvatures 1 and 2 are the κ₁ and κ₂ from [1] and are the eigenvalues of the Weingarten matrix. The Principal Directions 1 and 2 are the eigenvectors from the solution to the least-squares fit. The Mean Curvature is (κ₁ + κ₂) / 2, while the Gaussian curvature is (κ₁ * κ₂).

The principal directions can have their signs flipped: they come from eigenvectors, which are unique only up to a sign.

Note: Computing the Weingarten matrix values is an experimental feature, and there is no guarantee at this time that the values are correct.

Units

Principal curvatures and mean curvature are reported in 1/length (the reciprocal of the geometry length units; the radius of the best-fit circle is its reciprocal). Gaussian curvature, being a product of two curvatures, is reported in 1/length^2. Principal directions are dimensionless unit 3-vectors.

Ring Neighbor Schematic

Required Input Sources

• Triangle Geometry – a surface mesh, typically produced by a surface-meshing filter such as Create Surface Mesh (Surface Nets) or Create Surface Mesh (QuickMesh).

• Face Labels – the per-triangle pair of Feature Ids, produced alongside the mesh by the surface-meshing filter above.

• Feature Face Ids – computed by Compute Triangle Face Ids.

• Face Normals – computed by Compute Triangle Normals.

• Face Centroids – computed by Compute Triangle Centroids.

Input Parameter(s)

Parameter Name	Parameter Type	Parameter Notes	Description
Triangle Geometry	Geometry Selection	Triangle	The input Triangle Geometry to compute the curvature values
Neighborhood Ring Count	Scalar Value	Int32	The number of ring neighbors to use
Compute Principal Direction Vectors	Bool		Compute the Principal Direction Vectors
Compute Gaussian Curvature	Bool		Compute the Gaussian Curvature values
Compute Mean Curvature	Bool		Compute the Mean Curvature values
Compute Weingarten Matrix	Bool		Compute the Weingarten Matrix values
Use Face Normals for Curve Fitting	Bool		Use the face normals for curve fitting.

Input Triangle Face Data

Parameter Name	Parameter Type	Parameter Notes	Description
Face Attribute Matrix	AttributeMatrixSelection		The AttributeMatrix that holds the triangle face data.
Face Labels	Array Selection	Allowed Types: int32 Comp. Shape: 2	The DataPath to the ‘Face Labels’ DataArray
Feature Face Ids	Array Selection	Allowed Types: int32 Comp. Shape: 1	The DataPath to the ‘FeatureIds’ DataArray
Face Normals	Array Selection	Allowed Types: float64 Comp. Shape: 3	The DataPath to the ‘Feature Normals’ DataArray
Face Centroids	Array Selection	Allowed Types: float64 Comp. Shape: 3	The DataPath to the ‘Face Centroids’ DataArray

Output Face Data

Parameter Name	Parameter Type	Parameter Notes	Description
Principal Curvature 1	ArrayCreation		Output DataPath to hold the ‘Principal Curvature 1’ values
Principal Curvature 2	ArrayCreation		Output DataPath to hold the ‘Principal Curvature 2’ values
Principal Direction 1	ArrayCreation		Output DataPath to hold the ‘Principal Direction 1’ values
Principal Direction 2	ArrayCreation		Output DataPath to hold the ‘Principal Direction 2’ values
Gaussian Curvature	ArrayCreation		Output DataPath to hold the ‘Gaussian Curvature’ values
Mean Curvature	ArrayCreation		Output DataPath to hold the ‘Mean Curvature’ values
Weingarten Matrix	ArrayCreation		Output DataPath to hold the ‘Weingarten Matrix’ values

References

[1] J. Goldfeather, V. Interrante, “A Novel Cubic-Order Algorithm for Approximating Principal Direction Vectors”, ACM Transactions on Graphics 2004, 23(1), pp. 45 - 63.

Example Pipelines

• Compute_Feature_Face_Curvature

• Compute_Feature_Face_Curvature_2

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 GitHub site where the community of DREAM3D-NX users can help answer your questions.