Find 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 using the technique in [1]. The groups of Triangles over which to compute the curvatures is determines by the Features they are associated, denoted by their Face Labels. The curvature information will be stored in a Face Attribute Matrix.
Principal Curvatures 1 and 2 are the κ 1 and κ 2 from [1] and are the eigenvalues from the Wiengarten matrix. The Principal Directions 1 and 2 are the eigenvectors from the solution to the least squares fit algorithm. The Mean Curvature is (κ 1 + κ 2 ) / 2, while the Gaussian curvature is (κ 1 * κ 2 ).
@image latex FeatureFaceCurvatureFilter.png "Curvature Coloring of a Feature" width = 6in
Parameters¶
| Name | Type | Description |
|---|---|---|
| Neighborhood Ring Count | int32_t | The size of the neighborhood to use to calculate the curvature values |
| Compute Principal Direction Vectors | bool | Whether to compute the principal direction vectors |
| Compute Gaussian Curvature | bool | Whether to compute the Gaussian curvature values |
| Compute Mean Curvature | bool | Whether to compute the mean curvature values |
| Use Face Normals for Curve Fitting | bool | Whether to use the Face normals to improve the least squares fit |
Required Geometry¶
Triangle
Required Objects¶
| Kind | Default Name | Type | Component Dimensions | Description |
|---|---|---|---|---|
| Attribute Matrix | FaceData | Face | N / A | Specifies which Attribute Matrix to store the results |
| Face Attribute Array | FaceLabels | int32_t | (2) | Specifies which Features are on either side of each Face |
| Face Attribute Array | FeatureFaceIds | int32_t | (1) | Specifies to which Feature boundary each Face belongs |
| Face Attribute Array | FaceNormals | double | (3) | Specifies the normal of each Face |
| Face Attribute Array | FaceCentroids | double | (3) | Specifies the centroid of each Face |
Created Objects¶
| Kind | Default Name | Type | Component Dimensions | Description |
|---|---|---|---|---|
| Face Attribute Array | PrincipalCurvature1 | double | (1) | First set eigenvalues of the Wiengarten matrix (κ1). Only created if Compute Principal Direction Vectors is checked |
| Face Attribute Array | PrincipalCurvature2 | double | (1) | Second set eigenvalues of the Wiengarten matrix (κ2). Only created if Compute Principal Direction Vectors is checked |
| Face Attribute Array | PrincipalDirection1 | double | (3) | First set of eigenvectors. Only created if Compute Principal Direction Vectors is checked |
| Face Attribute Array | PrincipalDirection2 | double | (3) | Second set of eigenvectors. Only created if Compute Principal Direction Vectors is checked |
| Face Attribute Array | MeanCurvatures | double | (1) | Mean curvature values. Only created if Compute Mean Curvature is checked |
| Face Attribute Array | GaussianCurvatures | double | (1) | Gaussian curvature values. Only created if Compute Gaussian Curvature is checked |
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¶
License & Copyright¶
Please see the description file distributed with thisPlugin
DREAM.3D Mailing Lists¶
If you need more help with aFilter, please consider asking your question on the DREAM.3D Users Google group!