DREAM.3D v6 User Manual
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Surface Meshing (Curvature)
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 ).
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 |
Triangle
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 |
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 |
[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.
Please see the description file distributed with this**Plugin**
If you need more help with a**Filter**, please consider asking your question on the DREAM.3D Users Google group!