The ISD describes the distribution of grain interface curvatures in a 2/3-D material volume. The 2-tuple of the first and second principal curvatures define the genus of the interface. The following figure indicates the different genus of interfaces that are realized in a 3-D volume.
A 2-D volume will require one value to describe the curvature.
I personally find that ISD useful for a qualitative interpretation. The space itself is challenging to represent using feature identifiers. In the attached presentation I suggest some parsing of the spatial curvature information using a parametrized version of the principal curvatures.
- Rotate 45 deg Clockwise
- Convert κ1 and κ2 to polar coordinates r and Ɵ, respectively.
- Remove extreme outlying points.
- Use a cosine basis function for Ɵ and a Legendre polynomial basis for r.
Please see the following link for further explanation.
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Thank you so much Tony