- #1
meldraft
- 281
- 2
Hi all,
I am trying to argue that an ellipse is a good approximation for some discontinuity in a material. The ellipse and the interpolated curve I get from the photo look very much alike, but I need an actual number to show how much the two curves differ from each other. I thought of
[tex]\frac{Area_{actual} - Area_{ellipse}}{Area_{actual}}[/tex]
but it doesn't really give any information about how much the curves match (a square with the same area as the ellipse would give 0 deviation).
I'm kind of new to Riemannian geometry, but I thought that maybe I could use the Riemann curvature tensor, although I don't really know how to do it yet :P . I would appreciate any suggestions you are able to give!
I am trying to argue that an ellipse is a good approximation for some discontinuity in a material. The ellipse and the interpolated curve I get from the photo look very much alike, but I need an actual number to show how much the two curves differ from each other. I thought of
[tex]\frac{Area_{actual} - Area_{ellipse}}{Area_{actual}}[/tex]
but it doesn't really give any information about how much the curves match (a square with the same area as the ellipse would give 0 deviation).
I'm kind of new to Riemannian geometry, but I thought that maybe I could use the Riemann curvature tensor, although I don't really know how to do it yet :P . I would appreciate any suggestions you are able to give!