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Recipe for Curvature Measurement

... recipe for curvature measurement. Here it is.

1. Measure all the first partial derivatives which comprise the gradient, (little) g, and then compute n and P.
2. Then, measure all the second partial derivatives which comprise the Hessian, H.
3. Then you computer big G, the geometry tensor, as follows.

From G, you can get the curvature magnitudes, with two more steps:

1. Compute the trace and frobenious norm of G
2. Then use the quadratic formula to find kappa1 and kappa2.

If, in addition, you want the curvature directions, you can find those as the eigenvectors of G, knowing that kappa1 and kappa2 are the two non-zero eigenvalues.

Note that this started with measuring partial derivatives. And we do that based on ...