Singular Points
The affine focal set can be the following:
To find the singular points we simply differentiate p + tA in some tangent direction X:
The affine focal set is singular if, and only if, there exists non-zero X such that, i.e. if, and only if, X is an eigenvector of S and the derivative of t in that direction is zero. This means that the derivative of an affine principal curvature in its own affine principal direction is zero.
Read more about this topic: Affine Focal Set
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