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
Famous quotes containing the words singular and/or points:
“And that singular anomaly, the lady novelist—
I don’t think she’d be missed—I’m sure she’d not be
missed!”
—Sir William Schwenck Gilbert (1836–1911)
“Every man has to learn the points of the compass again as often as he awakes, whether from sleep or any abstraction.”
—Henry David Thoreau (1817–1862)