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:
“Each your doing,
So singular in each particular,
Crowns what you are doing in the present deeds,
That all your acts are queens.”
—William Shakespeare (1564–1616)
“He is the best sailor who can steer within the fewest points of the wind, and extract a motive power out of the greatest obstacles. Most begin to veer and tack as soon as the wind changes from aft, and as within the tropics it does not blow from all points of the compass, there are some harbors which they can never reach.”
—Henry David Thoreau (1817–1862)