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:
“Singularity is only pardonable in old age and retirement; I may now be as singular as I please, but you may not.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)
“Wonderful “Force of Public Opinion!” We must act and walk in all points as it prescribes; follow the traffic it bids us, realise the sum of money, the degree of “influence” it expects of us, or we shall be lightly esteemed; certain mouthfuls of articulate wind will be blown at us, and this what mortal courage can front?”
—Thomas Carlyle (1795–1881)