Hedgehog (geometry)

In differential geometry, a hedgehog or plane hedgehog is a type of plane curve, the envelope of a family of lines determined by a support function. More intuitively, sufficiently well-behaved hedgehogs are plane curves with one tangent line in each oriented direction. A projective hedgehog is a restricted type of hedgehog, defined from an anti-symmetric support function, and (again when sufficiently well-behaved) forms a curve with one tangent line in each direction, regardless of orientation.

Not to be confused with hedgehog (hypergraph) or hedgehog space.

Every closed strictly convex curve, the envelope of its supporting lines. The astroid forms a non-convex hedgehog, and the deltoid curve forms a projective hedgehog.

Hedgehogs can also be defined from support functions of hyperplanes in higher dimensions.

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