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About: Hedgehog (geometry)     Goto   Sponge   NotDistinct   Permalink

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