High Quality Content by WIKIPEDIA articles! In mathematics, an envelope of a family of manifolds (especially a family of curves) is a manifold that is tangent to each member of the family at some point.A one-parameter family Ct of smooth curves in the plane, parameterised by t in an open interval I, can be described as the zero loci of a family of smooth functions F : I x R2 -> R. Holding t fixed, F determines a function in x and y alone via ft(x,y) := F(t,(x,y)). The curve Ct is then identified with the zero locus of ft. Assume that, for all t, 0 R is a regular value or ft.

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