Envelope of A Family of Surfaces
A one-parameter family of surfaces in three-dimensional Euclidean space is given by a set of equations
depending on a real parameter a. For example the tangent planes to a surface along a curve in the surface form such a family.
Two surfaces corresponding to different values a and a' intersect in a common curve defined by
In the limit as a' approaches a, this curve tends to a curve contained in the surface at a
This curve is called the characteristic of the family at a. As a varies the locus of these characteristic curves defines a surface called the envelope of the family of surfaces.
The envelope of a family of surfaces is tangent to each surface in the family along the characteristic curve in that surface.
Read more about this topic: Envelope (mathematics)
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