Hedgehog

A hedgehog is an envelope parameterized by its Gauss map (Martinez-Maure 1996). Viewed another way, a hedgehog is a Minkowski difference of a convex body (Martinez-Maure 2003, 2004).

In two dimensions, the parametric equations for a hedgehog are

(1) (2)

(correcting a sign error in Martinez-Maure 1996). A plane convex hedgehog has at least four polygon vertices where the curvature has a stationary value. A plane convex hedgehog of constant width has at least six vertices (Martinez-Maure 1996).

For definitions of a hedgehog in dimensions, see Martinez-Maure (2001).