On evolutoids of regular surfaces in Euclidean 3-space

Abstract

Inspired by the concept of evolutoids of planar curves, we present the concept of evolutoids for regular surfaces as an envelope of a two-parameter family of lines in Euclidean 3-space. We give an explicit parametrization for such evolutoids. Besides, we used the theory of singularities to study the local behavior of regular points of this object and presented some relations between the geometry of the regular surface and its evolutoid.