Offset surface pencil with a common asymptotic curve

Abstract

Let [Formula: see text] be a parameter and an asymptotic curve on a surface [Formula: see text] We obtain conditions for offsets [Formula: see text] of [Formula: see text] such that the image [Formula: see text] of the curve [Formula: see text] is a common asymptotic on each offset. We illustrate the method with an example.

Surface family interpolating a common spherical indicatrix curve

“…The study of curves and surfaces has wide application areas such as architectural design, computer aided design, astronomy, astrophysics and genetics [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. We encounter curves and surfaces in every differential geometry book.…”

Involutive sweeping surfaces with Frenet frame in Euclidean 3-space

“…From a different point of view, the coupled non-dispersion (CD) equation from the motion of the involute evolute curve family, which provides a suitable interpretation for the integrability conditions is introduced in [15] . Further on, in order to synthesize interdisciplinary papers, we would like to note some of the important studies on ruled surfaces and surface family in different spaces [16] , [17] , [18] , [19] , [20] , [21] , [22] , [23] , [24] , [25] , [26] , [27] , [28] , [29] , [30] .…”

The Parallel Trajectory Ruled Surfaces

“…For example, in CAD, vehicle design, architecture etc. We can see research on these surfaces in related studies, [7][8][9][10][11]. In this paper, we defined the trajectory ruled surfaces with parallel curve which is defined using binormal vector field of given a curve.…”