Developable surface and line of curvature play an important role in geometric design and
surface analysis. This paper proposes a new method to construct a developable surface …

In this paper we first define the involutive sweeping surfaces as a new surface form. We then
investigate singularity, Gaussian and mean curvatures of these surfaces. By calculating the …

We construct a surface family possessing an involute of a given curve as an asymptotic
curve. We express necessary and sufficient conditions for that curve with the above property …

Offset surface pencil with a common asymptotic curve Page 1 International Journal of
Geometric Methods in Modern Physics Vol. 15, No. 11 (2018) 1850195 (11 pages) c© World …

In this paper, we analyzed surfaces family possessing a Mannheim partner of a given curve
as a asymptotic. Using the Frenet frame of the curve in Euclidean 3-space, we express the …

In this paper, we obtain the necessary and sufficient conditions of a surface pencil pair
interpolating a Bertrand pair as common asymptotic curves in Euclidean 3-space E 3 …

An orthonormal frame (f 1, f 2, f 3) is rotation-minimizing with respect to fi if its angular
velocity ω satisfies ω⋅ fi≡ 0—or, equivalently, the derivatives of fj and fk are both parallel to …

In this paper, we obtain the parametric representation for a family of surfaces through a
given asymptotic curve by using the Frenet frame in the Galilean space G3. Necessary and …

In recent years, 3D data has been widely used in archaeology and in the field of
conservation and restoration of cultural properties. Virtual restoration, which reconstructs the …

We analyzed the problem of finding a surfaces family through an asymptotic curve with
Cartan frame. We obtain the parametric representation for surfaces family whose members …