Abstract
In this paper, a new modified roller coaster surface according to a modified orthogonal frame is investigated in Euclidean 3-space. In this method, a new modified roller coaster surface is modeled. Both the Gaussian curvature and mean curvature of roller coaster surfaces are investigated. Subsequently, we obtain several characterizations in Euclidean 3-space.
Highlights
In differential geometry, the search for certain classes of surfaces with particular features in three-dimensional Euclidean space, such as ruled and developable surfaces which are 1-parameter smooth families of straight lines, has a significant role in the field of civil engineering and architecture (CAD) [1,2,3,4,5,6]
One aim of classical differential geometry is the investigation of several classes of surfaces with specific properties, for example, ruled surfaces and revolution surfaces
A canonical circular surface is characterised by a circle crosscut and in which the normal of the circle plane is usually parallel to that of the crosscut
Summary
The search for certain classes of surfaces with particular features in three-dimensional Euclidean space, such as ruled and developable surfaces which are 1-parameter smooth families of straight lines, has a significant role in the field of civil engineering and architecture (CAD) [1,2,3,4,5,6]. A canonical circular surface is characterised by a circle crosscut and in which the normal of the circle plane is usually parallel to that of the crosscut. A noncanonical circular surface is defined by a non-circular crosscut and the normal of the circle plane is usually not parallel to that of the crosscut. RR circular surface, the spine curve is a circle; the normal of a circle plane is generally not parallel with the normal of a crosscut. Tuncer et al [23,24] studied circular surfaces and roller coaster surfaces through theuse of unit quaternions. A modified roller coaster surface according to modified orthogonal frame isinvestigated in Euclidean 3-space. A novel, modified roller coaster is modeled. We obtain severalcharacterizations in the Euclidean 3-space
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