Curves in space are diicult to perceive and analyze, especially when they form dense sets as in typical 3D ow and volume deformation applications. We propose a technique that exposes essential properties of space curves by attaching an appropriate moving coordinate frame to each point, reexpressing that moving frame as a unit quaternion, and supporting interaction with the resulting quaternion ...

A novel geometrically exact model of the spatially curved Bernoulli–Euler beam is developed. The formulation utilizes Frenet–Serret frame as reference for updating orientation a cross section. weak form consistently derived and linearized, including contributions from kinematic constraints configuration-dependent load. nonlinear terms with respect to cross-sectional coordinates are strictly con...

There is increasing interest in the recovery of generalized cylinders (GCs) with curved spines. However, existing formulations of such GCs, for example those based on the Frenet-Serret frame or the tube model, suuer serious drawbacks: discontinuities, a lack of expressive power, \narrowing" in the plane normal to the spine, non-intuitive twisting behavior, and/or oo-axis nonorthogonality of the...

We consider a curve α = α(s) in Minkowski 3-space E31 and denote by {T,N,B} the Frenet frame of α. We say that α is a slant helix if there exists a fixed direction U of E31 such that the function 〈N(s), U〉 is constant. In this work we give characterizations of slant helices in terms of the curvature and torsion of α. MSC: 53C40, 53C50

In this study, we examine some properties of Salkowski curves in $\mathbb{E}^{3}$. We then make sense the angle $(nt)$ parametric equation curves. provide relationship between and binormal vector Darboux Through angle, obtain unit direction curve. Finally, calculate modified orthogonal frames with both curvature torsion give relationships Frenet frame

In this paper, we present a new method to evaluate the moving Frenet frame along intersection curves of two parametric surfaces in tangential situations. To resolve such situation, have combined perturbation with classical that works transversal situation. Unlike existent methods, our even if order contact point is more than one.

In this study, we investigate how to construct surfaces using a line of curvature in 3-dimensional Lie group. Then, by utilizing the Frenet frame, give conditions that curve becomes on surface when marching-scale functions are more general expressions. After then, provide some crucial examples efficient our method is these surfaces.

In this paper, the adjoint curve is defined by using alternative moving frame of a unit speed space in 3-dimensional Euclidean space. The relationships between Frenet vectors and are used to offer various characterizations. Besides, ruled surfaces constructed with its curve, their properties examined. last section, there examples curves previous sections.

A repetitive crystal-like pattern is spontaneously formed upon the twisting of straight ribbons. The pattern is akin to a tessellation with isosceles triangles, and it can easily be demonstrated with ribbons cut from an overhead transparency. We give a general description of developable ribbons using a ruled procedure where ribbons are uniquely described by two generating functions. This constr...

The projected deformation of stationary contours and markings on object surfaces is analyzed in this paper. It is shown that given a marked point on a stationary contour, an active observer can move deterministically to the osculating plane for that point by observing and controlling the deformation of the projected contour. Reaching the osculating plane enables the observer to recover the obje...