Recently, Savadjiev et al. introduced a generalized helicoid as an osculating object to characterize near parallel 3D curve patterns. This new model allows for patterns of different kinds to be examined and generated via three curvature parameters. The parameterization can be efficiently used to model hair strands. We present an investigation of the usability of the generalized helicoid model f...

A set of equations is developed to describe a curve in space given the curvature κ and the angle of rotation θ of the osculating plane. The set of equations has a solution (in terms of κ and θ) that indirectly solves the Frenet-Serret equations, with a unique value of θ for each specified value of τ . Explicit solutions can be generated for constant θ. The equations break down when the tangent ...

Abstract. Let X ⊂ Pr be a smooth algebraic curve in projective space, over an algebraically closed field of characteristic zero. For each m ∈ N, the m-flexes of X are defined as the points where the osculating hypersurface of degree m has higher contact than expected, and a hypersurface H ⊂ Pr is called a m-Hessian if it cuts X along its m-flexes. When X is a complete intersection, we give an e...

Basic sphere geometric principles are used to analyze approximation schemes of developable surfaces with cone spline surfaces, i.e. G1surfaces composed of segments of right circular cones. These approximation schemes are geometrically equivalent to the approximation of spatial curves with G1-arc splines, where the arcs are circles in an isotropic metric. Methods for isotropic biarcs and isotrop...

The theory of Finsler metric was introduced by Paul Finsler, in 1918. author defines this using the Minkowski norm instead inner product. Therefore, geometry is a more general and includes Riemannian metric. In present work, metric, we investigate position vector rectifying, normal osculating curves Finslerian 3-space $\mathbb{F}^{3}$. We obtain characterizations these Furthermore, show that re...

This paper is about new iso-parametric tool path planning for machining trimmed freeform surfaces. The trimmed surface has been re-parameterized by two different parameterization techniques, namely, the partial differential equation method and the newly developed boundary interpolation method. The efficiency of the scheme has been measured in terms of path length and computational time needed f...

Schubert curves are the spaces of solutions to certain one-dimensional Schubert problems involving žags osculating the rational normal curve. e real locus of a Schubert curve is known to be a natural covering space of RP1, so its real geometry is fully characterized by the monodromy of the cover. It is also possible, using K-theoretic Schubert calculus, to relate the real locus to the overall (...

ABSTRACT: In this paper we improve the known bound for the X-rank RX(P ) of an element P ∈ PN in the case in which X ⊂ Pn is a projective variety obtained as a linear projection from a general v-dimensional subspace V ⊂ Pn+v . Then, if X ⊂ Pn is a curve obtained from a projection of a rational normal curve C ⊂ Pn+1 from a point O ⊂ Pn+1, we are able to describe the precise value of the X-rank f...