Related papers: How can we construct a k-slant curve from a given …
In this paper we show how, under surprisingly weak assumptions, one can split a planar curve into three arcs and rearrange them (matching tangent directions) to obtain a closed curve. We also generalize this construction to curves split…
This paper proposes a simple technique of curve and surface construction with B-splines. Given a control polygon or a control mesh together with node ordinates corresponding to all control points, a rational curve or surface is obtained by…
A method is proposed to construct spiral curves by inversion of a spiral arc of parabola. The resulting curve is rational of 4-th order. Proper selection of the parabolic arc and parameters of inversion allows to match a wide range of…
In this note is we exhibit an elementary method to construct explicitly curves over finite fields with many points. Despite its elementary character the method is very efficient and can be regarded as a partial substitute for the use of…
We produce several algebraic curves, some well--known, some new, out of circles, by means of two classical (mutually reciprocal) algebraic methods: blow--down and blow--up.
In this paper we give several methods to construct curves over finite fields with many points and illustrate this with examples of the results.
We present a framework for constructing examples of smooth projective curves over number fields with explicitly given elements in their second K-group using elementary algebraic geometry. This leads to new examples for hyperelliptic curves…
In this paper, we give smoe characterizations of relatively normal-slant helices and isophotic curves on a smooth surface immersed in Euclidean 3-space with respect to their position vevtor. We also introduce the methods for generating an…
Surfaces and curves play an important role in geometric design. In recent years, problem of finding a surface passing through a given curve has attracted much interest. In the present paper, we propose a new method to construct a surface…
Cyclic curves, i.e. curves fixed by a cyclic collineation group, play a central role in the investigation of cyclic arcs in Desarguesian projective planes. In this paper, the genus of a cyclic curve arising from a cyclic k-arc of Singer…
This paper addresses a very classical topic that goes back at least to Pl\"ucker: how to understand a plane curve singularity using its polar curves. Here, we explicitly construct the singular points of a plane curve singularity directly…
We present an explicit method that, given a generic tuple of Dixmier-Ohno invariants, reconstructs a corresponding plane quartic curve.
Surfaces and curves play an important role in geometric design. In recent years, problem of finding a surface passing through a given curve have attracted much interest. In the present paper, we propose a new method to construct a surface…
In this paper, we de\"One a new type curve as V-Mannheim curve, V Mannheim partner curve and generating curve of Mannheim curve. We give characterization of these curve. In addition, we study a relation between Mannheim curve and spherical…
In this paper, we define a new special curve in Euclidean 3-space which we call {\it $k-$slant helix} and introduce some characterizations for this curve. This notation is generalization of a general helix and slant helix. Furthermore, we…
A method is proposed for constructing a spline curve of the Bezier type, which is continuous along with its first derivative by a piecewise polynomial function. Conditions for its existence and uniqueness are given. The constructed curve…
We show that we can obtain a reducible spherical curve from any non-trivial spherical curve by four or less inverse-half-twisted splices, i.e., the reductivity, which represents how reduced a spherical curve is, is four or less. We also…
We construct a conformally invariant random family of closed curves in the plane by welding of random homeomorphisms of the unit circle given in terms of the exponential of Gaussian Free Field. We conjecture that our curves are locally…
Geometric constructions are widely used in computer graphics and engineering drawing. A right generalized cylinder is a ruled surface whose base curve is a plane curve perpendicular to the rulings. The paper discusses relations between the…
For given convex set $K$ in the plane (not necessarily bounded), we can construct the curve $C$ for which the visibility (aperture) angle of this set has the same, prescribed value. We give the implicit formula for $C$, discuss some issues…