Given a point and a rational curve in the plane, their bisector curve is rational 2]. However, in general, the bisector of two rational curves in the plane is not rational 3]. Given a point and a rational space curve, this paper shows that the bisector surface is a rational ruled surface. Moreover, given two rational space curves, we show that the bisector surface is rational (except for the de...

In this paper, we study a geometric G^2 Hermite interpolation by planar rational cubic Bézier curves. Two data points, two tangent vectors and two signed curvatures interpolated per each rational segment. We give the necessary and the sufficient intrinsic geometric conditions for two C^2 parametric curves to be connected with G2 continuity. Locally, the free parameters w...

Given a faithful parameterization P(t) of a rational plane curve, an inversion formula t = f(x,y) gives the parameter value corresponding to a point (x,y) on the curve, where f is a rational function in x and y. We investigate the relationship between a point (x*, y*) not on the curve and the corresponding point P(t*) on the curve, where t* = f(x*, y*). It is shown that for a rational quadratic...

This paper presents a simple method for approximating a rational Bézier curve with Bézier curve sequence, whose control points are those of degree-elevated rational Bézier curves. It is proved that the derivatives with any given degree of the Bézier curve sequence constructed this way would uniformly converge to the corresponding derivatives of the original rational Bézier curve. © 2008 Publish...

We characterize all (n?2)-dimensional linear subspaces of Pn such that the induced projection, when restricted to rational normal curve, gives a Galois morphism. give an explicit description these spaces as disjoint union locally closed subvarieties in Grassmannian G(n?2,n).

This review provides the basic principle and rational for ROC analysis of rating and continuous diagnostic test results versus a gold standard. Derived indexes of accuracy, in particular area under the curve (AUC) has a meaningful interpretation for disease classification from healthy subjects. The methods of estimate of AUC and its testing in single diagnostic test and also comparative studies...

We exhibit a genus–2 curve C defined over Q(T ) which admits two independent morphisms to a rank–1 elliptic curve defined over Q(T ). We describe completely the set of Q(T )–rational points of the curve C and obtain a uniform bound for the number of Q–rational points of a rational specialization Ct of the curve C for a certain (possibly infinite) set of values t ∈ Q. Furthermore, for this set o...