An algorithm is presented to approximate planar offset curves within an arbitrary tolerance > 0. Given a planar parametric curve C(t) and an offset radius r, the circle of radius r is first approximated by piecewise quadratic Bézier curve segments within the tolerance . The exact offset curve Cr(t) is then approximated by the convolution of C(t) with the quadratic Bézier curve segments. For a p...

The parametric or geometric continuity of a rational polynomial curve has often been obtained by requiring the homogeneous polynomial curve associated with the rational curve to possess parametric or geometric continuity, respectively. Recently this approach has been shown overly restrictive. We make use of the necessary and su cient conditions of rational parametric continuity for de ning basi...

According to Western religion, galaxies are designed by the Creator. Dr. Jin He found many evidences that galaxies are rational distribution of stars. Rational structure in two dimension means that not only there exists an orthogonal net of curves in the plane but also, for each curve, the stellar density on one side of the curve is in constant ratio to the density on the other side of the curv...

The main goal of this paper is to propose a new practical method for hydrologic soil group estimation in surface runoff process based on geomorphology facieses and slop. The determination of CN based on this method can reduce the time and cost of project. In this research the upstream rivers of Glinak Watershed have been used as a case study to examine the efficiency of proposed method with a c...

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...

I. Introduction Rational spline is a commonly used spline function. In many cases the rational spline curves better approximating functions than the usual spline functions. It has been observed that many simple shapes including conic section and quadric surfaces can not be represented exactly by piecewise polynomials, whereas rational polynomials can exactly represent all conic sections and qua...

In this paper, a class of rational spatial curves that have a rational binormal is introduced. Such curves (called PB curves) play an important role in the derivation of rational rotation-minimizing conformal frames. The PB curve construction proposed is based upon the dual curve representation and the Euler-Rodrigues frame obtained from quaternion polynomials. The construction significantly si...

This paper presents an algorithm for optimal multi-degree reduction of rational disk Bézier curve in the L norm. We start by introducing a novel disk rational Bézier based on parallel projection, whose properties are also discussed. Then we transform multi-degree reduction of the error radius curve and the weight curve of the disk rational Bézier curve into solving a constrained quadratic progr...

Keywords: Arbitrary order derivative Derivative formula Rational Bézier curve a b s t r a c t In this paper, we develop the exact arbitrary order derivative formula of a rational Bézier curve at its corner. Some examples are presented to demonstrate the computation of the exact derivatives. Derivative formula of a parametric curve has important applications in geometric design and applied mathe...