A class of cubic Bézier-type curves based on the blending of algebraic and trigonometric polynomials, briefly CAT Bézier curves, is presented in this paper. The CAT Bézier curves retain the main superiority of cubic Bézier curves. The CAT Bézier curves can approximate the Bézier curves from the both sides, and the shapes of the curves can be adjusted totally or locally. With the shape parameter...

We present an efficient geometric algorithm for conic spline curve fitting and fairing through conic arc scaling. Given a set of planar points, we first construct a tangent continuous conic spline by interpolating the points with a quadratic Bézier spline curve or fitting the data with a smooth arc spline. The arc spline can be represented as a piecewise quadratic rational Bézier spline curve. ...

The objective of this paper is to provide an ef®cient and reliable algorithm for representing and evaluating the boundary of the interval Be Âzier curve in 2-and 3-D. The boundary of the planar Be Âzier curve is represented by a sequence of Be Âzier curve segments with same degree and line segments in the order they are encountered when marching counterclockwise along its boundary. The boundary...

We present the result and accuracy comparison of generalized positivitypreserving schemes for triangular Bézier patches of 1 C and 2 C scattered data interpolants that have been constructed. We compare three methods of 1 C schemes using cubic triangular Bézier patches and one 2 C scheme using quintic triangular Bézier patches. Our test case consists of four sets of node/test function pairs, wit...

Spiral segments are useful in the design of fair curves. They are important in CAD/CAM applications, the design of highway and railway routes, trajectories of mobile robots and other similar applications. Cubic Bézier curves are commonly used in curve and surface design because they are of low degree, are easily evaluated, and allow inflection points. This paper generalises earlier results on p...

The paper presents a technique for construction of C interpolating rational Bézier spline curves by means of blending rational quadric Bézier curves. A class of polynomials which satisfy special boundary conditions is used for blending. Properties of the polynomials are considered. The constructed spline curves have local shape control that make them useful in such geometric applications as rea...

Abstract Bezier curves are indispensable for geometric modelling and computer graphics. They have numerous favourable properties provide the user with intuitive tools editing shape of a parametric polynomial curve. Even more control flexibility can be achieved by associating parameter each point considering rational curves, which comes additional advantage being able to represent all conic sect...