This paper presents a simple matrix form for degree elevation of interval Bezier curve using LegendreBernstein basis transformations. The four fixed Kharitonov's polynomials (four fixed Bezier curves) associated with the original interval Bezier curve are obtained. These four fixed Bezier curves are expressed in terms of the Legendre polynomials. The process of degree elevations r times are app...

In this paper problem for converting a circular arc into cubic Bezier arc and approximation of cubic Bezier curve by a set of circular arcs are discussed. These questions occur in CAD/CAM systems during data exchange from data formats which support Bezier curves or during data exchange into data formats, which do not support Bezier curves. Some simple and practical solutions are proposed. An al...

We present two practical path planning algorithms based on Bezier curves for autonomous vehicles operating under waypoints and corridor constraints. Bezier curves have useful properties for the trajectory generation problem. This paper describes how the algorithms apply these properties to generate the reference trajectory for vehicles to satisfy the path constraints. Both algorithms generate t...

O. Ismail, Senior Member, IEEE Abstract— Fixed DP curve is a recent representation of the polynomial curves, proposed by Delgado and Pena in 2003. They introduced a new curve representation with linear computational complexity. An algorithmic approach to degree reduction of interval DP curve is presented in this paper. The four fixed Kharitonov's polynomials (four fixed DP curves) associated wi...

Ball basis was introduced for cubic polynomials by Ball, and was generalized for polynomials of higher degree by Said. An algorithmic approach to degree reduction of interval Said-Ball (SB) curve is presented in this paper. The four fixed Kharitonov's polynomials (four fixed SB curves) associated with the original interval SB curve are obtained. These four fixed SB curves are transformed into f...

We develop an efficient algorithm for the construction of common tangents between a set of Bezier curves. Common tangents are important in visibility, lighting, robot motion, and convex hulls. Common tangency is reduced to the intersection of parametric curves in a dual space, rather than the traditional intersection of implicit curves. We show how to represent the tangent space of a plane Bezi...

In this paper an improved version of an earlier proposed algorithm for approximating cubic Bezier curve by a set of circular arcs is presented. It is investigated how the improved algorithm fits for approximation of quadratic Bezier curves. These issues occur in CAD/CAM systems during data exchange into data formats which do not support Bezier curves. Experimental results on examples, widely us...

introduction 3d reconstruction of an object from its 2d cross-sections (slices) has many applications in different fields of sciences such as medical physics and biomedical engineering. in order to perform 3d reconstruction, at first, desired boundaries at each slice are detected and then using a correspondence between points of successive slices surface of desired object is reconstructed. mate...

Wang-Ball (WB) curve is one of the generalized cubic Ball basis which was first put forward in CONSURF system by Ball. Wang extended it to arbitrary odd and even degrees. An algorithmic approach to degree reduction of interval Wang-Ball curve is presented in this paper. The four fixed Kharitonov's polynomials (four fixed WB curves) associated with the original interval WB curve are obtained. Th...