The distance between a Be-....ier segment and its control polygon is bounded in terms of the second differences of the control point sequence and a constant that depends only on the degree of the polynomial. The constant derived here is the smallest possible and is sharp for the Hausdorff distance between control polygon and curve segment. The bound provides a straightforward proof of quadratic...

In this paper, we analyze the planar cubic Alternative curve to determine the conditions for convex, loops, cusps and inflection points. Thus cubic curve is represented by linear combination of three control points and basis function that consist of two shape parameters. By using algebraic manipulation, we can determine the constraint of shape parameters and sufficient conditions are derived wh...

In this paper we present an efficient technique for piecewise cubic Bézier approximation of digitized curve. An adaptive breakpoint detection method divides a digital curve into a number of segments and each segment is approximated by a cubic Bézier curve so that the approximation error is minimized. Initial approximated Bézier control points for each of the segments are obtained by interpolati...

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...

To determination the volume and weight of nonuniform bodies, such as in ore deposits evaluation for mining and rock cutting for construction, the methods of interpolation are usually used. The classic curves, which are frequently used to interpolate one-dimensional data are cubic spline, Bspline and Bezier curves. These methods have good efficiency for determination of geometric characteristics...

Non-self-intersection is both a topological and a geometric property. Recent theorems show how non-self-intersecting Bézier curves also have non-self-intersecting control polygons, after sufficiently many uniform subdivisions. As a partial generalization, a sufficient condition is given within R for a non-self-intersecting, C cubic Bézier curve to be ambient isotopic to its control polygon form...

wind power has been widely considered in recent years as an available and a clean renewable energy source. the cost of wind energy production is currently the main issue, and increasing the size of wind turbines can reduce wind energy production costs. hence, megawatt wind turbines are being rapidly developed in recent years. in this paper, an aerodynamic analysis of the nrel 5mw turbine is car...

Analogous to the cubic Bézier curve, a quartic trigonometric Bézier curve with a shape parameter is presented in this paper. Each curve segment is generated by four consecutive control points. The shape of the curve can be adjusted by altering the values of shape parameters while the control polygon is kept unchanged. These curves are closer to the control polygon than the cubic Bézier curves, ...