Properties of a parametric curve in R 3 are often determined by analysis of its piecewise linear (PL) approximation. For Bézier curves, there are standard algorithms, known as subdivision, that recursively create PL curves that converge to the curve in distance. The exterior angles of PL curves under subdivision are shown to converge to 0 at the rate of O(1 2 i), where i is the number of subdiv...

The use of Bezier curves and Bezier triangles has been extensively explored in the field of computer graphics. The purpose of this paper is to show that Bezier triangles and curves can be used for reducing the cost of Biquadratic Phong shading. A shading algorithm has been proposed which uses quadratic Bezier triangle’s blending functions for performing quadratic interpolation of normal vector ...

The generation of technical smooth surfaces from a mesh of three-dimensional data points is an important problem in geometric modelling. In this publication we give a survey of some new techniques based on a calculus of variation approach. Apart from the pure construction of these surfaces, the analysis of their quality is equally important in the design and manufacturing process. Generalized f...

A technique has been designed for capturing outlines by exploiting the properties of cubic Bezier curves. The planar images are used to extract the outline. The outline is divided into curve segments at high curvature points and each segment is processed independently for piecewise curve approximation. The proposed algorithm avoids the traditional method of least square fitting which is time co...

In this paper, we present an obstacle avoiding path planning method based on Voronoi diagram and composite Bezier curve algorithm which obtains the shortest path length. In our algorithm, a Voronoi diagram is constructed according to the global environment. The piecewise linear rough path in the Voronoi diagram which keeps away from the obstacles is obtained by performing Dijkstra’s shortest pa...

This paper presents a smooth path planning method considering physical limits for twowheeled mobile robots (TMRs). A Bezier curve is utilized to make an S-curve path. A convolution operator is used to generate the center velocity trajectory to travel the distance of the planned path while considering the physical limits. The trajectory gained through convolution does not consider the direction ...

Existing Bezier curve based shape description techniques primarily focus upon determining a set of pertinent Control Points (CP) to represent a particular shape contour. While many different approaches have been proposed, none adequately consider domain specific information about the shape contour like its gradualness and sharpness, in the CP generation process which can potentially result in l...