In this paper, we consider multi-degree reduction of Bézier curves with constraints of endpoints continuity with respect to L2 norm. The control points of the degree reduced Bézier curve can be obtained as a product of the degree reduction matrix and the vector of original control points. We find an explicit form of the multi-degree reduction matrix for Bézier curve with constraints of endpoint...

A new heuristic method of geometric Hermite interpolation is presented to construct a planar cubic rational Bézier curve with two points and two unit tangent directions. The integral, which shows the change rate of the curvature, is taken as the energy function to measure the fairness of the parameter curve. Hence the curvature of the new curve is more stable. Since that the energy function of ...

Quadratic Bézier curves are important geometric entities in many applications. However, it was often ignored by the literature the fact that a single segment of a quadratic Bézier curve may fail to fit arbitrary endpoint unit tangent vectors. The purpose of this paper is to provide a solution to this problem, i.e., constructing G quadratic Bézier curves satisfying given endpoint (positions and ...

In this paper, we improve the generalized Bernstein basis functions introduced by Han, et al. The new basis functions not only inherit the most properties of the classical Bernstein basis functions, but also reserve the shape parameters that are similar to the shape parameters of the generalized Bernstein basis functions. The degree elevation algorithm and the conversion formulae between the ne...

Based on the technique of C-shape G Hermite interpolation by cubic Pythagorean-Hodograph (PH) curve, we present a simple method for Cshape G Hermite interpolation by rational cubic Bézier curve. The method reproduces a circular arc when the input data come from it. Both the Bézier control points, which have the well understood geometrical meaning, and the weights of the resulting rational cubic...

We construct the Stancu-type generalization of q-Bernstein operators involving idea Bézier bases depending on shape parameter ?1???1 and obtain auxiliary lemmas. discuss local approximation results in term a Lipschitz-type function based two parameters maximal function, as well other related for our newly constructed operators. Moreover, we determine rate convergence by means Peetre’s K-functio...

We propose the extended Bézier spiral in this paper. The spiral is useful for both design purposes and improved aesthetics. This is because the spiral is one of the Bézier curves, which play an important role in interactive curve design, and because the assessment of the curve is based on the human reception of the curve. For the latter purpose we utilize the logarithmic distribution graph that...

In this paper a computationally effective trajectory generation algorithm of mobile robots is proposed. The algorithm plans a reference path based on Voronoi diagram and Bézier curves, that meet obstacle avoidance criteria. Bézier curves defining the path are created such that the circumference convex polygon of their control points miss all obstacles. To give smoothness, they are connected und...

We classify mutual position of a quadratic Bézier curve and a regular quadric in three dimensional Euclidean space. For given first and last control point, we find the set of all quadratic Bézier curves having no common point with a regular quadric. This system of such quadratic Bézier curves is represented by the set of their admissible middle control points. The spatial problem is reduced to ...

An explicit expression for the unique implicitization of any planar rational cubic Bézier curve is presented, the only exception being when the tangents at the ends of the curve are parallel. The representation is in the form of a cubic Bernstein-Bézier triangle and is invariant under affine transformations of the curve. The implicitization degenerates to zero if and only if the curve degenerat...