New derivative bounds for the rational quadratic Bézier paths are obtained, both for particular weight vectors and for classes of equivalent parametrisations. A comprehensive analysis of our bounds against existing bounds is made.

A class of single-valued curves in polar coordinates, which we refer to as p-B ezier curve, has been recently presented by SS anchez-Reyes and independently discovered by P.de Casteljau. From their deenition and expression in terms of the Fourier basis it is obvious that every curve of degree n can be expressed as a curve of degree kn, for any natural value k. In this paper, we provide a formul...

We consider a rational triangular Bézier surface of degree n and study conditions under which it is rationally parameterized by chord lengths (RCL surface) with respect to the reference circle. The distinguishing property of these surfaces is that the ratios of the three distances of a point to the three vertices of an arbitrary triangle inscribed to the reference circle and the ratios of the d...

In this paper we propose a tensor based description of the Bézier Shape Deformation (BSD) algorithm, denoted T-BSD. The BSD algorithm is a well-known technique, based on the deformation of a Bézier curve through a field of vectors. A critical point in the use of real-time applications is the cost in computational time. Recently, the use of tensors in numerical methods has been increasing becaus...

In this paper we propose a tensor based description of the Bézier Shape Deformation (BSD) algorithm, denoted T-BSD. The BSD algorithm is a well-known technique, based on the deformation of a Bézier curve through a field of vectors. A critical point in the use of real-time applications is the cost in computational time. Recently, the use of tensors in numerical methods has been increasing becaus...

Bézier curves are a widespread tool for the design of curves in Euclidian space. This paper generalizes the notion of Bézier curves to the infinite-dimensional space of images. To this end the space of images is equipped with a Riemannian metric which measures the cost of image transport and intensity variation in the sense of the metamorphosis model [MY01]. Bézier curves are then computed via ...

In this paper, a geometric model is introduced for Neutrosophic data problem for the first time. This model is based on neutrosophic sets and neutrosophic relations. Neutrosophic control points are defined according to these points, resulting in neutrosophic Bézier curves.

The offset surfaces to non-developable quadratic triangular Bézier patches are rational surfaces. In this paper we give a direct proof of this result and formulate an algorithm for computing the parameterization of the offsets. Based on the observation that quadratic triangular patches are capable of producing C smooth surfaces, we use this algorithm to generate rational approximations to offse...

We present a new method of surface generation from prescribed boundaries based on the elliptic partial differential operators. In particular, we focus on the study of the so-called harmonic and biharmonic Bézier surfaces. The main result we report here is that any biharmonic Bézier surface is fully determined by the boundary control points. We compare the new method, by way of practical example...

Using algebraic geometry methods and Bernstein-Bézier techniques we find the dimension of C1-continuous splines on the Alfeld split of a simplex in Rn and describe a minimal determining set for this space.