"How to find any $n^{th}$ order B\'{e}zier curve if we know its first, second, and third derivatives?" Hence have examined the way based on control points with matrix form, while derivatives are given in $\mathbf{E}^{3}$. Further, of a cubic as an example. In this study first how Bezier known second derivatives, which inherently, $\left( n-1\right) ^{th}$ order, $\left(n-2\right) n-3\right) cur...

The smooth interpolation of keyframes of a rigid body, in particular their orientations, is an important problem in animation . Using the quaternion as a representation for orientation, several papers have solved this problem through the generation of smooth curves on the quaternion sphere. However, none of these methods have constructed rational curves. This paper develops a method for generat...

It is an important problem to compute the geodesics on a surface in many fields. To find the geodesics in practice, however, the traditional discrete algorithms or numerical approaches can only find a list of discrete points. The first author proposed in 2010 a new, elegant and accurate method, the geodesic-like method, for approximating geodesics on a regular surface. This paper will present b...

However, we cannot easily control the curve locally. That is, any change to an individual control point will cause changes in the curve along its full length. In addition, we cannot create a local cusp in the curve, that is, we cannot create a sharp corner unless we create it at the beginning or end of a curve where it joins another curve. Finally, it is not possible to keep the degree of the B...

There are many ways to approximate cosine curve. In this study we have examined the way how curve can be written as any order Bezier As a result using Maclaurin series 4th and 6th based on control points with matrix form in E2. We give of coefficients. Also coefficients too.

We describe the structure and use of an interactive modeling and visualization tool used to help students understand various important concepts in curve and surface design. This paper describes those aspects of the tool related to NURBS curves, but Bezier and Hermite curves are also supported as are Bezier and B-Spline surfaces. The focus of this paper is almost exclusively on those features of...

The Bezier formulation for parametric curves has many quali ties, among them the intuitive relationship between the shape of the control polygon and the shape of the curve , and the case of computation and subdivision. Other formulations , however, have become more popular because they offer local control, or because they are interpolating, or even more recently because they provide the added f...