The present study discusses several approaches of representing curve boundaries with high-order Euler solvers. The aim is to minimize the solution entropy error. The traditional boundary representation based on interpolation polynomials is presented first. A new boundary representation based on the Bezier curve is then developed and analyzed. Several numerical tests are conducted to compare bot...

The paper consists of two parts. In the first, an interrogation method for a visualization of curvature behaviour is introduced. The method consists of a generalized focal analysis. The second part concerns the accurate computation of surface behaviour. Arithmetic operations on BBzier surfaces are used to achieve au exact representation of surface properties. With these property surfaces in Bez...

in this paper, a new numerical method is presented for solvingthe optimal control problems of bang-bang type with free or xed terminaltime. the method is based on bezier polynomials which are presented inany interval as [t0; tf ]. the problems are reduced to a constrained problemswhich can be solved by using lagrangian method. the constraints ofthese problems are terminal state and conditions....

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...

A range restricted C interpolation local scheme to scattered data is derived. Each macro triangle of the triangulated domain is split into three mini triangles and the interpolating surface on each mini triangle is a cubic Bézier triangle. Sufficient conditions derived for the non-negativity of these cubic Bézier triangles are expressed as lower bounds to the Bézier ordinates. The non-negativit...

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...

A design of a class of linkages is presented which are less complex than those suggested by Kapovich and Millson in the con…guration of conventional planar linkages. Conventional linkage constraints are relaxed allowing sliding joints and telescoping links. The precise number of …xed links, telescoping links, and sliding contacts is determined for this modern linkage to trace a Bézier curve of ...

The design of curves and surfaces in C.A.D. systems has many applications in car, plane or ship industry. Because they offer more flexibility, rational functions are often prefered to polynomial functions to modelize curves and surfaces. In this work, several methods to generate rational Bezier curves and surfaces which minimize some functionals are proposed. The functionals measure a technical...