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 goal of this paper is to characterize the evolute, involute and parallel curves a Bezier curve which applicable computer graphics related subjects. Especially, these couples are investigated at endpoints. Moreover, curvatures given.

An efficient method to segment eyed typhoon from a satellite cloud image is proposed. First, original satellite cloud image is enhanced by gray transform. Second, in order to reduce the computation burden to segment the whole satellite cloud image, single threshold segmentation based on Bezier histogram is implemented to the original satellite cloud image. Some small unrelated cloud masses are ...

This paper focuses on the optimal motion planning problem for cooperative aerial manipulation. We use the rapidly exploring random trees star (RRT*) algorithm that finds feasible paths quickly and optimizes them. For local planning within RRT*, we developed a trajectory planner using Bezier-curve which utilizes the differential flatness property of the aerial manipulator. Time-parameterization ...

This paper shows how to construct a rational Bezier model of a swept surface that interpolates N frames (i.e., N position/orientation pairs) of a fixed rational space curve c(s) and maintains the shape of the curve at all intermediate points of the sweep. Thus, the surface models an exact sweep of the curve, consistent with the given data. The primary novelty of the method is that this exact mo...

A strategy to obtain sets of initial configuration to design freeform reflector surfaces is presented. This strategy brings the initial configuration of the reflector surface using a collection of elemental facets defined by Bezier surfaces and able to face the optimization process of the illumination system. The purpose of this communication is to provide initial configurations to obtain a set...

We present a sufficient criterion for the Bernstein-Bezier (BB) form of a trivariate polynomial within a tetrahedron, such that the real zero contour of the polynomial defines a smooth and single sheeted algebraic surface patch. We call this an A-patch. We present algorithms to build a mesh of cubic A-patches to interpolate a given set of scattered point data in three dimensions, respecting the...