In this work, a new adaptive integration method for simulation of two-dimensional linear elasticity problems is presented. The main benefit the proposed reduction computational cost by lowering number points required to reach certain level accuracy. concept calculate weights trimmed cells employing advantage Bezier parametric curves. Within concept, it possible map square triangle with one curv...

"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...

Abstract Splines are one of the main methods mathematically representing complicated shapes, which have become primary technique in fields Computer Graphics (CG) and Computer-Aided Geometric Design (CAGD) for modeling complex surfaces. Among all, Bézier Catmull–Rom splines most common sub-fields engineering. In this paper, we focus on conversion between cubic curve segments, rather than going t...

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 new fast ray patch intersection algorithm is presented. The algorithm correctly handles all ray patch intersections. A number of parameters are derived from a numerical analysis of the algorithm and the data pad is re synthesized for higher accuracy. A global architecture for an ASIC for intersecting a ray with a bezier patch is presented. It is shown that a cache combined with pre pads can r...

Ghandmjit L. Bajaj t Department of Computer Science, Purdue University, West Lafayette, IN 47907 In this paper (part one of a trilogy), we introduce the concept of a discriminating family of regular algebraic curves (real, nonsingular and connected). Several discriminating families are obtained by different characterizations of the zero contours of the Bernstein-Bezier (BB) form of bivariate po...

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 ...

In this present paper, we introduce a new and simple integral modification of the Meyer-Konig and Zeller Bezier type operators and study the rate of convergence for functions of bounded variation. Our result improves and corrects the results of Guo (J. Approx. Theory, 56 (1989), 245–255 ), Zeng (Comput. Math. Appl., 39 (2000), 1–13; J. Math. Anal. Appl., 219 (1998), 364–376), etc.