By applying finite difference formula to time discretization and the cubic B-splines for spatial variable, a numerical method for solving the inverse system of Burgers equations is presented. Also, the convergence analysis and stability for this problem are investigated and the order of convergence is obtained. By using two test problems, the accuracy of presented method is verified. Additional...

Spline curves are very prominent in the mathematics due to their simple construction, accuracy of assessment and ability approximate complicated structures into interactive curved designs. A spline is a smooth piece-wise polynomial function. The primary goal this study use extended cubic B-spline (ExCuBS) functions with new second order derivative approximation obtain numerical solution weakly ...

We present a system for fast and accurate display of CSG constructive solid geome try models Such models have as primitives polyhedra and solids whose boundaries can be represented using rational spline surfaces As part of pre processing we compute the B rep boundary representation from the CSG tree and represent the resulting solid using trimmed spline surfaces No assumptions are made on the n...

We say that a system of functions is hodograph diminishing if the tangent directions of the curve are contained in the cone generated by the sides of the control polygon. We characterize such systems and conclude that Bézier curves, B-spline curves and, more generally, curves generated by totally positive bases are hodograph diminishing. A characterization is also found for rational curves. Hod...

An evolutionary algorithm based framework, a combination of modified breeder genetic algorithms incorporating characteristics of classic genetic algorithms, is utilized to design an offline/online path planner for unmanned aerial vehicles (UAVs) autonomous navigation. The path planner calculates a curved path line with desired characteristics in a three-dimensional (3-D) rough terrain environme...

Although curves can be generally described by using concepts such as NURBS, we will introduce subdivision curves as a lead-in to the more general concept of subdivision surfaces. Suppose we wanted to perform knot-insertion in the middle of a B-spline curve defined by four control points, p0 through p3. Using the blossoming technique, we would determine the control point to be as in Figure 1. Th...

Based on the matrix perturbation technique. a fast-fitting algorithm using uniform cubic B-spline curves is presented. Our algorithm entails much less floating-point operations when compared with Gaussian elimination method. In addition, our result can be applied to solve the closed cubic B-spline curve-fitting problem. Experimental results are included for a practical version. These experiment...