Despite the tremendous development in CNC programming facilities, linear and circular cuts parallel to the coordinate planes continue to be the standard motions of modern CNC machines. However, the increasing industrial demand for parts with intricate shapes cannot be satisfied with only these standard motions. The proportion of parts which are not covered by the standard CNC motions is certain...

Abstract This paper presents a new reward function that can be used for deep reinforcement learning in unmanned aerial vehicle (UAV) control and navigation problems. The is based on the construction estimation of time simplified trajectories to target, which are third-order Bezier curves. applied unchanged solve problems both two-dimensional three-dimensional virtual environments. effectiveness...

Transonic airfoil design problems are solved using a Genetic Algorithm (GA) based optimizer. At the desired operating point, the minimum drag and constant lift targets are achieved through either a scalarized objective function, involving an arbitrary weighting factor, or the Pareto technique. For the optimization of an airfoil at two operating points, similar approaches are used. The CPU cost ...

A gr'oup-theor'etic analysis is applied to find th e transf01'11wtion of the homogeneous control points of kdim ensional B ezier simplices {such as two dim ensional triangles and three dim ensional tetrah edra} under' a kdim ensional projec tive reparam eterization, This transf ormation has applications in the perspec tive projec ti on of textur'es represented as triangular spline intensity sur...

A near-optimal midcourse trajectory shaping guidance algorithm is proposed for both air and ballistic target engagement mission attributes for generic long range interceptor missile. This guidance methodology is based on the maximum final velocity as the objective function and maximum permissible flight altitude as the in-flight state constraint as well as the head-on orientation as the termina...

Recursive evaluation procedures based on spherical linear interpolation and stationary subdivision algorithms based on geodesic midpoint averaging are used to construct the analogues on spheres of arbitrary dimension of Lagrange and Hermite interpolation and Bezier and B-spline approximation.

We study Bezier surfaces defined over triangular domains. We have seen how spaces of bivariate polynomials can be constructed as tensor-products of the univariate ones. An alternative choice of polynomial space is, for each n ≥ 0, the space of polynomials of the form p(x, y) = 0≤i+j≤n a i,j x i y j , where we understand that i ≥ 0 and j ≥ 0 in the summation. As in the univariate case, we denote...