We present weighted quadrature for hierarchical B-splines to address the fast formation of system matrices arising from adaptive isogeometric Galerkin methods with suitably graded meshes. By exploiting a local tensor product structure, we extend construction rules spline setting. The proposed algorithm has computational cost proportional number degrees freedom and advantageous properties increa...

This paper discusses a design methodology of cooperative trajectory generation for multi-robot systems. The trajectory of achieving cooperative tasks, i.e., with temporal constraints, is constructed hy a nonlinear trajectory generation (NTG) algorithm. Three scenarios of multi-robot tasking are proposed at the cooperative task planning framework. The NTG algorithm is, then, used to generate rea...

In this paper some of the relationships between B-splines and linear control theory is examined. In particular, the controls that produce the B-spline basis is constructed and compared to the basis elements for dynamic splines.

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...

Analysis-suitable T-splines (AST-splines) are a promising candidate to achieve seamless integration between the design and analysis of thin-walled structures in industrial settings. In this work, we generalize AST-splines allow multiple extraordinary points within same face. This generalization drastically increases flexibility build geometries using AST-splines; e.g., much coarser meshes can b...

This paper deals with polynomial Hermite splines. In the first part, we provide a simple and fast procedure to compute refinement mask of B-splines any order in case general scaling factor. Our is solely derived from reproduction properties satisfied by splines it does not require explicit construction or evaluation basis functions. The second part discusses factorization B-spline masks terms a...

This paper discusses a Cooperative Path Planning (CPP) design methodology for multi-vehicle systems and a Nonlinear Trajectory Generation (NTG) algorithm. Three scenarios of multi-vehicle tasking are proposed at the CPP framework. The NTG algorithm is, then, used to generate realtime trajectory for desired vehicle activities. Given system dynamics and constraints, the NTG algorithm first finds ...

This paper discusses a Cooperative Path Planning (CPP) design methodology for multi-vehicle systems and a Nonlinear Trajectory Generation (NTG) algorithm. Three scenarios of multi-vehicle tasking are proposed at the CPP framework. The NTG algorithm is, then, used to generate realtime trajectory for desired vehicle activities. Given system dynamics and constraints, the NTG algorithm first finds ...

Recently in [7). a new multivariate B-spline scheme based on blending functions and control vertices was developed . This surface scheme allows CIo-1-continuous piecewise polynomial surfaces of degree k over arbitrary triangulations to be modelled . Actually, piecewise polynomial surfaces over a refined triangulation are produced given an arbitrary triangulation . The scheme exhibits both affin...

The reconstruction of a continuous function from discrete data is a basic task in many applications such as the visualization of 3D volumetric data sets. We use a local approximation method for quadratic C 1 splines on uniform tetrahedral partitions to achieve a globally smooth function. The spline is based on a truncated octahedral partition of the volumetric domain, where each truncated octah...