Generalized nth-Order Perturbation Method Based on Loop Subdivision Surface Boundary Element Method for Three-Dimensional Broadband Structural Acoustic Uncertainty Analysis

In this paper,a generalized nth-order perturbation method based on the isogeometric boundary element method is proposed for the uncertainty analysis of broadband structural acoustic scattering problems.The Burton-Miller method is employed to solve the problem of non-unique solutions that may be encountered in the external acoustic field,and the nth-order discretization formulation of the boundary integral equation is derived.In addition,the computation of loop subdivision surfaces and the subdivision rules are introduced.In order to confirm the effectiveness of the algorithm,the computed results are contrasted and analyzed with the results under Monte Carlo simulations(MCs)through several numerical examples.

A bound on the distance between Loop subdivision surface and its control mesh

By means of direct analysis of the connection between Loop subdivision surface and its control mesh and the computation of the basis functions, we obtain a bound on the distance between Loop subdivision surface patch and its control mesh. The bound can be used to compute the numbers of subdivision for a given tolerance. Finally, two examples are listed in this paper to demon- strate the applications of the bound.

Three-dimensional surface current loops in broadband responsive negative refractive metamaterial with isotropy

We propose a bulk negative refractive index （NRI） metamaterial composed of periodic array of tightly coupled metallic cross-pairs printed oR the six sides of a cube for applications of superlenses. The structural characteristics of the three-dimensional （3D） metamaterial consist in the high symmetry and the superposition of metallic cross-pairs, which can increase the magnetic inductive coupling between adjacent cross-pairs and realize a broadband and isotropic NRI. The proposed 3D structure is simulated using the CS~ Microwave Studio 2006 to verify the design validity. The simulation results show that the proposed structure can not only realize simultaneously an electric and magnetic response to an incident electromagnetic （EM） wave, but also exhibit a broadband NRI whose relative bandwidth can reach up to 56.7%. In addition, the NRI band is insensitive to tile polarization and the incident angle of the incident EM wave. Therefore, the proposed metamaterial is a good candidate material as three-dimensional broadband isotropic NRI metamaterial.

Loop Subdivision Surface Based Progressive Interpolation

A new method for constructing interpolating Loop subdivision surfaces is presented. The new method is an extension of the progressive interpolation technique for B-splines. Given a triangular mesh M, the idea is to iteratively upgrade the vertices of M to generate a new control mesh M such that limit surface of M would interpolate M. It can be shown that the iterative process is convergent for Loop subdivision surfaces. Hence, the method is well-defined. The new method has the advantages of both a local method and a global method, i.e., it can handle meshes of any size and any topology while generating smooth interpolating subdivision surfaces that faithfully resemble the shape of the given meshes. The meshes considered here can be open or closed.

Feature-Adaptive Rendering of Loop Subdivision Surfaces on Modern GPUs

We present a novel approach for real-time rendering Loop subdivision surfaces on modern graphics hardware. Our algorithm evaluates both positions and normals accurately, thus providing the true Loop subdivision surface. The core idea is to recursively refine irregular patches using a GPU compute kernel. All generated regular patches are then directly evaluated and rendered using tile hardware tessellation unit. Our approach handles triangular control meshes of arbitrary topologies and incorporates common subdivision surface features such as semi-sharp creases and hierarchical edits. While surface rendering is accurate up to machine precision, we also enforce a consistent bitwise evaluation of positions and normals at patch boundaries. This is particularly useful in the context of displacement mapping which strictly requires inatching surface normals. Furthermore, we incorporate efficient level-of-detail rendering where subdivision depth and tessellation density can be adjusted on-the-fly. Overall, our algorithm provides high-quality results at real-time frame rates, thus being ideally suited to interactive rendering applications such as video games or authoring tools.