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.

Reverse Loop subdivision with sharp features

In this paper we introduce a new reverse Loop subdivision method. In contrast to current wavelets based Loop subdivision scheme, our method applies the same rules to both regular and extraordinary vertices and reconstructs the sharp features easily. Furthermore, our method runs faster because it does not need analysis and synthesis procedural. Our main goal is the design of a reverse subdivision method that can reconstruct the coarser mesh from a finer subdivision surface with sharp features for multiresolution representation, The proposed method only needs a little memory storage and brings little error, and it is easy to implement.

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.

Conjugate-Gradient Progressive-Iterative Approximation for Loop and Catmull-Clark Subdivision Surface Interpolation

Loop and Catmull-Clark are the most famous approximation subdivision schemes,but their limit surfaces do not interpolate the vertices of the given mesh.Progressive-iterative approximation(PIA)is an efficient method for data interpolation and has a wide range of applications in many fields such as subdivision surface fitting,parametric curve and surface fitting among others.However,the convergence rate of classical PIA is slow.In this paper,we present a new and fast PIA format for constructing interpolation subdivision surface that interpolates the vertices of a mesh with arbitrary topology.The proposed method,named Conjugate-Gradient Progressive-Iterative Approximation(CG-PIA),is based on the Conjugate-Gradient Iterative algorithm and the Progressive Iterative Approximation(PIA)algorithm.The method is presented using Loop and Catmull-Clark subdivision surfaces.CG-PIA preserves the features of the classical PIA method,such as the advantages of both the local and global scheme and resemblance with the given mesh.Moreover,CG-PIA has the following features.1)It has a faster convergence rate compared with the classical PIA and W-PIA.2)CG-PIA avoids the selection of weights compared with W-PIA.3)CG-PIA does not need to modify the subdivision schemes compared with other methods with fairness measure.Numerous examples for Loop and Catmull-Clark subdivision surfaces are provided in this paper to demonstrate the efficiency and effectiveness of CG-PIA.