Mesh deformation on 3D complex configurations using multistep radial basis functions interpolation

The Radial Basis Function（RBF） method with data reduction is an effective way to perform mesh deformation. However, for large deformations on meshes of complex aerodynamic configurations, the efficiency of the RBF mesh deformation method still needs to be further improved to fulfill the demand of practical application. To achieve this goal, a multistep RBF method based on a multilevel subspace RBF algorithm is presented to further improve the efficiency of the mesh deformation method in this research. A whole deformation is divided into a series of steps, and the supporting radius is adjusted in accordance with the maximal displacement error. Furthermore, parallel computing is applied to the interpolation to enhance the efficiency. Typical deformation problems of the NASA Common Research Model（CRM） configuration, the DLR-F6 wing-body-nacellepylon configuration, and the DLR-F11 high-lift configuration are tested to verify the feasibility of this method. Test results show that the presented multistep RBF mesh deformation method is efficient and robust in dealing with large deformation problems over complex geometries.

Rigidity Constraints for Large Mesh Deformation

It is a challenging problem of surface-based deformation to avoid apparent volumetric distortions around largely deformed areas. In this paper, we propose a new rigidity constraint for gradient domain mesh deformation to address this problem. Intuitively the proposed constraint can be regarded as several small cubes defined by the mesh vertices through mean value coordinates. The user interactively specifies the cubes in the regions which are prone to volumetric distortions, and the rigidity constraints could make the mesh behave like a solid object during deformation. The experimental results demonstrate that our constraint is intuitive, easy to use and very effective.

An efficient large-scale mesh deformation method based on MPI/Open MP hybrid parallel radial basis function interpolation

An efficient MPI/OpenMP hybrid parallel Radial Basis Function (RBF) strategy for both continuous and discontinuous large-scale mesh deformation is proposed to reduce the computational cost and memory consumption.Unlike the conventional parallel methods in which all processors use the same surface displacement and implement the same operation,the present method employs different surface points sets and influence radius for each volume point movement,accompanied with efficient geometry searching strategy.The deformed surface points,also called Control Points (CPs),are stored in each processor.The displacement of spatial points is interpolated by using only 20-50 nearest control points,and the local influence radius is set to 5-20 times the maximum displacement of control points.To shorten the searching time for the nearest control point clouds,an Alternating Digital Tree (ADT) algorithm for 3D complex geometry is designed based on an iterative bisection technique.Besides,an MPI/OpenMP hybrid parallel approach is developed to reduce the memory cost in each High-Performance Computing (HPC) node for large-scale applications.Three 3D cases,including the ONERA-M6 wing and a commercial transport airplane standard model with up to 2.5 billion hybrid elements,are used to test the present mesh deformation method.The robustness and high parallel efficiency are demonstrated by a wing deflection case with a maximum bending angle of 450 and more than 80% parallel efficiency with 1024 MPI processors.In addition,the availability for both continuous and discontinuous surface deformation is verified by interpolating the projecting displacement with opposite directions surface points to the spatial points.

Mesh Deformation Method Based on Mean Value Coordinates Interpolation

Mesh deformation technique is widely used in many application fields, and has re- ceived a lot of attentions in recent years. This paper focuses on the methodology and algorithm of algebraic type mesh deformation for unstructured mesh in numerical discretization. To preserve mesh quality effectively, an algebraic approach for two and three dimensional unstructured mesh is developed based on mean value coordinates interpolation combined with node visibility analysis. The proposed approach firstly performs node visibility analysis to find out the visible boundary for each grid point to be moved, then evaluates the mean value coordinates of each grid point with respect to all vertices on its visible boundary. Thus the displacements of grid points can be calculated by interpolating the boundary movement by the mean value coordinates. Compared with other methods, the proposed method has good deformation capability and predictable com- putational cost, with no need to select parameters or functions. Applications of mesh deformation in different fields are presented to demonstrate the effectiveness of the proposed approach. The results of numerical experiments exhibit not only superior deformation capability of the method in traditional applications of fluid dynamic grid, but also great potential in modeling for large deformation analysis and inverse design problems.

Gradient Domain Mesh Deformation-A Survey

This survey reviews the recent development of gradient domain mesh deformation method. Different to other deformation methods, the gradient domain deformation method is a surface-based, variational optimization method. It directly encodes the geometric details in differential coordinates, which are also called Laplacian coordinates in literature. By preserving the Laplacian coordinates, the mesh details can be well preserved during deformation. Due to the locality of the Laplacian coordinates, the variational optimization problem can be casted into a sparse linear system. Fast sparse linear solver can be adopted to generate deformation result interactively, or even in real-time. The nonlinear nature of gradient domain mesh deformation leads to the development of two categories of deformation methods： linearization methods and nonlinear optimization methods. Basically, the linearization methods only need to solve the linear least-squares system once. They are fast, easy to understand and control, while the deformation result might be suboptimal. Nonlinear optimization methods can reach optimal solution of deformation energy function by iterative updating. Since the computation of nonlinear methods is expensive, reduced deformable models should be adopted to achieve interactive performance. The nonlinear optimization methods avoid the user burden to input transformation at deformation handles, and they can be extended to incorporate various nonlinear constraints, like volume constraint, skeleton constraint, and so on. We review representative methods and related approaches of each category comparatively and hope to help the user understand the motivation behind the algorithms. Finally, we discuss the relation between physical simulation and gradient domain mesh deformation to reveal why it can achieve physically plausible deformation result. Kun Zhou is currently a Cheung Kong professor in the Department of Computer Science, Zhejiang Uni- versity, and a member of the State Key Laboratory of CAD＆CG. He received his B.S. degree and Ph.D. degree from Zhejiang University in 1997 and 2002, respectively. Af- ter graduation, he joined Microsoft Research Asia as an associate re-

Quasi-angle-preserving mesh deformation using the least-squares approach

We propose an angle-based mesh representation, which is invariant under translation, rotation, and uniform scaling, to encode the geometric details of a triangular mesh. Angle-based mesh representation consists of angle quantities defined on the mesh, from which the mesh can be reconstructed uniquely up to translation, rotation,and uniform scaling. The reconstruction process requires solving three sparse linear systems: the first system encodes the length of edges between vertices on the mesh, the second system encodes the relationship of local frames between two adjacent vertices on the mesh, and the third system defines the position of the vertices via the edge length and the local frames. From this angle-based mesh representation, we propose a quasi-angle-preserving mesh deformation system with the least-squares approach via handle translation, rotation, and uniform scaling. Several detail-preserving mesh editing examples are presented to demonstrate the effectiveness of the proposed method.

RBFs-MSA Hybrid Method for Mesh Deformation

Simulating unsteady flow phenomena involving moving boundaries is a challenging task,one key requirement of which is a reliable and fast algorithm to deform the computational mesh.Radial basis functions（RBFs） interpolation is a very simple and robust method to deform the mesh.However,the number of operations and the requirement of memory storage will be increased rapidly as the number of grid nodes increases,which limits the application of RBFs to three-dimensional（3D） moving mesh.Moving submesh approach（MSA） is an efficient method,but its robustness depends on the method used to deform the background mesh.A hybrid method which combines the benefits of MSA and RBFs interpolation,which is called RBFs-MSA,has been presented.This hybrid method is proved to be robust and efficient via several numerical examples.From the aspect of the quality of deforming meshes,this hybrid method is comparable with the RBFs interpolation;from the aspect of computing efficiency,one test case shows that RBFs-MSA is about two orders of magnitude faster than RBFs interpolation.For these benefits of RBFs-MSA,the new method is suitable for unsteady flow simulation which refers to boundaries movement.

Exact mesh shape design of large cable-network antenna reflectors with flexible ring truss supports

An exact-designed mesh shape with favorable surface accuracy is of practical significance to the performance of large cable-network antenna reflectors. In this study, a novel design approach that could guide the generation of exact spatial parabolic mesh configurations of such reflector was proposed. By incorporating the traditional force density method with the standard finite element method, this proposed approach had taken the deformation effects of flexible ring truss supports into consideration, and searched for the desired mesh shapes that can satisfy the requirement that all the free nodes are exactly located on the objective paraboloid. Compared with the conventional design method,a remarkable improvement of surface accuracy in the obtained mesh shapes had been demonstrated by numerical examples. The present work would provide a helpful technical reference for the mesh shape design of such cable-network antenna reflector in engineering practice.

Mesh-Based Semi-Calibrated Photometric Stereo with Near Quasi Point Lights

Non-uniformity of light sources is one of the inevitable error factors causing poor shape recoveryaccuracy of photometric stereo methods under close-range lighting with quasi point lights. Semi-calibrated photometricstereo methods are required to avoid repeated, tedious and impractical photometric calibration. In thispaper, two simple, concise but effective mesh-based semi-calibrated photometric stereo methods are proposed.The proposed methods extend the traditional mesh-based photometric stereo methods and further allow joint andaccurate estimation of normals and non-uniform light intensities by alternatively updating normals, depth mapsand intensities. Extensive experiments are conducted to validate the effectiveness and robustness of the proposedalgorithms. Even under extremely severe non-uniform lighting, the proposed methods can still suppress the errorand improve the shape recovery accuracy by up to 65.6% in real-world experiments.

ALTERING CONNECTIVITY WITH LARGE DEFORMATION MESH FOR LAGRANGIAN METHOD AND ITS APPLICATION IN MULTIPLE MATERIAL SIMULATION

A new approach for treating the mesh with Lagrangian scheme of finite volume method is presented. It has been proved that classical Lagrangian method is difficult to cope with large deformation in tracking material particles due to severe distortion of cells, and the changing connectivity of the mesh seems especially attractive for solving such issues. The mesh with large deformation based on computational geometry is optimized by using new method. This paper develops a processing system for arbitrary polygonal unstructured grid,the intelligent variable grid neighborhood technologies is utilized to improve the quality of mesh in calculation process, and arbitrary polygonal mesh is used in the Lagrangian finite volume scheme. The performance of the new method is demonstrated through series of numerical examples, and the simulation capability is efficiently presented in coping with the systems with large deformations.

Nodes2STRNet for structural dense displacement recognition by deformable mesh model and motion representation

Displacement is a critical indicator for mechanical systems and civil structures.Conventional vision-based displacement recognition methods mainly focus on the sparse identification of limited measurement points,and the motion representation of an entire structure is very challenging.This study proposes a novel Nodes2STRNet for structural dense displacement recognition using a handful of structural control nodes based on a deformable structural three-dimensional mesh model,which consists of control node estimation subnetwork(NodesEstimate)and pose parameter recognition subnetwork(Nodes2PoseNet).NodesEstimate calculates the dense optical flow field based on FlowNet 2.0 and generates structural control node coordinates.Nodes2PoseNet uses structural control node coordinates as input and regresses structural pose parameters by a multilayer perceptron.A self-supervised learning strategy is designed with a mean square error loss and L2 regularization to train Nodes2PoseNet.The effectiveness and accuracy of dense displacement recognition and robustness to light condition variations are validated by seismic shaking table tests of a four-story-building model.Comparative studies with image-segmentation-based Structure-PoseNet show that the proposed Nodes2STRNet can achieve higher accuracy and better robustness against light condition variations.In addition,NodesEstimate does not require retraining when faced with new scenarios,and Nodes2PoseNet has high self-supervised training efficiency with only a few control nodes instead of fully supervised pixel-level segmentation.

An Efficient Dynamic Mesh Generation Method for Complex Multi-Block Structured Grid

Aiming at a complex multi-block structured grid,an efficient dynamic mesh generation method is presented in this paper,which is based on radial basis functions(RBFs)and transfinite interpolation(TFI).When the object is moving,the multi-block structured grid would be changed.The fast mesh deformation is critical for numerical simulation.In this work,the dynamic mesh deformation is completed in two steps.At first,we select all block vertexes with known deformation as center points,and apply RBFs interpolation to get the grid deformation on block edges.Then,an arc-lengthbased TFI is employed to efficiently calculate the grid deformation on block faces and inside each block.The present approach can be well applied to both two-dimensional(2D)and three-dimensional(3D)problems.Numerical results show that the dynamic meshes for all test cases can be generated in an accurate and efficient manner.

Model Transduction for Triangle Meshes

This paper proposes a novel method, called model transduction, to directly transfer pose between different meshes, without the need of building the skeleton configurations for meshes. Different from previous retargetting methods, such as deformation transfer, model transduction does not require a reference source mesh to obtain the source deformation, thus effectively avoids unsatisfying results when the source and target have different reference poses. Moreover, we show other two applications of the model transduction method： pose correction after various mesh editing operations, and skeleton-free deformation animation based on 3D Mocap （Motion capture） data. Model transduction is based on two ingredients： model deformation and model correspondence. Specifically, based on the mean-value manifold operator, our mesh deformation method produces visually pleasing deformation results under large angle rotations or big-scale translations of handles. Then we propose a novel scheme for shape-preserving correspondence between manifold meshes. Our method fits nicely in a unified framework, where the similar type of operator is applied in all phases. The resulting quadratic formulation can be efficiently minimized by fast solving the sparse linear system. Experimental results show that model transduction can successfully transfer both complex skeletal structures and subtle skin deformations.

An ultralight geometry processing library for parallel mesh refinement

In applications such as parallel mesh refinement,it remains a challenging issue to ensure the refined surface respects the original Computer-Aided Design(CAD)model accurately.In this paper,an ultralight geometry processing library is developed to resolve this issue effectively and efficiently.Here,we say the kernel is ultralight because it has a very small set of data-structures and algorithms by comparison with industrial-level geometry kernels.Within the library,a simplified surface boundary representation(B-rep)and a radial edge structure are developed respectively to depict the geometry model and the surface mesh,plus hash tables that record the connections between the geometry model and the surface mesh.Based on these data structures,a set of efficient algorithms are developed,which initializes the connection tables,projects a point back to the original geometry,etc.With these data-structure and algorithmic infrastructures set up,the callings of eight well-designed Application Programming Interfaces(APIs)are powerful enough to enable the parallel mesh refinement algorithm outputs a mesh respecting the input CAD model accurately.Numerical experiments will be finally presented to evaluate the performance of the overall parallel mesh refinement algorithm and the algorithms in relation with the developed library.

Flutter analysis of compressor blades under travelling wave modes using an efficient fluid–structure interaction method

Flutter is a self-sustained vibration which could create serious damage to compressor blades.Improving the efficiency and accuracy of Fluid-Structure Interaction(FSI)method is crucial to flutter analysis.An efficient FSI method which combines a fast mesh deformation technology and Double-Passage Shape Correction(DPSC)method is proposed to predict blades flutter under traveling wave modes.Firstly,regarding the fluid domain as a pseudo elastic solid,the flow mesh deformation and blade vibration response can be quickly obtained by solving the governing equations of the holistic system composed of blade and pseudo elastic solid.Then,by storing and updating the Fourier coefficients on the circumferential boundary,the phase-lagged boundary condition is introduced into the computational domain.Finally,the aerodynamic stability for the blades of an axial compressor under various Inter-Blade Phase Angle(IBPA)is analyzed.The results show that the proposed method can effectively predict the characteristics of aerodynamic damping,aerodynamic force and blade displacement.And a conceptual model is proposed to describe the motion behavior of the shock wave.Compared with the multi-passage method,the proposed method obtains almost the same unstable IBPA interval and the blade displacement error is less than 3.4%.But the calculation time is significantly shortened especially in small IBPA cases.

NUMERICAL STUDY OF THE PITCHING MOTIONS OF SUPERCAVITA-TING VEHICLES

The pitching motions of supercavitating vehicles could not be avoided due to the lost water buoyancy. In order to have some insight for the design of the supercavitating vehicles, the fixed frequency and free pitching motions are investigated. A numerical predicting method based on the relative motion principle and the non-inertia coordinate system is proposed to simulate the free pitching motions of supercavitating vehicles in the longitudinal plane. Homogeneous and two fluid multiphase models are used to predict the natural and the ventilated supercavitating flows. In the fixed frequency pitching motions, a variety of working conditions are considered, including the pitching angular velocities and the supercavity scales and the results are found to be consistent with the available experimental results in literature. The mesh deformation technology controlled by the moment of momentum equation is adopted to study the free pitching motions and finally to obtain the planing states proposed by Savchenko. The numerical method is validated for predicting the pitching motions of supercavitating vehicles and is found to enjoy better calculation efficiency as comparing with the mesh regeneration technology.

Numerical studies of static aeroelastic effects on grid fin aerodynamic performances

The grid fin is an unconventional control surface used on missiles and rockets. Although aerodynamics of grid fin has been studied by many researchers, few considers the aeroelastic effects.In this paper, the static aeroelastic simulations are performed by the coupled viscous computational fluid dynamics with structural flexibility method in transonic and supersonic regimes. The developed coupling strategy including fluid–structure interpolation and volume mesh motion schemes is based on radial basis functions. Results are presented for a vertical and a horizontal grid fin mounted on a body. Horizontal fin results show that the deformed fin is swept backward and the axial force is increased. The deformations also induce the movement of center of pressure, causing the reduction and reversal in hinge moment for the transonic flow and the supersonic flow,respectively. For the vertical fin, the local effective incidences are increased due to the deformations so that the deformed normal force is greater than the original one. At high angles of attack, both the deformed and original normal forces experience a sudden reduction due to the interference of leeward separated vortices on the fin. Additionally, the increment in axial force is shown to correlate strongly with the increment in the square of normal force.

A Revisit of Shape Editing Techniques:From the Geometric to the Neural Viewpoint

3D shape editing is widely used in a range of applications such as movie production,computer games and computer aided design.It is also a popular research topic in computer graphics and computer vision.In past decades,researchers have developed a series of editing methods to make the editing process faster,more robust,and more reliable.Traditionally,the deformed shape is determined by the optimal transformation and weights for an energy formulation.With increasing availability of 3D shapes on the Internet,data-driven methods were proposed to improve the editing results.More recently as the deep neural networks became popular,many deep learning based editing methods have been developed in this field,which are naturally data-driven.We mainly survey recent research studies from the geometric viewpoint to those emerging neural deformation techniques and categorize them into organic shape editing methods and man-made model editing methods.Both traditional methods and recent neural network based methods are reviewed.