isogeometric structural shape optimization an old dilemma in structural shape optimization is the needed tight link between design model or geometric description and analysis model the intention of this paper is to show that isogeometric analysis offers a potential and promising way out of this dilemma to this end we show a structural shape optimization framework based on the isogeometric analysis approach with the discretization based on non uniform rational b splines nurbs the analysis model represents the structural geometry exactly furthermore nurbs enable efficient geometry control together with smooth boundaries they are the de facto standard in cad systems but are also widely used in a shape optimal design context to define the geometry representation and the design variables with the presented isogeometric approach to shape optimization the analysis model is inherently merged with the design model omitting the typically involved interplay between both we derive analytical sensitivities for nurbs discretizations which allow application of efficient gradient based optimization algorithms the present contribution is restricted to two dimensional problems of linear elasticity but the extension to three dimensions and other problem classes is straightforward some representative examples demonstrate and validate the methodology further the potential of boundary continuity control within isogeometric structural shape optimization is explored to trigger smooth or less smooth angular designs

conjugate gradient methods applied to transonic finite difference and finite element calculations most transonic finite difference and finite element calculations are obtained by slor recently approximate factorization methods adi af2 sip have been used with finite differences application of such iterative methods to finite elements is not straightforward in this paper incomplete lu decomposition and ssor are used as preconditioning to second degree iterative methods with adaptive acceleration parameters as in conjugate gradient algorithms for both finite difference and finite element calculations based on the artificial density formulation different cases are tested and the results are demonstrated the present method is certainly more efficient than pure slor for obtaining results with reasonable accuracy

isogeometric boundary element analysis using unstructured t splines we couple collocated isogeometric boundary element methods and unstructured analysis suitable t spline surfaces for linear elastostatic problems we extend the definition of analysis suitable t splines to encompass unstructured control grids unstructured meshes and develop basis functions which are smooth rational polynomials defined in terms of the bezier extraction framework and which pass standard patch tests we then develop a collocation procedure which correctly accounts for sharp edges and corners extraordinary points and t junctions this approach is applied to several three dimensional problems including a real world t spline model of a propeller we believe this work clearly illustrates the power of combining new analysis suitable computer aided design technologies with established analysis methodologies in this case the boundary element method

convergence of the shifted qr algorithm on 3 3 normal matrices this paper concerns the convergence properties of the shifted qr algorithm on 3 3 normal hessenberg matrices the algorithm is viewed as an iteration on one dimensional subspaces a class of matrices is characterized for which hqr2 is unable to approximate a solution

rotation free isogeometric thin shell analysis using pht splines this paper presents a novel approach for isogeometric analysis of thin shells using polynomial splines over hierarchical t meshes pht splines the method exploits the flexibility of t meshes for local refinement the main advantage of the pht splines in the context of thin shell theory is that it achieves c1 continuity so the kirchhoff love theory can be used in pristine form no rotational degrees of freedom are needed numerical results show the excellent performance of the present method

part based 3d descriptions of complex objects from a single image volumetric 3d part based descriptions of complex objects in a scene can be highly beneficial for many tasks such as generic object recognition navigation and manipulation however it has been difficult to derive such descriptions from image data there has been some progress in getting such descriptions from range data or from perfect contours but analysis of a real intensity image presents many difficulties the object and part boundaries do not completely correspond to image boundaries the detected boundaries are often fragmented and many boundaries due to surface markings shadows and noise are present in addition inference of 3d from a 2d image is difficult the paper describes a method to compute the desired descriptions from a single image by exploiting projective properties of a class of generalized cylinders and of possible joints between them experimental results on some examples are given

isogeometric analysis using polynomial splines over hierarchical t meshes for two dimensional elastic solids isogeometric analysis has become a powerful alternative to standard finite elements due to its flexibility in handling complex geometries one of the major drawbacks of nurbs based isogeometric finite elements is the inefficiency of local refinement in this study we present an alternative to nurbs based isogeometric analysis that allows for local refinement the idea is based on polynomial splines and exploits the flexibility of t meshes for local refinement the shape functions satisfy important properties such as non negativity local support and partition of unity several numerical examples are used to demonstrate the reliability of the present method

line drawing interpretation bilateral symmetry results previously derived by the author are used to investigate the implication of bilateral symmetry in line drawings it is shown that the line drawing of an orthographically protected surface of revolution exhibits bilateral symmetry about the projection of its axis of revolution irrespective of the viewing direction barring one exception a bilaterally symmetric line drawing is necessarily the orthographic projection of a local surface of revolution whenever its symmetry axis continues to be the projection of a fixed line in space under perturbation of viewpoint the axis of revolution is the invariant preimage of the symmetry axis various line drawing causes are detailed which facilitate the deduction of invariant preimages of symmetry axes and consequently of local surfaces of revolution

the use of a preconditioned bi conjugate gradient method for hybrid plasma stability analysis abstract the numerical stability analysis of compact toroidal plasmas using implicit time differencing requires the solution of a set of coupled 2 dimensional elliptic partial differential equations for the field quantities at every timestep when the equations are spatially finite differenced and written in matrix form the resulting matrix is large sparse complex non hermitian and indefinite the use of the preconditioned bi conjugate gradient method for solving these equations is discussed the effect of block diagonal preconditioning and of incomplete block lu preconditioning on the convergence of the method is investigated for typical matrices arising in our studies the eigenvalue spectra of the original and preconditioned matrices are calculated as an illustration of the effectiveness of the preconditioning we show that the preconditioned bi conjugate gradient method converges more rapidly than the conjugate gradient method applied to the normal equations and that it is an effective iterative method for the class of non hermitian indefinite problems of interest

x fem in isogeometric analysis for linear fracture mechanics the extended finite element method x fem has proven to be an accurate robust method for solving problems in fracture mechanics x fem has typically been used with elements using linear basis functions although some work has been performed using quadratics in the current work the x fem formulation is incorporated into isogeometric analysis to obtain solutions with higher order convergence rates for problems in linear fracture mechanics in comparison with x fem with conventional finite elements of equal degree the nurbs based isogeometric analysis gives equal asymptotic convergence rates and equal accuracy with fewer degrees of freedom dof results for linear through quartic nurbs basis functions are presented for a multiplicity of one or a multiplicity equal the degree

domain decomposition methods for nonlinear problems in fluid dynamics abstract the numerical solution of finite element approximations of complicated two and three dimensional nonlinear problems can be a most formidable task in order to overcome this difficulty related to dimensionality domain splitting methods can be very effective particularly in view of obtaining a fast and economical conjugate gradient solver which can be used to precondition the solution of nonlinear problems by optimization methods via nonlinear least squares or weighted residual formulations a new technique of this type will be introduced and analysed and its efficiency will be discussed from numerical experiments concerning the numerical simulation of transonic flows for compressible inviscid fluids and incompressible viscous flows modelled by the navier stokes equations

an isogeometric continuum shell element for non linear analysis an isogeometric continuum shell formulation is proposed in which nurbs basis functions are used to construct the reference surface of the shell through the thickness behavior is interpolated using a higher order b spline which is in contrast to the standard continuum shell solid like shell formulation where a linear lagrange shape function is typically used in the thickness direction the present formulation yields a complete isogeometric representation of the continuum shell the shell element is implemented in a standard finite element code using bezier extraction which facilitates numerical integration on the reference surface of the shell through the thickness integration is done using a connectivity array which determines the support of a b spline basis function over an element the formulation has been verified using different linear and geometrically non linear examples the ability of the formulation in modelling buckling of static delaminations in composite materials is also demonstrated

shape from contour straight homogeneous generalized cylinders and constant cross section generalized cylinders we analyze the properties of straight homogeneous generalized cylinders shgcs and constant cross section generalized cylinders cgcs and derive the types of symmetries that the limb boundaries and cross sections of these objects produce on the image plane the constraints on the 3d shape of the objects are formulated based on the symmetries and from the geometry of the projection models finally the methods that recover the 3d shape from the image of their contours are discussed and recovered surfaces are shown for sample objects

an h hierarchical adaptive procedure for the scaled boundary finite element method note 374 reference lch article 2002 012view record in web of science record created on 2007 04 24 modified on 2016 08 08

epipolar geometry from profiles under circular motion addresses the problem of motion estimation from profiles apparent contours of an object rotating on a turntable in front of a single camera a practical and accurate technique for solving this problem from profiles alone is developed it is precise enough to reconstruct the shape of the object no correspondences between points or lines are necessary symmetry of the surface of revolution swept out by the rotating object is exploited to obtain the image of the rotation axis and the homography relating epipolar lines in two views robustly and elegantly these together with geometric constraints for images of rotating objects are used to obtain first the image of the horizon which is the projection of the plane that contains the camera centers and then the epipoles thus fully determining the epipolar geometry of the image sequence the estimation of this geometry by this sequential approach avoids many of the problems found in other algorithms the search for the epipoles by far the most critical step is carried out as a simple 1d optimization parameter initialization is trivial and completely automatic at all stages after the estimation of the epipolar geometry the euclidean motion is recovered using the fixed intrinsic parameters of the camera obtained either from a calibration grid or from self calibration techniques finally the spinning object is reconstructed from its profiles using the motion estimated in the previous stage results from real data are presented demonstrating the efficiency and usefulness of the proposed methods

recent developments in the algebraic multiblock method for euler equations abstract in this paper the algebraic multiblock method is presented and applied to the solution of the euler equations used to model inviscid compressible flow problems the method employs two extreme grids aimed at combining multigrid and domain decomposition ideas the fine grid is used by the discretization method the coarse grid results from the fine grid and defines the domain partitioning of the solution procedure the multigrid concept is practically simulated by applying the idea of the substructuring technique in which the inner finite volumes of a block are expressed by their boundary volumes through a matrix inversion process the conjugate gradient squared method is used for the approximate solution of numerous large block pentadiagonal systems emerging at each time step additionally efficient preconditioning and smoothing are employed to accelerate the iterative solution the proposed method is applied for the solution of the time marching euler equations using an implicit upwind finite volume method euflex numerical results and comparisons show the efficiency of the proposed method even for sequential processing

the scaled boundary finite element method in structural dynamics the scaled boundary finite element method is extended to solve problems of structural dynamics the dynamic stiffness matrix of a bounded finite domain is obtained as a continued fraction solution for the scaled boundary finite element equation the inertial effect at high frequencies is modeled by high order terms of the continued fraction without introducing an internal mesh by using this solution and introducing auxiliary variables the equation of motion of the bounded domain is expressed in high order static stiffness and mass matrices standard procedures in structural dynamics can be applied to perform modal analyses and transient response analyses directly in the time domain numerical examples for modal and direct time domain analyses are presented rapid convergence is observed as the order of continued fraction increases a guideline for selecting the order of continued fraction is proposed and validated high computational efficiency is demonstrated for problems with stress singularity

a stochastic scaled boundary finite element method abstract by extending the existing scaled boundary finite element method sbfem into the random field problem a stochastic scaled boundary finite element method ssbfem is developed in this paper to predict the structural responses with randomly distributed material properties the analyzed domain is discretized into a number of polygons modeled as sub domains of the sbfem so that the non homogeneous material properties are possible to be considered in establishment of the constitutive equation the random field represented by the karhunen loeve kl expansion is then directly incorporated into both the equilibrium equation of the sbfem and its sensitivity analysis formulation the perturbation method is employed to calculate the statistical moments of the structural responses and a semi analytical sensitivity analysis method is used to efficiently calculate the gradients involved particularly the proposed method is successfully applied to the stochastic fracture analysis with spatially varying random material properties four numerical examples are investigated to demonstrate the validity of the proposed method

line drawing interpretation straight lines and conic sections line drawings of man made scenes often exhibit instances of straight lines and conic sections i e ellipses parabolas and hyperbolas constraints imposed on the scene by such instances are investigated under the assumption of general viewpoint i e the mapping of the viewed surface onto the line drawing is stable under perturbation of the viewpoint within some open set both orthographic and perspective projection are considered the viewed surfaces are assumed to be piecewise c sup 3 it is shown that straight lines and conic sections in line drawings are projections of scene edges which are also straight lines and conic sections respectively it is also shown that scene events which project onto straight lines or conic sections cannot be combinations of view point independent and viewpoint dependent edges further continuous surface normal depth discontinuities which project onto straight lines can be locally described by developable surfaces and those which project onto conic sections can be locally described by nondevelopable quadric surfaces each of these quadric surfaces is determined up to four degrees of freedom by its projection

a generalized finite element formulation for arbitrary basis functions from isogeometric analysis to xfem many of the formulations of cm rent research interest including iosogeometric methods and the extended finite element method use nontraditional basis functions some such as subdivision surfaces may not have convenient analytical representations the concept of an element if appropriate at all no longer coincides with the traditional definition developing a new software for each new class of basis functions is a large research burden especially if the problems involve large deformations non linear materials and contact the objective of this paper is to present a method that separates as much as possible the generation and evaluation of the basis functions from the analysis resulting in a formulation that can be implemented within the traditional structure of a finite clement program but that permits the use of arbitrary sets of basis functions that are defined only through the input file elements ranging from a traditional linear four node tetrahedron through a higher order element combining xfem and isogeometric analysis may be specified entirely through an input file without any additional programming examples of this framework to applications with lagrange elements isogeometric elements and xfem basis functions for fracture are presented

robustness of isogeometric structural discretizations under severe mesh distortion abstract this paper investigates higher order and higher continuity functions in isogeometric structural analysis under distortion of the control and physical meshes first the concepts behind isogeometric analysis are briefly reviewed the effect of perturbing control points upon the geometrical mapping is observed in the one dimensional setting the concept is extended to multiple dimensions with a series of cases where the interior of a cube is distorted in different ways and patch tests are performed to assess accuracy a circular fillet patch is introduced through the appropriate degeneration of a control mesh in order to address the problem of modeling small features in finite element models the fillet patch is tested with two problems of linear elasticity and is shown to be accurate the investigation is further extended to the setting of large deformation nearly incompressible nonlinear elasticity with two examples which make use of the recently proposed f projection method

reproducing kernel triangular b spline based fem for solving pdes abstract we propose a reproducing kernel triangular b spline based finite element method fem as an improvement to the conventional triangular b spline element for solving partial differential equations pdes in the latter unexpected errors can occur throughout the analysis domain mainly due to the excessive flexibilities in defining the b spline the performance therefore becomes unstable and cannot be controlled in a desirable way to address this issue the proposed improvement adopts the reproducing kernel approximation in the calculation of b spline kernel function three types of pde problems are tested to validate the present element and compare against the conventional triangular b spline it has been shown that the improved triangular b spline satisfies the partition of unity condition even for extreme conditions including corners and holes

b spline contour representation and symmetry detection the detection of edges is only one of many steps in the understanding of images further processing necessarily involves grouping operations between contours we present a representation of edge contours by approximating b splines and show that such a representation facilitates the extraction of symmetries between contours our representation is rich compact stable and does not critically depend on feature extraction we turn our attention to the detection of three types of symmetries skew symmetries and parallel symmetries which have proven to be of great importance in inferring shape from contour and smooth local symmetries which have been used for planar shape description we show that our representation facilitates the computation of these symmetries

a multi element group preconditioned gmres algorithm for nonsymmetric systems arising in finite element analysis abstract a multi element group domain decomposition algorithm is presented for solving linear nonsymmetric systems arising in finite element analysis the iterative strategy employed is based on the generalized minimum residual gmres procedure originally proposed by saad and shultz two levels of preconditioning are investigated coding is presented which fully exploits vector architectured computers applications to problems of high speed compressible flow illustrate the effectiveness of the scheme

a displacement based finite element formulation for general polyhedra using harmonic shape functions summary a displacement based continuous galerkin finite element formulation for general polyhedra is presented for applications in nonlinear solid mechanics the polyhedra can have an arbitrary number of vertices or faces the faces of the polyhedra can have an arbitrary number of edges and can be nonplanar the polyhedra can be nonconvex with only the mild restriction of star convexity with respect to the vertex averaged centroid conforming shape functions are constructed using harmonic functions defined on the undeformed configuration thus requiring the use of a total lagrangian finite element formulation in large deformation applications for nonlinear applications with computationally intensive constitutive models it is important to minimize the number of element quadrature points for this reason an integration scheme is adopted in which the number of quadrature points is equal to the number of vertices as a first step toward verifying the element behavior in the general nonlinear setting several linear verification examples are presented using both random voronoi meshes and distorted hexahedral meshes for the hexahedral meshes results for the polyhedral formulation are compared to those of the standard trilinear hexahedral formulation the element behavior in the nearly incompressible regime is also examined copyright 2013 john wiley sons ltd

sensitivity analysis of the scaled boundary finite element method for elastostatics abstract as a semi analytical structural analysis algorithm the scaled boundary finite element method sbfem only discretizes the boundary of the analyzed domain without the need of fundamental solutions which makes it powerful for problems with stress singularity or unbounded foundation media in this paper a sensitivity analysis method of sbfem is proposed for elastostatics through which the first order derivatives of the structural responses with respect to the design parameters can be obtained efficiently and accurately an approach is suggested to compute the eigenvalue and eigenvector sensitivities of the hamilton matrix which are then used to calculate the analytical derivative of the stiffness matrix based on these calculations the sensitivities of displacements and stresses are further obtained by a series of differential equations the proposed sensitivity analysis method is also applied to the fracture mechanics problems three numerical examples are investigated to demonstrate the validity of the proposed method

extraction of parametric descriptions of circular gcs from a pair of contours for 3 d shape recognition this paper addresses the issue of recognizing 3 d three dimensional shapes of objects from their 2 d contour pairs a shape model that is represented by a family of spheres of varying radii with their centers on its axis is developed for the shape class of circular generalized cones gcs with a space curved axis the quasi invariant property of the shape model is defined and is used to recover the 3 d shapes of the object class by solving the problem of stereo matching between their contour pairs the recovered shapes are represented by a set of their parametric primitives and spatial relations between them so that they may be used for recognition even under occluded environment

isogeometric analysis enhanced by the scaled boundary finite element method abstract by leveraging the information of a typical cad model in the analysis the intensive process of discretization can be circumvented this unification has led to the isogeometric analysis iga hughes et al 2005 however as the cad model provides information only of the boundary a 2d 3d stress analysis is still one major step away in this work the concepts of isogeometric analysis and the scaled boundary finite element method sbfem are combined the sbfem requires only the boundary information and hence provides a seamless integration with the cad modeling within the proposed framework the nurbs basis functions are used to discretize the unknown fields in the circumferential direction whilst analytical solution is sought in the radial direction we further extend the framework to problems with singularities and to dynamic analysis the accuracy and the convergence properties of the proposed method are demonstrated with benchmark problems in the context of linear elasticity and linear elastic fracture mechanics

volumetric descriptions from a single intensity image since the early days of computer vision research shape from contour has been one of the most challenging problems many researchers in the field have attempted to understand this problem and proposed different approaches to solve it shape from contour still remains one of the hardest problems in the field the problem has two major difficulties first 2d properties of contours of viewed objects are generally not sufficient by themselves to uniquely determine 3d shape as one dimension is lost in the projection second real images produce imperfect contours that make their interpretation particularly difficult the first problem has received some attention in the research community but in the context of perfect contours the second one however has received very little in this work we propose a promising methodology to address this last problem for a large class of objects generalized cylinders it is based on exploiting mathematical invariant properties of the contours of generalized cylinders in a perceptual grouping approach we show that using these properties greatly helps addressing the figure ground problem in a more rigorous way than previous intuitive perceptual grouping methods our approach exploits the interplay between local and global features by handling different levels of the feature hierarchy we have developed and implemented a method that handles shgcs in complex seenes with markings and occlusion we demonstrate the application of our method of shape description and scene segmentation on complex real images we also demonstrate the usage of the obtained descriptions for recovery of complete 3 d object centered descriptions of viewed objects from a single intensity image

enriched isogeometric analysis of elliptic boundary value problems in domains with cracks and or corners summary the mapping method was introduced in jeong et al 2013 for highly accurate isogeometric analysis iga of elliptic boundary value problems containing singularities the mapping method is concerned with constructions of novel geometrical mappings by which push forwards of b splines from the parameter space into the physical space generate singular functions that resemble the singularities in other words the pullback of the singularity into the parameter space by the novel geometrical mapping a non uniform rational basis spline nurbs surface mapping becomes highly smooth one of the merits of iga is that it uses nurbs functions employed in designs for the finite element analysis however push forwards of rational nurbs may not be able to generate singular functions moreover the mapping method is effective for neither the k refinement nor the h refinement in this paper highly accurate stress analysis of elastic domains with cracks and or corners are achieved by enriched iga in which push forwards of nurbs via the design mapping are combined with push forwards of b splines via the novel geometrical mapping the mapping technique in a similar spirit of x fem or gfem we propose three enrichment approaches enriched iga for corners enriched iga for cracks and partition of unity iga for cracks copyright 2013 john wiley sons ltd

a two dimensional isogeometric boundary element method for elastostatic analysis the concept of isogeometric analysis where functions that are used to describe geometry in cad software are used to approximate the unknown fields in numerical simulations has received great attention in recent years the method has the potential to have profound impact on engineering design since the task of meshing which in some cases can add significant overhead has been circumvented much of the research effort has been focused on finite element implementations of the isogeometric concept but at present little has been seen on the application to the boundary element method the current paper proposes an isogeometric boundary element method bem which we term igabem applied to two dimensional elastostatic problems using non uniform rational b splines nurbs we find it is a natural fit with the isogeometric concept since both the nurbs approximation and bem deal with quantities entirely on the boundary the method is verified against analytical solutions where it is seen that superior accuracies are achieved over a conventional quadratic isoparametric bem implementation

polygon scaled boundary finite elements for crack propagation modelling summary an automatic crack propagation modelling technique using polygon elements is presented a simple algorithm to generate a polygon mesh from a delaunay triangulated mesh is implemented the polygon element formulation is constructed from the scaled boundary finite element method sbfem treating each polygon as a sbfem subdomain and is very efficient in modelling singular stress fields in the vicinity of cracks stress intensity factors are computed directly from their definitions without any nodal enrichment functions an automatic remeshing algorithm capable of handling any n sided polygon is developed to accommodate crack propagation the algorithm is simple yet flexible because remeshing involves minimal changes to the global mesh and is limited to only polygons on the crack paths the efficiency of the polygon sbfem in computing accurate stress intensity factors is first demonstrated for a problem with a stationary crack four crack propagation benchmarks are then modelled to validate the developed technique and demonstrate its salient features the predicted crack paths show good agreement with experimental observations and numerical simulations reported in the literature copyright 2012 john wiley sons ltd

a numerical study of various algorithms related to the preconditioned conjugate gradient method we present the results of a numerical study of the preconditioned conjugate gradient algorithm the minimal residual algorithm the biconjugate gradient algorithm and the bi minimal residual algorithm using both simple test matrices and more realistic test matrices derived from physical problems the application of the methods to unsymmetric matrices is considered we emphasize the importance of a good preconditioning look at various methods including icgg n and incomplete block factorization and make some practical recommendations some of the folk lore surrounding the semi iterative methods is dispelled

an extremum principle for shape from contour an extremum principle is developed that determines three dimensional surface orientation from a two dimensional contour the principle maximizes the ratio of the area to the square of the perimeter a measure of the compactness or symmetry of the three dimensional surface the principle interprets regular figures correctly and it interprets skew symmetries as oriented real symmetries the maximum likelihood method approximates the principle on irregular figures but we show that it consistently overestimates the slant of an ellipse

a comparison of direct and preconditioned iterative techniques for sparse unsymmetric systems of linear equations in this paper we compare direct and preconditioned iterative methods for the solution of nonsymmetric sparse systems of linear algebraic equations these problems occur in finite difference and finite element simulations of semiconductor devices and fluid flow problems we consider five iterative methods that appear to be the most promising for this class of problems the biconjugate gradient method the conjugate gradient squared method the generalized minimal residual method the generalized conjugate residual method and the method of orthogonal minimization each of these methods was tested using similar preconditioning incomplete lu factorization on a set of large sparse matrices arising from finite element simulation of semiconductor devices results are shown where we compare the computation time and memory requirements for each of these methods against one another as well as against a direct method that uses lu factorization to solve these problems the results of our numerical experiments show that preconditioned iterative methods are a practical alternative to direct methods in the solution of large sparse systems of equations and can offer significant savings in storage and cpu time

finding axes of symmetry from potential fields this paper addresses the problem of detecting axes of bilateral symmetry in images in order to achieve robustness to variation in illumination only edge gradient information is used to overcome the problem of edge breaks a potential field is developed from the edge map which spreads the information in the image plane pairs of points in the image plane are made to vote for their axes of symmetry with some confidence values to make the method robust to overlapping objects only local features in the form of taylor coefficients are used for quantifying symmetry we define an axis of symmetry histogram which is used to accumulate the weighted votes for all possible axes of symmetry to reduce the computational complexity of voting a hashing scheme is proposed wherein pairs of points whose potential fields are too asymmetric are pruned by not being counted for the vote experimental results indicate that the proposed method is fairly robust to edge breaks and is able to detect symmetries even when only 0 05 of the possible pairs are used for voting

application of elliptic fourier descriptors to symmetry detection under parallel projection in this paper the method of elliptic fourier descriptors using arc length parameterization is applied to tackle the problem of detection and recovery of symmetry under parallel projection a simple and fast iteration algorithm together with the invariants of symmetry provides sufficient information for the detection and recovery of symmetry under parallel projection the proposed method has been extensively tested using symmetric figures under different parallel projections simulation results of the algorithm are presented the extension of this method for planar object recognition under parallel projection is also addressed

multigrid domain decomposition methods for elliptic problems abstract the paper deals with a new approach to the construction of preconditioners of systems of mesh equations arising from finite element approximations of elliptic boundary value problems the approach is based on the idea of a multilevel decomposition of the mesh domain into small elementary subdomains estimates of the convergence rate and of the total arithmetic cost are derived for specific versions of the method applied to solve two and three dimensional model problems

three dimensional descriptions based on the analysis of the invariant and quasi invariant properties of some curved axis generalized cylinders we address the recovery of object level 3d descriptions of some classes of curved axis generalized cylinders for this the first part of the paper analyzes the projective properties of two common generic shapes planar right constant generalized cylinders prcgcs and circular planar right generalized cylinders circular prgcs the properties we analyze include new geometric invariant and quasi invariant properties of the orthographic projection of the above shapes and a useful classification of their structural properties as functions of their pose the second part of the paper describes an implemented system which detects and recovers prcgcs and circular prgcs from an intensity image in the presence of noise surface markings shadows and partial occlusion the methods exploit the projective properties to hypothesize and verify relevant curved axis objects thus explicitly using the three dimensionality of the objects and of the desired descriptions this work extends past work on the recovery of volumetric shapes from an intensity image by addressing new primitives deriving new properties and by developing a system that recovers them from an intensity image we demonstrate our method on several real intensity images

the scaled boundary finite element method a fundamental solution less boundary element method in this boundary element method based on finite elements only the boundary is discretized with surface finite elements yielding a reduction of the spatial dimension by one no fundamental solution is necessary and thus no singular integrals must be evaluated and general anisotropic material can be analysed for an unbounded semi infinite or infinite medium the radiation condition at infinity is satisfied exactly no discretization of free and fixed boundaries and interfaces between different materials is required the semi analytical solution inside the domain leads to an efficient procedure to calculate the stress intensity factors accurately without any discretization in the vicinity of the crack tip body loads are included without discretization of the domain thus the scaled boundary finite element method not only combines the advantages of the finite element and boundary element methods but also presents appealing features of its own after discretizing the boundary with finite elements the governing partial differential equations of linear elastodynamics are transformed to the scaled boundary finite element equation in displacement a system of linear second order ordinary differential equations with the radial coordinate as independent variable which can be solved analytically introducing the definition of the dynamic stiffness a system of nonlinear first order ordinary differential equations in dynamic stiffness with the frequency as independent variable is obtained besides the displacements in the interior the static stiffness and mass matrices of a bounded medium and the dynamic stiffness and unit impulse response matrices of an unbounded medium are calculated

scaled boundary fem solution of short crested wave diffraction by a vertical cylinder abstract the scaled boundary finite element method sbfem is a novel semi analytical method developed in the elasto statics and elasto dynamics areas that has the advantages of combining the finite element method with the boundary element method the sbfem method weakens the governing differential equation in the circumferential direction and solves the weakened equation analytically in the radial direction it has the inherent advantage of solving the unbounded fluid dynamic problem in this paper the boundary value problem composed of short crested waves diffracted by a vertical circular cylinder is solved by sbfem only the cylinder boundary is discretized with curved surface finite elements on the circumference of the cylinder while the radial differential equation is solved completely analytically the computation of the diffraction force based on the present sbfem solution demonstrates a high accuracy achieved with a small number of surface finite elements the method can be extended to solve more complex wave structure interaction problems resulting in direct engineering applications

isogeometric fluid structure interaction analysis with emphasis on non matching discretizations and with application to wind turbines abstract in this paper we develop a framework for fluid structure interaction fsi modeling and simulation with emphasis on isogeometric analysis iga and non matching fluid structure interface discretizations we take the augmented lagrangian approach to fsi as a point of departure here the lagrange multiplier field is defined on the fluid structure interface and is responsible for coupling of the two subsystems thus the fsi formulation does not rely on the continuity of the underlying function spaces across the fluid structure interface in order to produce the correct coupling conditions between the fluid and structural subdomains however in deriving the final fsi formulation the interface lagrange multiplier is formally eliminated and the formulation is written purely in terms of primal variables avoiding the use of lagrange multipliers adds efficiency to the proposed formulation as an added benefit the ability to employ non matching grids for multi physics simulations leads to significantly relaxed requirements that are placed on the geometry modeling and meshing tools for iga we show an application of the proposed fsi formulation to the simulation of the nrel 5 mw offshore wind turbine rotor where the aerodynamics domain is modeled using volumetric quadratic nurbs while the rotor structure is modeled using a cubic t spline based discretization of a rotation free kirchhoff love shell we conclude the article by showing fsi coupling of a t spline shell with a low order finite element method fem discretization of the aerodynamics equations this combined use of iga and fem is felt to be a good balance between speed robustness and accuracy of fsi simulations for this class of problems

irregular shape symmetry analysis theory and application to quantitative galaxy classification this paper presents a set of imperfectly symmetric measures based on a series of geometric transformation operations for quantitatively measuring the amount of symmetry of arbitrary shapes the definitions of both bilateral symmetricity and rotational symmetricity give new insight into analyzing the geometrical property of a shape and enable characterizing arbitrary shapes in a new way we developed a set of criteria for quantitative galaxy classification using our proposed irregular shape symmetry measures our study has demonstrated the effectiveness of the proposed method for the characterization of the shape of the celestial bodies the concepts described in the paper are applicable to many fields such as mathematics artificial intelligence digital image processing robotics biomedicine etc

efficient quadrature for nurbs based isogeometric analysis abstract we initiate the study of efficient quadrature rules for nurbs based isogeometric analysis a rule of thumb emerges the half point rule indicating that optimal rules involve a number of points roughly equal to half the number of degrees of freedom or equivalently half the number of basis functions of the space under consideration the half point rule is independent of the polynomial order of the basis efficient rules require taking into account the precise smoothness of basis functions across element boundaries several rules of practical interest are obtained and a numerical procedure for determining efficient rules is presented we compare the cost of quadrature for typical situations arising in structural mechanics and fluid dynamics the new rules represent improvements over those used previously in isogeometric analysis

interpreting line drawings of curved objects in this thesis we study the problem of interpreting line drawings of scenes composed or opaque regular solid objects bounded by piecewise smooth surfaces with no markings or texture on them it is assumed that the line drawing has been formed by orthographic projection of such a scene under general viewpoint that the line drawing is error free and that there are no lines due to shadows or specularities our definition implicitly excludes laminae wires and the apices of cones a major component of the interpretation of line drawings is line labelling by line labelling we mean a classification of each image curve as corresponding to either a depth or orientation discontinuity in the scene and b further subclassification of each kind of discontinuity for a depth discontinuity we determine whether it is a limb a locus of points on the surface where the line of sight is tangent to the surface or an occluding edge a tangent plane discontinuity of the surface for an orientation discontinuity we determine whether it corresponds to a convex or concave edge this thesis presents the first mathematically rigorous scheme for labelling line drawings of the class of scenes described by analysing the projection of the neighborhoods of different kinds of points on a piecewise smooth surface we are able to catalog all local labelling possibilities for the different types of junctions in a line drawing an algorithm is developed which utilizes this catalog to determine all legal labellings of the line drawing a local minimum complexity rule at each vertex select those labellings which correspond to the minimum number of faces meeting at the vertex is used in order to prune highly counter intuitive interpretations the labelling scheme was implemented and tested on a number of line drawings the labellings obtained are few and by and large in accordance with human interpretations

symmetry as a continuous feature symmetry is treated as a continuous feature and a continuous measure of distance from symmetry in shapes is defined the symmetry distance sd of a shape is defined to be the minimum mean squared distance required to move points of the original shape in order to obtain a symmetrical shape this general definition of a symmetry measure enables a comparison of the amount of symmetry of different shapes and the amount of different symmetries of a single shape this measure is applicable to any type of symmetry in any dimension the symmetry distance gives rise to a method of reconstructing symmetry of occluded shapes the authors extend the method to deal with symmetries of noisy and fuzzy data finally the authors consider grayscale images as 3d shapes and use the symmetry distance to find the orientation of symmetric objects from their images and to find locally symmetric regions in images

interpreting line drawings as three dimensional surfaces understanding how line drawings convey tri dimensionality is of fundamental importance in explaining surface perception when photometry is either uninformative or too complex to model analytically we put forward here a computational model for interpreting line drawings as three dimensional surfaces based on constraints on local surface orientation along extremal and discontinuity boundaries specific techniques are described for two key processes recovering the three dimensional conformation of a space curve e g a surface boundary from its two dimensional projection in an image and interpolating smooth surfaces from orientation constraints along extremal boundaries the relevance of the model to a general theory of low level vision is discussed

perception of 3 d surfaces from 2 d contours inference of 3 d shape from 2 d contours in a single image is an important problem in machine vision the authors survey classes of techniques proposed in the past and provide a critical analysis they show that two kinds of symmetries in figures which are known as parallel and skew symmetries give significant information about surface shape for a variety of objects they derive the constraints imposed by these symmetries and show how to use them to infer 3 d shape they also discuss the zero gaussian curvature zgc surfaces in depth and show results on the recovery of surface orientation for various zgc surfaces

the scaled boundary finite element method alias consistent infinitesimal finite element cell method for elastodynamics the scaled boundary finite element method alias the consistent infinitesimal finite element cell method is developed starting from the governing equations of linear elastodynamics only the boundary of the medium is discretized with surface finite elements yielding a reduction of the spatial dimension by one no fundamental solution is necessary and thus no singular integrals must be evaluated general anisotropic material is analysed without any increase in computational effort boundary conditions on free and fixed surfaces and on interfaces between different materials are enforced exactly without any discretization this method is exact in the radial direction and converges to the exact solution in the finite element sense in the circumferential directions for a bounded medium symmetric static stiffness and mass matrices with respect to the degrees of freedom on the boundary result without any additional assumption a stress singularity is represented very accurately as the condition on the boundary in the vicinity of the point of singularity is satisfied without spatial discretization

preconditioning and two level multigrid methods of arbitrary degree of approximation let h be a mesh parameter corresponding to a finite element mesh for an elliptic problem we describe preconditioning methods for two level meshes which for most prob lems solved in practice behave as methods of optimal order in both storage and computa tional complexity namely per mesh point these numbers are bounded above by relatively small constants for all h ho where ho is small enough to cover all but excessively fine meshes we note that in practice multigrid methods are actually solved on a finite often even a fixed number of grid levels in which case also these methods are not asymptotically optimal as h 0 numerical tests indicate that the new methods are about as fast as the best implementations of multigrid methods applied on general problems variable coefficients general domains and boundary conditions for all but excessively fine meshes furthermore most of the latter methods have been implemented only for difference schemes of second order of accuracy whereas our methods are applicable to higher order approximations we claim that our scheme could be added fairly easily to many existing finite element codes 1 introduction consider the numerical solution of elliptic boundary value prob lems discretized by finite element methods we assume that the boundary is polygonal or consists of planes we note that in practical problems one often has a fine enough grid already after the definition of the boundary and the minimal number of vertices needed for a first coarse triangulation anyhow if not so in most cases one makes only a few steps of mesh refinement hence the power of multigrid methods their optimal order of computational complexity is most often not achieved fully because optimality requires a large number of recursively defined meshes for details see e g 4 and for further references see 7 hence one might as well consider other methods perhaps simpler and more effective on a fixed mesh but which are not asymptotically optimal here we shall describe a method which uses only a fixed mesh but for which one nevertheless achieves a low order of computational complexity and of seemingly optimal order except for from a practical viewpoint excessively small meshes to be more precise the computational cost per mesh point is bounded by clog n for n no where n is the number of mesh points no is large enough to cover most applications and c is small enough that the method is competitive with multigrid methods as is well known the latter need recursion and the usual smoothing followed by corrections of the solutions on the different mesh levels we claim that the new method is more suitable for implementation in existing finite element packages in fact most packages for the multigrid methods are only for second order difference methods

acoustic isogeometric boundary element analysis an isogeometric boundary element method based on t splines is used to simulate acoustic phenomena we restrict our developments to low frequency problems to establish the fundamental properties of the proposed approach using t splines the computer aided design cad and boundary element analysis are integrated without recourse to geometry clean up or mesh generation a regularized burton miller formulation is used resulting in integrals which are at most weakly singular we employ a collocation based approach to generate the linear system of equations the method is verified against closed form solutions and direct comparisons are made with conventional lagrangian discretizations it is demonstrated that the superior accuracy of the isogeometric approach emanates from the exact geometric description encapsulated in the t spline the method is then applied to a real world application to illustrate the potential for integrated engineering design and analysis

recovery of the three dimensional shape of an object from a single view given a single picture which is a projection of a three dimensional scene onto the two dimensional picture plane we usually have definite ideas about the 3 d shapes of objects to do this we need to use assumptions about the world and the image formation process since there exist a large number of shapes which can produce the same picture the purpose of this paper is to identify some of these assumptions mostly geometrical ones by demonstrating how the theory and techniques which exploit such assumptions can provide a systematic shape recovery method the method consists of two parts the first is the application of the origami theory which models the world as a collection of plane surfaces and recovers the possible shapes qualitatively the second is the technique of mapping image regularities into shape constraints for recovering the probable shapes quantitatively actual shape recovery from a single view is demonstrated for the scenes of an object such as a box and a chair given a single image the method recovers the 3 d shapes of an object in it and generates images of the same object as we would see it from other directions

stress recovery and error estimation for the scaled boundary finite element method note 373 reference lch article 2002 011view record in web of science record created on 2007 04 24 modified on 2016 08 08