418 research outputs found
Fast Isogeometric Boundary Element Method based on Independent Field Approximation
An isogeometric boundary element method for problems in elasticity is
presented, which is based on an independent approximation for the geometry,
traction and displacement field. This enables a flexible choice of refinement
strategies, permits an efficient evaluation of geometry related information, a
mixed collocation scheme which deals with discontinuous tractions along
non-smooth boundaries and a significant reduction of the right hand side of the
system of equations for common boundary conditions. All these benefits are
achieved without any loss of accuracy compared to conventional isogeometric
formulations. The system matrices are approximated by means of hierarchical
matrices to reduce the computational complexity for large scale analysis. For
the required geometrical bisection of the domain, a strategy for the evaluation
of bounding boxes containing the supports of NURBS basis functions is
presented. The versatility and accuracy of the proposed methodology is
demonstrated by convergence studies showing optimal rates and real world
examples in two and three dimensions.Comment: 32 pages, 27 figure
Flexible G1 Interpolation of Quad Meshes
International audienceTransforming an arbitrary mesh into a smooth G1 surface has been the subject of intensive research works. To get a visual pleasing shape without any imperfection even in the presence of extraordinary mesh vertices is still a challenging problem in particular when interpolation of the mesh vertices is required. We present a new local method, which produces visually smooth shapes while solving the interpolation problem. It consists of combining low degree biquartic BĂ©zier patches with minimum number of pieces per mesh face, assembled together with G1-continuity. All surface control points are given explicitly. The construction is local and free of zero-twists. We further show that within this economical class of surfaces it is however possible to derive a sufficient number of meaningful degrees of freedom so that standard optimization techniques result in high quality surfaces
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Smooth parametric surfaces and n-sided patches
The theory of 'geometric continuity' within the subject of CAGD is reviewed. In particular, we are concerned with how parametric surface patches for CAGD can be pieced together to form a smooth Ck surface. The theory is applied to the problem of filling an n-sided hole occurring within a smooth rectangular patch complex. A number of solutions to this problem are surveyed
Extensions to OpenGL for CAGD.
Many computer graphic API’s, including OpenGL, emphasize modeling with rectangular patches, which are especially useful in Computer Aided Geomeric Design (CAGD). However, not all shapes are rectangular; some are triangular or more complex. This paper extends the OpenGL library to support the modeling of triangular patches, Coons patches, and Box-splines patches. Compared with the triangular patch created from degenerate rectangular Bezier patch with the existing functions provided by OpenGL, the triangular Bezier patches can be used in certain design situations and allow designers to achieve high-quality results that are less CPU intense and require less storage space. The addition of Coons patches and Box splines to the OpenGL library also give it more functionality. Both patch types give CAGD users more flexibility in designing surfaces. A library for all three patch types was developed as an addition to OpenGL
Arbitrary topology meshes in geometric design and vector graphics
Meshes are a powerful means to represent objects and shapes both in 2D and 3D, but the techniques based on meshes can only be used in certain regular settings and restrict their usage. Meshes with an arbitrary topology have many interesting applications in geometric design and (vector) graphics, and can give designers more freedom in designing complex objects. In the first part of the thesis we look at how these meshes can be used in computer aided design to represent objects that consist of multiple regular meshes that are constructed together. Then we extend the B-spline surface technique from the regular setting to work on extraordinary regions in meshes so that multisided B-spline patches are created. In addition, we show how to render multisided objects efficiently, through using the GPU and tessellation. In the second part of the thesis we look at how the gradient mesh vector graphics primitives can be combined with procedural noise functions to create expressive but sparsely defined vector graphic images. We also look at how the gradient mesh can be extended to arbitrary topology variants. Here, we compare existing work with two new formulations of a polygonal gradient mesh. Finally we show how we can turn any image into a vector graphics image in an efficient manner. This vectorisation process automatically extracts important image features and constructs a mesh around it. This automatic pipeline is very efficient and even facilitates interactive image vectorisation
Comparing faceted and smoothed tool surface descriptions in sheet metal forming simulation
This study deals with different tool surface description
methods used in the finite element analysis of sheet metal
forming processes. The description of arbitrarily-shaped tool
surfaces using the traditional linear finite elements is compared
with two distinct smooth surface description approaches:
(i) BĂ©zier patches obtained from the ComputerAided
Design model and (ii) smoothing the finite element
mesh using Nagata patches. The contact search algorithm is
presented for each approach, exploiting its special features in
order to ensure an accurate and efficient contact detection. The
influence of the tool modelling accuracy on the numerical
results is analysed using two sheet forming examples, the
unconstrained cylindrical bending and the reverse deep drawing
of a cylindrical cup. Smoothing the contact surfaces with
Nagata patches allows creating more accurate tool models,
both in terms of shape and normal vectors, when compared
with the conventional linear finite element mesh. The computational
efficiency is evaluated in this study through the total
number of increments and the required CPU time. The mesh
refinement in the faceted description approach is not effective
in terms of computational efficiency due to large discontinuities
in the normal vector field across facets, even when
adopting fine meshes.The authors gratefully acknowledge the financial
support of the Portuguese Foundation for Science and Technology (FCT)
via the projects PTDC/EME-TME/118420/2010 and PEst-C/EME/
UI0285/2013 and by FEDER funds through the program COMPETE –
Programa Operacional Factores de Competitividade, under the project
CENTRO-07-0224-FEDER-002001 (MT4MOBI). The first author is
also grateful to the FCT for the PhD grant SFRH/BD/69140/2010.info:eu-repo/semantics/publishedVersio
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