372 research outputs found
Curve network interpolation by quadratic B-spline surfaces
In this paper we investigate the problem of interpolating a B-spline curve
network, in order to create a surface satisfying such a constraint and defined
by blending functions spanning the space of bivariate quadratic splines
on criss-cross triangulations. We prove the existence and uniqueness of the
surface, providing a constructive algorithm for its generation. We also present
numerical and graphical results and comparisons with other methods.Comment: With respect to the previous version, this version of the paper is
improved. The results have been reorganized and it is more general since it
deals with non uniform knot partitions. Accepted for publication in Computer
Aided Geometric Design, October 201
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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
Reconstruction approximating method by biquadratic splines of offset surfaces holes
Funding for open access charge: Universidad de Granada / CBUA.Standard Offset surfaces are defined as locus of the points which are at constant distance
along the unit normal direction from the generator surfaces. Offset are widely
used in various practical applications, such as tolerance analysis, geometric optics
and robot path-planning. In some of the engineering applications, we need to extend
the concept of standard offset to the generalized offset where distance offset is not
necessarily constant and offset direction are not necessarily along the normal direction.
Normally, a generalized offset is functionally more complex than its progenitor
because of the square root appears in the expression of the unit normal vector. For
this, an approximation method of its construction is necessary. In many situation it
is necessary to fill or reconstruct certain function defined in a domain in which there
is a lack of information inside one or several sub-domains (holes). In some practical
cases, we may have some specific geometrical constrains, of industrial or design
type, for example, the case of a specified volume inside each one of these holes. The
problem of filling holes or completing a 3D surface arises in all sorts of computational
graphics areas, like CAGD, CAD-CAM, Earth Sciences, computer vision in
robotics, image reconstruction from satellite and radar information, etc. In this work
we present an approximation method of filling holes of the generalized offset of a
surface when there is a lack information in a sub-domain of the function that define
it. We prove the existence and uniqueness of solution of this problem, we show how
to compute it and we establish a convergence result of this approximation method.
Finally, we give some graphical and numerical examples.Universidad de Granada / CBU
An adaptive, hanging-node, discontinuous isogeometric analysis method for the first-order form of the neutron transport equation with discrete ordinate (SN) angular discretisation
In this paper a discontinuous, hanging-node, isogeometric analysis (IGA) method is developed and applied to the first-order form of the neutron transport equation with a discrete ordinate (SN) angular discretisation in two-dimensional space. The complexities involved in upwinding across curved element boundaries that contain hanging-nodes have been addressed to ensure that the scheme remains conservative. A robust algorithm for cycle-breaking has also been introduced in order to develop a unique sweep ordering of the elements for each discrete ordinates direction. The convergence rate of the scheme has been verified using the method of manufactured solutions (MMS) with a smooth solution. Heuristic error indicators have been used to drive an adaptive mesh refinement (AMR) algorithm to take advantage of the hanging-node discretisation. The effectiveness of this method is demonstrated for three test cases. The first is a homogeneous square in a vacuum with varying mean free path and a prescribed extraneous unit source. The second test case is a radiation shielding problem and the third is a 3×3 “supercell” featuring a burnable absorber. In the final test case, comparisons are made to the discontinuous Galerkin finite element method (DGFEM) using both straight-sided and curved quadratic finite elements
BĂ©zier Method For Image Processing
This project concerns about BĂ©zier method in Computer Aided GeometricDesign (CAGD) involving BĂ©zier Curve and BĂ©zier Surface which widely related to the other theorem and method. The aim of this project is to introduce the basic of BĂ©zier method and then generate the BĂ©zier curves, BĂ©zier surfaces, theory and properties and develop BĂ©zier method in image processing application specifically image compression by using MATLAB
PARAMETRIZATION AND SHAPE RECONSTRUCTION TECHNIQUES FOR DOO-SABIN SUBDIVISION SURFACES
This thesis presents a new technique for the reconstruction of a smooth surface from a set of 3D data points. The reconstructed surface is represented by an everywhere -continuous subdivision surface which interpolates all the given data points. And the topological structure of the reconstructed surface is exactly the same as that of the data points. The new technique consists of two major steps. First, use an efficient surface reconstruction method to produce a polyhedral approximation to the given data points. Second, construct a Doo-Sabin subdivision surface that smoothly passes through all the data points in the given data set. A new technique is presented for the second step in this thesis. The new technique iteratively modifies the vertices of the polyhedral approximation 1CM until a new control meshM, whose Doo-Sabin subdivision surface interpolatesM, is reached. It is proved that, for any mesh M with any size and any topology, the iterative process is always convergent with Doo-Sabin subdivision scheme. The new technique has the advantages of both a local method and a global method, and the surface reconstruction process can reproduce special features such as edges and corners faithfully
Almost- splines: Biquadratic splines on unstructured quadrilateral meshes and their application to fourth order problems
Isogeometric Analysis generalizes classical finite element analysis and
intends to integrate it with the field of Computer-Aided Design. A central
problem in achieving this objective is the reconstruction of analysis-suitable
models from Computer-Aided Design models, which is in general a non-trivial and
time-consuming task. In this article, we present a novel spline construction,
that enables model reconstruction as well as simulation of high-order PDEs on
the reconstructed models. The proposed almost- are biquadratic splines on
fully unstructured quadrilateral meshes (without restrictions on placements or
number of extraordinary vertices). They are smooth almost everywhere,
that is, at all vertices and across most edges, and in addition almost (i.e.
approximately) smooth across all other edges. Thus, the splines form
-nonconforming analysis-suitable discretization spaces. This is the
lowest-degree unstructured spline construction that can be used to solve
fourth-order problems. The associated spline basis is non-singular and has
several B-spline-like properties (e.g., partition of unity, non-negativity,
local support), the almost- splines are described in an explicit
B\'ezier-extraction-based framework that can be easily implemented. Numerical
tests suggest that the basis is well-conditioned and exhibits optimal
approximation behavior
Quadratic B-Spline Surfaces with Free Parameters for the Interpolation of Curve Networks
In this paper, we propose a method for constructing spline surfaces interpolating a B-spline curve network, allowing the presence of free parameters, in order to model the interpolating surface. We provide a constructive algorithm for its generation in the case of biquadratic tensor product B-spline surfaces and bivariate B-spline surfaces on criss-cross triangulations. Finally, we present graphical results
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