10,077 research outputs found
Constructing IGA-suitable planar parameterization from complex CAD boundary by domain partition and global/local optimization
In this paper, we propose a general framework for constructing IGA-suitable
planar B-spline parameterizations from given complex CAD boundaries consisting
of a set of B-spline curves. Instead of forming the computational domain by a
simple boundary, planar domains with high genus and more complex boundary
curves are considered. Firstly, some pre-processing operations including
B\'ezier extraction and subdivision are performed on each boundary curve in
order to generate a high-quality planar parameterization; then a robust planar
domain partition framework is proposed to construct high-quality patch-meshing
results with few singularities from the discrete boundary formed by connecting
the end points of the resulting boundary segments. After the topology
information generation of quadrilateral decomposition, the optimal placement of
interior B\'ezier curves corresponding to the interior edges of the
quadrangulation is constructed by a global optimization method to achieve a
patch-partition with high quality. Finally, after the imposition of
C1=G1-continuity constraints on the interface of neighboring B\'ezier patches
with respect to each quad in the quadrangulation, the high-quality B\'ezier
patch parameterization is obtained by a C1-constrained local optimization
method to achieve uniform and orthogonal iso-parametric structures while
keeping the continuity conditions between patches. The efficiency and
robustness of the proposed method are demonstrated by several examples which
are compared to results obtained by the skeleton-based parameterization
approach
Urn Models and Beta-splines
Some insight into the properties of beta-splines is gained by applying the techniques of urn models. Urn models are used to construct beta-spline basis functions and to derive the basic properties of these blending functions and the corresponding beta-spline curves. Only the simple notion of linear geometric continuity and with the most elementary beta parameter are outlined. Non-linear geometric continuity leads to additional beta parameters and to more complicated basis functions. Whether urn models can give us any insight into these higher order concepts still remains to be investigated
Polynomial-based non-uniform interpolatory subdivision with features control
Starting from a well-known construction of polynomial-based interpolatory 4-point schemes, in this paper we present
an original affine combination of quadratic polynomial samples that leads to a non-uniform 4-point scheme with edge
parameters. This blending-type formulation is then further generalized to provide a powerful subdivision algorithm
that combines the fairing curve of a non-uniform refinement with the advantages of a shape-controlled interpolation
method and an arbitrary point insertion rule. The result is a non-uniform interpolatory 4-point scheme that is unique
in combining a number of distinctive properties. In fact it generates visually-pleasing limit curves where special
features ranging from cusps and flat edges to point/edge tension effects may be included without creating undesired
undulations. Moreover such a scheme is capable of inserting new points at any positions of existing intervals, so that
the most convenient parameter values may be chosen as well as the intervals for insertion.
Such a fully flexible curve scheme is a fundamental step towards the construction of high-quality interpolatory subdivision surfaces with features control
Recent Results on Near-Best Spline Quasi-Interpolants
Roughly speaking, a near-best (abbr. NB) quasi-interpolant (abbr. QI) is an
approximation operator of the form where the 's are B-splines and the 's
are linear discrete or integral forms acting on the given function . These
forms depend on a finite number of coefficients which are the components of
vectors for . The index refers to this sequence of
vectors. In order that for all polynomials belonging to some
subspace included in the space of splines generated by the 's, each
vector must lie in an affine subspace , i.e. satisfy some
linear constraints. However there remain some degrees of freedom which are used
to minimize for each . It is easy to
prove that is an upper bound of
: thus, instead of minimizing the infinite norm of
, which is a difficult problem, we minimize an upper bound of this norm,
which is much easier to do. Moreover, the latter problem has always at least
one solution, which is associated with a NB QI. In the first part of the paper,
we give a survey on NB univariate or bivariate spline QIs defined on uniform or
non-uniform partitions and already studied by the author and coworkers. In the
second part, we give some new results, mainly on univariate and bivariate
integral QIs on {\sl non-uniform} partitions: in that case, NB QIs are more
difficult to characterize and the optimal properties strongly depend on the
geometry of the partition. Therefore we have restricted our study to QIs having
interesting shape properties and/or infinite norms uniformly bounded
independently of the partition
Geometrically nonlinear isogeometric analysis of laminated composite plates based on higher-order shear deformation theory
In this paper, we present an effectively numerical approach based on
isogeometric analysis (IGA) and higher-order shear deformation theory (HSDT)
for geometrically nonlinear analysis of laminated composite plates. The HSDT
allows us to approximate displacement field that ensures by itself the
realistic shear strain energy part without shear correction factors. IGA
utilizing basis functions namely B-splines or non-uniform rational B-splines
(NURBS) enables to satisfy easily the stringent continuity requirement of the
HSDT model without any additional variables. The nonlinearity of the plates is
formed in the total Lagrange approach based on the von-Karman strain
assumptions. Numerous numerical validations for the isotropic, orthotropic,
cross-ply and angle-ply laminated plates are provided to demonstrate the
effectiveness of the proposed method
Polynomial cubic splines with tension properties
In this paper we present a new class of spline functions with tension properties. These splines are composed by polynomial cubic pieces and therefore are conformal to the standard, NURBS based CAD/CAM systems
TiGL - An Open Source Computational Geometry Library for Parametric Aircraft Design
This paper introduces the software TiGL: TiGL is an open source high-fidelity
geometry modeler that is used in the conceptual and preliminary aircraft and
helicopter design phase. It creates full three-dimensional models of aircraft
from their parametric CPACS description. Due to its parametric nature, it is
typically used for aircraft design analysis and optimization. First, we present
the use-case and architecture of TiGL. Then, we discuss it's geometry module,
which is used to generate the B-spline based surfaces of the aircraft. The
backbone of TiGL is its surface generator for curve network interpolation,
based on Gordon surfaces. One major part of this paper explains the
mathematical foundation of Gordon surfaces on B-splines and how we achieve the
required curve network compatibility. Finally, TiGL's aircraft component module
is introduced, which is used to create the external and internal parts of
aircraft, such as wings, flaps, fuselages, engines or structural elements
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