4,428 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
Data-driven quasi-interpolant spline surfaces for point cloud approximation
In this paper we investigate a local surface approximation, the Weighted
Quasi Interpolant Spline Approximation (wQISA), specifically designed for large
and noisy point clouds. We briefly describe the properties of the wQISA
representation and introduce a novel data-driven implementation, which combines
prediction capability and complexity efficiency. We provide an extended
comparative analysis with other continuous approximations on real data,
including different types of surfaces and levels of noise, such as 3D models,
terrain data and digital environmental data
Efficient cosmological parameter sampling using sparse grids
We present a novel method to significantly speed up cosmological parameter
sampling. The method relies on constructing an interpolation of the
CMB-log-likelihood based on sparse grids, which is used as a shortcut for the
likelihood-evaluation. We obtain excellent results over a large region in
parameter space, comprising about 25 log-likelihoods around the peak, and we
reproduce the one-dimensional projections of the likelihood almost perfectly.
In speed and accuracy, our technique is competitive to existing approaches to
accelerate parameter estimation based on polynomial interpolation or neural
networks, while having some advantages over them. In our method, there is no
danger of creating unphysical wiggles as it can be the case for polynomial fits
of a high degree. Furthermore, we do not require a long training time as for
neural networks, but the construction of the interpolation is determined by the
time it takes to evaluate the likelihood at the sampling points, which can be
parallelised to an arbitrary degree. Our approach is completely general, and it
can adaptively exploit the properties of the underlying function. We can thus
apply it to any problem where an accurate interpolation of a function is
needed.Comment: Submitted to MNRAS, 13 pages, 13 figure
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