4,300 research outputs found
Combined 3D thinning and greedy algorithm to approximate realistic particles with corrected mechanical properties
The shape of irregular particles has significant influence on micro- and
macro-scopic behavior of granular systems. This paper presents a combined 3D
thinning and greedy set-covering algorithm to approximate realistic particles
with a clump of overlapping spheres for discrete element method (DEM)
simulations. First, the particle medial surface (or surface skeleton), from
which all candidate (maximal inscribed) spheres can be generated, is computed
by the topological 3D thinning. Then, the clump generation procedure is
converted into a greedy set-covering (SCP) problem.
To correct the mass distribution due to highly overlapped spheres inside the
clump, linear programming (LP) is used to adjust the density of each component
sphere, such that the aggregate properties mass, center of mass and inertia
tensor are identical or close enough to the prototypical particle. In order to
find the optimal approximation accuracy (volume coverage: ratio of clump's
volume to the original particle's volume), particle flow of 3 different shapes
in a rotating drum are conducted. It was observed that the dynamic angle of
repose starts to converge for all particle shapes at 85% volume coverage
(spheres per clump < 30), which implies the possible optimal resolution to
capture the mechanical behavior of the system.Comment: 34 pages, 13 figure
Computing a Compact Spline Representation of the Medial Axis Transform of a 2D Shape
We present a full pipeline for computing the medial axis transform of an
arbitrary 2D shape. The instability of the medial axis transform is overcome by
a pruning algorithm guided by a user-defined Hausdorff distance threshold. The
stable medial axis transform is then approximated by spline curves in 3D to
produce a smooth and compact representation. These spline curves are computed
by minimizing the approximation error between the input shape and the shape
represented by the medial axis transform. Our results on various 2D shapes
suggest that our method is practical and effective, and yields faithful and
compact representations of medial axis transforms of 2D shapes.Comment: GMP14 (Geometric Modeling and Processing
Generic, Geometric Finite Element Analysis of the Transtibial Residual Limb and Prosthetic Socket
Finite element analysis was used to investigate the stress distribution between the residual limb and prosthetic socket of persons with transtibial amputation (TTA). The purpose of this study was to develop a tool to provide a quantitative estimate of prosthetic interface pressures to improve our understanding of residual limb/prosthetic socket biomechanics and prosthetic fit. FE models of the residual limb and prosthetic socket were created. In contrast to previous FE models of the prosthetic socket/residual limb system, these models were not based on the geometry of a particular individual, but instead were based on a generic, geometric approximation of the residual limb. These models could then be scaled for the limbs of specific individuals. The material properties of the bulk soft tissues of the residual limb were based upon local in vivo indentor studies. Significant effort was devoted toward the validation of these generic, geometric FE models; prosthetic interface pressures estimated via the FE model were compared to experimentally determined interface pressures for several persons with TTA in a variety of socket designs and static load/alignment states. The FE normal stresses were of the same order of magnitude as the measured stresses (0-200 kPa); however, significant differences in the stress distribution were observed. Although the generic, geometric FE models do not appear to accurately predict the stress distribution for specific subjects, the models have practical applications in comparative stress distribution studies
Principal arc analysis on direct product manifolds
We propose a new approach to analyze data that naturally lie on manifolds. We
focus on a special class of manifolds, called direct product manifolds, whose
intrinsic dimension could be very high. Our method finds a low-dimensional
representation of the manifold that can be used to find and visualize the
principal modes of variation of the data, as Principal Component Analysis (PCA)
does in linear spaces. The proposed method improves upon earlier manifold
extensions of PCA by more concisely capturing important nonlinear modes. For
the special case of data on a sphere, variation following nongeodesic arcs is
captured in a single mode, compared to the two modes needed by previous
methods. Several computational and statistical challenges are resolved. The
development on spheres forms the basis of principal arc analysis on more
complicated manifolds. The benefits of the method are illustrated by a data
example using medial representations in image analysis.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS370 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Hybrid model for vascular tree structures
This paper proposes a new representation scheme of the cerebral blood
vessels. This model provides information on the semantics of the
vascular structure: the topological relationships between vessels and
the labeling of vascular accidents such as aneurysms and stenoses.
In addition, the model keeps information of the inner surface geometry
as well as of the vascular map volume properties, i.e. the tissue
density, the blood flow velocity and the vessel wall elasticity.
The model can be constructed automatically in a pre-process from a set
of segmented MRA images. Its memory requirements are optimized on the
basis of the sparseness of the vascular structure. It allows fast
queries and efficient traversals and navigations. The visualizations
of the vessel surface can be performed at different levels of
detail. The direct rendering of the volume is fast because the model
provides a natural way to skip over empty data.
The paper analyzes the memory requirements of the model along with the
costs of the most important operations on it.Postprint (published version
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