6,135 research outputs found
Faster ASV decomposition for orthogonal polyhedra using the Extreme Vertices Model (EVM)
The alternating sum of volumes (ASV) decomposition is a widely used
technique for converting a B-Rep into a CSG model. The obtained CSG
tree has convex primitives at its leaf nodes, while the contents of
its internal nodes alternate between the set union and difference
operators.
This work first shows that the obtained CSG tree T can also be
expressed as the regularized Exclusive-OR operation among all the
convex primitives at the leaf nodes of T, regardless the structure and
internal nodes of T. This is an important result in the case in which
EVM represented orthogonal polyhedra are used because in this model
the Exclusive-OR operation runs much faster than set union and
difference operations. Therefore this work applies this result to EVM
represented orthogonal polyhedra. It also presents experimental
results that corroborate the theoretical results and includes some
practical uses for the ASV decomposition of orthogonal polyhedra.Postprint (published version
Modeling of 2D and 3D Assemblies Taking Into Account Form Errors of Plane Surfaces
The tolerancing process links the virtual and the real worlds. From the
former, tolerances define a variational geometrical language (geometric
parameters). From the latter, there are values limiting those parameters. The
beginning of a tolerancing process is in this duality. As high precision
assemblies cannot be analyzed with the assumption that form errors are
negligible, we propose to apply this process to assemblies with form errors
through a new way of allowing to parameterize forms and solve their assemblies.
The assembly process is calculated through a method of allowing to solve the 3D
assemblies of pairs of surfaces having form errors using a static equilibrium.
We have built a geometrical model based on the modal shapes of the ideal
surface. We compute for the completely deterministic contact points between
this pair of shapes according to a given assembly process. The solution gives
an accurate evaluation of the assembly performance. Then we compare the results
with or without taking into account the form errors. When we analyze a batch of
assemblies, the problem is to compute for the nonconformity rate of a pilot
production according to the functional requirements. We input probable errors
of surfaces (position, orientation, and form) in our calculus and we evaluate
the quality of the results compared with the functional requirements. The pilot
production then can or cannot be validated
Perceptually Motivated Shape Context Which Uses Shape Interiors
In this paper, we identify some of the limitations of current-day shape
matching techniques. We provide examples of how contour-based shape matching
techniques cannot provide a good match for certain visually similar shapes. To
overcome this limitation, we propose a perceptually motivated variant of the
well-known shape context descriptor. We identify that the interior properties
of the shape play an important role in object recognition and develop a
descriptor that captures these interior properties. We show that our method can
easily be augmented with any other shape matching algorithm. We also show from
our experiments that the use of our descriptor can significantly improve the
retrieval rates
Deconstructing Approximate Offsets
We consider the offset-deconstruction problem: Given a polygonal shape Q with
n vertices, can it be expressed, up to a tolerance \eps in Hausdorff distance,
as the Minkowski sum of another polygonal shape P with a disk of fixed radius?
If it does, we also seek a preferably simple-looking solution P; then, P's
offset constitutes an accurate, vertex-reduced, and smoothened approximation of
Q. We give an O(n log n)-time exact decision algorithm that handles any
polygonal shape, assuming the real-RAM model of computation. A variant of the
algorithm, which we have implemented using CGAL, is based on rational
arithmetic and answers the same deconstruction problem up to an uncertainty
parameter \delta; its running time additionally depends on \delta. If the input
shape is found to be approximable, this algorithm also computes an approximate
solution for the problem. It also allows us to solve parameter-optimization
problems induced by the offset-deconstruction problem. For convex shapes, the
complexity of the exact decision algorithm drops to O(n), which is also the
time required to compute a solution P with at most one more vertex than a
vertex-minimal one.Comment: 18 pages, 11 figures, previous version accepted at SoCG 2011,
submitted to DC
Higher Sobolev Regularity of Convex Integration Solutions in Elasticity: The Dirichlet Problem with Affine Data in
In this article we continue our study of higher Sobolev regularity of
flexible convex integration solutions to differential inclusions arising from
applications in materials sciences. We present a general framework yielding
higher Sobolev regularity for Dirichlet problems with affine data in
. This allows us to simultaneously deal with linear and
nonlinear differential inclusion problems. We show that the derived higher
integrability and differentiability exponent has a lower bound, which is
independent of the position of the Dirichlet boundary data in
. As applications we discuss the regularity of weak
isometric immersions in two and three dimensions as well as the differential
inclusion problem for the geometrically linear hexagonal-to-rhombic and the
cubic-to-orthorhombic phase transformations occurring in shape memory alloys.Comment: 50 pages, 13 figure
Dense 3D Face Correspondence
We present an algorithm that automatically establishes dense correspondences
between a large number of 3D faces. Starting from automatically detected sparse
correspondences on the outer boundary of 3D faces, the algorithm triangulates
existing correspondences and expands them iteratively by matching points of
distinctive surface curvature along the triangle edges. After exhausting
keypoint matches, further correspondences are established by generating evenly
distributed points within triangles by evolving level set geodesic curves from
the centroids of large triangles. A deformable model (K3DM) is constructed from
the dense corresponded faces and an algorithm is proposed for morphing the K3DM
to fit unseen faces. This algorithm iterates between rigid alignment of an
unseen face followed by regularized morphing of the deformable model. We have
extensively evaluated the proposed algorithms on synthetic data and real 3D
faces from the FRGCv2, Bosphorus, BU3DFE and UND Ear databases using
quantitative and qualitative benchmarks. Our algorithm achieved dense
correspondences with a mean localisation error of 1.28mm on synthetic faces and
detected anthropometric landmarks on unseen real faces from the FRGCv2
database with 3mm precision. Furthermore, our deformable model fitting
algorithm achieved 98.5% face recognition accuracy on the FRGCv2 and 98.6% on
Bosphorus database. Our dense model is also able to generalize to unseen
datasets.Comment: 24 Pages, 12 Figures, 6 Tables and 3 Algorithm
Topomap: Topological Mapping and Navigation Based on Visual SLAM Maps
Visual robot navigation within large-scale, semi-structured environments
deals with various challenges such as computation intensive path planning
algorithms or insufficient knowledge about traversable spaces. Moreover, many
state-of-the-art navigation approaches only operate locally instead of gaining
a more conceptual understanding of the planning objective. This limits the
complexity of tasks a robot can accomplish and makes it harder to deal with
uncertainties that are present in the context of real-time robotics
applications. In this work, we present Topomap, a framework which simplifies
the navigation task by providing a map to the robot which is tailored for path
planning use. This novel approach transforms a sparse feature-based map from a
visual Simultaneous Localization And Mapping (SLAM) system into a
three-dimensional topological map. This is done in two steps. First, we extract
occupancy information directly from the noisy sparse point cloud. Then, we
create a set of convex free-space clusters, which are the vertices of the
topological map. We show that this representation improves the efficiency of
global planning, and we provide a complete derivation of our algorithm.
Planning experiments on real world datasets demonstrate that we achieve similar
performance as RRT* with significantly lower computation times and storage
requirements. Finally, we test our algorithm on a mobile robotic platform to
prove its advantages.Comment: 8 page
BSP-fields: An Exact Representation of Polygonal Objects by Differentiable Scalar Fields Based on Binary Space Partitioning
The problem considered in this work is to find a dimension independent algorithm for the generation of signed scalar fields exactly representing polygonal objects and satisfying the following requirements: the defining real function takes zero value exactly at the polygonal object boundary; no extra zero-value isosurfaces should be generated; C1 continuity of the function in the entire domain. The proposed algorithms are based on the binary space partitioning (BSP) of the object by the planes passing through the polygonal faces and are independent of the object genus, the number of disjoint components, and holes in the initial polygonal mesh. Several extensions to the basic algorithm are proposed to satisfy the selected optimization criteria. The generated BSP-fields allow for applying techniques of the function-based modeling to already existing legacy objects from CAD and computer animation areas, which is illustrated by several examples
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