11,238 research outputs found
A Note on Some Applications of Interval Arithmetic in Hierarchical Solid Modeling
Techniques of reliable computing like interval arithmetic can be used to
guarantee a reliable solution even in the presence of numerical round-off
errors. The need to trace bounds for the error function separately can be
eliminated using these techniques. In this talk, we focus on some
demonstrations how the techniques and algorithms of reliable computing
can be applied to the construction and further processing of hierarchical
solid representations using the octree model as an example.
An octree is a common hierarchical data structure to represent 3D
geometrical objects in solid modeling systems or to reconstruct a real
scene. The solid representation is based on recursive cell decompositions
of the space. Unfortunately, the data structure may require a large amount
of memory when it uses a set of very small cubic nodes to approximate a
solid.
In this talk, we present a novel generalization of the octree model created
from a CSG object that uses interval arithmetic and allows us to extend the
tests for classifying points in space as inside, on the boundary or outside
the object to handle whole sections of the space at once. Tree nodes with
additional information about relevant parts of the CSG object are
introduced in order to reduce the depth of the required subdivision.
Furthermore, this talk is concerned with interval-based algorithms for
reliable proximity queries between the extended octrees and with further
processing of the structure. We conclude the talk with some examples of
implementations
A Note on Some Applications of Interval Arithmetic in Hierarchical Solid Modeling
Abstract. Techniques of reliable computing, like interval arithmetic, can be used to guarantee reliable solutions even in the presence of numerical round-off errors. The need to trace bounds for the error function separately can be eliminated using these techniques. In this extended abstract, we focus on presenting how the techniques and algorithms of reliable computing can be applied to the construction and further processing of hierarchical solid representations using the octree model as an example
The Skip Quadtree: A Simple Dynamic Data Structure for Multidimensional Data
We present a new multi-dimensional data structure, which we call the skip
quadtree (for point data in R^2) or the skip octree (for point data in R^d,
with constant d>2). Our data structure combines the best features of two
well-known data structures, in that it has the well-defined "box"-shaped
regions of region quadtrees and the logarithmic-height search and update
hierarchical structure of skip lists. Indeed, the bottom level of our structure
is exactly a region quadtree (or octree for higher dimensional data). We
describe efficient algorithms for inserting and deleting points in a skip
quadtree, as well as fast methods for performing point location and approximate
range queries.Comment: 12 pages, 3 figures. A preliminary version of this paper appeared in
the 21st ACM Symp. Comp. Geom., Pisa, 2005, pp. 296-30
Design of multimedia processor based on metric computation
Media-processing applications, such as signal processing, 2D and 3D graphics
rendering, and image compression, are the dominant workloads in many embedded
systems today. The real-time constraints of those media applications have
taxing demands on today's processor performances with low cost, low power and
reduced design delay. To satisfy those challenges, a fast and efficient
strategy consists in upgrading a low cost general purpose processor core. This
approach is based on the personalization of a general RISC processor core
according the target multimedia application requirements. Thus, if the extra
cost is justified, the general purpose processor GPP core can be enforced with
instruction level coprocessors, coarse grain dedicated hardware, ad hoc
memories or new GPP cores. In this way the final design solution is tailored to
the application requirements. The proposed approach is based on three main
steps: the first one is the analysis of the targeted application using
efficient metrics. The second step is the selection of the appropriate
architecture template according to the first step results and recommendations.
The third step is the architecture generation. This approach is experimented
using various image and video algorithms showing its feasibility
Integration of reliable algorithms into modeling software
In this note we discuss strategies that would enhance modern modeling and simulation software (MSS) with reliable routines using validated data types, controlled rounding, algorithmic differentiation and interval equation or initial value problem solver. Several target systems are highlighted. In stochastic traffic modeling, the computation of workload distributions plays a prominent role since they influence the quality of service parameters. INoWaTIV is a workload analysis tool that uses two different techniques: the polynomial factorization approach and the Wiener-Hopf factorization to determine the work-load distributions of GI/GI/1 and SMP/GI/1 service systems accurately. Two extensions of a multibody modeling and simulation software were developed to model kinematic and dynamic properties of multibody systems in a validated way. Furthermore, an interface was created that allows the computation of convex hulls and reliable lower bounds for the distances between subpav-ing-encoded objects constructed with SIVIA (Set Inverter Via Interval Analysis)
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