476 research outputs found
Distance-Sensitive Planar Point Location
Let be a connected planar polygonal subdivision with edges
that we want to preprocess for point-location queries, and where we are given
the probability that the query point lies in a polygon of
. We show how to preprocess such that the query time
for a point~ depends on~ and, in addition, on the distance
from to the boundary of~---the further away from the boundary, the
faster the query. More precisely, we show that a point-location query can be
answered in time , where
is the shortest Euclidean distance of the query point~ to the
boundary of . Our structure uses space and
preprocessing time. It is based on a decomposition of the regions of
into convex quadrilaterals and triangles with the following
property: for any point , the quadrilateral or triangle
containing~ has area . For the special case where
is a subdivision of the unit square and
, we present a simpler solution that achieves a
query time of . The latter solution can be extended to
convex subdivisions in three dimensions
Colored Non-Crossing Euclidean Steiner Forest
Given a set of -colored points in the plane, we consider the problem of
finding trees such that each tree connects all points of one color class,
no two trees cross, and the total edge length of the trees is minimized. For
, this is the well-known Euclidean Steiner tree problem. For general ,
a -approximation algorithm is known, where is the
Steiner ratio.
We present a PTAS for , a -approximation algorithm
for , and two approximation algorithms for general~, with ratios
and
Approximating Dynamic Time Warping and Edit Distance for a Pair of Point Sequences
We give the first subquadratic-time approximation schemes for dynamic time
warping (DTW) and edit distance (ED) of several natural families of point
sequences in , for any fixed . In particular, our
algorithms compute -approximations of DTW and ED in time
near-linear for point sequences drawn from k-packed or k-bounded curves, and
subquadratic for backbone sequences. Roughly speaking, a curve is
-packed if the length of its intersection with any ball of radius
is at most , and a curve is -bounded if the sub-curve
between two curve points does not go too far from the two points compared to
the distance between the two points. In backbone sequences, consecutive points
are spaced at approximately equal distances apart, and no two points lie very
close together. Recent results suggest that a subquadratic algorithm for DTW or
ED is unlikely for an arbitrary pair of point sequences even for . Our
algorithms work by constructing a small set of rectangular regions that cover
the entries of the dynamic programming table commonly used for these distance
measures. The weights of entries inside each rectangle are roughly the same, so
we are able to use efficient procedures to approximately compute the cheapest
paths through these rectangles
Generating Kernel Aware Polygons
Problems dealing with the generation of random polygons has important applications for evaluating the performance of algorithms on polygonal domain. We review existing algorithms for generating random polygons. We present an algorithm for generating polygons admitting visibility properties. In particular, we propose an algorithm for generating polygons admitting large size kernels. We also present experimental results on generating such polygons
Multi-scale data storage schemes for spatial information systems
This thesis documents a research project that has led to the design and prototype
implementation of several data storage schemes suited to the efficient multi-scale
representation of integrated spatial data. Spatial information systems will benefit from
having data models which allow for data to be viewed and analysed at various levels
of detail, while the integration of data from different sources will lead to a more
accurate representation of reality.
The work has addressed two specific problems. The first concerns the design of an
integrated multi-scale data model suited for use within Geographical Information
Systems. This has led to the development of two data models, each of which allow for
the integration of terrain data and topographic data at multiple levels of detail. The
models are based on a combination of adapted versions of three previous data
structures, namely, the constrained Delaunay pyramid, the line generalisation tree and
the fixed grid.
The second specific problem addressed in this thesis has been the development of an
integrated multi-scale 3-D geological data model, for use within a Geoscientific
Information System. This has resulted in a data storage scheme which enables the
integration of terrain data, geological outcrop data and borehole data at various levels
of detail.
The thesis also presents details of prototype database implementations of each of the
new data storage schemes. These implementations have served to demonstrate the
feasibility and benefits of an integrated multi-scale approach.
The research has also brought to light some areas that will need further research before
fully functional systems are produced. The final chapter contains, in addition to
conclusions made as a result of the research to date, a summary of some of these areas
that require future work
HybridOctree_Hex: Hybrid Octree-Based Adaptive All-Hexahedral Mesh Generation with Jacobian Control
We present a new software package, "HybridOctree_Hex," for adaptive
all-hexahedral mesh generation based on hybrid octree and quality improvement
with Jacobian control. The proposed HybridOctree_Hex begins by detecting
curvatures and narrow regions of the input boundary to identify key surface
features and initialize an octree structure. Subsequently, a strongly balanced
octree is constructed using the balancing and pairing rules. Inspired by our
earlier preliminary hybrid octree-based work, templates are designed to
guarantee an all-hexahedral dual mesh generation directly from the strongly
balanced octree. With these pre-defined templates, the sophisticated hybrid
octree construction step is skipped to achieve an efficient implementation.
After that, elements outside and around the boundary are removed to create a
core mesh. The boundary points of the core mesh are connected to their
corresponding closest points on the surface to fill the buffer zone and build
the final mesh. Coupled with smart Laplacian smoothing, HybridOctree_Hex takes
advantage of a delicate optimization-based quality improvement method
considering geometric fitting, Jacobian and scaled Jacobian, to achieve a
minimum scaled Jacobian that is higher than . We empirically verify the
robustness and efficiency of our method by running the HybridOctree_Hex
software on dozens of complex 3D models without any manual intervention or
parameter adjustment. We provide the HybridOctree_Hex source code, along with
comprehensive results encompassing the input and output files and statistical
data in the following repository: https://github.com/CMU-CBML/HybridOctree_Hex
Shape representation and coding of visual objets in multimedia applications — An overview
Emerging multimedia applications have created the need for new functionalities in digital communications. Whereas existing compression standards only deal with the audio-visual scene at a frame level, it is now necessary to handle individual objects separately, thus allowing scalable transmission as well as interactive scene recomposition by the receiver. The future MPEG-4 standard aims at providing compression tools addressing these functionalities. Unlike existing frame-based standards, the corresponding coding schemes need to encode shape information explicitly. This paper reviews existing solutions to the problem of shape representation and coding. Region and contour coding techniques are presented and their performance is discussed, considering coding efficiency and rate-distortion control capability, as well as flexibility to application requirements such as progressive transmission, low-delay coding, and error robustnes
Terrain Representation And Reasoning In Computer Generated Forces : A Survey Of Computer Generated Forces Systems And How They Represent And Reason About Terrain
Report on a survey of computer systems used to produce realistic or intelligent behavior by autonomous entities in simulation systems. In particular, it is concerned with the data structures used by computer generated forces systems to represent terrain and the algorithmic approaches used by those systems to reason about terrain
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