1,726 research outputs found
Query processing of geometric objects with free form boundarie sin spatial databases
The increasing demand for the use of database systems as an integrating
factor in CAD/CAM applications has necessitated the development of database
systems with appropriate modelling and retrieval capabilities. One essential
problem is the treatment of geometric data which has led to the development of
spatial databases. Unfortunately, most proposals only deal with simple geometric
objects like multidimensional points and rectangles. On the other hand, there has
been a rapid development in the field of representing geometric objects with free
form curves or surfaces, initiated by engineering applications such as mechanical
engineering, aviation or astronautics. Therefore, we propose a concept for the realization
of spatial retrieval operations on geometric objects with free form
boundaries, such as B-spline or Bezier curves, which can easily be integrated in
a database management system. The key concept is the encapsulation of geometric
operations in a so-called query processor. First, this enables the definition of
an interface allowing the integration into the data model and the definition of the
query language of a database system for complex objects. Second, the approach
allows the use of an arbitrary representation of the geometric objects. After a
short description of the query processor, we propose some representations for free
form objects determined by B-spline or Bezier curves. The goal of efficient query
processing in a database environment is achieved using a combination of decomposition
techniques and spatial access methods. Finally, we present some experimental
results indicating that the performance of decomposition techniques is
clearly superior to traditional query processing strategies for geometric objects
with free form boundaries
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Stenomaps: Shorthand for shapes
We address some of the challenges in representing spatial data with a novel form of geometric abstraction-the stenomap. The stenomap comprises a series of smoothly curving linear glyphs that each represent both the boundary and the area of a polygon. We present an efficient algorithm to automatically generate these open, C1-continuous splines from a set of input polygons. Feature points of the input polygons are detected using the medial axis to maintain important shape properties. We use dynamic programming to compute a planar non-intersecting spline representing each polygon's base shape. The results are stylised glyphs whose appearance may be parameterised and that offer new possibilities in the 'cartographic design space'. We compare our glyphs with existing forms of geometric schematisation and discuss their relative merits and shortcomings. We describe several use cases including the depiction of uncertain model data in the form of hurricane track forecasting; minimal ink thematic mapping; and the depiction of continuous statistical data
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On the capture and representation of fonts
This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.The commercial need to capture, process and represent the shape and form of an outline has lead to the development of a number of spline routines. These use a mathematical curve format that approximates the contours of a given shape. The modelled outline lends itself to be used on, and for, a variety of purposes. These include graphic screens, laser printers and numerically controlled machines. The latter can be employed for cutting foil, metal. plastic and stone. One of the most widely used software design packages has been the lKARUS system. This, developed by URW of Hamburg (Gennany), employs a number of mathematical descriptions that facilitate the process of both modelling and representation of font characters. It uses a variety of curve formats, including Bezier cubics, general conics and parabolics. The work reported in this dissertation focuses on developing improved techniques, primarily. for the lKARUS system. This includes two algorithms
which allow a Bezier cubic description, two for a general conic representation and, yet another, two for the parabolic case. In addition, a number of algorithms are presented which promote conversions between these mathematical forms; for example, Bezier cubics to a general conic form. Furthennore, algorithms are developed to assist the process of rasterising both cubic and quadratic arcs.This study was partly funded by the Science and Education Research Council (SERC)
Elastic analysis of irregularly or sparsely sampled curves
We provide statistical analysis methods for samples of curves in two or more dimensions, where the image, but not the parameterization of the curves, is of interest and suitable alignment/registration is thus necessary. Examples are handwritten letters, movement paths, or object outlines. We focus in particular on the computation of (smooth) means and distances, allowing, for example, classification or clustering. Existing parameterization invariant analysis methods based on the elastic distance of the curves modulo parameterization, using the squareârootâvelocity framework, have limitations in common realistic settings where curves are irregularly and potentially sparsely observed. We propose using spline curves to model smooth or polygonal (FrĂ©chet) means of open or closed curves with respect to the elastic distance and show identifiability of the spline model modulo parameterization. We further provide methods and algorithms to approximate the elastic distance for irregularly or sparsely observed curves, via interpreting them as polygons. We illustrate the usefulness of our methods on two datasets. The first application classifies irregularly sampled spirals drawn by Parkinson's patients and healthy controls, based on the elastic distance to a mean spiral curve computed using our approach. The second application clusters sparsely sampled GPS tracks based on the elastic distance and computes smooth cluster means to find new paths on the Tempelhof field in Berlin. All methods are implemented in the Râpackage âelasdicsâ and evaluated in simulations.Peer Reviewe
Representing complex data using localized principal components with application to astronomical data
Often the relation between the variables constituting a multivariate data
space might be characterized by one or more of the terms: ``nonlinear'',
``branched'', ``disconnected'', ``bended'', ``curved'', ``heterogeneous'', or,
more general, ``complex''. In these cases, simple principal component analysis
(PCA) as a tool for dimension reduction can fail badly. Of the many alternative
approaches proposed so far, local approximations of PCA are among the most
promising. This paper will give a short review of localized versions of PCA,
focusing on local principal curves and local partitioning algorithms.
Furthermore we discuss projections other than the local principal components.
When performing local dimension reduction for regression or classification
problems it is important to focus not only on the manifold structure of the
covariates, but also on the response variable(s). Local principal components
only achieve the former, whereas localized regression approaches concentrate on
the latter. Local projection directions derived from the partial least squares
(PLS) algorithm offer an interesting trade-off between these two objectives. We
apply these methods to several real data sets. In particular, we consider
simulated astrophysical data from the future Galactic survey mission Gaia.Comment: 25 pages. In "Principal Manifolds for Data Visualization and
Dimension Reduction", A. Gorban, B. Kegl, D. Wunsch, and A. Zinovyev (eds),
Lecture Notes in Computational Science and Engineering, Springer, 2007, pp.
180--204,
http://www.springer.com/dal/home/generic/search/results?SGWID=1-40109-22-173750210-
Smooth Wilson Loops in N=4 Non-Chiral Superspace
We consider a supersymmetric Wilson loop operator for 4d N=4 super Yang-Mills
theory which is the natural object dual to the AdS_5 x S^5 superstring in the
AdS/CFT correspondence. It generalizes the traditional bosonic 1/2 BPS
Maldacena-Wilson loop operator and completes recent constructions in the
literature to smooth (non-light-like) loops in the full N=4 non-chiral
superspace. This Wilson loop operator enjoys global superconformal and local
kappa-symmetry of which a detailed discussion is given. Moreover, the
finiteness of its vacuum expectation value is proven at leading order in
perturbation theory. We determine the leading vacuum expectation value for
general paths both at the component field level up to quartic order in
anti-commuting coordinates and in the full non-chiral superspace in suitable
gauges. Finally, we discuss loops built from quadric splines joined in such a
way that the path derivatives are continuous at the intersection.Comment: 44 pages. v2 Added some clarifying comments. Matches the published
versio
Monotonicity Analysis over Chains and Curves
Chains are vector-valued signals sampling a curve. They are important to
motion signal processing and to many scientific applications including location
sensors. We propose a novel measure of smoothness for chains curves by
generalizing the scalar-valued concept of monotonicity. Monotonicity can be
defined by the connectedness of the inverse image of balls. This definition is
coordinate-invariant and can be computed efficiently over chains. Monotone
curves can be discontinuous, but continuous monotone curves are differentiable
a.e. Over chains, a simple sphere-preserving filter shown to never decrease the
degree of monotonicity. It outperforms moving average filters over a synthetic
data set. Applications include Time Series Segmentation, chain reconstruction
from unordered data points, Optical Character Recognition, and Pattern
Matching.Comment: to appear in Proceedings of Curves and Surfaces 200
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