9,540 research outputs found
The combination of spatial access methods and computational geometry in geographic database systems
Geographic database systems, known as geographic information systems (GISs) particularly among non-computer scientists, are one of the most important applications of the very active research area named spatial database systems. Consequently following the database approach, a GIS hag to be seamless, i.e. store the complete area of interest (e.g. the whole world) in one database map. For exhibiting acceptable performance a seamless GIS hag to use spatial access methods. Due to the complexity of query and analysis operations on geographic objects, state-of-the-art computational geomeny concepts have to be used in implementing these operations. In this paper, we present GIS operations based on the compuational geomeny technique plane sweep. Specifically, we show how the two ingredients spatial access methods and computational geomeny concepts can be combined für improving the performance of GIS operations. The fruitfulness of this combination is based on the fact that spatial access methods efficiently provide the data at the time when computational geomeny algorithms need it für processing. Additionally, this combination avoids page faults and facilitates the parallelization of the algorithms.
Green's functions for multiply connected domains via conformal mapping
A method is described for the computation of the Green's function in the complex plane corresponding to a set of K symmetrically placed polygons along the real axis. An important special case is a set of K real intervals. The method is based on a Schwarz-Christoffel conformal map of the part of the upper half-plane exterior to the problem domain onto a semi-infinite strip whose end contains K-1 slits. From the Green's function one can obtain a great deal of information about polynomial approximations, with applications in digital filters and matrix iteration. By making the end of the strip jagged, the method can be generalised to weighted Green's functions and weighted approximations
Analysis of existing mathematics textbooks for use in secondary schools.
Thesis (Ed.M.)--Boston University
Thesis (M.A.)--Boston Universit
Convexity preserving interpolatory subdivision with conic precision
The paper is concerned with the problem of shape preserving interpolatory
subdivision. For arbitrarily spaced, planar input data an efficient non-linear
subdivision algorithm is presented that results in limit curves,
reproduces conic sections and respects the convexity properties of the initial
data. Significant numerical examples illustrate the effectiveness of the
proposed method
Continuous cellular automata on irregular tessellations : mimicking steady-state heat flow
Leaving a few exceptions aside, cellular automata (CA) and the intimately related coupled-map lattices (CML), commonly known as continuous cellular automata (CCA), as well as models that are based upon one of these paradigms, employ a regular tessellation of an Euclidean space in spite of the various drawbacks this kind of tessellation entails such as its inability to cover surfaces with an intricate geometry, or the anisotropy it causes in the simulation results. Recently, a CCA-based model describing steady-state heat flow has been proposed as an alternative to Laplace's equation that is, among other things, commonly used to describe this process, yet, also this model suffers from the aforementioned drawbacks since it is based on the classical CCA paradigm. To overcome these problems, we first conceive CCA on irregular tessellations of an Euclidean space after which we show how the presented approach allows a straightforward simulation of steady-state heat flow on surfaces with an intricate geometry, and, as such, constitutes an full-fledged alternative for the commonly used and easy-to-implement finite difference method, and the more intricate finite element method
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