Search results for "geometric modeling"
showing 9 items of 19 documents
Solving the pentahedron problem
2015
Nowadays, all geometric modelers provide some tools for specifying geometric constraints. The 3D pentahedron problem is an example of a 3D Geometric Constraint Solving Problem (GCSP), composed of six vertices, nine edges, five faces (two triangles and three quadrilaterals), and defined by the lengths of its edges and the planarity of its quadrilateral faces. This problem seems to be the simplest non-trivial problem, as the methods used to solve the Stewart platform or octahedron problem fail to solve it. The naive algebraic formulation of the pentahedron yields an under-constrained system of twelve equations in eighteen unknowns. Even if the use of placement rules transforms the pentahedron…
Non-Desarguian geometries and the foundations of geometry from David Hilbert to Ruth Moufang
2004
Abstract In this work, we study the development of non-Desarguian geometry from David Hilbert to Ruth Moufang. We will see that a geometric model became a complicated interrelation between algebra and geometry.
Wavelength-flattened directional couplers for mirror-symmetric interferometers
2005
In the context of guided optics, we derive, analytically and geometrically, a rigorous general criterion to design wavelength insensitive interferometers with mirror symmetry, which are needed for wavelength multiplexing/demultiplexing. The criterion is applied to a practical case, resulting in an interferometer that works on a band wider than 70 nm.
A geometric street scattering channel model for car-to-car communication systems
2011
This paper presents a geometric street scattering channel model for car-to-car (C2C) communication systems under line-of-sight (LOS) and non-LOS (NLOS) propagation conditions. Starting from the geometric model, we develop a stochastic reference channel model, where the scatterers are uniformly distributed in rectangles in the form of stripes parallel to both sides of the street. We derive analytical expressions for the probability density functions (PDFs) of the angle-of-departure (AOD) and the angle-of-arrival (AOA). We also investigate the Doppler power spectral density (PSD) and the autocorrelation function (ACF) of the proposed model, assuming that the mobile transmitter (MT) and the mo…
An FPGA Implementation of a Quadruple-Based Multiplier for 4D Clifford Algebra
2008
Geometric or Clifford algebra is an interesting paradigm for geometric modeling in fields as computer graphics, machine vision and robotics. In these areas the research effort is actually aimed at finding an efficient implementation of geometric algebra. The best way to exploit the symbolic computing power of geometric algebra is to support its data types and operators directly in hardware. However the natural representation of the algebra elements as variable-length objects causes some problems in the case of a hardware implementation. This paper proposes a 4D Clifford algebra in which the variable-length elements are mapped into fixed-length elements (quadruples). This choice leads to a s…
Deducing self-interaction in eye movement data using sequential spatial point processes
2016
Eye movement data are outputs of an analyser tracking the gaze when a person is inspecting a scene. These kind of data are of increasing importance in scientific research as well as in applications, e.g. in marketing and man-machine interface planning. Thus the new areas of application call for advanced analysis tools. Our research objective is to suggest statistical modelling of eye movement sequences using sequential spatial point processes, which decomposes the variation in data into structural components having interpretation. We consider three elements of an eye movement sequence: heterogeneity of the target space, contextuality between subsequent movements, and time-dependent behaviou…
Applications of Kernel Methods
2009
In this chapter, we give a survey of applications of the kernel methods introduced in the previous chapter. We focus on different application domains that are particularly active in both direct application of well-known kernel methods, and in new algorithmic developments suited to a particular problem. In particular, we consider the following application fields: biomedical engineering (comprising both biological signal processing and bioinformatics), communications, signal, speech and image processing.
Symmetry as an Intrinsically Dynamic Feature
2010
Symmetry is one of the most prominent spatial relations perceived by humans, and has a relevant role in attentive mechanisms regarding both visual and auditory systems. The aim of this paper is to establish symmetry, among the likes of motion, depth or range, as a dynamic feature in artificial vision. This is achieved in the first instance by assessing symmetry estimation by means of algorithms, putting emphasis on erosion and multi- resolution approaches, and confronting two ensuing problems: the isolation of objects from the context, and the pertinence (or lack thereof) of some salient points, such as the centre of mass. Next a geometric model is illustrated and detailed, and the problem …
Development of helium coolant DEMO first wall model for SYCOMORE system code based on HCLL concept
2018
Abstract The conceptual design of the demonstration fusion power reactor, known as DEMO, is ongoing and several reactor configurations have to be investigated by exploring different design parameters. For these reasons, within the European framework, systems codes like SYCOMORE (SYstem COde for MOdelling tokamak REactor) have been developed. SYCOMORE includes several specific modules, one of which is aimed to define a suitable design of the helium breeding blanket. The research activity has been devoted to improve the method to define automatically the First Wall design starting from thermal-hydraulic and thermo-mechanical considerations, using analytical design formulae and, also, taking i…