117,824 research outputs found
Tutorial Appendix: Structure Preserving Representation of Euclidean Motions Through Conformal Geometric Algebra
No full textUsing conformal geometric algebra, Euclidean motions in n-D are represented as orthogonal transformations of a representational space of two extra dimensions, and a well-chosen metric. Orthogonal transformations are representable as multiple reflections, and by means of the geometric product this takes an efficient and structure preserving form as a ‘sandwiching product’. The antisymmetric part of the geometric product produces a spanning operation that permits the construction of lines, planes, spheres and tangents from vectors, and since the sandwiching operation distributes over this construction, ‘objects’ are fully integrated with ‘motions’. Duality and the logarithms complete the computational techniques.The resulting geometric algebra incorporates general conformal transformations and can be implemented to run almost as efficiently as classical homogeneous coordinates. It thus becomes a high-level programming language which naturally integrates quantitative computation with the automatic administration of geometric data structures.<br/
Jean Dorst — La force du vivant
No full textL. A. Jean Dorst — La force du vivant. In: Population, 36ᵉ année, n°3, 1981. p. 646
Newman L. H. et Murray W. J. C. — Nature’s way. Country life, Londres, 1952
No full textDorst Jean. Newman L. H. et Murray W. J. C. — Nature’s way. Country life, Londres, 1952. In: La Terre et La Vie, Revue d'Histoire naturelle, tome 7, n°1, 1953. p. 62
Reconstructing Rotations and Rigid Body Motions from Exact Point Correspondences Through Reflections
No full textWe describe a new algorithm to reconstruct a rigid body motion from point correspondences. The algorithm works by constructing a series of reflections which align the points with their correspondences one by one. This is naturally and efficiently implemented in the conformal model of geometric algebra, where the resulting transformation is represented by a versor. As a direct result of this algorithm, we also present a very compact and fast formula to compute a quaternion from two vector correspondences, a surprisingly elementary result which appears to be new. <br/
Estimating Motors from a Variety of Geometric Data in 3D Conformal Geometric Algebra
No full textThe motion rotors, or motors, are used to model Euclidean motion in 3D conformalgeometric algebra. In this chapter we present a technique for estimatingthe motor which best transforms one set of noisy geometric objects onto another.The technique reduces to an eigenrotator problem and has some advantages overmatrix formulations. It allows motors to be estimated from a variety of geometricdata such as points, spheres, circles, lines, planes, directions, and tangents; andthe different types of geometric data are combined naturally in a single framework.Also, it excludes the possibility of a reflection unlike some matrix formulations.It returns the motor with the smallest translation and rotation angle whenthe optimal motor is not unique
Square Root and Logarithm of Rotors in 3D Conformal Geometric Algebra Using Polar Decomposition
No full textConformal transformations are described by rotors in the conformal model of geometric algebra (CGA). In applications there is a need for interpolation of such transformations, especially for the subclass of 3D rigid body motions. This chapter gives explicit formulas for the square root and the logarithm of rotors in 3D CGA. It also classifies the types of conformal transformations and their orbits. To derive the results, we employ a novel polar decomposition for the even subalgebra of 3D CGA and an associated norm-like expression. <br/
Perceived Control and Liveability: Environment and behaviour interaction in two urban villages of Shenzhen
No full textUrban village is a very special type of neighbourhood, created in the fast urbanisation process in Chinese cities like Shenzhen in the past three decades, playing an essential role in accommodating migrant groups, including rural-urban migrant workers and the young professionals. Built by the villagers whose farmland was transformed into urban use, these high-density informal settlements have become places where the daily life of the migrant groups happens. Nowadays, along with the processes of fast urban development and upgrading of industries, urban villages located in the central urban districts are being considered as problematic neighbourhoods that need to be reconstructed. The current model is still based on large-scale redevelopment, replacing the urban villages with new urban functions. In response to such radical approach, this paper will present an alternative argument of maintaining and improving urban villages as arrival cities for migrant groups. It is based on an environmental-behaviour study in the framework of liveability. This study is based on the theory that perceived control over the built environment is an important condition for liveability (Altman 1975, Van Dorst 2011). It indicates the changing life styles inside the urban villages, as well as the way space is socially produced in two urban villages in Shenzhen: Hubei and Baishizhou.UrbanismArchitecture and The Built Environmen
Home and Mortgage Ownership of the Dutch Elderly: Explaining Cohort, Time and Age Effects
No full textThe relationship between home ownership of Dutch elderly households and age is strongly negative. Other studies suggest that this age gradient should be attributed to a cohort effect. In this paper we investigate where those cohort effects come from. We also observe that mortgage ownership among elderly home-owners increased considerably during the nineties. Using panel data we estimate models explaining home and mortgage ownership by age, cohort, and time effects, as well as other factors. Cohort and time effects are modelled explicitly using macro economic and housing market related variables. We find that the level of GDP per capita when the household head was young is the main factor explaining generation effects in home ownership among the elderly. After accounting for cohort effects it also appears that home ownership decreases slightly with age. Mortgage ownership among elderly home owners rose considerably during the nineties due to house price increases and due to financial innovation in the mortgage market. Cohort effects are also important. A supplementary analysis suggests that those cohort effects are due to the fact that the accidental bequest motive is becoming less important.home ownership, mortgages, cohort effects
Phraseology in children’s literature: a contrastive analysis
No full textThis dissertation investigates Dutch and Italian phraseology in a corpus of Children’s Literature. Phraseological units notoriously pose challenges for both translators and language learners. However, the presence and nature of phraseological units in lower language proficiency levels have received very little attention. As both authors and translators of children’s books base their linguistic choices, and their phraseological choices specifically, on the assumptions they have of the still limited linguistic, phraseological, and cultural knowledge of their young receivers, Children’s Literature could be a source for a core phraseological inventory.
Through a contrastive, bidirectional analysis of phraseological units and their translatants (Dutch↔Italian), a first attempt is made to evaluate if Children’s Literature (CL) could prove a fruitful corpus for identifying a core phraseological inventory. Furthermore, the similarities and differences between the phraseological inventories of the two languages involved are explored, and the translational equivalence between phraseological units and their translatants is examined
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