Passive-Active Geometric Calibration for View-Dependent Projections onto Arbitrary Surfaces

In this paper we present a hybrid technique for correcting distortions that appear when projecting images onto geometrically complex, colored and textured surfaces. It analyzes the optical flow that results from perspective distortions during motions of the observer and tries to use this information for computing the correct image warping. If this fails due to an unreliable optical flow, an accurate -but slower and visiblestructured light projection is automatically triggered. Together with an appropriate radiometric compensation, view-dependent content can be projected onto arbitrary everyday surfaces. An implementation mainly on the GPU ensures fast frame rates.

hp-dGFEM for Second-Order Elliptic Problems in Plyhedra I: Stability and Quasioptimality on Geometric Meshes

We introduce and analyze hp-version discontinuous Galerkin (dG) finite element methods for the numerical approximation of linear second-order elliptic boundary-value problems in three-dimensional polyhedral domains. To resolve possible corner-, edge- and corner-edge singularities, we consider hexahedral meshes that are geometrically and anisotropically refined toward the corresponding neighborhoods. Similarly, the local polynomial degrees are increased linearly and possibly anisotropically away from singularities. We design interior penalty hp-dG methods and prove that they are well-defined for problems with singular solutions and stable under the proposed hp-refinements. We establish (abstract) error bounds that will allow us to prove exponential rates of convergence in the second part of this work.

Geometric properties of the lung parenchyma after postnatal glucocorticoid treatment in rats

While glucocorticoid (GC) administration appears to be beneficial during the acute phase of treatment of neonates at risk of developing chronic lung disease, it is still not clear whether steroid application has an adverse long-term effect on the lung maturation. Thus, the goal of the present work was to analyze GC effects on the pulmonary structure in a rat model where dosage and timing of drug administration were adapted to the therapeutic situation in human neonatology. The animals received daily a maximum of 0.1 mg dexamethasone phosphate per kilogram body weight during the first 4 postnatal days. Investigations were performed at the light microscopic level by means of a digital image analysis system. While there were no differences in the lung architecture between experimental animals and controls on day 4, the earliest time point of observation, we found a widening of airspaces with a concomitant decrease in the alveolar surface area density, representing a loss of parenchymal complexity, on days 10 and 21 in treated rats. On days 36 and 60, however, no alterations in the pulmonary parenchyma could be detected in experimental animals. We conclude from these findings that the GC-induced initial inhibition of development (days 10 and 21) was completely reversed, so that a normal parenchymal architecture and also a normal alveolar surface area density were found in adult rats (days 36 and 60). From the results obtained using the regimen of GC administration described, mimicking more closely the steroid treatment in human neonatology, we conclude that the observed short-term adverse effects on lung development can be fully compensated until adult age.

Genetic Control of Plant Development by Overriding a Geometric Division Rule

Formative cell divisions are critical for multicellular patterning. In the early plant embryo, such divisions follow from orienting the division plane. A major unanswered question is how division plane orientation is genetically controlled, and in particular whether this relates to cell geometry. We have generated a complete 4D map of early Arabidopsis embryogenesis and used computational analysis to demonstrate that several divisions follow a rule that uses the smallest wall area going through the center of the cell. In other cases, however, cell division clearly deviates from this rule, which invariably leads to asymmetric cell division. By analyzing mutant embryos and through targeted genetic perturbation, we show that response to the hormone auxin triggers a deviation from the ``shortest wall'' rule. Our work demonstrates that a simple default rule couples division orientation to cell geometry in the embryo and that genetic regulation can create patterns by overriding the default rule.

Geometric parameters of shoreface profiles of Laptev Sea erosion coast (Table 1)

Field investigations of the Laptev Sea shoreface morphology were carried out (1) off erosional shores composed of unconsolidated sediments, (2) off the modern delta shores of the Lena River, and (3) off rocky shores. It was found that profiles off erosional shores had a concave shape. This shape is not well described by commonly applied power functions, a feature, which is in disagreement with the generally accepted concept of the equilibrium shape of shoreface profiles. The position of the lower shoreface boundary is determined by the elevation of the coastal lowland inundated during the last transgression (at -5 to -10 m) and may easily be recognized by a sharp, an order of magnitude decrease in the mean inclination of the sea floor. The mean shoreface inclination depends on sediment grain-size and ranges from 0.0022 to 0.033. The concave shape of the shoreface did not change substantially during the last 20-30 years, which indicates that shoreline retreat did not slow down and hence suggests continued intensive coastal erosion in the 21st century. The underwater part of the Lena River delta extends up to 35 km offshore. Its upper part is formed by a shallow and up to 18-km wide bench, which reaches depths of 2-3 m along the outer edge. The evolution of the delta was irregular. Whereas some parts of the delta are advancing rapidly (58 m/year), other parts are eroding. Comparison of measured profiles with older bathymetric data gave an opportunity to evaluate the changes of the underwater delta over past decades. Bathymetric surveys of the seabed around the delta can thus contribute towards a quantification of the sediment budget of the river-sea system. In addition, some sections of the Laptev Sea coast are composed of bedrock that has a comparatively low resistance to wave erosion. These sections may supply a considerable amount of sediment, especially if the cliffs are high. This source must therefore also be taken into account when assessing the contribution of shore erosion to the Laptev Sea sediment budget.

Atmospheric, oceanic and hydrological polar motion excitation mechanisms based on a combination of geometric and gravimetric space observations

The goal of our study is to determine accurate time series of geophysical Earth rotation excitations to learn more about global dynamic processes in the Earth system. For this purpose, we developed an adjustment model which allows to combine precise observations from space geodetic observation systems, such as Satellite Laser Ranging (SLR), Global Navigation Satellite Systems (GNSS), Very Long Baseline Interferometry (VLBI), Doppler Orbit determination and Radiopositioning Integrated on Satellite (DORIS), satellite altimetry and satellite gravimetry in order to separate geophysical excitation mechanisms of Earth rotation. Three polar motion time series are applied to derive the polar motion excitation functions (integral effect). Furthermore we use five time variable gravity field solutions from Gravity Recovery and Climate Experiment (GRACE) to determine not only the integral mass effect but also the oceanic and hydrological mass effects by applying suitable filter techniques and a land-ocean mask. For comparison the integral mass effect is also derived from degree 2 potential coefficients that are estimated from SLR observations. The oceanic mass effect is also determined from sea level anomalies observed by satellite altimetry by reducing the steric sea level anomalies derived from temperature and salinity fields of the oceans. Due to the combination of all geodetic estimated excitations the weaknesses of the individual processing strategies can be reduced and the technique-specific strengths can be accounted for. The formal errors of the adjusted geodetic solutions are smaller than the RMS differences of the geophysical model solutions. The improved excitation time series can be used to improve the geophysical modeling.

Geometric Integrability of the Camassa-Holm Equation. II

It is known that the Camassa–Holm (CH) equation describes pseudo-spherical surfaces and that therefore its integrability properties can be studied by geometrical means. In particular, the CH equation admits nonlocal symmetries of “pseudo-potential type”: the standard quadratic pseudo-potential associated with the geodesics of the pseudo-spherical surfaces determined by (generic) solutions to CH, allows us to construct a covering π of the equation manifold of CH on which nonlocal symmetries can be explicitly calculated. In this article, we present the Lie algebra of (first-order) nonlocal π-symmetries for the CH equation, and we show that this algebra contains a semidirect sum of the loop algebra over sl(2,R) and the centerless Virasoro algebra. As applications, we compute explicit solutions, we construct a Darboux transformation for the CH equation, and we recover its recursion operator. We also extend our results to the associated Camassa–Holm equation introduced by J. Schiff.

Geometric characteristics of conics in Bézier form

Derive coordinate-free expressions for geometric characteristics of conics written in Bézier form in terms of their control points and weights.

Aerodynamic study of airfoils geometric imperfections at low Reynolds number

The interest of this study is based on the observation that some manufacturing processes of various vehicles wings, such as unmanned aerial vehicle (UAV), or blades, such as wind turbine blades, or other devices that use aerodynamic profiles, produce imperfections in the leading edge or open trailing edge with bigger thickness than original airfoil, because, for example, they are manufactured in two parts, top surface and bottom surface and subsequently joined. In this last step might appear a sliding between the top surface and the bottom surface having a small step on the leading edge or a small thickness gain can occur on the trailing edge. Normally these imperfections are corrected through a refill and/or sanding processes using many hours of manual labor. Therefore the initial objective of this research is to determine the level of influence in the aerodynamic characteristics at low Reynolds numbers (Lissaman, 1981, Carmichael, 1981, Nagamatsu and Cuche, 1981, Schmitz, 1957, Cebeci, 1989, Mueller and Batill, 1982) of these imperfections in the manufacture, and determine whether there may be a value for which it would not be necessary to correct them

Synchronization waves in geometric networks

We report synchronization of networked excitable nodes embedded in a metric space, where the connectivity properties are mostly determined by the distance between units. Such a high clustered structure, combined with the lack of long-range connections, prevents full synchronization and yields instead the emergence of synchronization waves. We show that this regime is optimal for information transmission through the system, as it enhances the options of reconstructing the topology from the dynamics. Measurements of topological and functional centralities reveal that the wave-synchronization state allows detection of the most structurally relevant nodes from a single observation of the dynamics, without any a priori information on the model equations ruling the evolution of the ensemble

A geometric characterization of the upper bound for the span of the jones polynomial

Let D be a link diagram with n crossings, sA and sB be its extreme states and |sAD| (respectively, |sBD|) be the number of simple closed curves that appear when smoothing D according to sA (respectively, sB). We give a general formula for the sum |sAD| + |sBD| for a k-almost alternating diagram D, for any k, characterizing this sum as the number of faces in an appropriate triangulation of an appropriate surface with boundary. When D is dealternator connected, the triangulation is especially simple, yielding |sAD| + |sBD| = n + 2 - 2k. This gives a simple geometric proof of the upper bound of the span of the Jones polynomial for dealternator connected diagrams, a result first obtained by Zhu [On Kauffman brackets, J. Knot Theory Ramifications6(1) (1997) 125–148.]. Another upper bound of the span of the Jones polynomial for dealternator connected and dealternator reduced diagrams, discovered historically first by Adams et al. [Almost alternating links, Topology Appl.46(2) (1992) 151–165.], is obtained as a corollary. As a new application, we prove that the Turaev genus is equal to the number k of dealternator crossings for any dealternator connected diagram

Geometric tools in Juan de Álava's stonecutting workshop

Stonemasonry of the Gothic vault in its totality is based upon geometry of the line, whereas classic stereotomy relies on the comprehensive knowledge of the surface and the highly sophisticated sides of the voussoirs necessary for its vaults. It is obvious that this leap in the art of construction was paralleled and accompanied by an extension of the horizons of geometry. In Spain, it was made possible thanks to the centuries-old tradition of stone building begun in the most remote medieval times and to the presence of outstanding architects or stonemasons such as Juan de Álava, whose professional work surpassed the established limits and provided the art of building with new instruments.

Analysis of the geometric altimetry to support aircraft optimal profiles within future 4D trajectory management

The use of barometric altimetry is to some extent a limiting factor on safety, predictability and efficiency of aircraft operations, and reduces the potential of the trajectory based operations capabilities. However, geometric altimetry could be used to improve all of these aspects. Nowadays aircraft altitude is estimated by applying the International Standard Atmosphere which differs from real altitude. At different temperatures for an assigned barometric altitude, aerodynamic forces are different and this has a direct relationship with time, fuel consumption and range of the flight. The study explores the feasibility of using sensors providing geometric reference altitude, in particular, to supply capabilities for the optimization of vertical profiles and also, their impact on the vertical Air Traffic Management separation assurance processes. One of the aims of the thesis is to assess if geometric altitude fulfils the aeronautical requirements through existing sensors. Also the thesis will elaborate on the advantages of geometric altitude over the barometric altitude in terms of efficiency for vertical navigation. The evidence that geometric altitude is the best choice to improve the efficiency in vertical profile and aircraft capacity by reducing vertical uncertainties will also be shown. In this paper, an atmospheric study is presented, as well as the impact of temperature deviation from International Standard Atmosphere model is analyzed in order to obtain relationship between geometric and barometric altitude. Furthermore, an aircraft model to study aircraft vertical profile is provided to analyse trajectories based on geometric altitudes.