The Alignment of Objects With Smooth Surfaces: Error Analysis of the Curvature Method

The recognition of objects with smooth bounding surfaces from their contour images is considerably more complicated than that of objects with sharp edges, since in the former case the set of object points that generates the silhouette contours changes from one view to another. The "curvature method", developed by Basri and Ullman [1988], provides a method to approximate the appearance of such objects from different viewpoints. In this paper we analyze the curvature method. We apply the method to ellipsoidal objects and compute analytically the error obtained for different rotations of the objects. The error depends on the exact shape of the ellipsoid (namely, the relative lengths of its axes), and it increases a sthe ellipsoid becomes "deep" (elongated in the Z-direction). We show that the errors are usually small, and that, in general, a small number of models is required to predict the appearance of an ellipsoid from all possible views. Finally, we show experimentally that the curvature method applies as well to objects with hyperbolic surface patches.

Wrinkling of Atomic Planes in Ultrathin Au Nanowires

A detailed understanding of structure and stability of nanowires is critical for applications. Atomic resolution imaging of ultrathin single crystalline Au nanowires using aberration-corrected microscopy reveals an intriguing relaxation whereby the atoms in the close-packed atomic planes normal to the growth direction are displaced in the axial direction leading to wrinkling of the (111) atomic plane normal to the wire axis. First-principles calculations of the structure of such nanowires confirm this wrinkling phenomenon, whereby the close-packed planes relax to form saddle-like surfaces. Molecular dynamics studies of wires with varying diameters and different bounding surfaces point to the key role of surface stress on the relaxation process. Using continuum mechanics arguments, we show that the wrinkling arises due to anisotropy in the surface stresses and in the elastic response, along with the divergence of surface-induced bulk stress near the edges of a faceted structure. The observations provide new understanding on the equilibrium structure of nanoscale systems and could have important implications for applications in sensing and actuation.

On the structure of quasi-two-dimensional foams

S.J. Cox and E. Janiaud (2008) On the structure of quasi-two-dimensional foams. Phil. Mag. Letts. 88:693-701 Philosophical Magazine Letters Volume 88, Issue 9-10, 2008 Special Issue: Solid and Liquid Foams. In commemoration of Manuel Amaral Fortes The full text will be available 12 months after publication Sponsorship: We thank K. Brakke for his development and maintenance of the Surface Evolver code, I. Cantat, N. Denkov and F. Graner for their insightful comments on this work, and the participants in the Grenoble Foam Mechanics Workshop (2008) for their suggestions. EJ thanks D. Weaire and S. Hutzler for support, and ESA (MAP AO-99-108:C14914/02/NL/SH, MAP AO-99-075:C14308/00/NL/SH) for funding. SJC thanks the British Council Alliance programme, CNRS and EPSRC (EP/D048397/1, EP/D071127/1) for financial support.

Proposta metodológica para o imageamento, caracterização, parametrização e geração de modelos virtuais de afloramentos

The aim of this work was to describe the methodological procedures that were mandatory to develop a 3D digital imaging of the external and internal geometry of the analogue outcrops from reservoirs and to build a Virtual Outcrop Model (VOM). The imaging process of the external geometry was acquired by using the Laser Scanner, the Geodesic GPS and the Total Station procedures. On the other hand, the imaging of the internal geometry was evaluated by GPR (Ground Penetrating Radar).The produced VOMs were adapted with much more detailed data with addition of the geological data and the gamma ray and permeability profiles. As a model for the use of the methodological procedures used on this work, the adapted VOM, two outcrops, located at the east part of the Parnaiba Basin, were selected. On the first one, rocks from the aeolian deposit of the Piaui Formation (Neo-carboniferous) and tidal flat deposits from the Pedra de Fogo Formation (Permian), which arises in a large outcrops located between Floriano and Teresina (Piauí), are present. The second area, located at the National Park of Sete Cidades, also at the Piauí, presents rocks from the Cabeças Formation deposited in fluvial-deltaic systems during the Late Devonian. From the data of the adapted VOMs it was possible to identify lines, surfaces and 3D geometry, and therefore, quantify the geometry of interest. Among the found parameterization values, a table containing the thickness and width, obtained in canal and lobes deposits at the outcrop Paredão and Biblioteca were the more relevant ones. In fact, this table can be used as an input for stochastic simulation of reservoirs. An example of the direct use of such table and their predicted radargrams was the identification of the bounding surface at the aeolian sites from the Piauí Formation. In spite of such radargrams supply only bi-dimensional data, the acquired lines followed of a mesh profile were used to add a third dimension to the imaging of the internal geometry. This phenomenon appears to be valid for all studied outcrops. As a conclusion, the tool here presented can became a new methodology in which the advantages of the digital imaging acquired from the Laser Scanner (precision, accuracy and speed of acquisition) were combined with the Total Station procedure (precision) using the classical digital photomosaic technique

Mapeamento digital de análogos a reservatórios petrolíferos: exemplos para depósitos fluviais da Unidade Açu-3 - Bacia Potiguar

In the current work are presented the results about the study of digital mapping of analogs referents the fluvial oil reservoirs in the Açu Formation. With the regional recognizing in the south corner of Potiguar Basin was selected a area of 150 Km square in the west of Assu city. In this area was chosen the outcrops for the digital mapping and from the data fields and remote sensors were done the depositional architectural for the fluvial deposits, which it was named coarse meandering fluvial systems. In the deposits were individualized 3 (three) fluvial cycles, which they was separated by bounding surface of fifth order. Such cycles are preferentially sandy, with fining-upward sequence finished in flood plain deposits. Inner of the sandy levels of the filling channels were characterized least cycles, normaly incomplete, constituted by braided sandy bodies and bounding surfaces of fourth order. In the mapped area was chosen a outcrop with great exposition, where it was possible to see tipical deposits of filling channel and was in this outcrop that was done the digital mapping. In this outcrop was used diverse technics and tools, which they integrated sedimentological, altimetric (GPS, Total Station), LIDAR (Light Detection and Ranging), digital photomosaic of high resolution and of the inner geometries (Ground Penetration Radar) data sets. For the integrating, interpretation and visualization of data was used software GoCAD®. The final product of the outcrop digital mapping was the photorealistic model of part of the cliff (or slope) because the observed reflectors in the radargrams were absents. A part of bar oblique accretion was modeled according to GPR gride of 200x200 meters in the alluvial Assu river probable recent analog. With the data of inner geometries was developed the three-dimentional sedimentary architectural, where it was possible characterize sand sheet deposits and many hierarchy of braided channels. At last, simulations of sedimentary geometries and architectures of the Potiguar Basin Fluvial Reservoirs were done with PetBool software, in order to understand the capacity of this program in simulations with a lot of numbers of conditioning wells. In total, 45 simulations was acquired, where the time and the channel numbers increase in relation of the conditioning wells quantity. The deformation of the meanders was detected from the change of simulated dominion dimensions. The presence of this problem was because the relationship between the simulated dominion and the width of the meander

Dois testes de imageamento com GPR em problemas de controle ambiental em regiões tropicais: migração de dunas e localização de dutos de óleo enterrados

Because the penetration depth of Ground Penetrating Radar (GPR) signals is very limited in high conductive soils, the usefullness of this method in tropical regions is not yet completly known. The main objective of this researh is to test the usefullness of the method in Brazil. Two typical problems where GPR has been used in Europe and North American were choosed for this test: the first one is to characterize the internal structures of a sand body and the second problem is the localization of old buried pipes lines. The first test was done near the city of São Bento do Norte, in the northern coast of Rio Grande do Norte state, NE Brazil. In this region, there is a sand dune that is migrating very fast in the direction of adjacent settling areas. To characterize the internal structure of the dune and its relationship to the prevailing wind direction, as a preliminary step to understand the dune migration, GPR profiles using the 400 MHz frequency were performed in E-W, N-S, NE-SW, and SE-NW directions over the sand dune intersecting at the top of the dune. The practical resolution of the GPR data is around 30 cm; this was sufficient to distinguish individual foresets inside the dune. After applying the elevation correction to the data, we identified that dips of bedding structures are smallest for the N-S profile, which is perpendicular to the dominant wind direction, largest for the E-W profile, and intermediate for the SW-NE and SE-NW profiles. Foresets in the E-W profile dip with angles varying from 2 to 6 degrees. In the E-W profile, the water table and a horizontal truncation interface separating two generations of dunes were identified, as well as an abrupt directional change in the foreset patterns associated to a lateral contact between two dune generations, the older one extending to the west. The used high frequency of 400 Mhz does not allow a penetration deep enough to map completely these internal contacts. The second test was done near Estreito, a small town near Carnaúbais city, also in Rio Grande do Norte state. In this locality, there are several old pipe lines buried in area covered by plantations where digging should be minimized. Several GPR profiles using the 400 and 200 MHz frequency were performed trying to intercept perpendicularly the possible pipe lines. Because of the high conductivity of the soil, the raw original data can hardly be use to identify the pipe lines. However, after an adequate processing over the 200 MHz profiles, six pipe lines were identified. As a global result of the tests, GPR can be very usefull if the conductivity of the ground is low or, in the case of medium conductivities of the soils, if adequate processing is performed

Interpretação de dados de GPR com base na hierarquização de superfícies limitantes e na adaptação de critérios sismoestratigráficos

Due to its high resolution, Ground Penetrating Radar (GPR) has been used to image subsurface sedimentary deposits. Because GPR and Seismic methods share some principles of image construction, the classic seismostratigraphic interpretation method has been also applied as an attempt to interpret GPR data. Nonetheless some advances in few particular contexts, the adaptations from seismic to GPR of seismostratigraphic tools and concepts unsuitable because the meaning given to the termination criteria in seismic stratigraphy do not represent the adequate geologic record in the GPR scale. Essentially, the open question relies in proposing a interpretation method for GPR data which allow not only relating product and sedimentary process in the GPR scale but also identifying or proposing depositional environments and correlating these results with the well known Sequence Stratigraphy cornerstones. The goal of this dissertation is to propose an interpretation methodology of GPR data able to perform this task at least for siliciclastic deposits. In order to do so, the proposed GPR interpretation method is based both on seismostratigraphic concepts and on the bounding surface hierarchy tool from Miall (1988). As consequence of this joint use, the results of GPR interpretation can be associated to the sedimentary facies in a genetic context, so that it is possible to: (i) individualize radar facies and correlate them to the sedimentary facies by using depositional models; (ii) characterize a given depositional system, and (iii) determine its stratigraphic framework highligthing how it evolved through geologic time. To illustrate its use the proposed methodology was applied in a GPR data set from Galos area which is part of the Galinhos spit, located in Rio Grande do Norte state, Northeastern Brazil. This spit presents high lateral sedimentary facies variation, containing in its sedimentary record from 4th to 6th cicles caused by high frequency sea level oscillation. The interpretation process was done throughout the following phases: (i) identification of a vertical facies succession, (ii) characterization of radar facies and its associated sedimentary products, (iii) recognition of the associated sedimentary process in a genetic context, and finally (iv) proposal of an evolutionay model for the Galinhos spit. This model proposes that the Galinhos spit is a barrier island constituted, from base to top, of the following sedimentary facies: tidal channel facies, tidal flat facies, shore facies, and aeolic facies (dunes). The tidal channel facies, in the base, is constituted of lateral accretion bars and filling deposits of the channels. The base facies is laterally truncated by the tidal flat facies. In the foreshore zone, the tidal flat facies is covered by the shore facies which is the register of a sea transgression. Finally, on the top of the stratigraphic column, aeolic dunes are deposited due to areal exposition caused by a sea regression

Caracterização geológica tridimensional e monitoramento de dunas no litoral oriental do Rio Grande do Norte

This work presents geophysical and geological results obtained in a dunefield located in the east coast of Rio Grande do Norte State, with the aim to recognize the aeolian body depositional geometries to a future geologic modeling of the aeolian petroliferous reservoirs. The research, which was done in blowouts region situated at Nisia Floresta Municipally, included the characterization of external geometries with GPS and internal geometry analysis by GPR. Data was integrated in GoCAD software, where it was possible the three-dimensional characterization and interpretation of the studied deposits. The interpretation of GPR profiling allowed identifying: First-order bounding surfaces that separated the aeolian deposits of the Barreiras Formation rocks; Second-order bounding surfaces, which limit dune generations and Third-order bounding surfaces, a reactivation surface. This classification was based and adapted by the Brookfield (1977) and Kocurek (1996) propose. Four radarfacies was recognized: Radarfacies 1, progradational reflectors correlated to foresets of the dunes, Radarfacies 2, plain parallels reflectors related to sand sheets, Radarfacies 3, plain parallels reflectors associated to reworking of the blowout dune crest and Radarfacies 4, mounded reflectors associated to vegetated mound of sand or objects buried in subsurface. The GPR and GPS methods was also employed to the monitoring of dunefields susceptible to human activities in Buzios Beach, where the constructions along the blowout region and the tourism are changing the natural evolution of the deposits. This fact possibly to cause negative impacts to the coastal zone. Data obtained in Dunas Park, a unit environmental conservation, was compared with information of the Buzios Beach. There is a major tendency of erosion in Buzios, specifically in blowout corridor and blowout dune

Adding constrained discontinuities to Gaussian process models of wind fields

Gaussian Processes provide good prior models for spatial data, but can be too smooth. In many physical situations there are discontinuities along bounding surfaces, for example fronts in near-surface wind fields. We describe a modelling method for such a constrained discontinuity and demonstrate how to infer the model parameters in wind fields with MCMC sampling.

Adding constrained discontinuities to Gaussian process models of wind fields

Gaussian Processes provide good prior models for spatial data, but can be too smooth. In many physical situations there are discontinuities along bounding surfaces, for example fronts in near-surface wind fields. We describe a modelling method for such a constrained discontinuity and demonstrate how to infer the model parameters in wind fields with MCMC sampling.

The sedimentology and diagenesis of Lower Permian (Rotliegend) sediments: (onshore U.K. and southern North Sea). Available in 2 volumes.

The thesis provides a comparative study of both sedimentology and diagenesis of Lower Permian (Rotliegend) strata, onshore and offshore U.K. (Southern North Sea). Onshore formations studied include the Bridgnorth, Penrith and Hopeman Sandstone, and are dominated by aeolian facies, with lesser amounts of interbedded fluvial sediments. Aeolian and fluvial strata in onshore basins typically grade laterally into alluvial fan breccias at basin margins. Onshore basins represent proximal examples of Rotliegend desert sediments. The Leman Sandstone Formation of the Ravenspurn area in the Southern North Sea displays a variety of facies indicative of a distal sedimentological setting; Aeolian, fluvial, sabkha, and playa lake sediments all being present. "Sheet-like" geometry of stratigraphical units within the Leman Sandstone, and alternation of fluvial and aeolian deposition was climatically controlled. Major first order bounding surfaces are laterally extensive and were produced by lacustrine transgression and regression from the north-west. Diagenesis within Permian strata was studied using standard petrographic microscopy, scanning electron microscopy, cold cathodo-Iuminescence, X-ray diffraction clay analysis, X-ray fluorescence spectroscopy, fluid inclusion microthermometry, and K-Ar dating of illites. The diagenesis of Permian sediments within onshore basins is remarkably similar, and a paragenetic sequence of early haematite, illitic clays, feldspar, kaolinite, quartz and late calcite is observed. In the Leman Sandstone formation, authigenic mineralogy is complex and includes early quartz, sulphates and dolomite, chlorite, kaolinite, late quartz, illite and siderite. Primary lithological variation, facies type, and the interdigitation and location of facies within a basin are important initial controls upon diagenesis. Subsequently, burial history, structure, the timing of gas emplacement, and the nature of sediments within underlying formations may also exersize significant controls upon diagenesis within Rotliegend strata.

Revisiting the Late Jurassic-Early Cretaceous of the NW South Iberian Basin: new ages and sedimentary environments

The study of the Upper Jurassic-Lower Cretaceous deposits (Higueruelas, Villar del Arzobispo and Aldea de Cortés Formations) of the South Iberian Basin (NW Valencia, Spain) reveals new stratigraphic and sedimentological data, which have significant implications on the stratigraphic framework, depositional environments and age of these units. The Higueruelas Fm was deposited in a mid-inner carbonate platform where oncolitic bars migrated by the action of storms and where oncoid production progressively decreased towards the uppermost part of the unit. The overlying Villar del Arzobispo Fm has been traditionally interpreted as an inner platform-lagoon evolving into a tidal-flat. Here it is interpreted as an inner-carbonate platform affected by storms, where oolitic shoals protected a lagoon, which had siliciclastic inputs from the continent. The Aldea de Cortés Fm has been previously interpreted as a lagoon surrounded by tidal-flats and fluvial-deltaic plains. Here it is reinterpreted as a coastal wetland where siliciclastic muddy deposits interacted with shallow fresh to marine water bodies, aeolian dunes and continental siliciclastic inputs. The contact between the Higueruelas and Villar del Arzobispo Fms, classically defined as gradual, is also interpreted here as rapid. More importantly, the contact between the Villar del Arzobispo and Aldea de Cortés Fms, previously considered as unconformable, is here interpreted as gradual. The presence of Alveosepta in the Villar del Arzobispo Fm suggests that at least part of this unit is Kimmeridgian, unlike the previously assigned Late Tithonian-Middle Berriasian age. Consequently, the underlying Higueruelas Fm, previously considered Tithonian, should not be younger than Kimmeridgian. Accordingly, sedimentation of the Aldea de Cortés Fm, previously considered Valangian-Hauterivian, probably started during the Tithonian and it may be considered part of the regressive trend of the Late Jurassic-Early Cretaceous cycle. This is consistent with the dinosaur faunas, typically Jurassic, described in the Villar del Arzobispo and Aldea de Cortés Fms.

Sea-level control on the connection between shelf-edge deltas and the Bourcart canyon head (western Mediterranean) during the last glacial/interglacial cycle

A dense grid of high- and very high resolution seismic data, together with piston cores and borehole data providing time constraints, enables us to reconstruct the history of the Bourcart canyon head in the western Mediterranean Sea during the last glacial/interglacial cycle. The canyon fill is composed of confined channel–levee systems fed by a series of successively active shelf fluvial systems, originating from the west and north. Most of the preserved infill corresponds to the interval between Marine Isotope Stage (MIS) 3 and the early deglacial (19 cal ka BP). Its deposition was strongly controlled by a relative sea level that impacted the direct fluvial/canyon connection. During a period of around 100 kyr between MIS 6 and MIS 2, the canyon “prograded” by about 3 km. More precisely, several parasequences can be identified within the canyon fill. They correspond to forced-regressed parasequences (linked to punctuated sea-level falls) topped by a progradational-aggradational parasequence (linked to a hypothetical 19-ka meltwater pulse (MWP)). The bounding surfaces between forced-regressed parasequences are condensed intervals formed during intervals of relative sediment starvation due to flooding episodes. The meandering pattern of the axial incision visible within the canyon head, which can be traced landward up to the Agly paleo-river, is interpreted as the result of hyperpycnal flows initiated in the river mouth in a context of increased rainfall and mountain glacier flushing during the early deglacial.

Collision Cones for Quadric Surfaces

The problem of collision prediction in dynamic environments appears in several diverse fields, which include robotics, air vehicles, underwater vehicles, and computer animation. In this paper, collision prediction of objects that move in 3-D environments is considered. Most work on collision prediction assumes objects to be modeled as spheres. However, there are many instances of object shapes where an ellipsoidal or a hyperboloid-like bounding box would be more appropriate. In this paper, a collision cone approach is used to determine collision between objects whose shapes can be modeled by general quadric surfaces. Exact collision conditions for such quadric surfaces are obtained in the form of analytical expressions in the relative velocity space. For objects of arbitrary shapes, exact representations of planar sections of the 3-D collision cone are obtained.

Triangular mesh parameterization with trimmed surfaces

Given a 2manifold triangular mesh \(M \subset {\mathbb {R}}^3\), with border, a parameterization of \(M\) is a FACE or trimmed surface \(F=\{S,L_0,\ldots, L_m\}\) -- \(F\) is a connected subset or region of a parametric surface \(S\), bounded by a set of LOOPs \(L_0,\ldots ,L_m\) such that each \(L_i \subset S\) is a closed 1manifold having no intersection with the other \(L_j\) LOOPs -- The parametric surface \(S\) is a statistical fit of the mesh \(M\) -- \(L_0\) is the outermost LOOP bounding \(F\) and \(L_i\) is the LOOP of the ith hole in \(F\) (if any) -- The problem of parameterizing triangular meshes is relevant for reverse engineering, tool path planning, feature detection, redesign, etc -- Stateofart mesh procedures parameterize a rectangular mesh \(M\) -- To improve such procedures, we report here the implementation of an algorithm which parameterizes meshes \(M\) presenting holes and concavities -- We synthesize a parametric surface \(S \subset {\mathbb {R}}^3\) which approximates a superset of the mesh \(M\) -- Then, we compute a set of LOOPs trimming \(S\), and therefore completing the FACE \(F=\ {S,L_0,\ldots ,L_m\}\) -- Our algorithm gives satisfactory results for \(M\) having low Gaussian curvature (i.e., \(M\) being quasi-developable or developable) -- This assumption is a reasonable one, since \(M\) is the product of manifold segmentation preprocessing -- Our algorithm computes: (1) a manifold learning mapping \(\phi : M \rightarrow U \subset {\mathbb {R}}^2\), (2) an inverse mapping \(S: W \subset {\mathbb {R}}^2 \rightarrow {\mathbb {R}}^3\), with \ (W\) being a rectangular grid containing and surpassing \(U\) -- To compute \(\phi\) we test IsoMap, Laplacian Eigenmaps and Hessian local linear embedding (best results with HLLE) -- For the back mapping (NURBS) \(S\) the crucial step is to find a control polyhedron \(P\), which is an extrapolation of \(M\) -- We calculate \(P\) by extrapolating radial basis functions that interpolate points inside \(\phi (M)\) -- We successfully test our implementation with several datasets presenting concavities, holes, and are extremely nondevelopable -- Ongoing work is being devoted to manifold segmentation which facilitates mesh parameterization