Teorema de Pitágoras: algumas extensões/generalizações e atividades com o Software GeoGebra

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Home ranges of Guiana dolphins (Sotalia guianensis) (Cetacea: Delphinidae) in the Cananeia estuary, Brazil

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Simplificação de malhas visando representações em multirresolução

The representation of real objects in virtual environments has applications in many areas, such as cartography, mixed reality and reverse engineering. The generation of these objects can be performed through two ways: manually, with CAD (Computer Aided Design) tools, or automatically, by means of surface reconstruction techniques. The simpler the 3D model, the easier it is to process and store it. However, this methods can generate very detailed virtual elements, that can result in some problems when processing the resulting mesh, because it has a lot of edges and polygons that have to be checked at visualization. Considering this context, it can be applied simplification algorithms to eliminate polygons from resulting mesh, without change its topology, generating a lighter mesh with less irrelevant details. The project aimed the study, implementation and comparative tests of simplification algorithms applied to meshes generated through a reconstruction pipeline based on point clouds. This work proposes the realization of the simplification step, like a complement to the pipeline developed by (ONO et al., 2012), that developed reconstruction through cloud points obtained by Microsoft Kinect, and then using Poisson algorithm

Área e volume: a transição da noção de medida à de área e de volume

Pós-graduação em Matemática em Rede Nacional - IBILCE

Sobre pavimentações do plano euclidiano

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Construções euclidianas e o desfecho de problemas famosos da geometria

Construction techniques with ruler and the compasses, fundamental on Euclidean geometry, have been related to modern algebraic theories such as solving equations and extension of bodies from the works by Paolo Ruffini (1765-1822), Niels Henrik Abel (1802-1829) and Evariste Galois (1811-1832). This relation could provide an answer to some famous problems, from ancient Greece, such as doubling the cube, the trisection Angle, the Quadrature of the Circle and the construction of regular polygons, which remained unsolved for over two thousand years. Also important for our purposes are the notions of algebraic numbers, transcendental and the criteria for constructability, of those numbers. The objective of this study is to reconstruct relevant steps of geometric constructions with ruler (unmarked) and the compasses, from the elementary to the outcome buildings, in the nineteenth century, considering those mentioned problems.

O ensino de geometria através da pavimentação do plano

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Refinamento geométrico de contornos e cumeeiras de telhados de edifícios extraídos de dados laser com uso de imagem aérea

In this paper, a method is proposed to refine the LASER 3D roofs geometrically by using a high-resolution aerial image and Markov Random Field (MRF) models. In order to do so, a MRF description for grouping straight lines is developed, assuming that each projected side contour and ridge is topologically correct and that it is only necessary to improve its accuracy. Although the combination of laser data with data from image is most justified for refining roof contour, the structure of ridges can give greater robustness in the topological description of the roof structure. The MRF model is formulated based on relationships (length, proximity, and orientation) between the straight lines extracted from the image and projected polygon and also on retangularity and corner injunctions. The energy function associated with MRF is minimized by the genetic algorithm optimization method, resulting in the grouping of straight lines for each roof object. Finally, each grouping of straight lines is topologically reconstructed based on the topology of the corresponding LASER scanning polygon projected onto the image-space. The results obtained were satisfactory. This method was able to provide polygons roof refined buildings in which most of its contour sides and ridges were geometrically improved.

Áreas de polígonos via determinantes

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Collision free region determination by modified polygonal Boolean operations

Cutting and packing problems are found in numerous industries such as garment, wood and shipbuilding. The collision free region concept is presented, as it represents all the translations possible for an item to be inserted into a container with already placed items. The often adopted nofit polygon concept and its analogous concept inner fit polygon are used to determine the collision free region. Boolean operations involving nofit polygons and inner fit polygons are used to determine the collision free region. New robust non-regularized Boolean operations algorithm is proposed to determine the collision free region. The algorithm is capable of dealing with degenerated boundaries. This capability is important because degenerated boundaries often represent local optimal placements. A parallelized version of the algorithm is also proposed and tests are performed in order to determine the execution times of both the serial and parallel versions of the algorithm.

Parallel Layout Construction Algorithm for Irregular Shape Packing Problems

Cutting and packing problems arise in a variety of industries, including garment, wood and shipbuilding. Irregular shape packing is a special case which admits irregular items and is much more complex due to the geometry of items. In order to ensure that items do not overlap and no item from the layout protrudes from the container, the collision free region concept was adopted. It represents all possible translations for a new item to be inserted into a container with already placed items. To construct a feasible layout, collision free region for each item is determined through a sequence of Boolean operations over polygons. In order to improve the speed of the algorithm, a parallel version of the layout construction was proposed and it was applied to a simulated annealing algorithm used to solve bin packing problems. Tests were performed in order to determine the speed improvement of the parallel version over the serial algorithm

The Fundamental Gap For Hyperbolic Triangles

In 1983, M. van den Berg made his Fundamental Gap Conjecture about the difference between the first two Dirichlet eigenvalues (the fundamental gap) of any convex domain in the Euclidean plane. Recently, progress has been made in the case where the domains are polygons and, in particular, triangles. We examine the conjecture for triangles in hyperbolic geometry, though we seek an for an upper bound for the fundamental gap rather than a lower bound.

Isospectrality and Heat Content

We present examples of isospectral operators that do not have the same heat content. Several of these examples are planar polygons that are isospectral for the Laplace operator with Dirichlet boundary conditions. These include examples with infinitely many components. Other planar examples have mixed Dirichlet and Neumann boundary conditions. We also consider Schrodinger operators acting in L-2[0,1] with Dirichlet boundary conditions, and show that an abundance of isospectral deformations do not preserve the heat content.

Effect of Methodological and Ecological Approaches on Heterogeneity of Nest-Site Selection of a Long-Lived Vulture

The application of scientific-based conservation measures requires that sampling methodologies in studies modelling similar ecological aspects produce comparable results making easier their interpretation. We aimed to show how the choice of different methodological and ecological approaches can affect conclusions in nest-site selection studies along different Palearctic meta-populations of an indicator species. First, a multivariate analysis of the variables affecting nest-site selection in a breeding colony of cinereous vulture (Aegypius monachus) in central Spain was performed. Then, a meta-analysis was applied to establish how methodological and habitat-type factors determine differences and similarities in the results obtained by previous studies that have modelled the forest breeding habitat of the species. Our results revealed patterns in nesting-habitat modelling by the cinereous vulture throughout its whole range: steep and south-facing slopes, great cover of large trees and distance to human activities were generally selected. The ratio and situation of the studied plots (nests/random), the use of plots vs. polygons as sampling units and the number of years of data set determined the variability explained by the model. Moreover, a greater size of the breeding colony implied that ecological and geomorphological variables at landscape level were more influential. Additionally, human activities affected in greater proportion to colonies situated in Mediterranean forests. For the first time, a meta-analysis regarding the factors determining nest-site selection heterogeneity for a single species at broad scale was achieved. It is essential to homogenize and coordinate experimental design in modelling the selection of species' ecological requirements in order to avoid that differences in results among studies would be due to methodological heterogeneity. This would optimize best conservation and management practices for habitats and species in a global context.

Patterned-ground plant communities along a bioclimate gradient in the High Arctic, Canada

Non-sorted circles, non-sorted polygons, and earth hummocks are common ground-surface features ill arctic regions. The), are caused by a variety of physical processes that Occur in permafrost regions including contraction cracking and frost heave. Here we describe the vegetation of patterned-ground forms on zonal sites at three location!: along an N-S transect through the High Arctic of Canada. We made 75 releves on patterned-ground features (circles, polygons, earth hummocks) and adjacent tundra (Interpolygon, intercircle, interhummock areas) and identified and classified the vegetation according to the Braun-Blanquet Method. Environmental factors were correlated with the vegetation data using a nonmetric multidimensional scaling ordination (NMDS). We identified eleven commnunities: (1) Puccinellia angustata-Papaver radicalum community in xeromesic non-sorted polygons of subzone A of the Circumpolar Arctic Vegetation Map; (2) Saxifraga-Parmelia omphalodes ssp. glacialis community in hydromesic interpolygon areas of subzone A; (3) Hypogymnia subobscura-Lecanora epibryon community In xeromesic non-sorted polygons of subzone B; (4) Orthotrichum speciosum-Salix arctica community In xeromesic interpolygon areas of subzone B; (5) Cochlearia groenlandica-Luzula nivalis community in hydromesic earth Mocks Of subzone B; (6) Salix arctica-Eriophorum angustifolium ssp. triste community in hygric earth hummocks of subzone 13; (7) Puccinellia angustata-Potentilla vahliana community in xeromesic non-sorted circles and bare patches of subzone Q (8) Dryas integrifolia-Carex rupestris community in xeromesic intercircle areas and vegetated patches of subzone C; (9) Braya glabella ssp. purpurascens-Dryas integrifolia community In hydromesic non-sorted circles of subzone Q (10) Dryas integrifolia-Carex aquatilis community in hydromesic intercircle areas of subzone C; and (11) Eriophorum angustifolium ssp. triste-Carex aquatilis community ill hygric intercircle areas of subzone C. The NMDS ordination displayed the vegetation types with respect to complex environmental gradients. The first axis of the ordination corresponds to a complex soil moisture gradient and the second axis corresponds to a complex geology/elevation/climate gradient. The tundra plots have a greater moss and graminoid cover than the adjacent frost-heave communities. In general, frost-heave features have greater thaw depths, more bare ground, thinner organic horizons, and lower soil moisture than the surrounding tundra. The morphology of the investigated patterned ground forms changes along the climatic gradient, with non-sorted pollygons dominating in the northernmost sites and non-sorted circles dominating, in the southern sites.