ResearchPad - polygons https://www.researchpad.co Default RSS Feed en-us © 2020 Newgen KnowledgeWorks <![CDATA[Mesh smoothing algorithm based on exterior angles split]]> https://www.researchpad.co/article/elastic_article_13823 Since meshes of poor quality give rise to low accuracy in finite element analysis and kinds of inconveniences in many other applications, mesh smoothing is widely used as an essential technique for the improvement of mesh quality. With respect to this issue, the main contribution of this paper is that a novel mesh smoothing method based on an exterior-angle-split process is proposed. The proposed method contains three main stages: the first stage is independent element geometric transformation performed by exterior-angle-split operations, treating elements unconnected; the second stage is to offset scaling and displacement induced by element transformation; the third stage is to determine the final positions of nodes with a weighted strategy. Theoretical proof describes the regularity of this method and many numerical experiments illustrate its convergence. Not only is this method applicable for triangular mesh, but also can be naturally extended to arbitrary polygonal surface mesh. Quality improvements of demonstrations on triangular and quadrilateral meshes show the effectiveness of this method.

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<![CDATA[A quadratic trigonometric spline for curve modeling]]> https://www.researchpad.co/article/5c40f762d5eed0c48438600c

An imperative curve modeling technique has been established with a view to its applications in various disciplines of science, engineering and design. It is a new spline method using piecewise quadratic trigonometric functions. It possesses error bounds of order 3. The proposed curve model also owns the most favorable geometric properties. The proposed spline method accomplishes C2 smoothness and produces a Quadratic Trigonometric Spline (QTS) with the view to its applications in curve design and control. It produces a C2 quadratic trigonometric alternative to the traditional cubic polynomial spline (CPS) because of having four control points in its piecewise description. The comparison analysis of QTS and CPS verifies the QTS as better alternate to CPS. Also, the time analysis proves QTS computationally efficient than CPS.

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<![CDATA[Tiled vector data model for the geographical features of symbolized maps]]> https://www.researchpad.co/article/5989db5aab0ee8fa60bdf54a

Electronic maps (E-maps) provide people with convenience in real-world space. Although web map services can display maps on screens, a more important function is their ability to access geographical features. An E-map that is based on raster tiles is inferior to vector tiles in terms of interactive ability because vector maps provide a convenient and effective method to access and manipulate web map features. However, the critical issue regarding rendering tiled vector maps is that geographical features that are rendered in the form of map symbols via vector tiles may cause visual discontinuities, such as graphic conflicts and losses of data around the borders of tiles, which likely represent the main obstacles to exploring vector map tiles on the web. This paper proposes a tiled vector data model for geographical features in symbolized maps that considers the relationships among geographical features, symbol representations and map renderings. This model presents a method to tailor geographical features in terms of map symbols and ‘addition’ (join) operations on the following two levels: geographical features and map features. Thus, these maps can resolve the visual discontinuity problem based on the proposed model without weakening the interactivity of vector maps. The proposed model is validated by two map data sets, and the results demonstrate that the rendered (symbolized) web maps present smooth visual continuity.

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<![CDATA[High-Resolution Underwater Mapping Using Side-Scan Sonar]]> https://www.researchpad.co/article/5989db3cab0ee8fa60bd50a0

The goal of this study is to generate high-resolution sea floor maps using a Side-Scan Sonar(SSS). This is achieved by explicitly taking into account the SSS operation as follows. First, the raw sensor data is corrected by means of a physics-based SSS model. Second, the data is projected to the sea-floor. The errors involved in this projection are thoroughfully analysed. Third, a probabilistic SSS model is defined and used to estimate the probability of each sea-floor region to be observed. This probabilistic information is then used to weight the contribution of each SSS measurement to the map. Because of these models, arbitrary map resolutions can be achieved, even beyond the sensor resolution. Finally, a geometric map building method is presented and combined with the probabilistic approach. The resulting map is composed of two layers. The echo intensity layer holds the most likely echo intensities at each point in the sea-floor. The probabilistic layer contains information about how confident can the user or the higher control layers be about the echo intensity layer data. Experimental results have been conducted in a large subsea region.

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<![CDATA[MorphoTester: An Open Source Application for Morphological Topographic Analysis]]> https://www.researchpad.co/article/5989daa8ab0ee8fa60ba83ee

The increased prevalence and affordability of 3D scanning technology is beginning to have significant effects on the research questions and approaches available for studies of morphology. As the current trend of larger and more precise 3D datasets is unlikely to slow in the future, there is a need for efficient and capable tools for high-throughput quantitative analysis of biological shape. The promise and the challenge of implementing relatively automated methods for characterizing surface shape can be seen in the example of dental topographic analysis. Dental topographic analysis comprises a suite of techniques for quantifying tooth surfaces and component features. Topographic techniques have provided insight on mammalian molar form-function relationships and these methods could be applied to address other topics and questions. At the same time implementing multiple complementary topographic methods can have high time and labor costs, and comparability of data formats and approaches is difficult to predict. To address these challenges I present MorphoTester, an open source application for visualizing and quantifying topography from 3D triangulated polygon meshes. This application is Python-based and is free to use. MorphoTester implements three commonly used dental topographic metrics–Dirichlet normal energy, relief index, and orientation patch count rotated (OPCR). Previous OPCR algorithms have used raster-based grid data, which is not directly interchangeable with vector-based triangulated polygon meshes. A 3D-OPCR algorithm is provided here for quantifying complexity from polygon meshes. The efficacy of this metric is tested in a sample of mandibular second molars belonging to four species of cercopithecoid primates. Results suggest that 3D-OPCR is at least as effective for quantifying complexity as previous approaches, and may be more effective due to finer resolution of surface data considered here. MorphoTester represents an advancement in the automated quantification of morphology, and can be modified to adapt to future needs and priorities.

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<![CDATA[Automatic extraction of endocranial surfaces from CT images of crania]]> https://www.researchpad.co/article/5989db52ab0ee8fa60bdc538

The authors present a method for extracting polygon data of endocranial surfaces from CT images of human crania. Based on the fact that the endocast is the largest empty space in the crania, we automate a procedure for endocast extraction by integrating several image processing techniques. Given CT images of human crania, the proposed method extracts endocranial surfaces by the following three steps. The first step is binarization in order to fill void structures, such as diploic space and cracks in the skull. We use a void detection method based on mathematical morphology. The second step is watershed-based segmentation of the endocranial part from the binary image of the CT image. Here, we introduce an automatic initial seed assignment method for the endocranial region using the distance field of the binary image. The final step is partial polygonization of the CT images using the segmentation results as mask images. The resulting polygons represent only the endocranial part, and the closed manifold surfaces are computed even though the endocast is not isolated in the cranium. Since only the isovalue threshold and the size of void structures are required, the procedure is not dependent on the experience of the user. The present paper also demonstrates that the proposed method can extract polygon data of endocasts from CT images of various crania.

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<![CDATA[Hexahedral mesh generation via constrained quadrilateralization]]> https://www.researchpad.co/article/5989db5cab0ee8fa60bdfecb

Decomposing a volume into high-quality hexahedral cells is a challenging task in finite element simulations and computer graphics. Inspired by the use of a spatial twist continuum and frame field in previous hexahedral mesh generation methods, we present a method of hexahedral mesh generation via constrained quadrilateralization that combines a spatial twist continuum and frame fields. Given a volume represented by a tetrahedral mesh, surface quadrilateral mesh and frame field, we first extend the loop of the surface of a solid to a layer of hexahedral elements, then divide the solid into two smaller sub-solids by the layer, and finally handle them recursively until all of the sub-solids are empty. In our hexahedral mesh generation framework, we apply constrained quadrilateralization to extend the loop to a layer of hexahedral elements. The “divide-and-conquer” strategy used in this method is suitable for parallelization. This method can potentially lead to easier and more robust implementations that are more parallelizable and less dependent on heavy numerical libraries. The testing results show that the quality of the meshes generated by this method is similar to those produced by current state-of-the-art mesh generation methods.

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