A novel progressive lossy-to-lossless coding method is proposed for mesh models of images whose underlying triangulations have arbitrary connectivity. For a triangulation T of a set P of points, our proposed method represents the connectivity of T as a sequence of edge flips that maps a uniquely-determined Delaunay triangulation (i.e., preferred-directions Delaunay triangulation) of P to T. The coding efficiency of our method is highest when the underlying triangulation connectivity is close to Delaunay, and slowly degrades as connectivity moves away from being Delaunay. Through experimental results, we show that our proposed coding method is able to significantly outperform a simple baseline coding scheme. Furthermore, our proposed method can outperform traditional connectivity coding methods for meshes that do not deviate too far from Delaunay connectivity. This result is of practical significance since, in many applications, mesh connectivity is often not so far from being Delaunay, due to the good approximation properties of Delaunay triangulations. / Graduate

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In this work, a triangulation method, a classic algorithm for Sammon’s projection and the combination of Sammon’s algorithm and the triangulation method for mapping of new points are examined in details. The combination of Sammon’s algorithm and triangulation method is created. The algorithms of triangulation method, Sammon’s algorithm and their combination are realized in Microsoft Visual Basic 5.0. These algorithms are developed and examined on the view on the following stand points: * Visual evaluation of data projection; * Evaluation of time of data mapping; * Evaluation of projection error. The triangulation method is quite fast, however only (2m-3) distances among examined data points are exactly preserved. Sammon’s algorithm tries to preserve all m(m-1)/2 distances among data points, but it is quite slow: whenever a new point must be mapped, all visualization procedure must be repeated over. This question is solved using the combination of the triangulation method and Sammon’s projection. On purpose to get the more exact data projection onto a plane, we must to map more initial points using Sammon’s projection and less new points using the triangulation method. The combination of these methods is used, whenever new points of the data must be quickly mapped. This method performs quite fast and quite a little precision is lost. The discovered new ways for fast mapping of points in a high-dimensional space onto a plane and it makes a background for the further research... [to full text]

Subject of this paper is triangulation of given domain also called as mesh generation. Overview of main mesh types (structured, unstructured and hybrid) is given. Groups of triangulation methods are defined and include collective triangulation, incremental triangulation, pliant mesh generation with post-triangulation and plaint mesh generation with retriangulation. Delaunay triangulation is described in greater detail and variuos Delaunay triangulation algorithms are presented including use of Delaunay triangulation for anisotropic mesh generation and method to generate Constrained Delaunay triangulation. Greedy insertion Delaunay and data dependent allgorithms are developed for hight fields surface aproximation. Significant improvements are made to these algorithms including faster recalculation, node selection and use of supplementary data sets in order to maximise efficiency of calculations. Main criteria to evaluate developed algorithms is overall error of approximation and speed of calculation. Data dependent algorithm generates better quality mesh (less approximation error), however Delaunay triangulation algorithm is significantly faster. Results and conclusions are presented at the end of paper.

Urbanization and the globalization of the food system are causing social, environmental, economic and political problems worldwide. Rapid urbanization is increasing environmental degradation and food insecurity. Urban agriculture is one tool for sustainable development that has the potential to provide food or related services within or on the edges of urban areas. The goal of this research was to determine the current situation and the future potential of urban agriculture in Kingston. A literature review, questionnaires, interviews and case studies were used to determine the perceptions of relevant stakeholders, barriers and ways to overcome those barriers. Conservative estimates of urban agriculture's value to Kingston's environmental, social, community health, food security and economic dimensions were made through modeling. Study participants demonstrated a relatively greater awareness of environmental and community benefits of urban agriculture compared to food security, health or economic benefits. Modeling and calculations indicated that urban agriculture could contribute at least $190 to $860 million per year in positive environmental, health and economic benefits. Modeling indicated that sourcing more local urban produced foods could reduce greenhouse gas emissions by at least 1300 to 14000 tonnes annually for 39 common fresh fruits and vegetables. Urban agriculture could meet the fresh fruits and vegetables needs of up to 76% or more of the Kingston CMA population. There appeared to be 5600 ha of area in the inner-city that could be used for food production. Major challenges identified were perceptions of limited space, limited resources and education. Recommendations to address these challenges are also provided. Overall, urban agriculture has potential to contribute to sustainability in Kingston. / Thesis (Master, Environmental Studies) -- Queen's University, 2007-08-28 14:26:18.048

The problem of generating a surface triangulation from a set of points with normal information arises in several mesh processing tasks like surface reconstruction or surface resampling. In this paper we present a surface triangulation approach which is based on local 2d delaunay triangulations in tangent space. Our contribution is the extension of this method to surfaces with sharp corners and creases. We demonstrate the robustness of the method on difficult meshing problems that include nearby sheets, self intersecting non manifold surfaces and noisy point samples.

The problem of generating a surface triangulation from a set of points with normal information arises in several mesh processing tasks like surface reconstruction or surface resampling. In this paper we present a surface triangulation approach which is based on local 2d delaunay triangulations in tangent space. Our contribution is the extension of this method to surfaces with sharp corners and creases. We demonstrate the robustness of the method on difficult meshing problems that include nearby sheets, self intersecting non manifold surfaces and noisy point samples.

Thesis (M.B.A.)--North-West University, Potchefstroom Campus, 2009.

Thesis (M.B.A.)--North-West University, Potchefstroom Campus, 2009.

In this thesis, we will present examples of Voronoi diagrams that are not tessellations. Moreover, we will find sufficient conditions on subspaces of E2, S2 and the Poincaré disk and the sets of sites that guarantee that the Voronoi diagrams are pre-triangulations. We will also study g-spaces, which are metric spaces with ‘extendable’ geodesics joining any 2 points and give properties for a set of sites in a g-space that again guarantees that the Voronoi diagram is a pre-triangulation.