title: Three dimensional extension of Bresenham’s algorithm with Voronoi diagram

authors: Au, Chi Kit

subjects: voronoi diagram

abstract: Bresenham’s algorithm for plotting a two-dimensional line segment is elegant and efficient in its deployment of mid-point comparison and integer arithmetic. It is natural to investigate its three-dimensional extensions. In so doing, this paper uncovers the reason for little prior work. The concept of the mid-point in a unit interval generalizes to that of nearest neighbours involving a Voronoi diagram. Algorithmically, there are challenges. While a unit interval in two-dimension becomes a unit square in three-dimension, “squaring” the number of choices in Bresenham’s algorithm is shown to have difficulties. In this paper, the three-dimensional extension is based on the main idea of Bresenham’s algorithm of minimum distance between the line and the grid points. The structure of the Voronoi diagram is presented for grid points to which the line may be approximated. The deployment of integer arithmetic and symmetry for the three-dimensional extension of the algorithm to raise the computation efficiency are also investigated.

text: Three dimensional extension of Bresenham’s algorithm with Voronoi diagram Bresenham’s algorithm for plotting a two-dimensional line segment is elegant and efficient in its deployment of mid-point comparison and integer arithmetic. It is natural to investigate its three-dimensional extensions. In so doing, this paper uncovers the reason for little prior work. The concept of the mid-point in a unit interval generalizes to that of nearest neighbours involving a Voronoi diagram. Algorithmically, there are challenges. While a unit interval in two-dimension becomes a unit square in three-dimension, “squaring” the number of choices in Bresenham’s algorithm is shown to have difficulties. In this paper, the three-dimensional extension is based on the main idea of Bresenham’s algorithm of minimum distance between the line and the grid points. The structure of the Voronoi diagram is presented for grid points to which the line may be approximated. The deployment of integer arithmetic and symmetry for the three-dimensional extension of the algorithm to raise the computation efficiency are also investigated.

year: 2010

title: On the accuracy of simulations of turbulence

authors: Wan, Minping

subjects: turbulence

abstract: The widely recognized issue of adequate spatial resolution in numerical simulations of turbulence is studied in the context of two-dimensional magnetohydrodynamics. The familiar criterion that the dissipation scale should be resolved enables accurate computation of the spectrum, but fails for precise determination of higher-order statistical quantities. Examination of two straightforward diagnostics, the maximum of the kurtosis and the scale-dependent kurtosis, enables the development of simple tests for assessing adequacy of spatial resolution. The efficacy of the tests is confirmed by examining a sample problem, the distribution of magnetic reconnection rates in turbulence. Oversampling the Kolmogorov dissipation scale by a factor of 3 allows accurate computation of the kurtosis, the scale-dependent kurtosis, and the reconnection rates. These tests may provide useful guidance for resolution requirements in many plasma computations involving turbulence and reconnection.

text: On the accuracy of simulations of turbulence The widely recognized issue of adequate spatial resolution in numerical simulations of turbulence is studied in the context of two-dimensional magnetohydrodynamics. The familiar criterion that the dissipation scale should be resolved enables accurate computation of the spectrum, but fails for precise determination of higher-order statistical quantities. Examination of two straightforward diagnostics, the maximum of the kurtosis and the scale-dependent kurtosis, enables the development of simple tests for assessing adequacy of spatial resolution. The efficacy of the tests is confirmed by examining a sample problem, the distribution of magnetic reconnection rates in turbulence. Oversampling the Kolmogorov dissipation scale by a factor of 3 allows accurate computation of the kurtosis, the scale-dependent kurtosis, and the reconnection rates. These tests may provide useful guidance for resolution requirements in many plasma computations involving turbulence and reconnection.

year: 2010

title: Kūkū te kererū, ketekete te kākā: The role of literature in indigenous methods of naming native and introduced birds to Aotearoa New Zealand

authors: Raharuhi, Te Urukeiha

subjects: indigenous methods of naming

abstract: This thesis describes the role of academic literature in indigenous epistemology with a focus on indigenous methods of naming native and introduced birds to Aotearoa New Zealand. The story of the role of academic literature in mātauranga Māori transmission presented in this thesis, describes a narrative of indigenous people being increasingly excluded from transmission of mātauranga Māori in literature production. Importantly the exclusion of original sources from participation in literature production and revision resulted in a high degree of persistent error in academic literature presenting oral narratives and te reo Māori bird names.

Currently, te reo Māori names of native and introduced birds are represented in English language academic literature, as subject matter or topic of interest predominately within a scientific research paradigm, in the fields of linguistics, ornithology, ethnology or disciplines where these are combined such as ethno-ornithology or folk-taxonomy. Research inquiry conducted in this study is influenced by a potential to explore indigenous methods of naming in terms of what they reveal about our ways of being (ontology) and our ways of knowing (epistemology).

This thesis presents two literature reviews and the findings of seven semi-structured interviews to explore the complexities of the role of academic literature in indigenous epistemology with a focus on indigenous methods of naming native and indigenous birds to Aotearoa New Zealand. Exploring indigenous methods of naming in this way provides an opportunity to tease out the influence of translation, Western scientific paradigms and the medium of academic literature on the transmission of mātauranga Māori as well as identify opportunities and limitations for indigenous epistemology offered through the medium of academic literature.

A comprehensive index of te reo Māori bird names with attention to the variety of linguistic nuances of geographically specific vernacular presented consistently in the context of indigenous methods of naming, potentially provides an accessible and meaningful taxonomic reference document. At the present time such an index has not been published. The findings of the research presented in this thesis support the potential of academic literature to meaningfully contribute to indigenous methods of naming when it records or facilitates direct participation of hapū in indigenous epistemology rather than predetermine or prematurely theorise indigenous methods of naming native and introduced birds to Aotearoa New Zealand. Equally, it presents findings to support potential for academic literature to contribute to mātauranga Māori when it articulates indigenous epistemology as a valuable way of knowing and does not assume to replace memory arts as the primary methods of mātauranga Māori transmission. Furthermore, the application of an indigenous paradigm to the production of literature about indigenous methods of naming as an aspect of mātauranga Māori has the potential to constitute an accurate and authentic body of knowledge.

text: Kūkū te kererū, ketekete te kākā: The role of literature in indigenous methods of naming native and introduced birds to Aotearoa New Zealand This thesis describes the role of academic literature in indigenous epistemology with a focus on indigenous methods of naming native and introduced birds to Aotearoa New Zealand. The story of the role of academic literature in mātauranga Māori transmission presented in this thesis, describes a narrative of indigenous people being increasingly excluded from transmission of mātauranga Māori in literature production. Importantly the exclusion of original sources from participation in literature production and revision resulted in a high degree of persistent error in academic literature presenting oral narratives and te reo Māori bird names.

Currently, te reo Māori names of native and introduced birds are represented in English language academic literature, as subject matter or topic of interest predominately within a scientific research paradigm, in the fields of linguistics, ornithology, ethnology or disciplines where these are combined such as ethno-ornithology or folk-taxonomy. Research inquiry conducted in this study is influenced by a potential to explore indigenous methods of naming in terms of what they reveal about our ways of being (ontology) and our ways of knowing (epistemology).

This thesis presents two literature reviews and the findings of seven semi-structured interviews to explore the complexities of the role of academic literature in indigenous epistemology with a focus on indigenous methods of naming native and indigenous birds to Aotearoa New Zealand. Exploring indigenous methods of naming in this way provides an opportunity to tease out the influence of translation, Western scientific paradigms and the medium of academic literature on the transmission of mātauranga Māori as well as identify opportunities and limitations for indigenous epistemology offered through the medium of academic literature.

A comprehensive index of te reo Māori bird names with attention to the variety of linguistic nuances of geographically specific vernacular presented consistently in the context of indigenous methods of naming, potentially provides an accessible and meaningful taxonomic reference document. At the present time such an index has not been published. The findings of the research presented in this thesis support the potential of academic literature to meaningfully contribute to indigenous methods of naming when it records or facilitates direct participation of hapū in indigenous epistemology rather than predetermine or prematurely theorise indigenous methods of naming native and introduced birds to Aotearoa New Zealand. Equally, it presents findings to support potential for academic literature to contribute to mātauranga Māori when it articulates indigenous epistemology as a valuable way of knowing and does not assume to replace memory arts as the primary methods of mātauranga Māori transmission. Furthermore, the application of an indigenous paradigm to the production of literature about indigenous methods of naming as an aspect of mātauranga Māori has the potential to constitute an accurate and authentic body of knowledge.

year: 2015