Wavelets Defined Over Non Nested Tetrahedral Grids: a Theoretical Approach

• Boscardin, Liliana B. ^[1] ; Castro, Silvia M. ^[1] ; Castro, Liliana R. ^[1]
  1. [1] Universidad Nacional del Sur

     Universidad Nacional del Sur

     Argentina

     
• Localización: Journal of Computer Science and Technology, ISSN-e 1666-6038, Vol. 19, Nº. 1, 2019 (Ejemplar dedicado a: Forty-Nineth; e08), págs. 8-21
• Idioma: inglés
• DOI: 10.24215/16666038.19.e02
• Títulos paralelos:
  • Wavelets Definidas sobre Grillas Tetraédricas no Anidadas: un Abordaje Teórico
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• Resumen
  • español

    La principal contribuci´on de este art´ıculo es la definici´on de wavelets sobre grillas tetra´edricas no anidadas lo cual permite la representaci´on de funciones definidas sobre una tetraedrizaci´on irregular. De esta manera es posible representar distintos atributos de un objeto 3D como pueden ser su color, su densidad, su brillo, etc. Esta representaci´on consiste de un conjunto de coeficientes correspondientes a una resoluci´on m´as gruesa y de un conjunto de coeficientes de detalle que miden el error entre dos aproximaciones sucesivas. En este trabajo se presentan la matriz de an´alisis, que se necesita para pasar de una resoluci´on m´as fina a una m´as gruesa, y la matriz de an´alisis, necesaria para pasar de una resoluci´on gruesa a una m´as fina. El marco general de trabajo para todo el art´ıculo es el de grillas tetra´edricas no anidadas.

  • English

    The main contribution of this paper is the definition of wavelets over non nested tetrahedral grids, allowing the representation of functions defined on an a irregular tetrahedralization. In this way, it is possible to represent different attributes of a 3D object such as its color, brightness, density, etc. This representation consists of a set of coefficients corresponding to a coarse resolution followed by a set of detail coefficients that measures the error between two successive approximations. In this work the analysis matrix that allows going from a fine to a coarser resolution and the synthesis matrix needed for going from a coarse resolution to a finer one, are presented. All this is within the framework of non nested tetrahedral grids.

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