Cuadrilaterización de una malla triangular usando análisis espectral y teoría de Morse

La reparametrización de las mallas triangulares es uno de los procesos fundamentales usados por casi todos los sistemas de procesamiento geométrico. La mayoría de trabajos se han enfocado en el remallado triangular; el problema igualmente importante de la reparametrización de superficies trianguladas en cuadriláteros ha permanecido por mucho tiempo sin dirección. A pesar de la falta relativa de atención, la necesidad de métodos de reparametrización cuadrilaterales de calidad es de gran importancia en varias áreas de computación gráfica y visión por computador. En este artículo se muestra un acercamiento al problema de cuadrilaterización de mallas triangulares. Aplicando un análisis de la teoría de Morse a los valores propios de una malla laplaciana, se implementa un algoritmo que cuadrilateriza superficies triangulares. Debido a las propiedades del operador laplaciano, los parches cuadrilaterales resultantes se forman adecuadamente y se levantan directamente de las propiedades intrínsecas de la superficie

Cuadrilaterización de una malla triangular usando análisis espectral y teoría de Morse

La reparametrización de las mallas triangulares es uno de los procesos fundamentales usados por casi todos los sistemas de procesamiento geométrico. La mayoría de trabajos se han enfocado en el remallado triangular; el problema igualmente importante de la reparametrización de superficies trianguladas en cuadriláteros ha permanecido por mucho tiempo sin dirección. A pesar de la falta relativa de atención, la necesidad de métodos de reparametrización cuadrilaterales de calidad es de gran importancia en varias áreas de computación gráfica y visión por computador. En este artículo se muestra un acercamiento al problema de cuadrilaterización de mallas triangulares. Aplicando un análisis de la teoría de Morse a los valores propios de una malla laplaciana, se implementa un algoritmo que cuadrilateriza superficies triangulares. Debido a las propiedades del operador laplaciano, los parches cuadrilaterales resultantes se forman adecuadamente y se levantan directamente de las propiedades intrínsecas de la superficie

Digital Alchemy: Matter and Metamorphosis in Contemporary Digital Animation and Interface Design

The recent proliferation of special effects in Hollywood film has ushered in an era of digital transformation. Among scholars, digital technology is hailed as a revolutionary moment in the history of communication and representation. Nevertheless, media scholars and cultural historians have difficulty finding a language adequate to theorizing digital artifacts because they are not just texts to be deciphered. Rather, digital media artifacts also invite critiques about the status of reality because they resurrect ancient problems of embodiment and transcendence.In contrast to scholarly approaches to digital technology, computer engineers, interface designers, and special effects producers have invented a robust set of terms and phrases to describe the practice of digital animation. In order to address this disconnect between producers of new media and scholars of new media, I argue that the process of digital animation borrows extensively from a set of preexisting terms describing materiality that were prominent for centuries prior to the scientific revolution. Specifically, digital animators and interface designers make use of the ancient science, art, and technological craft of alchemy. Both alchemy and digital animation share several fundamental elements: both boast the power of being able to transform one material, substance, or thing into a different material, substance, or thing. Both seek to transcend the body and materiality but in the process, find that this elusive goal (realism and gold) is forever receding onto the horizon.The introduction begins with a literature review of the field of digital media studies. It identifies a gap in the field concerning disparate arguments about new media technology. On the one hand, scholars argue that new technologies like cyberspace and digital technology enable radical new forms of engagement with media on individual, social, and economic levels. At the same time that media scholars assert that our current epoch is marked by a historical rupture, many other researchers claim that new media are increasingly characterized by ancient metaphysical problems like embodiment and transcendence. In subsequent chapters I investigate this disparity

Contributions dans le domaine de l'analyse multirésolution de maillages surfaciques semi-réguliers. Application à la compression géométrique

The goal of this work is to find solutions for the compression and the visualization of surface meshes at different levels of details. the first part is focused on static meshes, the second part is focused on dynamic meshes, used to represent 3D animations.L’objectif de cette thèse de doctorat est de proposer des solutions aux problèmes de compression et d’affichage de maillages surfaciques à plusieurs niveaux de détails. La première partie est réservée à l’étude des maillages statiques. La deuxième partie, elle concerne l’étude des maillagesdynamiques, où nous détaillons les solutions proposées pour les objets 3D animés

Variational normal meshes

Hierarchical representations of surfaces have many advantages for digital geometry processing applications. Normal meshes are particularly attractive since their level-to-level displacements are in the local normal direction only. Consequently, they only require scalar coefficients to specify. In this article, we propose a novel method to approximate a given mesh with a normal mesh. Instead of building an associated parameterization on the fly, we assume a globally smooth parameterization at the beginning and cast the problem as one of perturbing this parameterization. Controlling the magnitude of this perturbation gives us explicit control over the range between fully constrained (only scalar coefficients) and unconstrained (3-vector coefficients) approximations. With the unconstrained problem giving the lowest approximation error, we can thus characterize the error cost of normal meshes as a function of the number of nonnormal offsets---we find a significant gain for little (error) cost. Because the normal mesh construction creates a geometry driven approximation, we can replace the difficult geometric distance minimization problem with a much simpler least squares problem. This variational approach reduces magnitude and structure (aliasing) of the error further. Our method separates the parameterization construction into an initial setup followed only by subsequent perturbations, giving us an algorithm which is far simpler to implement, more robust, and significantly faster

Variational normal meshes

Hierarchical representations of surfaces have many advantages for digital geometry processing applications. Normal meshes are particularly attractive since their level-to-level displacements are in the local normal direction only. Consequently, they only require scalar coefficients to specify. In this article, we propose a novel method to approximate a given mesh with a normal mesh. Instead of building an associated parameterization on the fly, we assume a globally smooth parameterization at the beginning and cast the problem as one of perturbing this parameterization. Controlling the magnitude of this perturbation gives us explicit control over the range between fully constrained (only scalar coefficients) and unconstrained (3-vector coefficients) approximations. With the unconstrained problem giving the lowest approximation error, we can thus characterize the error cost of normal meshes as a function of the number of nonnormal offsets---we find a significant gain for little (error) cost. Because the normal mesh construction creates a geometry driven approximation, we can replace the difficult geometric distance minimization problem with a much simpler least squares problem. This variational approach reduces magnitude and structure (aliasing) of the error further. Our method separates the parameterization construction into an initial setup followed only by subsequent perturbations, giving us an algorithm which is far simpler to implement, more robust, and significantly faster

Variational Normal Meshes

this article, we propose a novel method to approximate a given mesh with a normal mesh. Instead of building an associated parameterization on the fly, we assume a globally smooth parameterization at the beginning and cast the problem as one of perturbing this parameterization. Controlling the magnitude of this perturbation gives us explicit control over the range between fully constrained (only scalar coefficients) and unconstrained (3-vector coefficients) approximations. With the unconstrained problem giving the lowest approximation error, we can thus characterize the error cost of normal meshes as a function of the number of nonnormal offsets---we find a significant gain for little (error) cost. Because the normal mesh construction creates a geometry driven approximation, we can replace the difficult geometric distance minimization problem with a much simpler least squares problem. This variational approach reduces magnitude and structure (aliasing) of the error further. Our method separates the parameterization construction into an initial setup followed only by subsequent perturbations, giving us an algorithm which is far simpler to implement, more robust, and significantly faste

Approximation of Surfaces by Normal Meshes

This thesis introduces a novel geometry processing pipeline based on unconstrained spherical parameterization and normal remeshing. We claim three main contributions: First we show how to increase the stability of Normal Mesh construction, while speeding it up by decomposing the process into two stages: parameterization and remeshing. We show that the remeshing step can be seen as resampling under a small perturbation of the given parameterization. Based on this observation we describe a novel algorithm for efficient and stable (interpolatory) normal mesh construction via parameterization perturbation. Our second contribution is the introduction of Variational Normal Meshes. We describe a novel algorithm for encoding these meshes, and use our implementation to argue that variational normal meshes have a higher approximation quality than interpolating normal meshes, as expected. In particular we demonstrate that interpolating normal meshes have about 60 percent higher Hausdorff approximation error for the same number of vertices than our novel variational normal meshes. We also show that variational normal meshes have less aliasing artifacts than interpolatory normal meshes. The third contribution is on creating parameterizations for unstructured genus zero meshes. Previous approaches could only avoid collapses by introducing artificial constraints or continuous reprojections, which are avoided by our method. The key idea is to define upper bound energies that are still good approximations. We achieve this by dividing classical planar triangle energies by the minimum distance to the sphere center. We prove that these simple modifaction provides the desired upper bounds and are good approximations in the finite element sense. We have implemented all algorithms and provide example results and statistical data supporting our theoretical observations