3D Compression: from A to Zip a first complete example

Imagens invadiram a maioria das publicacações e comunicacões contemporâneas. Esta expansão acelerou-se com o desenvolvimento de métodos eficientes de compressão da imagem. Hoje o processo da criação de imagens é baseado nos objetos multidimensionais gerados por CAD, simulações físicas, representações de dados ou soluções de problemas de otimização. Esta variedade das fontes motiva o desenho de esquemas de compressão adaptados a classes específicas de modelos. O lançamento recente do Google Sketch’up com o seu armazém de modelos 3D acelerou a passagem das imagens bidimensionais às tridimensionais. Entretanto, este o tipo de sistemas requer um acesso rápido aos modelos 3D, possivelmente gigantes, que é possível somente usando de esquemas eficientes da compressão. Esse trabalho faz parte de um tutorial ministrado no Sibgrapi 2007.Images invaded most of contemporary publications and communications. This expansion has accelerated with the development of efficient schemes dedicated to image compression. Nowadays, the image creation process relies on multidimensional objects generated from computer aided design, physical simulations, data representation or optimisation problem solutions. This variety of sources motivates the design of compression schemes adapted to specific class of models. The recent launch of Google Sketch’up and its 3D models warehouse has accelerated the shift from two-dimensional images to three-dimensional ones. However, these kind of systems require fast access to eventually huge models, which is possible only through the use of efficient compression schemes. This work is part of a tutorial given at the XXth Brazilian Symposium on Computer Graphics and Image Processing (Sibgrapi 2007)

Schnyder woods for higher genus triangulated surfaces, with applications to encoding

Schnyder woods are a well-known combinatorial structure for plane triangulations, which yields a decomposition into 3 spanning trees. We extend here definitions and algorithms for Schnyder woods to closed orientable surfaces of arbitrary genus. In particular, we describe a method to traverse a triangulation of genus $g$ and compute a so-called $g$-Schnyder wood on the way. As an application, we give a procedure to encode a triangulation of genus $g$ and $n$ vertices in $4n+O(g \log(n))$ bits. This matches the worst-case encoding rate of Edgebreaker in positive genus. All the algorithms presented here have execution time $O((n+g)g)$, hence are linear when the genus is fixed.Comment: 27 pages, to appear in a special issue of Discrete and Computational Geometr

Schnyder woods for higher genus triangulated surfaces

The final version of this extended abstract has been published in "Discrete and Computational Geometry (2009)"International audienceSchnyder woods are a well known combinatorial structure for planar graphs, which yields a decomposition into 3 vertex-spanning trees. Our goal is to extend definitions and algorithms for Schnyder woods designed for planar graphs (corresponding to combinatorial surfaces with the topology of the sphere, i.e., of genus 0) to the more general case of graphs embedded on surfaces of arbitrary genus. First, we define a new traversal order of the vertices of a triangulated surface of genus g together with an orientation and coloration of the edges that extends the one proposed by Schnyder for the planar case. As a by-product we show how some recent schemes for compression and compact encoding of graphs can be extended to higher genus. All the algorithms presented here have linear time complexity

Vector field reconstruction from sparse samples with applications

Abstract. We present a novel algorithm for 2D vector field reconstruction from sparse set of points–vectors pairs. Our approach subdivides the domain adaptively in order to make local piecewise polynomial approximations for the field. It uses partition of unity to blend those local approximations together, generating a global approximation for the field. The flexibility of this scheme allows handling data from very different sources. In particular, this work presents important applications of the proposed method to velocity and acceleration fields ’ analysis, in particular for fluid dynamics visualization

Particle-based non-Newtonian fluid animation for melting objects

Abstract. This paper presents a new visually realistic animation technique for objects that melt and flow. It simulates viscoplastic properties of materials such as metal, plastic, wax, polymer and lava. The technique consists in modeling the object by the transition of a non–Newtonian fluid with high viscosity to a liquid of low viscosity. During the melting, the viscosity is formulated using the General Newtonian fluids model, whose properties depend on the local temperature. The phase transition is then driven by the heat equation. The fluid simulation framework uses a variation of the Lagrangian method called Smoothed Particle Hydrodynamics. This paper also includes several schemes that improve the efficiency and the numerical stability of the equations