Workshop on Computational Manifolds

NOVEMBER 22-24, 2011

Location: Auditório 3, IMPA

The workshop on Computational Manifolds and Applications will consist
of keynote lectures, contributed talks and project presentations by the participants of the program.


13h30 - 14h15 :: Douglas Cedrim
14h15 - 15h00 :: Mattia Natali, Javier Lezama
15h00 - 15h30 :: Break
15:30 - 16h15 :: Francisco Ganacim
16:15 - 17h00 :: Andre Maximo

13h30 - 14h15 :: Francisco Benavides
14h15 - 15h00 :: Leandro Cruz
15h00 - 15h30 :: Break
15:30 - 16h15 :: Maria Andrade, Leonardo Carvalho, Dalia Bonilla
16:15 - 17h00 :: Aldo Rene Zang

13h30 - 14h30 :: Geovan Tavares
14h30 - 15h00 :: Break
15h00 - 16h00 :: Jean Gallier
16h00 - 17h00 :: Wolfgang Ziller


Douglas Cedrim (USP)
Title: Voronoi based clustering
Abstract: Discrete Voronoi Diagrams are a common and powerful tool to handle geometric properties of discrete surfaces. In some geometric processing algorithms, for sake of complexity, one has to work just with a subset of the original data. In this talk we discuss a particular construction of these subsets by using a Voronoi clustering algorithm regarding the adaptivity of the mesh.

Mattia Natali (University of Bergen), Javier Lezama (Universidad de Cordoba)
Title: Discussion of semi-regular remeshing
Abstract: The described technique proposed by Igor Guskov aims to generate a new semi-regular triangulation starting from an initial mesh and passing through a manifold construction of the underlying surface. The parameterization process is based on the definition of a base mesh, on which a differential structure is built. At the same time, it is possible to control the anisotropy of the final regular mesh.

Francisco Benavides (IMPA)
Title: A Direct texture placement and editing surface
Abstract: The authors present an approach for texture placement and editing based on direct manipulation of textures on the surface. The theoretical foundations of the applied discrete operators can be found in the article "Discrete Differential-Geometry Operators for Triangulated 2-Manifolds", which presents theoretical results on which the texture placement is based. These derivations are based on Voronoi cells and Finite Element-Volume methods.

Aldo Rene Zang (IMPA)
Title: BRDFs Evolution: from analytical models to measured data
Abstract: A fundamental problem in computer graphics rendering is modeling how lights is reflected from surfaces. A class of functions called Bidirectional Reflectance Distribution Functions (BRDFs) characterizes the process where light transport occurs at an idealized surface point. First we will talk a little bit about the physically inspired analytic reflection models that provide the BRDFs used in computer graphics today. Before talking about measured approaches for BRDFs we will talk about a change of variables for get a efficient BRDF representation introduced by Rusinkiewicz in 1998. We will talk too about the new approaches for measuring the BRDFs from real materials using the Rusinkiewicz parametrization, and techniques for constructing new BRDFs from measured data sets. Finally we will talk about a non-parametric Inverse Shade Tree (IST) framework for representing and editing measured spatially- and directionally-dependent surface appearance (SVBRDF). The IST framework allow us to edit a captured SVBRDF editing simples 1D and 2D functions in the leaves of the tree.

Leandro Cruz (IMPA)
Title: Fitting Subdivision Surfaces
Abstract: In this talk we will show how to fit a subdivision surface using the Quasi-Interpolation method. This method calculates the position of control points of a Catmul-Clark surface that better fit the given surface. It obtains an approximation of original surface with a desired accuracy, without need to solve a Linear System, like the Least-Square Method. Thus, this is a fast, local, and scale well algorithm. Its convergence rate is optimal for regular meshes and, empirically, was observed that it behave well for irregular meshes.

Francisco Ganacim (IMPA)
Title: Parametrization of Triangular Meshes using Angle-Based Flattening
Abstract: Computing a low distortion parameterization for a mesh is a key step in many algorithms (e.g. texture mapping). The distortion occurs when areas of high surface curvature are flattened. By cutting this areas, we can reduce the parameterization's distortion at the expense of introducing additional seams to the mesh. After eliminating the high distortion areas, we compute a low-distortion parameterization using the angles in the mesh. In this talk we are going to show how to compute the seams and the parameterization using two techniques: Seamster and ABF.

Andre Maximo (IMPA)
Title: M4G: A Surface Representation for Adaptive CPU-GPU Coupled Computation
Abstract: Discrete surfaces are represented in different ways depending on the application and the target computational domain. In this work, we explore a new surface representation, called Manifolds-for-GPUs (M4G), aiming at describing discrete surfaces with adaptive control of the resolution and combining the different computational granularities of the CPU and the GPU.

Maria Andrade, Leonardo Carvalho, Dalia Bonilla (IMPA)
Title: Fluid simulation on surfaces
Abstract: In this work, we show how to calculate the Navier-Stokes equations on a smooth surface, where we want to simulate a fluid flow. We used a parametrization of a Catmull-Clark surface, from which we calculate a metric that depends on its tangent vectors and use this metric to get the necessary differential operators to solve the problem. The Navier-Stokes equations are solved on a discretization of the surface, dealing with the transition of the fluid between the patches that form the surface.

Geovan Tavares
Title: On the Combinatorics of Implicit Manifolds
Abstract: Implicit manifolds have been at the forefront of geometric modeling for over 20 years now. Its use in mathematics is more than a century old and it is at the very definition of general manifolds. In this talk we will describe a combinatorics for implicit manifolds and its application to numerical methods in implicit differential equations. Along the talk we will point several unsolved problems on the mathematical and combinatorial aspects of implicit manifolds.

Jean Gallier
Title: The classification theorem for compact surfaces
Abstract: The classification theorem for compact surfaces is one of the great achievements of early 20th century mathematics. The statement of this theorem is quite intuitive but it took about sixty years until a rigorous proof was finally given by Brahana in 1921. Early versions of the classification theorem were given by Mobius in 1861, and by Jordfan in 1866. More definite proofs were given later by von Dyck in 1888 and Dehn and Heegaard in 1907. A complete and rigorous proof requires a significant amount of machinery. In this talk, we will give a guided tour of the proof, pointing out which tools from algebraic topology are needed. We will also give an abbreviated  history of the "proof", and briefly explain how the theorem leads to "global parametrizations," using fundamental domains.

Wolfgang Ziller
Title: Ricci Flow and the Uniformization Theorem
Abstract: The Ricci flow is a natural flow that changes a metric on a manifold to something that is "nicer". We will discuss some applications, in particular how one can use it to prove the uniformization theorem for surfaces.

Submission of contributors
Please send a one-page extended abstract of your presentation
in PDF format to until October 28th, 2011.
Submissions will be selected based on suitability to the event
and time limitations.