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"Damiand, Guillaume"
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Combinatorial maps : efficient data structures for computer graphics and image processing
\"Although they are less widely known than other models, combinatorial maps are very powerful data structures and can be useful in many applications, including computer graphics and image processing. The book introduces these data structures, describes algorithms and data structures associated with them, makes connections to other common structures, and demonstrates how to use these structures in geometric modeling and image processing. The data structures and algorithms introduced in the book will be available in a C++ library on the authors' website\"-- Provided by publisher.
Book
Combinatorial Maps
This book gathers important ideas related to combinatorial maps and explains how the maps are applied in geometric modeling and image processing. It focuses on two subclasses of combinatorial maps: n-Gmaps and n-maps. The book presents the data structures, operations, and algorithms that are useful in handling subdivided geometric objects. It shows how to study data structures for the explicit representation of subdivided geometric objects and describes operations for handling the structures. The book also illustrates results of the design of data structures and operations.
eBook
Distributed Combinatorial Maps for Parallel Mesh Processing
We propose a new strategy for the parallelization of mesh processing algorithms. Our main contribution is the definition of distributed combinatorial maps (called n-dmaps), which allow us to represent the topology of big meshes by splitting them into independent parts. Our mathematical definition ensures the global consistency of the meshes at their interfaces. Thus, an n-dmap can be used to represent a mesh, to traverse it, or to modify it by using different mesh processing algorithms. Moreover, an nD mesh with a huge number of elements can be considered, which is not possible with a sequential approach and a regular data structure. We illustrate the interest of our solution by presenting a parallel adaptive subdivision method of a 3D hexahedral mesh, implemented in a distributed version. We report space and time performance results that show the interest of our approach for parallel processing of huge meshes.
Journal Article
Generic volume transfer for distributed mesh dynamic repartitioning
Efficient and distributed adaptive mesh construction and editing pose several challenges, including selecting the appropriate distributed data structure, choosing strategies for distributing computational load, and managing inter-processor communication. Distributed Combinatorial Maps permit the representation and editing of distributed 3D meshes. This paper addresses computation load and expands communication aspects through volume transfer operation and repartitioning strategies. This work is the first one defining such transfer for cells of any topology. We demonstrate the benefits of our method by presenting a parallel adaptive hexahedral subdivision operation, involving fully generic volumes, in a process including a conversion to conformal mesh and surface fitting. Our experiments compare different strategies using multithreading and MPI implementations to highlight the benefits of volume transfer. Special attention has been paid to generic aspects and adaptability of the framework.
Journal Article
High-order elements in position-based dynamics
The simulation of deformable objects has been the subject of a great deal of work in the field of computer graphics. The constraint-based PBD (Position-Based Dynamics) approach has been proven to be effective in this field for real-time and stable deformable objects simulation. Finite element method with linear tetrahedron discretization is the most widely used in computer graphics despite producing less accurate results than hexahedral or higher-order elements. In this context, our proposal is to integrate higher degree elements within the
pbd
framework. In addition, we propose a solution to improve convergence of unstable energies (like Neo-Hooke) when used as constraints. We show that our approach improves accuracy compared to linear tetrahedra. We also highlight the time savings, since fewer elements are needed.
Journal Article
Stripped halfedge data structure for parallel computation of arrangements of segments
Computing an arrangement of segments with some geometrical and topological guarantees is a critical step in many geometry processing applications. In this paper, we propose a method to efficiently compute arrangements of segments using a strip-based data structure. Thanks to this new data structure, the arrangement computation algorithm can easily be parallelized as the per strip computations are independent. Another interest of our approach is that we can propose an out-of-core and streamed construction for large datasets, while keeping a low memory footprint. We prove the correctness of our structure and provide a complete comparative evaluation with respect to state-of-the-art demonstrating the interest of our construction for the computation of an exact arrangement.
Journal Article
Hybrid 3D mass-spring system for simulation of isotropic materials with any Poisson’s ratio
Mass-spring systems (MSS) simulating elastic materials obey constraints known in elasticity as the
Cauchy relations
, restricting the Poisson ratio of isotropic systems to be exactly
ν
=
1
/
4
. We remind that this limitation is intrinsic to centrosymmetric spring systems (where each node is a center of symmetry), forbidding them for instance to simulate incompressible materials (with
ν
=
1
/
2
). To overcome this restriction, we propose to supplement the spring deformation energy with an energy depending on the volume only, insensitive to change of shape, permitting MSS to simulate any real isotropic materials. In addition, the freedom in choosing the spring constants realizing a given elastic behavior allows to manage instabilities. The proposed hybrid model is evaluated by comparing its response to various deformation geometries with analytical model and/or finite element model. The results show that the hybrid MSS model allows to simulate any compressible isotropic elastic material and in particular the nearly incompressible (Poisson ratio
ν
≃
1
/
2
) biological soft tissues to which it is dedicated.
Journal Article
Combinatorial Maps
A Versatile Framework for Handling Subdivided Geometric ObjectsCombinatorial Maps: Efficient Data Structures for Computer Graphics and Image Processing gathers important ideas related to combinatorial maps and explains how the maps are applied in geometric modeling and image processing. It focuses on two subclasses of combinatorial maps: n-Gmaps and n-maps.Suitable for researchers and graduate students in geometric modeling, computational and discrete geometry, computer graphics, and image processing and analysis, the book presents the data structures, operations, and algorithms that are useful in handling subdivided geometric objects. It shows how to study data structures for the explicit representation of subdivided geometric objects and describes operations for handling the structures. The book also illustrates results of the design of data structures and operations.
eBook
Homology of Cellular Structures Allowing Multi-incidence
This paper focuses on homology computation over ‘cellular’ structures that allow multi-incidence between cells. We deal here with combinatorial maps, more precisely chains of maps and subclasses such as maps and generalized maps. Homology computation on such structures is usually achieved by computing simplicial homology on a simplicial analog. But such an approach is computationally expensive because it requires computing this simplicial analog and performing the homology computation on a structure containing many more cells (simplices) than the initial one. Our work aims at providing a way to compute homologies directly on a cellular structure. This is done through the computation of incidence numbers. Roughly speaking, if two cells are incident, then their incidence number characterizes how they are attached. Having these numbers naturally leads to the definition of a boundary operator, which induces a homology. Hence, we propose a boundary operator for chains of maps and provide optimization for maps and generalized maps. It is proved that, under specific conditions, the homology of a combinatorial map as defined in the paper is equivalent to the homology of its simplicial analogue.
Journal Article