DOCSLIB.ORG

Automatic Higher Order Mesh Generation and Movement Utilizing Spring-Field and Vector-Adding

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Automatic Higher Order Mesh Generation and Movement Utilizing Spring-Field and Vector-Adding AUTOMATIC HIGHER ORDER MESH GENERATION AND MOVEMENT UTILIZING SPRING-FIELD AND VECTOR-ADDING By Tuo Liu C. Bruce Hilbert Kidambi Sreenivas Algorithms/Optimization Associate Professor of Branch Technology Mechanical Engineering (Chair) (Committee Member) James C. Newman III Steve L. Karman Jr. Professor of Computational Engineering Staff Specialist (Committee Member) Pointwise (Committee Member) AUTOMATIC HIGHER ORDER MESH GENERATION AND MOVEMENT UTILIZING SPRING-FIELD AND VECTOR-ADDING By Tuo Liu A Dissertation Submitted to the Faculty of the University of Tennessee at Chattanooga in Partial Fulfillment of the Requirements of the Degree of Doctor of Philosophy in Computational Engineering The University of Tennessee at Chattanooga Chattanooga, Tennessee December 2017 ii Copyright © 2017 By Tuo Liu All Rights Reserved iii ABSTRACT In this research, an automatic unstructured curved 2D mesh generation method is developed. It can handle complex geometries. Based on this 2D method, an extension to 3D geometries is developed. The methodology of this mesh generation is to provide near-body and off-body meshes by an advancing-layer method to avoid mesh quality problems in transition areas, while using spring models to complement the advancing-layers by smoothing the mesh, especially in medial axis regions. After generating the linear mesh, a higher-order finite-element ready, curved mesh is obtained by deforming the linear mesh through “pipes” using a simple Vector- Adding approach. Different from most curved viscous mesh generation approaches, this method eschews a linear or nonlinear elasticity analogy while still providing positive-Jacobian mesh elements. In addition, the transformation from linear to curved meshes can be achieved by only deforming the necessary edges of the elements near domain boundaries while retaining the remaining non-curved edges to the benefit of numerical solvers. The CFD results of 30P30N airfoil on the curved mesh are given and are in good agreement with the experimental data. Further, a new method for moving boundary problems with viscous mesh layers is also presented. This method is an extension of the mesh generation approach above. It can be used not only for high-order mesh moving but also for high-order mesh generation. Also, based on the curved mesh deformation strategy, the method can handle high-order mesh movement or regeneration with minimal extra computational time compared with linear mesh movement. Several 2D boundary motion cases are tested including boundary translations, boundary rotations, iv and boundary morphing. The CFD results on the curved mesh after rotation are given and are in good agreement with the experimental data. This technique is also tested through the optimization of an airfoil to achieve a maximized lift and drag ratio. The results demonstrate that this approach can handle large boundary movements while preserving a good mesh quality. v DEDICATION This dissertation is dedicated to my parents. Mom and Dad, I love you. vi ACKNOWLEDGMENTS I would like to express my special appreciation and thanks to my advisor Dr. C. Bruce Hilbert for devoting a great deal of time to answer my questions and offer suggestions, and his company Branch Technology for supporting him to do this. I also would like to express my gratitude to my previous advisors Dr. Li Wang and Dr. Steve Karman for their guidance and precious advice. Without their guidance and encouragement throughout my time as a graduate student, this work would not have been possible. I also thank my other committee members, Dr. Kidambi Sreenivas and Dr. James Newman for their guidance regarding this work. In addition, I would like to express my appreciation to Dr. Timothy Swafford for his support and for believing in me. My gratitude also goes to my wife Siman Wei. I cannot imagine sailing my vessel without her support and encouragement. Finally, I would like to thank all the teachers who impart knowledge to me, all my classmates with whom I study and play soccer and basketball, all the staff who offer me help and care, and all my friends, especially my friends in Chattanooga, who guided me towards more scenic lookout points when I hit the rocks. You light up my life. vii TABLE OF CONTENTS ABSTRACT ................................................................................................................................................. iv DEDICATION ............................................................................................................................................. vi ACKNOWLEDGMENTS .......................................................................................................................... vii LIST OF TABLES ....................................................................................................................................... xi LIST OF FIGURES .................................................................................................................................... xii LIST OF ABBREVIATIONS .................................................................................................................... xvi LIST OF SYMBOLS ................................................................................................................................ xvii CHAPTER I. INTRODUCTION ............................................................................................................................. 1 II. SPRING-FIELD AND VECTOR-ADDING ................................................................................... 11 2.1 Spring-Field ............................................................................................................................. 11 2.2 Vector-Adding ......................................................................................................................... 16 2.2.1 What is Vector-Adding? ................................................................................................ 16 2.2.2 Stop conditions ............................................................................................................. 19 III. 2D MESH GENERATION.............................................................................................................. 21 3.1 Boundary Mesh Generation Procedure .................................................................................... 22 3.1.1 Linear boundary mesh generation ................................................................................ 22 3.1.2 Curved boundary mesh generation .............................................................................. 25 3.1.3 Mesh results .................................................................................................................. 25 3.1.3.1 Bat Shape Geometry .......................................................................................... 26 3.1.3.2 30P30N airfoil ..................................................................................................... 27 3.2 Linear Domain Mesh Generation Procedure ........................................................................... 27 3.2.1 Procedure of the linear domain mesh generation ........................................................ 28 viii 3.2.2 Original AFSF method and mesh results ....................................................................... 30 3.2.2.1 Spring models ..................................................................................................... 30 3.2.2.2 Mesh results ....................................................................................................... 35 3.2.3 Improved AFSF method and mesh results .................................................................... 41 3.2.3.1 Two main adjustments ....................................................................................... 41 3.2.3.2 Mesh Results ...................................................................................................... 45 3.3 Curved Mesh Deformation Procedure ..................................................................................... 50 3.3.1 Positive Jacobian ........................................................................................................... 51 3.3.2 Mesh results .................................................................................................................. 55 3.3.3 CFD Results .................................................................................................................... 59 IV. 2D MESH MOVEMENT ................................................................................................................ 63 4.1 Further Adjustments in the Improved AFSF Method .............................................................. 63 4.2 Mesh Results ............................................................................................................................ 67 4.3 CFD Results ............................................................................................................................. 72 4.4 Optimization ............................................................................................................................ 76 V. 3D MESH GENERATION.............................................................................................................. 80 5.1 Boundary Surface Mesh Generation ........................................................................................ 82 5.2 Linear Domain Mesh Generation ............................................................................................
Load more

Recommended publications
  • Compression and Streaming of Polygon Meshes
    Compression and Streaming of Polygon Meshes by Martin Isenburg A dissertation submitted to the faculty of the University of North Carolina at Chapel Hill in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Computer Science. Chapel Hill 2005 Approved by: Jack Snoeyink, Advisor Craig Gotsman, Reader Peter Lindstrom, Reader Dinesh Manocha, Committee Member Ming Lin, Committee Member ii iii ABSTRACT MARTIN ISENBURG: Compression and Streaming of Polygon Meshes (Under the direction of Jack Snoeyink) Polygon meshes provide a simple way to represent three-dimensional surfaces and are the de-facto standard for interactive visualization of geometric models. Storing large polygon meshes in standard indexed formats results in files of substantial size. Such formats allow listing vertices and polygons in any order so that not only the mesh is stored but also the particular ordering of its elements. Mesh compression rearranges vertices and polygons into an order that allows more compact coding of the incidence between vertices and predictive compression of their positions. Previous schemes were designed for triangle meshes and polygonal faces were triangulated prior to compression. I show that polygon models can be encoded more compactly by avoiding the initial triangulation step. I describe two compression schemes that achieve better compression by encoding meshes directly in their polygonal representation. I demonstrate that the same holds true for volume meshes by extending one scheme to hexahedral meshes. Nowadays scientists create polygonal meshes of incredible size. Ironically, com- pression schemes are not capable|at least not on common desktop PCs|to deal with giga-byte size meshes that need compression the most.
    [Show full text]
  • Mesh Compression
    Mesh Compression Dissertation der Fakult¨at f¨ur Informatik der Eberhard-Karls-Universit¨at zu T¨ubingen zur Erlangung des Grades eines Doktors der Naturwissenschaften (Dr. rer. nat.) vorgelegt von Dipl.-Inform. Stefan Gumhold aus Tubingen¨ Tubingen¨ 2000 Tag der m¨undlichen Qualifikation: 19.Juli 2000 Dekan: Prof. Dr. Klaus-J¨orn Lange 1. Berichterstatter: Prof. Dr.-Ing. Wolfgang Straßer 2. Berichterstatter: Prof. Jarek Rossignac iii Zusammenfassung Die Kompression von Netzen ist eine weitgef¨acherte Forschungsrichtung mit Anwen- dungen in den verschiedensten Bereichen, wie zum Beispiel im Bereich der Hand- habung extrem großer Modelle, beim Austausch von dreidimensionalem Inhaltuber ¨ das Internet, im elektronischen Handel, als anpassungsf¨ahige Repr¨asentation f¨ur Vo- lumendatens¨atze usw. In dieser Arbeit wird das Verfahren der Cut-Border Machine beschrieben. Die Cut-Border Machine kodiert Netze, indem ein Teilbereich durch das Netz w¨achst (region growing). Kodiert wird die Art und Weise, wie neue Netzele- mente dem wachsenden Teilbereich einverleibt werden. Das Verfahren der Cut-Border Machine kann sowohl auf Dreiecksnetze als auch auf Tetraedernetze angewendet wer- den. Trotz der einfachen Struktur des Verfahrens kann eine sehr hohe Kompression- srate erzielt werden. Im Falle von Tetraedernetzen erreicht die Cut-Border Machine die beste Kompressionsrate von allen bekannten Verfahren. Die einfache Struktur der Cut-Border Machine erm¨oglicht einerseits die Realisierung direkt in Hardware und ist auch als Implementierung in Software extrem schnell. Auf der anderen Seite erlaubt die Einfachheit eine theoretische Analyse des Algorithmus. Gezeigt werden konnte, dass f¨ur ebene Triangulierungen eine leicht modifizierte Version der Cut-Border Machine lineare Laufzeiten in der Zahl der Knoten erzielt und dass die komprimierte Darstellung nur linearen Speicherbedarf ben¨otigt, d.h.
    [Show full text]
  • From Segmented Images to Good Quality Meshes Using Delaunay Refinement
    Mesh generation Applications CGAL-mesh From Segmented Images to Good Quality Meshes using Delaunay Refinement Jean-Daniel Boissonnat INRIA Sophia-Antipolis Geometrica Project-Team Emerging Trends in Visual Computing From Segmented Images to Good Quality Meshes Grid-based methods (MC and variants) I Produces unnecessarily large meshes I Regularization and decimation are difficult tasks I Imposes dominant axis-aligned edges Mesh generation Applications CGAL-mesh A determinant step towards numerical simulations Challenges I Quality of the mesh : accurary, topological correctness, size and shape of the elements I Number of elements, processing time I Robustness issues Emerging Trends in Visual Computing From Segmented Images to Good Quality Meshes Mesh generation Applications CGAL-mesh A determinant step towards numerical simulations Challenges I Quality of the mesh : accurary, topological correctness, size and shape of the elements I Number of elements, processing time I Robustness issues Grid-based methods (MC and variants) I Produces unnecessarily large meshes I Regularization and decimation are difficult tasks I Imposes dominant axis-aligned edges Emerging Trends in Visual Computing From Segmented Images to Good Quality Meshes Mesh generation Applications CGAL-mesh Affine Voronoi diagrams and Delaunay triangulations Emerging Trends in Visual Computing From Segmented Images to Good Quality Meshes Mesh generation Applications CGAL-mesh Mesh generation by Delaunay refinement A simple greedy technique that goes back to the early 80’s [Frey, Hermeline]
    [Show full text]
  • Polyhedral Mesh Generation and a Treatise on Concave Geometrical Edges
    Available online at www.sciencedirect.com ScienceDirect Procedia Engineering 124 ( 2015 ) 174 – 186 24th International Meshing Roundtable (IMR24) Polyhedral Mesh Generation and A Treatise on Concave Geometrical Edges Sang Yong Leea,* aKEPCO International Nuclear Graduate School, 658-91 Haemaji-ro Seosaeng-myeon Ulju-gun, Ulsan 689-882, Republic of Korea Abstract Three methods are investigated to remove the concavity at the boundary edges and/or vertices during polyhedral mesh generation by a dual mesh method. The non-manifold elements insertion method is the first method examined. Concavity can be removed by inserting non-manifold surfaces along the concave edges and using them as an internal boundary before applying Delaunay mesh generation. Conical cell decomposition/bisection is the second method examined. Any concave polyhedral cell is decomposed into polygonal conical cells first, with the polygonal primal edge cut-face as the base and the dual vertex on the boundary as the apex. The bisection of the concave polygonal conical cell along the concave edge is done. Finally the cut-along-concave-edge method is examined. Every concave polyhedral cell is cut along the concave edges. If a cut cell is still concave, then it is cut once more. The first method is very promising but not many mesh generators can handle the non-manifold surfaces especially for complex geometries. The second method is applicable to any concave cell with a rather simple procedure but the decomposed cells are too small compared to neighbor non-decomposed cells. Therefore, it may cause some problems during the numerical analysis application. The cut-along-concave-edge method is the most viable method at this time.
    [Show full text]
  • Tetrahedral Meshing in the Wild
    Tetrahedral Meshing in the Wild YIXIN HU, New York University QINGNAN ZHOU, Adobe Research XIFENG GAO, New York University ALEC JACOBSON, University of Toronto DENIS ZORIN, New York University DANIELE PANOZZO, New York University Fig. 1. A selection of the ten thousand meshes in the wild tetrahedralized by our novel tetrahedral meshing technique. We propose a novel tetrahedral meshing technique that is unconditionally Additional Key Words and Phrases: Mesh Generation, Tetrahedral Meshing, robust, requires no user interaction, and can directly convert a triangle soup Robust Geometry Processing into an analysis-ready volumetric mesh. The approach is based on several core principles: (1) initial mesh construction based on a fully robust, yet ACM Reference Format: eicient, iltered exact computation (2) explicit (automatic or user-deined) Yixin Hu, Qingnan Zhou, Xifeng Gao, Alec Jacobson, Denis Zorin, and Daniele tolerancing of the mesh relative to the surface input (3) iterative mesh Panozzo. 2018. Tetrahedral Meshing in the Wild . ACM Trans. Graph. 37, 4, improvement with guarantees, at every step, of the output validity. The Article 1 (August 2018), 14 pages. https://doi.org/10.1145/3197517.3201353 quality of the resulting mesh is a direct function of the target mesh size and allowed tolerance: increasing allowed deviation from the initial mesh and 1 INTRODUCTION decreasing the target edge length both lead to higher mesh quality. Our approach enables łblack-boxž analysis, i.e. it allows to automatically Triangulating the interior of a shape is a fundamental subroutine in solve partial diferential equations on geometrical models available in the 2D and 3D geometric computation.
    [Show full text]
  • A Parallel Mesh Generator in 3D/4D
    Portland State University PDXScholar Portland Institute for Computational Science Publications Portland Institute for Computational Science 2018 A Parallel Mesh Generator in 3D/4D Kirill Voronin Portland State University, [email protected] Follow this and additional works at: https://pdxscholar.library.pdx.edu/pics_pub Part of the Theory and Algorithms Commons Let us know how access to this document benefits ou.y Citation Details Voronin, Kirill, "A Parallel Mesh Generator in 3D/4D" (2018). Portland Institute for Computational Science Publications. 11. https://pdxscholar.library.pdx.edu/pics_pub/11 This Pre-Print is brought to you for free and open access. It has been accepted for inclusion in Portland Institute for Computational Science Publications by an authorized administrator of PDXScholar. Please contact us if we can make this document more accessible: [email protected]. A parallel mesh generator in 3D/4D∗ Kirill Voronin Portland State University [email protected] Abstract In the report a parallel mesh generator in 3d/4d is presented. The mesh generator was developed as a part of the research project on space-time discretizations for partial differential equations in the least-squares setting. The generator is capable of constructing meshes for space-time cylinders built on an arbitrary 3d space mesh in parallel. The parallel implementation was created in the form of an extension of the finite element software MFEM. The code is publicly available in the Github repository [1]. Introduction Finite element method is nowadays a common approach for solving various application problems in physics which is known first of all for its easy-to-implement methodology.
    [Show full text]
  • Polyhedral Mesh Generation
    POLYHEDRAL MESH GENERATION W. Oaks1, S. Paoletti2 adapco Ltd, 60 Broadhollow Road, Melville 11747 New York, USA [email protected], [email protected] ABSTRACT A new methodology to generate a hex-dominant mesh is presented. From a closed surface and an initial all-hex mesh that contains the closed surface, the proposed algorithm generates, by intersection, a new mostly-hex mesh that includes polyhedra located at the boundary of the geometrical domain. The polyhedra may be used as cells if the field simulation solver supports them or be decomposed into hexahedra and pyramids using a generalized mid-point-subdivision technique. This methodology is currently used to provide hex-dominant automatic mesh generation in the preprocessor pro*am of the CFD code STAR-CD. Keywords: mesh generation, polyhedra, hexahedra, mid-point-subdivision, computational geometry. 1. INTRODUCTION to create a mesh that satisfies the boundary constraint, while the second family does not require a quadrilateral In the past decade automatic mesh generation has received surface mesh. Its creation becomes part of the generation significant attention from researchers both in academia and process. in the industry with the result of considerable advances in The first family of methodologies such as spatial twist understanding the underlying topological and geometrical continuum STC and related whisker weaving [1], properties of meshes. hexahedral advancing-front [2], rely on a proof of existence Most of the practical methodologies that have been [3],[4] for combinatorial hexahedral meshes whose only developed rely on using simplical cells such as triangles in requirement is an even number of quadrilaterals on the 2D and tetrahedra in 3D, due to the availability of relatively boundary surface.
    [Show full text]
  • Topological Issues in Hexahedral Meshing
    Topological Issues in Hexahedral Meshing David Eppstein Univ. of California, Irvine Dept. of Information and Computer Science Topological issues in hexahedral meshing D. Eppstein, UC Irvine, ATMCS 2001 Outline I. What is meshing? Problem statement — Types of mesh — Quality issues — Duality II. What can we mesh? Necessary conditions — Sufficient conditions for topological mesh — Geometric existence problem — bicuboid III. How well can we mesh? Mesh complexity — Provable quality IV. How can we make our meshes better? Point placement — topological changes — flipping — flip graph connectivity — bicuboid revisited Topological issues in hexahedral meshing D. Eppstein, UC Irvine, ATMCS 2001 I. What is Meshing? Given an input domain (manifold with boundary or possibly non-manifold geometry) Partition it into simple cells (triangles, quadrilaterals, tetrahedra, cuboids) Essential preprocessing step for finite element method (numerical solution of differential equations e.g. airflow) Other applications e.g. computer graphics Topological issues in hexahedral meshing D. Eppstein, UC Irvine, ATMCS 2001 Triangle mesh of Lake Superior [Ruppert] Topological issues in hexahedral meshing D. Eppstein, UC Irvine, ATMCS 2001 Quadrilateral mesh of an irregular polygon (all quadrilaterals kite-shaped) Topological issues in hexahedral meshing D. Eppstein, UC Irvine, ATMCS 2001 Triangle mesh on three-dimensional surface [Chew] Topological issues in hexahedral meshing D. Eppstein, UC Irvine, ATMCS 2001 Tetrahedral mesh of a cube Topological issues in hexahedral
    [Show full text]
  • Parallel Adaptive Mesh Generation and Decomposition
    Purdue University Purdue e-Pubs Department of Computer Science Technical Reports Department of Computer Science 1995 Parallel Adaptive Mesh Generation and Decomposition Poting Wu Elias N. Houstis Purdue University, [email protected] Report Number: 95-012 Wu, Poting and Houstis, Elias N., "Parallel Adaptive Mesh Generation and Decomposition" (1995). Department of Computer Science Technical Reports. Paper 1190. https://docs.lib.purdue.edu/cstech/1190 This document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact [email protected] for additional information. PARALLEL ADAPTIVE MESH GENERAnON AND DECOMPOSITION Poling Wu Elias N. HOlISm Department of Computer Sciences Purdue University West Lafayette, IN 47907 CSD·TR·9S..()12 February 1995 Parallel Adaptive Mesh Generation and Decomposition Poting Wu and Elias N. Houstis Department of Computer Sciences Purdue University West Lafayette, Indiana 47907-1398, U.S.A. e-mail: [email protected] October, 1994 Abstract An important class of methodologies for the parallel processing of computational models defined on some discrete geometric data structures (i.e., meshes, grids) is the so called geometry decomposition or splitting approach. Compared to the sequential processing of such models, the geometry splitting parallel methodology requires an additional computational phase. It consists of the decomposition of the associated geometric data structure into a number of balanced subdomains that satisfy a number of conditions that ensure the load balancing and minimum communication requirement of the underlying computations on a parallel hardware platform. It is well known that the implementation of the mesh decomposition phase requires the solution of a computationally intensive problem.
    [Show full text]
  • Computational Meshing for CFD Simulations
    Chapter 6 Computational Meshing for CFD Simulations Andreas Lintermann1 The original article is available under https://10.1007/978-981-15-6716-2_6 Abstract In computational fluid dynamics modelling, small cells or elements are created to fill the volume to simulate the flow in. They constitute a mesh where each cell represents a discrete space that represents the flow locally. Mathematical equations that represent the flow physics are then applied to each cell of the mesh. Generating a high quality mesh is extremely important to obtain reliable solutions and to guarantee numerical stability. This chapter begins with a basic introduction to a typical workflow and guidelines for generating high quality meshes, and concludes with some more advanced topics, i.e., how to generate meshes in parallel, a discussion on mesh quality, and examples on the application of lattice-Boltzmann methods to simulate flow without any turbulence modelling on highly-resolved meshes. 6.1 Introduction The segmented airway region from CT/MRI scans provides surface boundary informa- tion (see Chapter 5). The internal space, where inhaled air or particles pass through, is an enclosed volume formed by the surface boundaries. In computational fluid dynamics CFD modelling, small cells or elements are created to fill this volume. They constitute a mesh and thereby discretise the space. The mathematical equations that represent the flow physics (Chapter 6, and 7) are then applied to each cell of the mesh. The end result is the ability to store time-dependent flow properties such as pressure, velocity, or temperature in each individual cell. 1A. Lintermann Forschungszentrum Jülich GmbH email:[email protected] 85 86 CHAPTER 6.
    [Show full text]
  • Variational Tetrahedral Mesh Generation from Discrete Volume Data Julien Dardenne, Sébastien Valette, Nicolas Siauve, Noël Burais, Rémy Prost
    Variational tetrahedral mesh generation from discrete volume data Julien Dardenne, Sébastien Valette, Nicolas Siauve, Noël Burais, Rémy Prost To cite this version: Julien Dardenne, Sébastien Valette, Nicolas Siauve, Noël Burais, Rémy Prost. Variational tetrahedral mesh generation from discrete volume data. The Visual Computer, Springer Verlag, 2009, 25 (5), pp.401-410. hal-00537029 HAL Id: hal-00537029 https://hal.archives-ouvertes.fr/hal-00537029 Submitted on 17 Nov 2010 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Noname manuscript No. (will be inserted by the editor) Variational tetrahedral mesh generation from discrete volume data J. Dardenne · S. Valette · N. Siauve · N. Burais · R. Prost the date of receipt and acceptance should be inserted later Abstract In this paper, we propose a novel tetrahedral mesh measured in terms of minimal dihedral angle. Indeed, the ac- generation algorithm, which takes volumic data (voxels) as curacy and convergence speed of a FEM-based simulation an input. Our algorithm performs a clustering of the origi- depends on the mesh objective quality. As a consequence, a nal voxels within a variational framework. A vertex replaces lot of research was carried out on the topic of mesh gener- each cluster and the set of created vertices is triangulated in ation.
    [Show full text]
  • From Triangulation to Simplex Mesh: a Simple and Efficient
    From Triangulation to Simplex Mesh: a Simple and Efficient Transformation Francisco J. GALDAMESa;c, Fabrice JAILLETb;c (a) Department of Electrical Engineering, Universidad de Chile, Av. Tupper 2007, Santiago, Chile (b) Universit´ede Lyon, IUT Lyon 1, D´epartement Informatique, F-01000, France (c) Universit´ede Lyon, CNRS, Universit´eLyon 1, LIRIS, ´equipe SAARA, UMR5205, F-69622, France Preprint { April 2010 Abstract In the field of 3D images, relevant information can be difficult to in- terpret without further computer-aided processing. Generally, and this is particularly true in medical imaging, a segmentation process is run and coupled with a visualization of the delineated structures to help un- derstanding the underlying information. To achieve the extraction of the boundary structures, deformable models are frequently used tools. Amongst all techniques, Simplex Meshes are valuable models thanks to their good propensity to handle a large variety of shape alterations alto- gether with a fine resolution and stability. However, despite all these great characteristics, Simplex Meshes are lacking to cope satisfyingly with other related tasks, as rendering, mechanical simulation or reconstruction from iso-surfaces. As a consequence, Triangulation Meshes are often preferred. In order to face this problem, we propose an accurate method to shift from a model to another, and conversely. For this, we are taking advantage of the fact that triangulation and simplex meshes are topologically duals, turning it into a natural swap between these two models. A difficulty arise as they are not geometrically equivalent, leading to loss of informa- tion and to geometry deterioration whenever a transformation between these dual meshes takes place.
    [Show full text]