A Survey on Implicit Surface Polygonization

Implicit surfaces (IS) are commonly used in image creation, modeling environments, modeling objects, and scientific data visualization. In this article, we present a survey of different techniques for fast visualization of IS. The main classes of visualization algorithms are identified along with the advantages of each in the context of the different types of IS commonly used in computer graphics. We focus closely on polygonization methods, as they are the most suited to fast visualization. Classification and comparison of existing approaches are presented using criteria extracted from current research. This enables the identification of the best strategies according to the number of specific requirements, such as speed, accuracy, quality, or stylization.

[1]  James F. O'Brien,et al.  Shape transformation using variational implicit functions , 1999, SIGGRAPH Courses.

[2]  Roberto Scopigno,et al.  A modified look-up table for implicit disambiguation of Marching Cubes , 1994, The Visual Computer.

[3]  J. Sethian,et al.  FRONTS PROPAGATING WITH CURVATURE DEPENDENT SPEED: ALGORITHMS BASED ON HAMILTON-JACOB1 FORMULATIONS , 2003 .

[4]  Shengjun Liu,et al.  High quality triangulation of implicit surfaces , 2005, Ninth International Conference on Computer Aided Design and Computer Graphics (CAD-CG'05).

[5]  John Hart Morse Theory for Implicit Surface Modeling , 1997, VisMath.

[6]  Ronald Fedkiw,et al.  Level set methods and dynamic implicit surfaces , 2002, Applied mathematical sciences.

[7]  Gert Vegter,et al.  Isotopic approximation of implicit curves and surfaces , 2004, SGP '04.

[8]  Mario Botsch,et al.  Feature sensitive surface extraction from volume data , 2001, SIGGRAPH.

[9]  Dietmar Saupe,et al.  Interactive Visualization of Implicit Surfaces with Singularities , 1997, Comput. Graph. Forum.

[10]  Gregory M. Nielson,et al.  Dual marching cubes , 2004, IEEE Visualization 2004.

[11]  Alfred Gray,et al.  Modern differential geometry of curves and surfaces withmathematica , 1997 .

[12]  Bing-Yu Chen,et al.  Cubical Marching Squares: Adaptive Feature Preserving Surface Extraction from Volume Data , 2005, Comput. Graph. Forum.

[13]  Jules Bloomenthal,et al.  An Implicit Surface Polygonizer , 1994, Graphics Gems.

[14]  Gert Vegter,et al.  Isotopic meshing of implicit surfaces , 2006, The Visual Computer.

[15]  Markus Hadwiger,et al.  Real-time volume graphics , 2006, Eurographics.

[16]  Charles D. Hansen,et al.  Massively parallel isosurface extraction , 1992, Proceedings Visualization '92.

[17]  Richard K. Beatson,et al.  Reconstruction and representation of 3D objects with radial basis functions , 2001, SIGGRAPH.

[18]  J. Hughes,et al.  Rapid Approximate Silhouette Rendering Of Implicit Surfaces , 1998 .

[19]  Steve Oudot,et al.  Provably good sampling and meshing of surfaces , 2005, Graph. Model..

[20]  Michael Garland,et al.  Optimal triangulation and quadric-based surface simplification , 1999, Comput. Geom..

[21]  L. Formaggia,et al.  Shape reconstruction from medical images and quality mesh generation via implicit surfaces , 2007 .

[22]  Irina Voiculescu,et al.  Implicit Curves and Surfaces: Mathematics, Data Structures and Algorithms , 2009 .

[23]  Yongjian Xi,et al.  A novel region-growing based iso-surface extraction algorithm , 2008, Comput. Graph..

[24]  Weijun Liu,et al.  A Robust and Topological Correct Marching Cube Algorithm Without Look-Up Table , 2005, The Fifth International Conference on Computer and Information Technology (CIT'05).

[25]  Brian Wyvill,et al.  Shrinkwrap: An efficient adaptive algorithm for triangulating an iso-surface , 2004, The Visual Computer.

[26]  Brian Wyvill,et al.  Introduction to Implicit Surfaces , 1997 .

[27]  Raymond A Wildman,et al.  Postprocessing of Voxel-Based Topologies for Additive Manufacturing Using the Computational Geometry Algorithms Library (CGAL) , 2015 .

[28]  Afonso Paiva,et al.  Robust adaptive meshes for implicit surfaces , 2006, 2006 19th Brazilian Symposium on Computer Graphics and Image Processing.

[29]  Cláudio T. Silva,et al.  High-Quality Extraction of Isosurfaces from Regular and Irregular Grids , 2006, IEEE Transactions on Visualization and Computer Graphics.

[30]  Brian Wyvill,et al.  THE BLOB TREE- WARPING, BLENDING AND BOOLEAN OPERATIONS IN ANIMPLICIT SURFACE MODELING SYSTEM , 1998 .

[31]  William E. Lorensen,et al.  Marching cubes: A high resolution 3D surface construction algorithm , 1987, SIGGRAPH.

[32]  Alexander G. Belyaev,et al.  Detection of Surface Creases in Range Data , 2005, IMA Conference on the Mathematics of Surfaces.

[33]  Christophe Chaillou,et al.  Fast Polygonization of Implicit Surfaces , 2001, WSCG.

[34]  Václav Skala,et al.  Adaptive edge spinning algorithm for polygonization of implicit surfaces , 2004, Proceedings Computer Graphics International, 2004..

[35]  Z. H. Jiang,et al.  Tetrahedra Based Adaptive Polygonization of Implicit Surface Patches , 1999, Comput. Graph. Forum.

[36]  共立出版株式会社 コンピュータ・サイエンス : ACM computing surveys , 1978 .

[37]  Hans-Peter Seidel,et al.  3D scattered data interpolation and approximation with multilevel compactly supported RBFs , 2005, Graph. Model..

[38]  Benoît Crespin Dynamic triangulation of variational implicit surfaces using incremental Delaunay tetrahedralization , 2002, Symposium on Volume Visualization and Graphics, 2002. Proceedings. IEEE / ACM SIGGRAPH.

[39]  Vadim Shapiro,et al.  Semi-analytic geometry with R-functions , 2007, Acta Numerica.

[40]  Sundaresan Raman,et al.  Quality Isosurface Mesh Generation Using an Extended Marching Cubes Lookup Table , 2008, Comput. Graph. Forum.

[41]  Ken Brodlie,et al.  Improving the Robustness and Accuracy of the Marching Cubes Algorithm for Isosurfacing , 2003, IEEE Trans. Vis. Comput. Graph..

[42]  Peter Kipfer GPU Construction and Transparent Rendering of Iso-Surfaces , 2005 .

[43]  L. Paul Chew,et al.  Guaranteed-quality mesh generation for curved surfaces , 1993, SCG '93.

[44]  Cláudio T. Silva,et al.  Direct (Re)Meshing for Efficient Surface Processing , 2006, Comput. Graph. Forum.

[45]  Pierre Alliez,et al.  State of the Art in Surface Reconstruction from Point Clouds , 2014, Eurographics.

[46]  Kalpathi R. Subramanian,et al.  Interpolating implicit surfaces from scattered surface data using compactly supported radial basis functions , 2001, Proceedings International Conference on Shape Modeling and Applications.

[47]  H. Hege,et al.  A Generalized Marching Cubes Algorithm Based On Non-Binary Classifications , 1997 .

[48]  C.W.A.M. van Overveld,et al.  How to shrinkwrap a critical point : an algorithm for the adaptive triangulation of iso-surfaces with arbitrary topology , 1996 .

[49]  Xin Wang,et al.  Fast Visualization Algorithm for Implicit Surfaces , 2006, 16th International Conference on Artificial Reality and Telexistence--Workshops (ICAT'06).

[50]  V. Skala,et al.  POLYGONIZATION BY THE EDGE SPINNING , 2002 .

[51]  Dinesh Manocha,et al.  Reliable implicit surface polygonization using visibility mapping , 2006, SGP '06.

[52]  Andrea Bottino,et al.  How to Shrinkwrap through a Critical Point : an Algorithm for the Adaptive Triangulation of Iso-Surfaces with Arbitrary Topology , 1996 .

[53]  Leif Kobbelt,et al.  Feature sensitive mesh processing , 2003, SCCG '03.

[54]  Tosiyasu L. Kunii,et al.  Ridges and ravines on implicit surfaces , 1998, Proceedings. Computer Graphics International (Cat. No.98EX149).

[55]  Paul-Louis George,et al.  Meshing Implicit Curves and Surfaces , 2010 .

[56]  Brian Wyvill,et al.  Polygonization of Implicit Surfaces with Constructive solid Geometry , 1996, Int. J. Shape Model..

[57]  Pauline Jepp Using multi agent systems for illustrative rendering of implicit surfaces , 2007 .

[58]  B. Natarajan On generating topologically consistent isosurfaces from uniform samples , 1994, The Visual Computer.

[59]  Paul S. Heckbert,et al.  Using particles to sample and control implicit surfaces , 1994, SIGGRAPH.

[60]  Bernd Hamann,et al.  The asymptotic decider: resolving the ambiguity in marching cubes , 1991, Proceeding Visualization '91.

[61]  A. James Stewart,et al.  Curvature-Dependent Triangulation of Implicit Surfaces , 2001, IEEE Computer Graphics and Applications.

[62]  Mathieu Desbrun,et al.  Adaptive Sampling of Implicit Surfaces for Interactive Modelling and Animation , 1995, Comput. Graph. Forum.

[63]  James F. Blinn,et al.  A Generalization of Algebraic Surface Drawing , 1982, TOGS.

[64]  Daniel Simões Lopes,et al.  Tangent vectors to a 3-D surface normal: A geometric tool to find orthogonal vectors based on the Householder transformation , 2013, Comput. Aided Des..

[65]  Erich Hartmann,et al.  A marching method for the triangulation of surfaces , 1998, The Visual Computer.

[66]  Jules Bloomenthal,et al.  Polygonization of implicit surfaces , 1988, Comput. Aided Geom. Des..

[67]  Joaquim A. Jorge,et al.  Adaptive polygonization of implicit surfaces , 2005, Comput. Graph..

[68]  Per-Olof Persson,et al.  A Simple Mesh Generator in MATLAB , 2004, SIAM Rev..

[69]  Patrick Reuter Reconstruction and Rendering of Implicit Surfaces from Large Unorganized Point Sets , 2003 .

[70]  Leif Kobbelt,et al.  A survey of point-based techniques in computer graphics , 2004, Comput. Graph..

[71]  Brian Wyvill,et al.  Interactive implicit modeling with hierarchical spatial caching , 2005, International Conference on Shape Modeling and Applications 2005 (SMI' 05).

[72]  Shigeru Muraki,et al.  Volumetric shape description of range data using “Blobby Model” , 1991, SIGGRAPH.

[73]  Antonio A. F. Oliveira,et al.  Fast polygonization of variational implicit surfaces , 2004, Proceedings. 17th Brazilian Symposium on Computer Graphics and Image Processing.

[74]  I. Wald,et al.  Interactive Isosurface Ray Tracing of Large Octree Volumes , 2006, 2006 IEEE Symposium on Interactive Ray Tracing.

[75]  J. E. Glynn,et al.  Numerical Recipes: The Art of Scientific Computing , 1989 .

[76]  Roberto Scopigno,et al.  Discretized Marching Cubes , 1994, Proceedings Visualization '94.

[77]  Andrew H. Gee,et al.  Regularised marching tetrahedra: improved iso-surface extraction , 1999, Comput. Graph..

[78]  Alexander A. Pasko,et al.  Dynamic meshes for accurate polygonization of implicit surfaces with sharp features , 2001, Proceedings International Conference on Shape Modeling and Applications.

[79]  Hans-Peter Seidel,et al.  Multi-level partition of unity implicits , 2003, ACM Trans. Graph..

[80]  Jules Bloomenthal,et al.  Polygonization of non-manifold implicit surfaces , 1995, SIGGRAPH.

[81]  Yutaka Ohtake,et al.  Dual/Primal mesh optimization for polygonized implicit surfaces , 2002, SMA '02.

[82]  K. Klein,et al.  Adaptive Triangulation Of Objects Reconstructed From Multiple Range Images , 2001 .

[83]  Christian Rössl,et al.  Feature Sensitive Remeshing , 2001, Comput. Graph. Forum.

[84]  Anath Fischer,et al.  Anisotropic meshing of implicit surfaces , 2005, International Conference on Shape Modeling and Applications 2005 (SMI' 05).

[85]  Brian Wyvill,et al.  Polygonization of Implicit Surfaces on Multi-Core Architectures with SIMD Instructions , 2012, EGPGV@Eurographics.

[86]  John C. Hart,et al.  A programmable particle system framework for shape modeling , 2005, International Conference on Shape Modeling and Applications 2005 (SMI' 05).

[87]  Thomas Lewiner,et al.  Efficient Implementation of Marching Cubes' Cases with Topological Guarantees , 2003, J. Graphics, GPU, & Game Tools.

[88]  Yutaka Ohtake,et al.  GPU-based rendering of sparse low-degree implicit surfaces , 2006, GRAPHITE '06.

[89]  Ross T. Whitaker,et al.  Topology, Accuracy, and Quality of Isosurface Meshes Using Dynamic Particles , 2007, IEEE Transactions on Visualization and Computer Graphics.

[90]  Valerio Pascucci,et al.  Accelerated IsoContouring of Scalar Fields , 1998 .

[91]  Samir Akkouche,et al.  Adaptive Implicit Surface Polygonization Using Marching Triangles , 2001, Comput. Graph. Forum.

[92]  Thomas Ertl,et al.  Twofold adaptive partition of unity implicits , 2008, The Visual Computer.

[93]  Patrick Reuter,et al.  Anisotropic Sampling for Differential Point Rendering of Implicit Surfaces , 2005, WSCG.

[94]  Enrico O. Purisima,et al.  A new tetrahedral tesselation scheme for isosurface generation , 1998, Comput. Graph..

[95]  Abel J. P. Gomes,et al.  Polygonization of non-homogeneous non-manifold implicit surfaces with tentative topological guarantees , 2010, IEEE Congress on Evolutionary Computation.

[96]  Devendra Kalra,et al.  Guaranteed ray intersections with implicit surfaces , 1989, SIGGRAPH.

[97]  Alexander A. Pasko,et al.  Geometric modeling in the analysis of trivariate functions , 1988, Comput. Graph..

[98]  Mark Hall,et al.  Adaptive polygonalization of implicitly defined surfaces , 1990, IEEE Computer Graphics and Applications.

[99]  M. Cerm Ak,et al.  POLYGONIZATION BY THE EDGE SPINNING , 2002 .

[100]  Michael M. Kazhdan,et al.  Unconstrained isosurface extraction on arbitrary octrees , 2007, Symposium on Geometry Processing.

[101]  Robert B. Fisher,et al.  Edge-constrained marching triangles , 2002, Proceedings. First International Symposium on 3D Data Processing Visualization and Transmission.

[102]  Tao Ju,et al.  Manifold Dual Contouring , 2007, IEEE Transactions on Visualization and Computer Graphics.

[103]  Sergey V. Matveyev Approximation of isosurface in the Marching Cube: ambiguity problem , 1994, Proceedings Visualization '94.

[104]  Tamal K. Dey,et al.  Sampling and meshing a surface with guaranteed topology and geometry , 2004, SCG '04.

[105]  Zoë J. Wood,et al.  Isosurface Topology Simplification , 2002 .

[106]  Gregory M. Nielson,et al.  On Marching Cubes , 2003, IEEE Trans. Vis. Comput. Graph..

[107]  Paul Ning,et al.  An evaluation of implicit surface tilers , 1993, IEEE Computer Graphics and Applications.

[108]  Steven P. Callahan,et al.  A Survey of GPU-Based Volume Rendering of Unstructured Grids , 2005, RITA.

[109]  Laurent Rineau,et al.  A generic software design for Delaunay refinement meshing , 2007, Comput. Geom..

[110]  Hamish A. Carr,et al.  Accelerating marching cubes with graphics hardware , 2006, CASCON.

[111]  Raphaëlle Chaine,et al.  The HybridTree: Mixing skeletal implicit surfaces, triangle meshes, and point sets in a free-form modeling system , 2006, Graph. Model..

[112]  Gabriel Taubin,et al.  Smooth Signed Distance Surface Reconstruction and Applications , 2012, CIARP.

[113]  Neil A. Dodgson,et al.  Interactive Implicit Modelling Based on C1 Continuous Reconstruction of Regular Grids , 2002, Int. J. Shape Model..

[114]  Katsushi Ikeuchi,et al.  Non-manifold implicit surfaces based on discontinuous implicitization and polygonization , 2002, Geometric Modeling and Processing. Theory and Applications. GMP 2002. Proceedings.

[115]  Tosiyasu L. Kunii,et al.  Color ridges on implicit polynomial surfaces , 2003 .

[116]  Dinesh Manocha,et al.  Topology preserving surface extraction using adaptive subdivision , 2004, SGP '04.

[117]  Brian Wyvill,et al.  Pen‐and‐Ink for BlobTree Implicit Models , 2005, Comput. Graph. Forum.

[118]  Gabriel Taubin,et al.  SSD: Smooth Signed Distance Surface Reconstruction , 2011, Comput. Graph. Forum.

[119]  Joshua A. Levine,et al.  Delaunay Meshing of Isosurfaces , 2007, IEEE International Conference on Shape Modeling and Applications 2007 (SMI '07).

[120]  Alexei Sourin,et al.  Function representation in geometric modeling: concepts, implementation and applications , 1995, The Visual Computer.

[121]  E Chernyaev,et al.  Marching cubes 33 : construction of topologically correct isosurfaces , 1995 .

[122]  John C. Hart,et al.  Guaranteeing the topology of an implicit surface polygonization for interactive modeling , 1997, SIGGRAPH Courses.

[123]  Luiz Velho,et al.  Physically-based methods for polygonization of implicit surfaces , 1992 .

[124]  B. Mourrain,et al.  Meshing implicit algebraic surfaces : the smooth case , 2004 .

[125]  Brian Wyvill,et al.  Using Multi-agent Systems for Sampling and Rendering Implicit Surfaces , 2008, 2008 XXI Brazilian Symposium on Computer Graphics and Image Processing.

[126]  Tao Ju,et al.  Dual contouring of hermite data , 2002, ACM Trans. Graph..

[127]  Luiz Velho,et al.  Simple and Efficient Polygonization of Implicit Surfaces , 1996, J. Graphics, GPU, & Game Tools.

[128]  Marco Attene,et al.  Edge-Sharpener: Recovering Sharp Features in Triangulations of non-adaptively re-meshed surfaces , 2003, Symposium on Geometry Processing.

[129]  A. Edelman,et al.  Mesh generation for implicit geometries , 2005 .

[130]  Antoine Bouthors,et al.  Twinned meshes for dynamic triangulation of implicit surfaces , 2007, GI '07.

[131]  Luciana Porcher Nedel,et al.  Marching Cubes without Skinny Triangles , 2009, Computing in Science & Engineering.

[132]  Barton T. Stander,et al.  Interactive Re-Polygonization of Blobby Implicit Curves , 2007 .

[133]  Václav Skala,et al.  Polygonisation of disjoint implicit surfaces by the adaptive edge spinning algorithm of implicit objects , 2007, Int. J. Comput. Sci. Eng..

[134]  Adrian Hilton,et al.  Marching triangles: range image fusion for complex object modelling , 1996, Proceedings of 3rd IEEE International Conference on Image Processing.

[135]  Samir Akkouche,et al.  Incremental Polygonization of Implicit Surfaces , 2000, Graph. Model..

[136]  Jan J. Koenderink,et al.  Solid shape , 1990 .

[137]  Ron Goldman,et al.  Curvature formulas for implicit curves and surfaces , 2005, Comput. Aided Geom. Des..

[138]  Laurent Grisoni,et al.  Realtime visualization of implicit objects with contact control , 2003, GRAPHITE '03.

[139]  Patrick Reuter,et al.  Reconstructing multi-scale variational partition of unity implicit surfaces with attributes , 2006, Graph. Model..

[140]  Hans-Peter Seidel,et al.  Ridge-valley lines on meshes via implicit surface fitting , 2004, ACM Trans. Graph..

[141]  Scott Schaefer,et al.  Dual marching cubes: primal contouring of dual grids , 2004, 12th Pacific Conference on Computer Graphics and Applications, 2004. PG 2004. Proceedings..

[142]  Christian Sigg,et al.  Representation and rendering of implicit surfaces , 2006 .

[143]  Luiz Velho,et al.  Implicit Objects in Computer Graphics , 2002, Springer New York.

[144]  Dinesh Manocha,et al.  Feature-sensitive subdivision and isosurface reconstruction , 2003, IEEE Visualization, 2003. VIS 2003..

[145]  Aaron Knoll,et al.  Ray tracing implicit surfaces for interactive visualization , 2009 .

[146]  Luiz Velho,et al.  A unified approach for hierarchical adaptive tesselation of surfaces , 1999, TOGS.

[147]  Joaquim A. Jorge,et al.  A Calligraphic Interface for Interactive Free-Form Modeling with Large Datasets , 2005, XVIII Brazilian Symposium on Computer Graphics and Image Processing (SIBGRAPI'05).

[148]  Luciana Porcher Nedel,et al.  Edge Transformations for Improving Mesh Quality of Marching Cubes , 2009, IEEE Transactions on Visualization and Computer Graphics.