{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,16]],"date-time":"2026-05-16T08:54:16Z","timestamp":1778921656797,"version":"3.51.4"},"publisher-location":"Berlin, Heidelberg","reference-count":93,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783540708223","type":"print"},{"value":"9783540708230","type":"electronic"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2007]]},"DOI":"10.1007\/978-3-540-70823-0_1","type":"book-chapter","created":{"date-parts":[[2007,5,24]],"date-time":"2007-05-24T00:52:26Z","timestamp":1179967946000},"page":"1-19","source":"Crossref","is-referenced-by-count":118,"title":["Topology-Based Flow Visualization, The State of the Art"],"prefix":"10.1007","author":[{"given":"Robert S.","family":"Laramee","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Helwig","family":"Hauser","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lingxiao","family":"Zhao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Frits H.","family":"Post","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"1_CR1_Ref","unstructured":"R. H. Abraham and C. D. Shaw. \u00a0Dynamics - the Geometry of Behavior. Addison-Wesley, 1992."},{"key":"1_CR2_Ref","doi-asserted-by":"crossref","unstructured":"D. C. Banks and B. A. Singer. Vortex Tubes in Turbulent Flows: Identification, Representation, Reconstruction. In Proceedings IEEE Visualization \u201994, pages 132-139, October 1994.","DOI":"10.1109\/VISUAL.1994.346327"},{"issue":"2","key":"1_CR3_Ref","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1109\/2945.468404","volume":"1","author":"D. C. Banks","year":"1995","unstructured":"D. C. Banks and B. A. Singer. A Predictor-Corrector Technique for Visualizing Unsteady Flow. IEEE Transactions on Visualization and Computer Graphics, 1(2):151-163, June 1995.","journal-title":"IEEE Transactions on Visualization and Computer Graphics"},{"key":"1_CR4_Ref","unstructured":"D. Bauer and R. Peikert. Vortex Tracking in Scale-Space. In Proceedings of the Symposium on Data Visualisation 2002, pages 233-240. Eurographics Association, 2002."},{"key":"1_CR5_Ref","doi-asserted-by":"crossref","unstructured":"P.-T. Bremer, H. Edelsbrunner, B. Hamann, and V. Pascucci. A Multi-resolution Data Structure for Two-Dimensional Morse-Smale Functions. In Proceedings IEEE Visualization 2003, pages 139-146, October 2003.","DOI":"10.1109\/VISUAL.2003.1250365"},{"issue":"4","key":"1_CR6_Ref","doi-asserted-by":"publisher","first-page":"385","DOI":"10.1109\/TVCG.2004.3","volume":"10","author":"P.-T. Bremer","year":"2004","unstructured":"P.-T. Bremer, H. Edelsbrunner, B. Hamann, and V. Pascucci. \u00a0Topological Hierarchy for Functions on Triangulated Surfaces. IEEE Transactions on Visualization and Computer Graphics, 10(4):385-396, July\/Aug 2004.","journal-title":"IEEE Transactions on Visualization and Computer Graphics"},{"key":"1_CR7_Ref","doi-asserted-by":"crossref","unstructured":"C. Carner, M. Jin, X. Gu, and H. Qiu. \u00a0Topology-driven Surface Mappings with Robust Feature Alignment. In Proceedings IEEE Visualization 2005, pages 543-550, October 2005.","DOI":"10.1109\/VISUAL.2005.1532840"},{"key":"1_CR8_Ref","doi-asserted-by":"crossref","unstructured":"W. de Leeuw and R. van Liere. Visualization of Global Flow Structures Using Multiple Levels of Topology. In Data Visualization \u201999 (VisSym \u201999), pages 45-52. May 1999.","DOI":"10.1007\/978-3-7091-6803-5_5"},{"issue":"3","key":"1_CR9_Ref","doi-asserted-by":"publisher","first-page":"325","DOI":"10.1016\/S0097-8493(00)00028-5","volume":"24","author":"W. de Leeuw","year":"2000","unstructured":"W. de Leeuw and R. van Liere. Multi-level Topology for Flow Visualization. Computers and Graphics, 24(3):325-331, June 2000.","journal-title":"Computers and Graphics"},{"key":"1_CR10_Ref","doi-asserted-by":"crossref","unstructured":"W. C. de Leeuw and R. van Liere. Collapsing Flow Topology Using Area Metrics. In Proceedings IEEE Visualization \u201999, pages 349-354, 1999.","DOI":"10.1109\/VISUAL.1999.809907"},{"key":"1_CR11_Ref","doi-asserted-by":"crossref","unstructured":"T. Delmarcelle and L. Hesselink. The Topology of Symmetric, Second-Order Tensor Fields. In Proceedings IEEE Visualization \u201994, 1994.","DOI":"10.1109\/VISUAL.1994.346326"},{"key":"1_CR12_Ref","unstructured":"H. Doleisch, M. Mayer, M. Gasser, P. Priesching, and H. Hauser. Interactive Feature Specification for Simulation Data on Time-Varying Grids. In Conference on Simulation and Visualization 2005 (SimVis 2005), pages 291-304, 2005."},{"key":"1_CR13_Ref","doi-asserted-by":"crossref","unstructured":"J. El-Sana and A. Varshney. Controlled Simplification of Genus for Polygonal Models. In Proceedings IEEE Visualization \u201997, pages 403-412, October 1997.","DOI":"10.1109\/VISUAL.1997.663909"},{"key":"1_CR14_Ref","unstructured":"C. Garth, X. Tricoche, T. Salzbrunn, T. Bobach, and G. Scheuermann. Surface Techniques for Vortex Visualization. In Data Visualization, Proceedings of the 6th Joint IEEE TCVG-EUROGRAPHICS Symposium on Visualization (VisSym 2004), pages 155-164, May 2004."},{"key":"1_CR15_Ref","doi-asserted-by":"crossref","unstructured":"C. Garth, X. Tricoche, and G. Scheuermann. Tracking of Vector Field Singularities in Unstructured 3D Time-Dependent Datasets. In Proceedings IEEE Visualization 2004, pages 329-335, 2004.","DOI":"10.1109\/VISUAL.2004.107"},{"key":"1_CR16_Ref","unstructured":"I. Guskov and Z. Wood. Topological Noise Removal. In Proceedings, Graphics Interface 2001, pages 19-26, 2001."},{"key":"1_CR17_Ref","doi-asserted-by":"crossref","unstructured":"A. Gyulassy, V. Natarajan, V. Pascucci, P.-T. Bremer, and B. Hamann. Topology-based Simplification for Feature Extraction from 3D Scalar Fields. In Proceedings IEEE Visualization 2005, pages 535-542, 2005.","DOI":"10.1109\/VISUAL.2005.1532839"},{"key":"1_CR18_Ref","doi-asserted-by":"crossref","unstructured":"R. Haimes and D. Kenwright. \u00a0On the Velocity Gradient Tensor and Fluid Feature Extraction. Technical Report AIAA Paper 99-3288, American Institute of Aeronautics and Astronautics, 1999.","DOI":"10.2514\/6.1999-3288"},{"issue":"1","key":"1_CR19_Ref","doi-asserted-by":"publisher","first-page":"28","DOI":"10.1016\/0734-189X(83)90094-4","volume":"22","author":"R. M. Haralick","year":"1983","unstructured":"R. M. Haralick. Ridges and valleys on digital images. Computer Vision, Graphics, and Image Processing, 22(1):28-38, April 1983.","journal-title":"Computer Vision, Graphics, and Image Processing"},{"key":"1_CR20_Ref","doi-asserted-by":"crossref","unstructured":"B. Heckel, G. H. Weber, B. Hamann, and K. I. Joy. Construction of vector field hierarchies. In Proceedings IEEE Visualization \u201999, pages 19-26, 1999.","DOI":"10.1109\/VISUAL.1999.809863"},{"issue":"8","key":"1_CR21_Ref","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1109\/2.35197","volume":"22","author":"J. L. Helman","year":"1989","unstructured":"J. L. Helman and L. Hesselink. Representation and Display of Vector Field Topology in Fluid Flow Data Sets. IEEE Computer, 22(8):27-36, August 1989.","journal-title":"IEEE Computer"},{"key":"1_CR22_Ref","doi-asserted-by":"crossref","unstructured":"J. L. Helman and L. Hesselink. Surface Representations of Two- and ThreeDimensional Fluid Flow Topology. In Proceedings IEEE Visualization \u201990, pages 6-13, 1990.","DOI":"10.1109\/VISUAL.1990.146359"},{"issue":"3","key":"1_CR23_Ref","doi-asserted-by":"publisher","first-page":"36","DOI":"10.1109\/38.79452","volume":"11","author":"J. L. Helman","year":"1991","unstructured":"J. L. Helman and L. Hesselink. Visualizing Vector Field Topology in Fluid Flows. IEEE Computer Graphics and Applications, 11(3):36-46, May 1991.","journal-title":"IEEE Computer Graphics and Applications"},{"issue":"1","key":"1_CR24_Ref","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1109\/2945.582332","volume":"3","author":"L. Hesselink","year":"1997","unstructured":"L. Hesselink, Y. Levy, and Y. Lavin. The Topology of Symmetric, Second-Order 3D Tensor Fields. IEEE Transactions on Visualization and Computer Graphics, 3 (1):1-11, March 1997.","journal-title":"IEEE Transactions on Visualization and Computer Graphics"},{"key":"1_CR25_Ref","doi-asserted-by":"crossref","unstructured":"M. Hlawitschka and G. Scheuermann. HOT Lines: Tracking Lines in Higher Order Tensor Fields. \u00a0In Proceedings IEEE Visualization 2005, pages 27-34, 2005.","DOI":"10.1109\/VISUAL.2005.1532773"},{"key":"1_CR26_Ref","doi-asserted-by":"crossref","unstructured":"V. Interrante, H. Fuchs, and S. Pizer. Enhancing Transparent Skin Surfaces with Ridge and Valley Lines. \u00a0In Proceedings IEEE Visualization \u201995, pages 52-59, 1995.","DOI":"10.1109\/VISUAL.1995.480795"},{"key":"1_CR27_Ref","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1017\/S0022112095000462","volume":"285","author":"J. Jeong","year":"1995","unstructured":"J. Jeong and F. Hussain. On the Identification of a Vortex. Journal of Fluid Mechanics, 285:69-94, 1995.","journal-title":"Journal of Fluid Mechanics"},{"key":"1_CR28_Ref","unstructured":"M. Jiang, R. Machiraju, and D. Thompson. A Novel Approach to Vertex Core Region Detection. In Proceedings of the Symposium on Data Visualisation 2002 (VisSym \u201902), pages 217-225. Eurographics Association, 2002."},{"key":"1_CR29_Ref","doi-asserted-by":"crossref","unstructured":"D. Kenwright and R. Haimes. Vortex Identification-Applications in Aerodynamics. In Proceedings IEEE Visualization \u201997, pages 413-416, November 1997.","DOI":"10.1109\/VISUAL.1997.663910"},{"key":"1_CR30_Ref","doi-asserted-by":"crossref","unstructured":"D. N. Kenwright. Automatic Detection of Open and Closed Separation and Attachment Lines. In Proceedings IEEE Visualization \u201998, pages 151-158, 1998.","DOI":"10.1109\/VISUAL.1998.745297"},{"issue":"4","key":"1_CR31_Ref","doi-asserted-by":"publisher","first-page":"70","DOI":"10.1109\/38.689668","volume":"18","author":"D. N. Kenwright","year":"1998","unstructured":"D. N. Kenwright and R. Haimes. Automatic Vortex Core Detection. IEEE Computer Graphics and Applications, 18(4):70-74, July\/August 1998.","journal-title":"IEEE Computer Graphics and Applications"},{"issue":"2","key":"1_CR32_Ref","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1109\/2945.773805","volume":"5","author":"D. N. Kenwright","year":"1999","unstructured":"D. N. Kenwright, C. Henze, and C. Levit. Features Extraction of Separation and Attachment Lines. IEEE Transactions on Visualization and Computer Graphics, 5(2):135-144, 1999.","journal-title":"IEEE Transactions on Visualization and Computer Graphics"},{"key":"1_CR33_Ref","doi-asserted-by":"crossref","unstructured":"R. S. Laramee, C. Garth, H. Doleisch, J. Schneider, H. Hauser, and H. Hagen. Visual Analysis and Exploration of Fluid Flow in a Cooling Jacket. In Proceedings IEEE Visualization 2005, pages 623-630, 2005.","DOI":"10.1109\/VISUAL.2005.1532850"},{"key":"1_CR34_Ref","unstructured":"R. S. Laramee, C. Garth, J. Schneider, and H. Hauser. Texture-Advection on Stream Surfaces: A Novel Hybrid Visualization Applied to CFD Results. In Data Visualization, The Joint Eurographics-IEEE VGTC Symposium on Visualization (EuroVis 2006), pages 155-162,368. Eurographics Association, 2006."},{"key":"1_CR35_Ref","doi-asserted-by":"crossref","unstructured":"R. S. Laramee, D. Weiskopf, J. Schneider, and H. Hauser. Investigating Swirl and Tumble Flow with a Comparison of Visualization Techniques. In Proceedings IEEE Visualization 2004, pages 51-58, 2004.","DOI":"10.1109\/VISUAL.2004.59"},{"key":"1_CR36_Ref","doi-asserted-by":"crossref","unstructured":"Y. Lavin, R. Kumar Batra, and L. Hesselink. Feature comparisons of vector fields using earth mover\u2019s distance. \u00a0In Proceedings IEEE Visualization \u201998, pages 103-110, 1998.","DOI":"10.1145\/280953.282225"},{"key":"1_CR37_Ref","doi-asserted-by":"publisher","first-page":"1347","DOI":"10.2514\/3.25224","volume":"28","author":"Y. Levy","year":"1990","unstructured":"Y. Levy, D. Degani, and A. Seginer. Graphical Visualization of Vortical Flows by Means of Helicity. AIAA Journal, 28:1347-1352, 1990.","journal-title":"AIAA Journal"},{"key":"1_CR38_Ref","doi-asserted-by":"crossref","unstructured":"S. K. Lodha, J. C. Renteria, and K. M. Roskin. Topology Preserving Compression of 2D Vector Fields. In Proceedings IEEE Visualization 2000, pages 343-350, 2000.","DOI":"10.1109\/VISUAL.2000.885714"},{"key":"1_CR39_Ref","doi-asserted-by":"crossref","unstructured":"H. L\u00f6ffelmann and M. E. Gr\u00f6ller. Enhancing the Visualization of Characteristic Structures in Dynamical Systems. In Proceedings of the 9th Eurographics Workshop on Visualization in Scientific Computing, pages 35-46, 1998.","DOI":"10.1007\/978-3-7091-7517-0_6"},{"key":"1_CR40_Ref","unstructured":"K. Ma and V. Interrante. Extracting Feature Lines from 3D Unstructured Grids. In Proceedings IEEE Visualization \u201997, pages 285-292, 1997."},{"issue":"2","key":"1_CR41_Ref","doi-asserted-by":"publisher","first-page":"198","DOI":"10.1109\/TVCG.2004.1260771","volume":"10","author":"K. Mahrous","year":"2004","unstructured":"K. Mahrous, J. C. Bennett, G. Scheuermann, B. Hamann, and K. I. Joy. Topological segmentation in three-dimensional vector fields. IEEE Transactions on Visualization and Computer Graphics, 10(2):198-205, 2004.","journal-title":"IEEE Transactions on Visualization and Computer Graphics"},{"key":"1_CR42_Ref","unstructured":"K. M. Mahrous, J. C. Bennett, B. Hammann, and K. I. Joy. Improving Topological Segmentation of Three-dimensional Vector Fields. In Proceedings of the Joint Eurographics - IEEE TCVG Symposium on Visualization (VisSym 2003), pages 203-212, 2003."},{"key":"1_CR43_Ref","doi-asserted-by":"crossref","unstructured":"S. Mann and A. Rockwood. Computing Singularities of 3D Vector Fields with Geometric Algebra. In Proceedings of IEEE Visualization 2002, pages 283-290, October 2002.","DOI":"10.1109\/VISUAL.2002.1183786"},{"key":"1_CR44_Ref","unstructured":"O. Monga, S. Benayoun, and O. Faugeras. \u00a0From Partial Derivatives of 3D Density Images to Ridge Lines. In Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern, pages 163-169, 1992."},{"key":"1_CR45_Ref","doi-asserted-by":"crossref","unstructured":"X. Ni, M. Garland, and J. C. Hart. Fair Morse Functions for Extracting the Topological Structure of a Surface Mesh. ACM Transactions on Graphics (SIGGRAPH 2004), 23(3), 2004.","DOI":"10.1145\/1015706.1015769"},{"key":"1_CR46_Ref","doi-asserted-by":"crossref","unstructured":"R. Peikert and M. Roth. The Parallel Vectors Operator - A Vector Field Visualization Primitive. In Proceedings of IEEE Visualization \u201999, pages 263-270. IEEE Computer Society, 1999.","DOI":"10.1109\/VISUAL.1999.809896"},{"issue":"4","key":"1_CR47_Ref","doi-asserted-by":"publisher","first-page":"775","DOI":"10.1111\/j.1467-8659.2003.00723.x","volume":"22","author":"F. H. Post","year":"2003","unstructured":"F. H. Post, B. Vrolijk, H. Hauser, R. S. Laramee, and H. Doleisch. The State of the Art in Flow Visualization: Feature Extraction and Tracking. Computer Graphics Forum, 22(4):775-792, Dec. 2003.","journal-title":"Computer Graphics Forum"},{"issue":"1","key":"1_CR48_Ref","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1007\/PL00013399","volume":"17","author":"F. Reinders","year":"2001","unstructured":"F. Reinders, F. H. Post, and H. J. W. Spoelder. \u00a0Visualization of Time-Dependent Data with Feature Tracking and Event Detection,. In The Visual Computer, volume 17(1), pages 55-71. 2001.","journal-title":"In The Visual Computer"},{"issue":"4","key":"1_CR49_Ref","doi-asserted-by":"publisher","first-page":"675","DOI":"10.1111\/1467-8659.00625","volume":"21","author":"F. Reinders","year":"2002","unstructured":"F. Reinders, I. A. Sadarjoen, B. Vrolijk, and F. H. Post. Vortex Tracking and Visualisation in a Flow Past a Tapered Cylinder. In Computer Graphics Forum, volume 21(4), pages 675-682. November 2002.","journal-title":"In Computer Graphics Forum"},{"key":"1_CR50_Ref","doi-asserted-by":"crossref","unstructured":"M. Roth and R. Peikert. Flow Visualization for Turbomachinery Design. In Proceedings IEEE Visualization \u201996, pages 381-384, October 1996.","DOI":"10.1109\/VISUAL.1996.568137"},{"key":"1_CR51_Ref","doi-asserted-by":"crossref","unstructured":"M. Roth and R. Peikert. A Higher-Order Method For Finding Vortex Core Lines. In Proceedings IEEE Visualization \u201998, pages 143-150, 1998.","DOI":"10.1109\/VISUAL.1998.745296"},{"key":"1_CR52_Ref","unstructured":"Y. Rubner, C. Tomasi, and L. J. Guibas. \u00a0A Metric for Distributions with Applications to Image Databases. 1998."},{"issue":"3","key":"1_CR53_Ref","doi-asserted-by":"publisher","first-page":"333","DOI":"10.1016\/S0097-8493(00)00029-7","volume":"24","author":"I. A. Sadarjoen","year":"2000","unstructured":"I. A. Sadarjoen and F. H. Post. \u00a0Detection, Quantification, and Tracking of Vortices using Streamline Geometry. Computers and Graphics, 24(3):333-341, June 2000.","journal-title":"Computers and Graphics"},{"key":"1_CR54_Ref","unstructured":"J. Sahner, T. Weinkauf, and H. C. Hege. Galilean Invariant Extraction and Iconic Representation of Vortex Core Lines. In Proceedings of the Joint Eurographics - IEEE VGTC Symposium on Visualization (EuroVis 05), 2005."},{"key":"1_CR55_Ref","doi-asserted-by":"crossref","unstructured":"G. Scheuermann, H. Hagen, H. Kr\u00fcger, M. Menzel, and A. Rockwood. Visualization of Higher Order Singularities in Vector Fields. In Proceedings IEEE Visualization \u201997, pages 67-74, October 1997.","DOI":"10.1109\/VISUAL.1997.663858"},{"issue":"2","key":"1_CR56_Ref","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1109\/2945.694953","volume":"4","author":"G. Scheuermann","year":"1998","unstructured":"G. Scheuermann, H. Kr\u00fcger, M. Menzel, and A. P. Rockwood. Visualizing Nonlinear Vector Field Topology. IEEE Transactions on Visualization and Computer Graphics, 4(2):109-116, April\/June 1998.","journal-title":"IEEE Transactions on Visualization and Computer Graphics"},{"key":"1_CR57_Ref","doi-asserted-by":"crossref","unstructured":"G. Scheuermann and X. Tricoche. Topological Methods in Flow Visualization. In C.D. Hansen and C.R. Johnson, editors, The Visualization Handbook, pages 341-358. Elsevier, 2005.","DOI":"10.1016\/B978-012387582-2\/50019-8"},{"key":"1_CR58_Ref","doi-asserted-by":"crossref","unstructured":"S. Stegmaier and T. Ertl. A Graphics Hardware-based Vortex Detection and Visualization System. In Proceedings IEEE Visualization 2004, pages 195-202, 2004.","DOI":"10.1109\/VISUAL.2004.3"},{"key":"1_CR59_Ref","doi-asserted-by":"crossref","unstructured":"D. Sujudi and R. Haimes. Identification of Swirling Flow in 3D Vector Fields. Technical Report AIAA Paper 95-1715, American Institute of Aeronautics and Astronautics, 1995.","DOI":"10.2514\/6.1995-1715"},{"key":"1_CR60_Ref","doi-asserted-by":"crossref","unstructured":"L. Sun, R Batra, X. Shi, and L. Hesselink. Topology Visualization of the Optical Power Flow through a Novel C-Shaped Nano-Aperture. In Proceedings IEEE Visualization 2004, pages 337-344, 2004.","DOI":"10.1109\/VISUAL.2004.106"},{"key":"1_CR61_Ref","doi-asserted-by":"crossref","unstructured":"A. Szymczak and J. Vanderhyde. Extraction of Topologically Simple Isosurfaces from Volume Datasets. In Proceedings IEEE Visualization 2003, pages 67-74, 2003.","DOI":"10.1109\/VISUAL.2003.1250356"},{"key":"1_CR62_Ref","doi-asserted-by":"crossref","unstructured":"C. K. Tang and G. G. Medioni. Extremal Feature Extraction From 3D Vector and Noisy Scalar Fields. In Proceedings IEEE Visualization \u201998, pages 95-102. IEEE, 1998.","DOI":"10.1109\/VISUAL.1998.745290"},{"key":"1_CR63_Ref","doi-asserted-by":"crossref","unstructured":"A. Telea and J.J. van Wijk. Simplified Representation of Vector Fields. In Proceedings IEEE Visualization \u201999, pages 35-42, 1999.","DOI":"10.1109\/VISUAL.1999.809865"},{"issue":"3","key":"1_CR64_Ref","doi-asserted-by":"publisher","first-page":"595","DOI":"10.1111\/1467-8659.t01-1-00710","volume":"21","author":"H. Theisel","year":"2002","unstructured":"H. Theisel. Designing 2D Vector Fields of Arbitrary Topology. Computer Graphics Forum (Eurographics 2002), 21(3):595-595, 2002.","journal-title":"Computer Graphics Forum (Eurographics 2002)"},{"key":"1_CR65_Ref","unstructured":"H. Theisel, C. R\u00f6ssl, and H. Seidel. Using Feature Flow Fields for Topologi- cal Comparison of Vector Fields. In Proceedings of the Conference on Vision, Modeling and Visualization 2003 (VMV-03), pages 521-528, November 19-21 2003."},{"key":"1_CR66_Ref","doi-asserted-by":"crossref","unstructured":"H. Theisel, Ch. R\u00f6ssl, and H.-P. Seidel. Combining Topological Simplification and Topology Preserving Compression for 2D Vector Fields. In Pacific Graphics, pages 419-423, 2003.","DOI":"10.1109\/PCCGA.2003.1238287"},{"key":"1_CR67_Ref","doi-asserted-by":"crossref","unstructured":"H. Theisel, Ch. R\u00f6ssl, and H.-P. Seidel. Compression of 2D Vector Fields Under Guaranteed Topology Preservation. In Eurographics (EG 03), volume 22(3) of Computer Graphics forum, pages 333-342, September 1-6 2003.","DOI":"10.1111\/1467-8659.00680"},{"key":"1_CR68_Ref","unstructured":"H. Theisel and H.-P. Seidel. Feature Flow Fields. In Proceedings of the Joint Eurographics - IEEE TCVG Symposium on Visualization (VisSym 03), pages 141-148, 2003."},{"key":"1_CR69_Ref","doi-asserted-by":"crossref","unstructured":"H. Theisel, J. Sahner, T. Weinkauf, H.-C. Hege, and H.-P. Seidel. Extraction of Parallel Vector Surfaces in 3D Time-Dependent Fields and Application to Vortex Core Line Tracking. \u00a0In Proceedings IEEE Visualization 2005, pages 631-638, 2005.","DOI":"10.1109\/VISUAL.2005.1532851"},{"key":"1_CR70_Ref","doi-asserted-by":"crossref","unstructured":"H. Theisel, T. Weinkauf, H.-C. Hege, and H.-P. Seidel. Saddle Connectors-An Approach to Visualizing the Topological Skeleton of Complex 3D Vector Fields. In Proceedings IEEE Visualization 2003, pages 225-232, 2003.","DOI":"10.1109\/VISUAL.2003.1250376"},{"key":"1_CR71_Ref","doi-asserted-by":"crossref","unstructured":"H. Theisel, T. Weinkauf, H.-C. Hege, and H.-P. Seidel. Stream Line and Path Line Oriented Topology for 2D Time-Dependent Vector Fields. In Proceedings IEEE Visualization 2004, pages 321-328, 2004.","DOI":"10.1109\/VISUAL.2004.99"},{"key":"1_CR72_Ref","doi-asserted-by":"crossref","unstructured":"H. Theisel, T. Weinkauf, H.-C. Hege, and H.-P. Seidel. Topological Methods for 2D Time-Dependent Vector Fields Based On Stream Lines and Path Lines. IEEE Transactions on Visualization and Computer Graphics, 11(4), 2005.","DOI":"10.1109\/TVCG.2005.68"},{"key":"1_CR73_Ref","unstructured":"H. Theisel, T. Weinkauf, H.-P. Seidel, and H. Seidel. Grid-Independent Detection of Closed Stream Lines in 2D Vector Fields. In Proceedings of the Conference on Vision, Modeling and Visualization 2004 (VMV 04), pages 421-428, November 2004."},{"key":"1_CR74_Ref","doi-asserted-by":"crossref","unstructured":"X. Tricoche, C. Garth, G. Kindlmann, E. Deines, G. Scheuermann, and H. Hagen.\u00a0 Visualization of Intricate Flow Structures for Vortex Breakdown Analysis. In Proceedings IEEE Visualization 2004, pages 187-194, 2004.","DOI":"10.1109\/VISUAL.2004.113"},{"key":"1_CR75_Ref","unstructured":"X. Tricoche, C. Garth, and G. Scheuermann. Fast and Robust Extraction of Separation Line Features. In Proceedings of Seminar on Scientific Visualization 2003, Schloss Dagstuhl, 2003."},{"key":"1_CR76_Ref","doi-asserted-by":"crossref","unstructured":"X. Tricoche and G. Scheuermann. Continuous Topology Simplification of Planar Vector Fields. In Proceedings IEEE Visualization 2001, pages 159-166, 2001.","DOI":"10.1109\/VISUAL.2001.964507"},{"key":"1_CR77_Ref","doi-asserted-by":"crossref","unstructured":"X. Tricoche, G. Scheuermann, and H. Hagen. A Topology Simplification Method For 2D Vector Fields. In Proceedings IEEE Visualization 2000, 2000.","DOI":"10.1109\/VISUAL.2000.885716"},{"key":"1_CR78_Ref","unstructured":"X. Tricoche, G. Scheuermann, and H. Hagen. Scaling the Topology of Symmetric, Second-Order Planar Tensor Fields. In Proceedings of NSF\/DOE Lake Tahoe Workshop on Hierarchical Approximation and Geometrical Methods for Scientific Visualization, 2001."},{"issue":"3","key":"1_CR79_Ref","doi-asserted-by":"publisher","first-page":"461","DOI":"10.1111\/1467-8659.00539","volume":"20","author":"X. Tricoche","year":"2001","unstructured":"X. Tricoche, G. Scheuermann, and H. HagenTensor Topology Tracking: A Visualization Method for Time-Dependent 2D Symmetric Tensor Fields. \u00a0In Computer Graphics Forum 20(3) (Eurographics 2001), pages 461-470, September 2001.","journal-title":"Computer Graphics Forum"},{"key":"1_CR80_Ref","doi-asserted-by":"crossref","unstructured":"X. Tricoche, G. Scheuermann, and H. Hagen. Topology-Based Visualization of Time-Dependent 2D Vector Fields. In Proceedings of the Joint Eurographics - IEEE TCVG Symposium on Visualization (VisSym-01), pages 117-126, May 28-30 2001.","DOI":"10.1007\/978-3-7091-6215-6_13"},{"key":"1_CR81_Ref","doi-asserted-by":"crossref","unstructured":"X. Tricoche, G. Scheuermann, and H. Hagen. Topology Simplification of Symmetric, Second-Order 2D Tensor Fields, Hierarchical and Geometrical Methods in Scientific Visualization. 2003.","DOI":"10.1007\/978-3-662-07443-5_17"},{"key":"1_CR82_Ref","doi-asserted-by":"crossref","unstructured":"X. Tricoche, G. Scheuermann, H. Hagen, and S. Clauss. Vector and Tensor Field Topology Simplification on Irregular Grids. In Proceedings of the Joint Eurographics - IEEE TCVG Symposium on Visualization (VisSym-01), pages 107-116. Springer-Verlag, May 28-30 2001.","DOI":"10.1007\/978-3-7091-6215-6_12"},{"issue":"2","key":"1_CR83_Ref","doi-asserted-by":"publisher","first-page":"249","DOI":"10.1016\/S0097-8493(02)00056-0","volume":"26","author":"X. Tricoche","year":"2002","unstructured":"X. Tricoche, T. Wischgoll, G. Scheuermann, and H. Hagen. Topology Tracking for the Visualization of Time-Dependent Two-Dimensional Flows. Computers & Graphics, 26(2):249-257, 2002.","journal-title":"Computers & Graphics"},{"key":"1_CR84_Ref","unstructured":"T. Weinkauf, H. Theisel, H. C. Hege, and H.-P. Seidel. Boundary Switch Connectors for Topological Visualization of Complex 3D Vector Fields. In Proceedings of the Joint Eurographics - IEEE TCVG Symposium on Visualization (VisSym 04), pages 183-192, 2004."},{"issue":"3","key":"1_CR85_Ref","doi-asserted-by":"publisher","first-page":"469","DOI":"10.1111\/j.1467-8659.2004.00778.x","volume":"23","author":"T. Weinkauf","year":"2004","unstructured":"T. Weinkauf, H. Theisel, H.-C. Hege, and H.-P. Seidel. Topological Construction and Visualization of Higher Order 3D Vector Fields. Computer Graphics Forum, 23(3):469-478, 2004.","journal-title":"Computer Graphics Forum"},{"key":"1_CR86_Ref","doi-asserted-by":"crossref","unstructured":"T. Weinkauf, H. Theisel, H. C. Hege, and H.-P. Seidel. Extracting Higher Order Critical Points and Topological Simplification of 3D Vector Fields. In Proceedings IEEE Visualization 2005, pages 559-566, 2005.","DOI":"10.1109\/VISUAL.2005.1532842"},{"key":"1_CR87_Ref","doi-asserted-by":"crossref","unstructured":"T. Wischgoll and G. Scheuermann. \u00a0Detection and Visualization of Closed Streamlines in Planar Fields. IEEE Transactions on Visualization and Computer Graphics, 7(2), 2001.","DOI":"10.1109\/2945.928168"},{"key":"1_CR88_Ref","unstructured":"T. Wischgoll and G. Scheuermann. Locating Closed Streamlines in 3D Vector Fields. In Proceedings of the Joint Eurographics - IEEE TCVG Symposium on Visualization (VisSym 02), pages 227-280, May 2002."},{"key":"1_CR89_Ref","unstructured":"T. Wischgoll, G. Scheuermann, and H. Hagen. Tracking Closed Streamlines in Time Dependent Planar Flows. In Proceedings of the Vision Modeling and Visualization Conference 2001 (VMV 01), pages 447-454, November 21-23 2001."},{"key":"1_CR90_Ref","doi-asserted-by":"crossref","unstructured":"X. Zheng and A. Pang. Topological Lines in 3D Tensor Fields. In Proceedings IEEE Visualization \u201904, pages 313-320, 2004.","DOI":"10.1109\/VISUAL.2004.105"},{"key":"1_CR91_Ref","doi-asserted-by":"crossref","unstructured":"X. Zheng and A. Pang. 2D Asymmetric Tensor Fields. In Proceedings IEEE Visualization 2005, pages 3-10, 2005.","DOI":"10.1109\/VISUAL.2005.1532770"},{"issue":"4","key":"1_CR92_Ref","doi-asserted-by":"publisher","first-page":"395","DOI":"10.1109\/TVCG.2005.67","volume":"11","author":"X. Zheng","year":"2005","unstructured":"X. Zheng, B. Parlett, and A. Pang. Topological Lines in 3D Tensor Fields and Discriminant Hessian Factorization. IEEE Transactions on Visualization and Computer Graphics, 11(4):395-407, July 2005.","journal-title":"IEEE Transactions on Visualization and Computer Graphics"},{"key":"1_CR93_Ref","doi-asserted-by":"crossref","unstructured":"X. Zheng, B. Parlett, and A. Pang. Topological Structures of 3D Tensor Fields. In Proceedings IEEE Visualization 2005, pages 551-558, 2005.","DOI":"10.1109\/VISUAL.2005.1532841"}],"container-title":["Mathematics and Visualization","Topology-based Methods in Visualization"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-540-70823-0_1.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,16]],"date-time":"2025-01-16T15:55:58Z","timestamp":1737042958000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-540-70823-0_1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007]]},"ISBN":["9783540708223","9783540708230"],"references-count":93,"URL":"https:\/\/doi.org\/10.1007\/978-3-540-70823-0_1","relation":{},"ISSN":["1612-3786"],"issn-type":[{"value":"1612-3786","type":"print"}],"subject":[],"published":{"date-parts":[[2007]]}}}