Poisson-based tools for flow visualization

This paper applies Poisson-based methods to assist in interactive exploration of steady flow fields. Using data-driven deformations we obtain flow-orthogonal and flow-tangential surfaces by a flux-based optimization. Surfaces are positioned interactively and deformed in real-time according to local flow. The deformed surfaces are particularly useful for defining seed structures. We show how the same gradient-based computational framework can be applied to obtain parametrizations of flow-aligned surfaces. This way it is easy to define nontrivial seed structures for integration-based flow visualization methods. Additionally, the flow-aligned parametrizations are employed for view-independent surface-based LIC visualizations. We apply our method to a number of data sets to show the effectiveness of our deformations and parametrization-based seed extraction methods for interactive flow exploration.

[1]  Christian Rössl,et al.  Stream Surface Parametrization by Flow‐Orthogonal Front Lines , 2012, Comput. Graph. Forum.

[2]  Christian Rössl,et al.  As-Perpendicular-as-possible surfaces for flow visualization , 2012, 2012 IEEE Pacific Visualization Symposium.

[3]  Hans Hagen,et al.  IRIS: Illustrative Rendering for Integral Surfaces , 2010, IEEE Transactions on Visualization and Computer Graphics.

[4]  Marc Alexa,et al.  As-rigid-as-possible surface modeling , 2007, Symposium on Geometry Processing.

[5]  Hans-Christian Hege,et al.  Advected Tangent Curves: A General Scheme for Characteristic Curves of Flow Fields , 2012, Comput. Graph. Forum.

[6]  H.-J. Kaltenbach,et al.  Direct numerical simulation of flow separation behind a swept, rearward-facing step at ReH=3000 , 2000 .

[7]  Robert S. Laramee,et al.  Automatic Stream Surface Seeding: A Feature Centered Approach , 2012, Comput. Graph. Forum.

[8]  Detlev Stalling,et al.  Fast texture based algorithms for vector field visualization , 1999 .

[9]  Min Chen,et al.  Over Two Decades of Integration-Based, Geometric Flow Visualization , 2009, Eurographics.

[10]  Kenneth I. Joy,et al.  Generation of Accurate Integral Surfaces in Time-Dependent Vector Fields , 2008, IEEE Transactions on Visualization and Computer Graphics.

[11]  Rüdiger Westermann,et al.  A particle system for interactive visualization of 3D flows , 2005, IEEE Transactions on Visualization and Computer Graphics.

[12]  Silvia Born,et al.  Illustrative Stream Surfaces , 2010, IEEE Transactions on Visualization and Computer Graphics.

[13]  Robert S. Laramee,et al.  Texture Advection on Stream Surfaces: A Novel Hybrid Visualization Applied to CFD Simulation Results , 2006, EuroVis.

[14]  Keenan Crane,et al.  Geodesics in heat: A new approach to computing distance based on heat flow , 2012, TOGS.

[15]  Hujun Bao,et al.  Poisson shape interpolation , 2006, Graph. Model..

[16]  Robert S. Laramee,et al.  The State of the Art in Flow Visualisation: Feature Extraction and Tracking , 2003, Comput. Graph. Forum.

[17]  Jovan Popović,et al.  Deformation transfer for triangle meshes , 2004, SIGGRAPH 2004.

[18]  Robert S. Laramee,et al.  The State of the Art in Flow Visualization: Dense and Texture‐Based Techniques , 2004, Comput. Graph. Forum.

[19]  Keenan Crane,et al.  Geodesics in heat: A new approach to computing distance based on heat flow , 2012, TOGS.

[20]  David Bommes,et al.  Efficient Linear System Solvers for Mesh Processing , 2005, IMA Conference on the Mathematics of Surfaces.

[21]  Hujun Bao,et al.  Output-coherent image-space LIC for surface flow visualization , 2012, 2012 IEEE Pacific Visualization Symposium.

[22]  Daniel Weiskopf,et al.  Animation of Orthogonal Texture Patterns for Vector Field Visualization , 2008, IEEE Transactions on Visualization and Computer Graphics.

[23]  Rüdiger Westermann,et al.  Interactive Streak Surface Visualization on the GPU , 2009, IEEE Transactions on Visualization and Computer Graphics.

[24]  Christian Rössl,et al.  Harmonic Guidance for Surface Deformation , 2005, Comput. Graph. Forum.

[25]  Patrick H. Worley,et al.  Algorithm 888: Spherical Harmonic Transform Algorithms , 2008, TOMS.

[26]  R. Abraham,et al.  Manifolds, Tensor Analysis, and Applications , 1983 .

[27]  Anders Ynnerman,et al.  Flow field visualization using vector field perpendicular surfaces , 2009, SCCG.

[28]  Ligang Liu,et al.  A Local/Global Approach to Mesh Parameterization , 2008, Comput. Graph. Forum.

[29]  Thomas Ertl,et al.  Point-based stream surfaces and path surfaces , 2007, GI '07.

[30]  Hans-Christian Hege,et al.  Dual streamline seeding , 2009, 2009 IEEE Pacific Visualization Symposium.

[31]  Kun Zhou,et al.  Mesh editing with poisson-based gradient field manipulation , 2004, SIGGRAPH 2004.

[32]  Patrick Pérez,et al.  Poisson image editing , 2003, ACM Trans. Graph..

[33]  Sang Uk Lee,et al.  Multiview normal field integration using level set methods , 2007, 2007 IEEE Conference on Computer Vision and Pattern Recognition.

[34]  Charles D. Hansen,et al.  Flow Charts: Visualization of Vector Fields on Arbitrary Surfaces , 2008, IEEE Transactions on Visualization and Computer Graphics.

[35]  Jeff P. Hultquist,et al.  Constructing stream surfaces in steady 3D vector fields , 1992, Proceedings Visualization '92.

[36]  D. Bommes,et al.  Mixed-integer quadrangulation , 2009, SIGGRAPH 2009.

[37]  Kenneth I. Joy,et al.  Time and Streak Surfaces for Flow Visualization in Large Time-Varying Data Sets , 2009, IEEE Transactions on Visualization and Computer Graphics.

[38]  Christian Rössl,et al.  Discrete tensorial quasi-harmonic maps , 2005, International Conference on Shape Modeling and Applications 2005 (SMI' 05).

[39]  Maria Vittoria Salvetti,et al.  Simulation of the three-dimensional flow around a square cylinder between parallel walls at moderate Reynolds numbers , 2005 .

[40]  Olga Sorkine-Hornung,et al.  On Linear Variational Surface Deformation Methods , 2008, IEEE Transactions on Visualization and Computer Graphics.

[41]  Holger Theisel,et al.  Streak Lines as Tangent Curves of a Derived Vector Field , 2010, IEEE Transactions on Visualization and Computer Graphics.

[42]  YANQING CHEN,et al.  Algorithm 8 xx : CHOLMOD , supernodal sparse Cholesky factorization and update / downdate ∗ , 2006 .

[43]  Hans-Peter Seidel,et al.  Smoke Surfaces: An Interactive Flow Visualization Technique Inspired by Real-World Flow Experiments , 2008, IEEE Transactions on Visualization and Computer Graphics.