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Ronny Peikert 1 Over Two Decades of Integration-Based, Geometric Vector Field Visualization Part III:

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Presentation on theme: "Ronny Peikert 1 Over Two Decades of Integration-Based, Geometric Vector Field Visualization Part III:"— Presentation transcript:

1 Ronny Peikert peikert@inf.ethz.ch 1 http://graphics.ethz.ch/~peikert Over Two Decades of Integration-Based, Geometric Vector Field Visualization Part III: Curve based seeding Planar based seeding Ronny Peikert ETH Zurich 1 http://graphics.ethz.ch/~peikert

2 Ronny Peikert peikert@inf.ethz.ch 2 http://graphics.ethz.ch/~peikert Overview Curve-based seeding objects  steady flow stream surfaces  unsteady flow "path surfaces" "streak surfaces" Planar-based seeding objects  steady flow  unsteady flow Orthogonal surfaces of a vector field Discussion, future research opportunities 2 http://graphics.ethz.ch/~peikert

3 Ronny Peikert peikert@inf.ethz.ch 3 http://graphics.ethz.ch/~peikert Stream surfaces 3 http://graphics.ethz.ch/~peikert Definition  A stream surface is the union of the stream lines seeded at all points of a curve (the seed curve).  Motivation  separates (steady) flow, flow cannot cross the surface  surfaces offer more rendering options than lines (perception!)‏

4 Ronny Peikert peikert@inf.ethz.ch 4 http://graphics.ethz.ch/~peikert Stream surfaces 4 http://graphics.ethz.ch/~peikert First stream surface computation  done before SciVis existed!  Early use in flow visualization (Helman and Hesselink 1990) for flow separation Image: Ying et al.

5 Ronny Peikert peikert@inf.ethz.ch 5 http://graphics.ethz.ch/~peikert Stream surface integration Problem: naïve algorithm fails if streamlines diverge or grow at largely different speeds. Example of failure: seed curve which extends to no-slip boundary: 5 http://graphics.ethz.ch/~peikert fixed time steps slightly better: fixed spatial steps wall (u = 0)‏ streamli nes

6 Ronny Peikert peikert@inf.ethz.ch 6 http://graphics.ethz.ch/~peikert Hultquist's algorithm Hultquist's algorithm (Hultquist 1992) does optimized triangulation:  Of two possible connections choose the one which is closer to orthogonal to both streamlines. 6 http://graphics.ethz.ch/~peikert systematic triangulation optimized triangulation strea mline s

7 Ronny Peikert peikert@inf.ethz.ch 7 http://graphics.ethz.ch/~peikert Hultquist's algorithm (2)‏ The problem of divergence or convergence is solved by inserting or terminating streamlines. 7 http://graphics.ethz.ch/~peikert inserted streamline terminated streamline

8 Ronny Peikert peikert@inf.ethz.ch 8 http://graphics.ethz.ch/~peikert Curvature of front curve controlled by limiting the dihedral angle of the mesh (Garth et al. 2004)‏ Adaptive refinement Intricate structure of vortex breakdown bubble Curvature of front curve controlled by limiting the dihedral angle of the mesh (Garth et al. 2004)‏ Adaptive refinement Intricate structure of vortex breakdown bubble 8 http://graphics.ethz.ch/~peikert

9 Ronny Peikert peikert@inf.ethz.ch 9 http://graphics.ethz.ch/~peikert Refined Hultquist methods (2)‏ Cubic Hermite interpolation along the front curves. Runge-Kutta used to propagate front and its covariant derivatives (Schneider et al. 2009)‏ 9 http://graphics.ethz.ch/~peikert

10 Ronny Peikert peikert@inf.ethz.ch 10 http://graphics.ethz.ch/~peikert Analytical methods In a tetrahedral cell the vector field is linearly interpolated: Streamline has equation Stream surface seeded on straight line (entry curve) is a ruled surface. Exit curve is computed analytically respecting boundary switch curves 10 http://graphics.ethz.ch/~peikert HultquistScheuermann (Sche uerm ann et al., 2001).

11 Ronny Peikert peikert@inf.ethz.ch 11 http://graphics.ethz.ch/~peikert Implicit methods A stream function is a special*) solution of the PDE [don't confuse with a potential which has PDE ] 11 http://graphics.ethz.ch/~peikert streamline stream surfaces *) mass flux =  ‏

12 Ronny Peikert peikert@inf.ethz.ch 12 http://graphics.ethz.ch/~peikert Implicit methods (2)‏ Stream functions  exist for divergence-free vector fields (= incompressible flow)‏  … and for compressible flow, if there are no sinks/sources  are computed by solving a PDE (with appropriate boundary conditions)‏  yield stream surfaces by isosurface extraction  Advantage of stream function method (Kenwright and Mallinson, 1992, van Wijk, 1993): conservation of mass! 12 http://graphics.ethz.ch/~peikert

13 Ronny Peikert peikert@inf.ethz.ch 13 http://graphics.ethz.ch/~peikert Implicit methods (3)‏ Computational space method, implicit method per cell, respects conservation of mass (van Gelder, 2001)‏ 13 http://graphics.ethz.ch/~peikert Delta wing. Stream surface close to boundary. Flow separation and attachment.

14 Ronny Peikert peikert@inf.ethz.ch 14 http://graphics.ethz.ch/~peikert Rendering of stream surfaces Stream arrows (Löffelmann et al. 1997)‏ Texture advection on stream surfaces (Laramee et al. 2006)‏ 14 http://graphics.ethz.ch/~peikert

15 Ronny Peikert peikert@inf.ethz.ch 15 http://graphics.ethz.ch/~peikert Rendering of stream surfaces (2)‏ 15 http://graphics.ethz.ch/~peikert

16 Ronny Peikert peikert@inf.ethz.ch 16 http://graphics.ethz.ch/~peikert Invariant 2D manifolds Critical points of types saddle and focus saddle (spiral saddle) have a stream surface converging to them. And so do periodic orbits of types saddle and twisted saddle. 16 http://graphics.ethz.ch/~peikert

17 Ronny Peikert peikert@inf.ethz.ch 17 http://graphics.ethz.ch/~peikert Invariant 2D manifolds Saddle connectors (Theisel et al, 2003)‏  Visualization of topological skeleton of 3D vector fields  Intersection of 2D manifolds of (focus) saddles 17 http://graphics.ethz.ch/~peikert Flow past a cylinder saddle-connector of a pair of focus saddle crit. points

18 Ronny Peikert peikert@inf.ethz.ch 18 http://graphics.ethz.ch/~peikert Geodesic circles stream surface algorithm (Krauskopf and Osinga 1999)‏  Front grows radially (not along stream lines)‏  by solving a boundary value problem  "immune" against spiraling Geodesic circles stream surface algorithm (Krauskopf and Osinga 1999)‏  Front grows radially (not along stream lines)‏  by solving a boundary value problem  "immune" against spiraling 18 http://graphics.ethz.ch/~peikert

19 Ronny Peikert peikert@inf.ethz.ch 19 http://graphics.ethz.ch/~peikert Invariant 2D manifolds (3)‏ Topology-aware stream surface method (Peikert and Sadlo, 2009)‏  starts at critical point, periodic orbit, or given seed curve  handles convergence to saddle or sink 19 http://graphics.ethz.ch/~peikert

20 Ronny Peikert peikert@inf.ethz.ch 20 http://graphics.ethz.ch/~peikert Path surfaces Particle based path surfaces (Schafhitzel et al. 2007)‏  Density control a la Hultquist  Point splatting  1st order Euler integration  GPU implementation interactive seeding! 20 http://graphics.ethz.ch/~peikert Path surface of unsteady flow past a cylinder

21 Ronny Peikert peikert@inf.ethz.ch 21 http://graphics.ethz.ch/~peikert Streak surfaces Smoke surfaces are a technique based on streak surfaces (von Funck et al. 2008)  advected mesh is not retriangulated, but  size/shape of triangles is mapped to opacity  simplified optical model for smoke 21 http://graphics.ethz.ch/~peikert

22 Ronny Peikert peikert@inf.ethz.ch 22 http://graphics.ethz.ch/~peikert Planar based seeding Planar-based seeding for steady flow  Stream polygons (Schroeder et al. 1991)‏  Flow volumes (Max et al. 1993)‏  Implicit flow volumes (Xue et al. 2004) 22 http://graphics.ethz.ch/~peikert

23 Ronny Peikert peikert@inf.ethz.ch 23 http://graphics.ethz.ch/~peikert Planar based seeding (2)‏ Planar-based seeding for unsteady flow  Extension of flow volume technique to unsteady vector fields (Becker et at. 1995). 23 http://graphics.ethz.ch/~peikert Image: Crawfis, Shen, Max Unsteady flow volume

24 Ronny Peikert peikert@inf.ethz.ch 24 http://graphics.ethz.ch/~peikert Orthogonal surfaces Surfaces (approximately) orthogonal to a vector (or eigen- vector) field as a visualization technique (Zhang et al. 2003). If a vector field is conservative,, its potential can be visualized with a scalar field visualization technique, such as isosurfaces. Orthogonal surfaces exist also in the slightly more general case of helicity-free vector fields. However, 3D flow fields usually have helicity. Also eigenvector fields of symmetric 3D tensors. Consequence: For many applications, orthogonal surfaces are less suitable (discussed by Schultz et al. 2009). 24 http://graphics.ethz.ch/~peikert

25 Ronny Peikert peikert@inf.ethz.ch 25 http://graphics.ethz.ch/~peikert Discussion, future research There is no single best flow vis technique! Most effort spent so far on streamlines  Extension to unsteady flow somewhat lacking behind  Also extension to stream surfaces (and unsteady variants)‏  Other areas needing more research:  Uncertainty visualization tools for geometric techniques  Comparative visualization tools for geometric techniques  Improved surface and volume construction methods  Automatic seeding for surfaces and volumes 25 http://graphics.ethz.ch/~peikert

26 Ronny Peikert peikert@inf.ethz.ch 26 http://graphics.ethz.ch/~peikert The End 26 http://graphics.ethz.ch/~peikert  Thank you for your attention! Any questions?  We would like to thank the following:  R. Crawfis, W. v. Funck, C. Garth, J.L. Helman, J. Hultquist, H. Loeffelmann, N. Max, H. Osinga, T. Schafhitzel, G. Scheuermann, D. Schneider, W. Schroeder, H.W. Shen, H. Theisel, T. Weinkauf, S.X. Ying, D. Xue  PDF versions of STAR and MPEG movies available at:  http://cs.swan.ac.uk/~csbob

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