1. Flow Visualization Overview
“Line Integral Convolution”
Szigyarto Tamas Peter,
Saint-Petersburg State University,
Faculty of Applied Mathematics – Control Processes
Department of Computer Modeling and Multiple Processors Systems

2. Agenda Introduction Mathematical Model
Classification of visualization approach
LIC technique
Conclusion
Agenda

3. Introduction Application: Automotive industry Aerodynamics
Turbo machinery design
Weather simulation
Medical visualization
Climate modeling
Introduction

4. Mathematical Model Basic definitions Particle-Tracing Numerical model
Mathematical Model >> Overview

5. Vector fields and Integral curves
Time-dependent vector field
Integral curves
The collection of all possible integral curves for a vector field constitutes the corresponding flow
Mathematical Model >> Basic Definitions

6. Two types of flow fields
Steady flows
Unsteady flows
Mathematical Model >> Basic Definitions

7. Streamlines, pathlines and streaklines
Mathematical Model >> Particle Tracing

8. Reconstruction of flow data
velocity is usually not given in analytic form, but requires reconstruction from the discrete simulation output
The output of flow simulation usually represented by many sample vectors , which are discretely represent the solution of the simulation process on large-sized grids
Reconstruction filter
we need to get a continuous velocity
Mathematical Model >> Numerical Model

9. Numerical integration
Mathematical Model >> Numerical Model

10. Grids Grids involved in flow simulation: cartesian, (b) regular,
(c) general rectilinear,
(d) structured or curvilinear,
(e) unstructured,
(f) unstructured triangular.
Mathematical Model >> Numerical Model

11. Classification of visualization approach
Overview
Point-based direct flow visualization
Sparse representation for particle-tracing technique
Dense representation for particle-tracing technique
Feature-based visualization approach
Classification Of Visualization Approach

12. Overview
Direct flow visualization: common approaches are drawing arrows or color coding velocity. Intuitive pictures can be provided, especially in the case of two dimensions. Solutions of this kind allow immediate investigation of the flow data.
Dense, texture-based flow visualization: similar to direct flow visualization, a texture is computed that is used to generate a dense representation of the flow. A notion of where the flow moves is incorporated through co-related texture values along the vector field.
Geometric flow visualization: integration-based approaches first integrate the flow data and then use geometric objects as a basis for flow visualization. Examples include streamlines, streaklines, and pathlines.
Feature-based flow visualization: another approach makes use of an abstraction and/or extraction step which is performed before visualization. Special features are extracted from the original dataset, such as important phenomena or topological information of the flow.
Classification Of Visualization Approach >> Overview

13. Example of circular flow at the surface of a ring
direct visualization
by the use of
arrow glyphs
texture-based by
the use of LIC
visualization based
on geometric objects,
here streamlines
Classification Of Visualization Approach >> Overview

14. Point-Based Direct Flow Visualization
Traditional techniques:
arrow plots based on glyphs
direct line segments (the length represent the magnitude of the velocity)
Additional features:
applying arrow-plots to time-dependent flow fields
illumination and shadows
use complex glyphs with respect to velocity, acceleration, curvature, local rotation, shear, or convergence
Classification Of Visualization Approach >> Point-Based Direct Flow Visualization

15. Examples Glyph-based 3D flow visualization, Traditional arrow plot
combined with illuminated streamlines
Traditional arrow plot
Classification Of Visualization Approach >> Point-Based Direct Flow Visualization

16. Problems 3D representation issues: Solutions:
the position and orientation of an arrow is more difficult to understand due to the projection onto the 2D image plane
arrow might occlude other arrows in the background
the problem of clutter
Solutions:
use of semi-transparency to avoid occlusion problems
highlighting arrows with orientations in a range specified by the user, or by selectively seeding the arrows to avoid clutter problem
Classification Of Visualization Approach >> Point-Based Direct Flow Visualization

17. Feature-based visualization approach
Basic concept:
seek to compute a more abstract representation that already contains the important properties in a condensed form and suppresses superfluous information
Examples of the abstract data:
flow topology based on
critical points
vortices
shockwaves
Methods:
to emphasize special attributes for each type of feature, suitable representations must be used
glyphs or icons can be employed for vortices or for critical points
ellipses or ellipsoids to encode the rotation speed and other attributes of vortices
Classification Of Visualization Approach >> Feature-based Visualization Approach

18. Examples Large vortex formed by detatching
flow at the stay vane leading edge
Topology-based visualization
Classification Of Visualization Approach >> Feature-based Visualization Approach

19. Sparse Representations for Particle-Tracing Techniques
Traditional approach:
compute characteristic curves (streamlines, pathlines, streaklines) and draws them as thin lines
streamlets – lines generated by particles traced for a very short time
use of geometric objects of finite extent perpendicular to the particle trace
streamribbon:
an area swept out by a deformable line segment along a streamline. The strip-like shape of a streamribbon displays the rotational behavior of a 3D flow.
streamtubes:
is a thick tube-shaped streamline whose radial extent shows the expansion of the flow
stream polygons
Classification Of Visualization Approach >> Sparse Representation For Partical Tracing Technique

20. Examples Combination of streamlines, streamribbons, arrows, and
color coding for a 3D flow
(courtesy of
BMW Group and Martin Schulz).
Classification Of Visualization Approach >> Sparse Representation For Partical Tracing Technique

21. Examples Sparse representation based on the use of streamlets
Classification Of Visualization Approach >> Sparse Representation For Partical Tracing Technique

22. Dense Representations for Particle-Tracing Techniques
Dense representation typically built upon texture-based techniques among their:
Spot Noise
Line Integral Convolution (LIC)
Classification Of Visualization Approach >> Dense Representation For Partical Tracing Technique

23. Spot noise
produces a texture by generating a set of spots on the spatial domain (spot is an ellipse or another shape that wrapes and distributed over domain)
each spot represents a particle moving over a short period of time and results in a streak in the direction of the flow at the position of the spot
enhanced spot noise adds the visualization of the velocity magnitude and allows for curved spots
common form
Classification Of Visualization Approach >> Dense Representation For Partical Tracing Technique

24. Examples
A snapshot of the unsteady spot noise algorithm. Image courtesy of De Leeuw and Van Liere
Classification Of Visualization Approach >> Dense Representation For Partical Tracing Technique

25. Line Integral Convolution (LIC)
common form
LIC was one of the first dense, texture-based algorithms able to accurately reflect velocity fields with high local curvature
Line Integral Convolution >> Foundation

26. LIC-based hierarchy LIC extends directions:
adding flow orientation cues;
(2) showing local velocity magnitude;
(3) adding support for non-rectilinear grids;
(4) animating the resulting textures such that the animation shows the upstream and downstream flow direction;
(5) allowing real-time and interactive exploration;
(6) extending LIC to 3D;
(7) extending LIC to unsteady vector fields;
Line Integral Convolution >> Foundation

27. Curvilinear and unsteady LIC
Basic challenges for original LIC:
LIC portrays a vector field with uniform velocity magnitude
LIC operates over a steady flows
LIC uses only a Cartesian grids
Solutions (by Forsell and Cohen):
curvilinear LIC introduces technique for displaying vector magnitude
use streaklines instead streamlines, so the LIC can trace a path that incorporates multiple time steps
Line Integral Convolution >> Extentions

28. Fast LIC (by Stalling and Hege)
Fast LIC comparison with original technique:
Fast LIC approximately one order magnitude faster than original LIC
Key parts of the fast LIC:
fast LIC minimizes the computation of redundant streamlines present in the original method
fast LIC exploits similar convolution integrals along a single streamline and thus reuses parts of the convolution computation from neighboring streamline texels
Line Integral Convolution >> Extentions

29. Fast LIC modifications
Parallel fast LIC: computes animation sequences on a massively parallel distributed memory computer.
Fast LIC on the surfaces: The approach by Forssell and Cohen was limited to surfaces represented by curvilinear grids. The proposed method works by tessellating a given surface representation with triangles.
Volume LIC: introduces the use of halos in order to enhance depth perception such that the user has a better chance at perceiving the 3D space covered in the visualization
Enhanced fast LIC and LIC with normal: Hege and Stalling experiment with higher order filter kernels in order to enhance the quality of the resulting LIC textures. Scheuermann address this missing orthogonal vector field component by extending fast LIC to incorporate a normal component into the visualization.
Line Integral Convolution >> Extentions

30. Fast LIC example
A result from the volume LIC method. Image courtesy of Interrante and Grosch
Line Integral Convolution >> Extentions

31. Dynamic LIC
DLIC: Sundquist presents an extension to fast LIC in order to visualize time-dependent electromagnetic fields
Assumption: the motion of the field is not necessarily along the direction of the field itself in the case of electromagnetic fields
Result: proposed algorithm handles the case of when the vector field and the direction of the motion of the field lines are independent
Line Integral Convolution >> Extentions

32. Directional problems with LIC
Dye injection: Shen address the problem of directional cues in LIC by incorporating animation and introducing dye advection into the computation. The simulation of dye may be used to highlight features of the flow. But, modelling of dye transport is not always physically correct since dye is dispersed not only by advection, but also by diffusion.
Oriented LIC: address the problem of direction of flow in still images. By orientation, means the upstream and downstream directions of the flow, not visible in the original LIC implementation. Conceptually, the OLIC algorithm makes use of a sparse texture consisting of many separated spots that are smeared in the direction of the local vector field through integration.
Fast Rendering OLIC: A fast version of OLIC is achieved by Wegenkittl and Groller via a trade-off of accuracy for time.
Line Integral Convolution >> Extentions

33. Dye injection examples
Dye injection is used to highlight areas of the flow:
in combination on the boundary,
in combination with a low-contrast LIC texture.
The data set is a slice through an intake port and combustion chamber from CFD
Line Integral Convolution >> Extentions

34. Unsteady Flow LIC
UFLIC: Shen and Kao extend the original LIC algorithm to handle unsteady flows
Idea: introduce a new convolution filter that better models the nature of unsteady flow
Why? According to Shen and Kao, Forssell and Cohens approach (ULIC) has multiple limitations including:
lack of clarity with respect to spatial coherence
deriving current flow values from future flow values
unclear exposition with respect to temporal coherence
lack of accurate time stepping
All of these problems are addressed by UFLIC!!!
Line Integral Convolution >> Extentions

35. UFLIC in action
Results from A Texture-Based Framework for Spacetime-Coherent Visualization of Time-Dependent
Vector Fields, by D. Weiskopf, G. Erlabacher, and T. Ertl.
Line Integral Convolution >> Extentions

36. 3D LIC
Rezk-Salama propose rendering methods to effectively display the results of 3D LIC computations. They utilize texture-based volume rendering in an effort to provide exploration of 3D LIC textures at interactive frame rates
Proposed approach:
use of transfer functions
allow user to see through portions of the LIC textures deemed uninteresting by the user
use of clipping planes
Line Integral Convolution >> Extentions

37. 3D LIC examples
An LIC visualization showing a simulation of flow around a wheel. The appropriate choice of transfer function results in a sparser noise texture. Image courtesy of
Rezk-Salama.
Line Integral Convolution >> Extentions

38. Spot Noise vs. LIC
Spot noise is capable of reflecting velocity magnitude within the amount of smearing in the texture, thus freeing up hue for the visualization of another attribute such as pressure, temperature etc.
LIC is more suited for the visualization of critical points which is a key element in conveying the flow topology. The vector magnitudes are normalized thus retaining lower spatial frequency texture in areas of low velocity magnitude
Line Integral Convolution >> Conclusion

39. Spot Noise vs. LIC (visual comparison)
Visualization of flow past a box using (left) spot noise and (right) LIC.
Line Integral Convolution >> Conclusion

40. References
[1] The State of the Art in Flow Visualization: Dense and Texture-Based Techniques, Robert S. Laramee, Helwig Hauser, Helmut Doleisch, Benjamin Vrolijk, Frits H. Post, and Daniel Weiskopf,
[2] Flow Visualization Overview, Daniel Weiskopf and Gordon Erlebacher
[3] Scientific Visualization of Large-Scale Unsteady Fluid Flows, David A. Lane
[4] Analysis and Visualization of Features in Turbomachinery Fluid Flow, Turbomachinery CFD Flow Visualization,
References

41. Thanx for your attention!!!