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

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

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

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

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

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

Streamlines, pathlines and streaklines Mathematical Model >> Particle Tracing

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

Numerical integration Mathematical Model >> Numerical Model

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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, http://www.vrvis.at/ar3/pr2/star/ [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, http://www.cg.inf.ethz.ch/~ebauer/turbo/ References

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