Image Space Based Visualization of Unsteady Flow on Surfaces Robert Laramee Bruno Jobard Helwig Hauser Presenter: Bob Armstrong 24 January 2007

What's This About? New Algorithm: ISBV  Generates dense representations of arbitrary fluid flow on computational fluid dynamics (CFD) surfaces Applied to unsteady flow on boundary surfaces of complex meshes from CFDs of more than 250K polygons, dynamic meshes, medical data Seeing is believing

Visualization of flow on the surface of an intake manifold. The ideal intake manifold distributes flow evenly to the piston valves.

Visualization of flow at the complex surface of a cooling jacket – a composite of over 250,000 polygons

The Baldwin-Lomax model is a classical algebraic turbulence model which is suitable for high-speed flows with thin attached boundary-layers, typically present in aerospace and turbomachinery applications.

What's the Problem? Traditional direct visualization of unsteady flow is computationally expensive  No real-time production  Animation/Simulation is expensive

Their Approach Build off of Past Work  LEA  IBFV Reduce complexity by generating 3D vector fields onto 2D image space

Past Work Foundation for the ISBV Algorithm Both produce dense representations of unsteady, 2D vector fields LEA:  Lagrangian-Eulerian Advection IBFV:  Image Based Flow Visualization

Lagrangian-Eulerian Advection Produces animations with high spatio- temporal correlation All data stored in 2D arrays Each frame depicts instantaneous flow structure Generates animations at interactive frame rates

Image Based Flow Visualization Simulation of 2D fluid flow Each frame of a flow animation is a blend between a warped version of the previous image and a number of background images. Relies on graphics hardware

IBFV Method image kdistortrenderblend k = k + 1 Note Distortion Phase: There is nothing to stop the image from being advected outside of the geometrical boundary.

Definition: CFD Computational Fluid Dynamics  Branch of Fluid Mechanics  Relies on Numerical Methods & Algorithms

More CFD How does one treat a continuous fluid in a discretized fashion on a computer?  Widely used: Discretize the spatial domain into small cells that form a grid or mesh  Apply suitable algorithm to solve the equations of motion.

Definition: Advection Advection is transport of a conserved scalar quantity in a vector field. A good example is the transport of pollutants or silt in a river: the motion of the water carries these impurities downstream.

Different Advections VelocityVorticityVorticity mapped to helicity More information here:

A hybrid stream surface-texture advection visualization showing tumble motion inside a gas engine cylinder. Texture is advected according to the velocity field and color is mapped to velocity magnitude.

The same stream surface geometry. Texture is advected according to the vorticity field and color is mapped to vorticity magnitude. The relationship to the velocity field can be explored in a novel fashion.

The same stream surface geometry. Texture is advected according to the vorticity field and color is mapped to helicity. Mapping color to helicity indicates candidate vortex core regions.

Traditional Visualization Methods Maps one or more 2D textures to a 3D geometrical surface Textured geometry rendered to an image space

ISBV Algorithm Project surface geometry to image space Apply texturing Texture properties are advected in image space

ISBV Method (1) Associate the 3D flow data with polygons at boundary surface Project the surface and vector field onto the image plane Identify geometric discontinuities Advect texture properties according to the vector field in image space

ISBV Method (2) Inject and blend noise Apply additional blending along the geometric discontinuities previously identified Overlay all optional visualization cues such as showing a semi-transparent representation of the surface with shading

Flow Diagram Vector Field Projection Edge Detection Compute Advection Mesh Edge Blending Noise Blending Image Overlay Application Image Advection Dynamic Case k = k+1 Static Case k = k+1 k = time as a frame #

Vector Edge Projection Project vector field to the image plane Velocity vectors stored at the polygon vertices Encode velocity vectors as color values at the mesh vertices

Color & Velocity Component Color assignment done as a scaling operation Each color component assigned velocity

Why Use Velocity Image Fields? Advection computation, noise blending simpler in image space Vector field and polygon mesh decoupled Hardware-accelerated occlusion culling Supported on graphics hardware

Velocity Vectors Decoded vectors used to compute advection mesh, then projected upon the image plane

Timing of Projection of Vectors Project vectors to image plane after velocity image construction  Don't have to project all vectors  Use original 3D vectors for the velocity mask

Example Velocity Image Field

Edge Detection Edge detection solves the problem of artificial flow continuity because of artifacts from 3D to 2D image space projection Selectively detects only edges affecting flow texture properties

Problem with Sharp Edges

Geometric Edge Boundaries

Edge Blending During this phase of the algorithm  Introduce discontinuities in the texture aligned with discontinuities from the surface  Essentially, ensure that edges are accounted for visually

Geometric Edge Detection DisabledEnabled

Compute Advection Mesh Distort regular, rectilinear mesh according to velocity vectors stored at mesh grid intersections p is a path line, k is a frame Above ensures that distortion does not extend beyond geometric boundaries.

Image Advection & Texture Clipping Coarse Resolution Advection Mesh, With Artifacts Texture Clipping applied

Noise Blending Use IBVF method for noise injection and blending

Blending Sample Noise Image Sample Blended Image

No Edge Blending With Edge Blending

Image Overlay Application Optional step Overlay enhances visualization with colorization, shading, etc. Overlay Applied Composite of All

Vector Projection The projection of the vectors to the image plane is done after velocity image construction for 2 reasons:  not all of the vectors have to be projected, thus saving computation time  can use the original 3D vectors for the velocity mask

Performance

Performance Discussed Authors looking for speedup; specifically, increased frame rates  up to 20 fps Performance tied to image resolution & polygon count (unsteady state flow) Don't have any good comparative figures

79K polygons dynamic geometry dynamic topology time-lapsed pics

221K Polygonal Intake Port

Intake Port Mesh Close-Up