1 Streamtube example Streamtube example 6 streamlines 6 - - PDF document

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Advection methods comparison

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Stream-ribbon

We really would like to see vorticities, I.e. places were the flow twists. A point primitive or an icon can hardly convey this idea: trace neighboring particles and connect them with polygons shade those polygons appropriately and

• ne will detect twists

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Stream-ribbon Problem - when flow diverges Solution: Just trace one streamline and a constant size vector with it:

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Stream-tube

Generate a stream-line and connect circular crossflow sections along the stream-line

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First of two other line icons ...

Narrow surfaces between two adjacent streamlines Built from a front with only two particles Reflect flow divergence through changing width, and Vortices are shown in the degree of twist in the ribbon

Stream Ribbons

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Vorticity

Formally

⌧Vorticity ω - measure of rotation of vector field

Streamwise vorticity where v - instantaneous velocity

Flow divergence

Measure of the spread of the flow

Streamribbons

Ω = v . ω |v| . |ω|

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Streamtube example

• 6 streamlines
• Streamline added for

comparison

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Streamtube example

• 6 streamlines
• Alternative generation
• Stream polygon
• Rotation of edges vorticity
• Area of polygon divergence

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Stream-balls Another way to get around diverging stream- lines simply put implicit surface primitives at particle traces - at places where they are close they’ll merge elegantly ...

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Streamballs

Stream balls:

Display stream lines as chains of balls and use their radius and Color to encode scalar values

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Global Texture Techniques

Two approaches:

Advection-based

⌧Streamline placement

Icon placement or smearing

⌧Spot Noise ⌧Vector Kernel ⌧Line Integral Convolution ⌧Line Bundles

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2D vector field visualization

We want to visualize a function with F given only at certain vertices

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: F I R Ω

x ij ij y ij

F F F F   ↔ =      

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Mappings - Hedgehogs, Glyphs

analogous to tufts or vanes from experimental flow visualization clutter the image real quick maybe ok for 2D not very informative

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2D vector field visualization

First idea

Visualize the two scalar fields Fx and Fy As the two components are normally not independent, this usually provides no insight.

Second idea

Data is supposed to represent the direction of moving particles Visualize the “flow“ Do it by means of glyphs or particle tracing

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2D vector field visualization

Glyphs

We display the vectors using arrows as geometric primitives Draw an arrow at every vertex of the grid

⌧Length corresponds to magnitude of velocity ⌧Direction corresponds to flow direction

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2D vector field visualization

Pros and Cons of glyphs

Simple 3D effects Heavy load in the graphics subsystem Inherent occlusion effects Poor results if magnitude of velocity changes fast Use arrows of constant length and color code magnitude

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Global techniques

• Display the entire flow field in a single picture
• Minimum user intervention
• Example: Hedgehogs (global arrow plots)

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Mappings - Hedgehogs, Glyphs

Put “icons” at certain places in the flow

e.g. arrows - represent direction & magnitude

• ther primitives are

possible

• riented

lines glyphs vortex

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2D vector field visualization

Example

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Advection-Based Textures

Streamline placement

Banks and Turk

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Streamline Placement

Movie

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Icon Placement

Hedgehogs or arrow plots: uniform grid

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Icon Placement

Image-filling and randomized

Banks and Turk

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More artistic

David Laidlaw

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Arrows Arrows

But in 3D it suffers from perception problems:

Is it this?

• r this?

Of course the picture quickly gets cluttered too

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Arrows Arrows

Arrows can be used successfully in 3D as follows:

by slicing the volume, and attaching arrows (with shadow effects) to the slice plane - this gives a hedgehog effect by giving more spatial cues - drawing arrows as true 3D objects

but clutter again a problem!

{BTW - Eulerian or Lagrangian?}

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Example of a complex Glyph

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Vector Kernel

An image kernel moves in a discrete and jittered path left to right and top to bottom across the image screen. The kernel samples the scalar and vector fields. The vector field uses a weighted probability of drawing an anti-aliased line across the kernel. The line is oriented in the vector field direction. The line may also be semi-transparent. The probability is proportional to the vector magnitude.

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Vector Kernel

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Spot Noise for Flow Visualization Spot Noise for Flow Visualization

Spots of random size and intensity drawn in a plane give a texture effect

Texture defined as an intensity function f: f( x ) = Σ ai h( x - xi ) where xi is random position, ai is random scale (zero mean), and h is the spot function - zero everywhere except for small area (here circular)

• ne spot

many spots spot texture

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Spot Noise for Flow Visualization

Different textures result from different spot shapes Aligning the shape of the spot with the direction

• f flow gives a good visualization effect

In direction of flow, scale proportional to ( 1 + |v | ) , |v| = velocity magnitude At 90 degrees to flow, scale proportional to 1 / ( 1 + | v | )

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Spot Noise Example

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Spot Noise

Uses small motion blurred particles to visualize flows on stream surfaces Particles represented as ellipses with their long axes oriented along the direction of the flow I.e. we multiply our kernel h with an amplitude and add a phase shift! Hence - we convolve a spot kernel in spatial domain with a random sequence (white noise)

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Spot Noise

examples of white noise:

set of random values on a grid Poisson point process - a set of randomly scaled delta functions randomly placed (dart throwing)

variation of the data visualization can be realized via variation of the spot:

d - data value m - parameter mapping

( ) ( ) ( ) ( )

∑

− =

k k k k

x x x d m h a x f ,

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Rendering - Spot Noise

Different size Different profiles

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Rendering - Spot Noise

bla

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Rendering - Spot Noise

Scalar - use +-shape for positive values, x- shape for negative values change the size of the spot according to the norm of the gradient vector data - use an ellipse shaped spot in the direction of the flow ...

scalar gradients flow Velocity potential

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Spot Noise for Flow Visualization Spot Noise for Flow Visualization

If velocity direction varies rapidly, result is not very successful

Improvement achieved by ‘bending’ spot along the streamline

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Flow Over a Surface

Wall friction displayed using oil and paint - wind evaporates oil and paint leaves white traces Numerical simulation

• f flow, visualized

using spot noise

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Spot Noise Example

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Spot Noise Movie

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Learning More about Spot Noise

Spot noise has been developed by researchers in the Netherlands

van Wijk and de Leeuw see http://www.cwi.nl/~wimc/spotnoise.html Thanks to Wim de Leeuw for the images used in these slides

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Rendering - LIC

Similar to spot noise embed a noise texture under the vector field difference - integrates along a streamline

LIC Spot Noise

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Line Integral Convolution (LIC)

Essence of method is:

consider a white noise texture, T(x,y) for each pixel, set its intensity as a function (eg average) of values of T along a short streamline segment through the pixel this has effect of correlating the resulting pixel values along streamlines, so a sense of the flow direction is

• btained

white noise flow lines LIC

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LIC Example

Flow over surface of car - from CIRA, Italy Italian Aerospace Research Centre

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LIC Example

Flow underneath car - from CIRA, Italy

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LIC Developments - Oriented LIC LIC Developments - Oriented LIC

Original LIC shows direction of flow but not orientation (ie -> or <- ) Oriented LIC uses a sparse texture and a weighting of samples along streamline to give orientation effect

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Learning More about LIC Learning More about LIC

Original LIC

B Cabral and C Leedom, Imaging Vector Fields Using Line Integral Convolution, SIGGRAPH93, ACM Computer Graphics, pp263-270, 1993

Fast LIC

www.zib.de/Visual/projects/vector includes the Lic Factory - Java applet

Oriented LIC

R Wegenkittl and E Groller www.cg.tuwien.ac.at/research/vis/dynsys/frolic/

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Algorithm - Cabral & Leedom ‘93

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Line Integral Convolution

Rather than deposit energy

• n each pixel,

integrate the icon weights with a white noise function.

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2D LIC

What do LIC–images look like?

smooth change of color along time line, but rough alternation perpendicular to it visual impression like a painting depicts the directional structure of the vector field but not the magnitude of the flow

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LIC Example: 2D Airfoil

Han-Wei Shen

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Streamline and LIC Comparison

Han-Wei Shen

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Line Integral Convolution (LIC)

Han-Wei Shen

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LIC Example: Space Shuttle

Han-Wei Shen

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Enhancements

LIC is computationally expensive

Fast LIC (Stalling and Hege ‘95) PLIC (Verma et al ‘99)

LIC is primarily for regular Cartesian grids

Curvilinear LIC (Forsell ‘95)

LIC is primarily 2D

3D Volume LIC (Shen et al ‘96, Interrante ‘97, Rezk-Salama ‘99)

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Fast LIC: an order of magnitude faster

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(Rezk-Salaman ‘99)

3D Volume LIC

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LIC and Stream Surfaces

http://www.zib.de/Visual/projects/vector/

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LIC Factory

Cool website

LIC Factory

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Movement Without Motion

An oscillating filter weight can produce the appearance of motion.

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Movement in LIC

The integral weights are shifted to form an oscillation along the streamline. Global Winds movie of a single timestep.

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Changing the Texture

By controlling the white noise to band- limited noise with varying frequencies, different textures can be generated.

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Textured Splats

Use graphics hardware at the data points to brush a texture image canvas for that data point. Do this in a depth-sorted

• rder to get a

volume rendering.

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Texture Splats

Crawfis, Max 1993 extended splatting to visualize vector fields used simple idea of “textured vectors” for visualization of vector fields

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Texture Splats - Vector Viz

The splat would be a Gaussian type texture how about setting this to an arbitrary image? How about setting this to an image including some elongated particles representing the flow in the field? Texture must represent whether we are looking at the vector head on or sideways

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Texture Splats

Texture images Appropriate opacities

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Texture Splats - Vector Viz

How do you get them to “move”? Just cycle over a periodic number of different textures (rows)

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More global techniques Texture Splats

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Textured Splats

See VectorVizNotes

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Line Bundles

For vector fields

• nly, just use a

collection of semi-transparent lines.

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Line bundles

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Spot Noise