Flow Visualisation - University of Edinburgh

Taku Komura Flow Visualisation 1

Visualisation : Lecture 13

Visualisation – Lecture 13

Taku Komura

Institute for Perception, Action & BehaviourSchool of Informatics

Flow Visualisation



Flow Visualisation .... so far● Vector Field Visualisation

– vector fields indicate transport (i.e. flow)— local methods for local direction and magnitude— global methods for flow sources and paths

● global methods require:— numerical integration— particle trace calculation— rakes for initialisation



Rakes – a reminder● Shape (or topology) of stream origin



Stream Ribbons & Surfaces● Concept : initialise two streamlines together

– flow rotation: lines will rotate around each other– flow convergence/divergence: relative distance between lines– both not visible with regular separate streamlines

● Streamribbon– initialise 2 streamlines from a rake line and connect with polygons

● Streamsurface– initialise multiple streamlines along a base curve or line rake and

connect with polygons



Streamribbons● Initialisation : two connected streamlines

– Global view of vector field flow – as per streamlines– Local view of vector field variation

— width of ribbon (distance between connected lines)= cross-flow divergence

— twisting of ribbon = streamwise vorticity– rotation of the vector field flow around the streamline– axis of rotation = vector field direction (in stream)– magnitude of rotation = vorticity



Example : streamribbonsLocal information clearer using ribbons

– cannot show vorticity rotation with un-orientated line

● Problem if streamlines diverge significantly– expect ribbon orientation to

be tangent to vector field

Streamribbons

Streamlines



Streamsurfaces● Initialisation: infinite number of connected streamlines

originating from a given base curve (i.e. the rake)– streamribbons are special case of streamsurfaces– by using a closed base curve – streamtubes– generate multiple streamlines from user specified rake,

connect adjacent lines with polygons● Properties:

– surface orientation at any point on surface tangent to vector field– no visual interpolation required by viewer– additional information : divergence & vorticity



Example : streamtubes

● Local variance in flow clearer than with glyphs / lines /dots

Size of tube varies with temperature and velocity of the flow.



Flow Volumes : simulated smoke– initialise with a seed polygon – the rake– calculate streamlines at the vertices.– split the edges if the points diverge.



Rendering Flow Volumes● Temporal Volume Rendering of Flow

– define colour based on vorticity– good property to render due to persistence – dependence

on previous states

[Max, Becker, Crawfis http://www.llnl.gov/graphics/sciviz.html]



Flow Visualisation Limitations● “Plotting” Methods

– take up too much space to plot– wasted space in between glyphs when used– simulations getting larger and larger

● Streamline methods (global view lecture 12/13)– also take up a lot of space– user definition of rakes – domain/task specific

● Particle methods (e.g. storm, lecture 12)– particles tend to bunch and poorly sample the domain



Flow Visualisation Ideals - ?● High Density Data – ability to visualise dense vector

fields● Effective Space Utilisation – each output pixel

(in rendering) should contain useful information● Visually Intuitive – understandable● Geometry independent – not requiring user or

algorithmic sampling decisions that can miss data ● Efficient – for large data sets, real-time interaction● Dimensional Generality – handle at least 2D & 3D data



Direct Image Synthesis● Concept : modify an image directly with reference to the

vector flow field– alternative to graphics primitives (e.g. in VTK)– modified image allows visualisation of flow

● Practice :– use image operator to modify image– modify operator based on local value of vector field– use initial image with no structure

— e.g. white noise (then modified by operator to create structure)



Example : Direct Image Synthesis● Line Integral Convolution (LIC)

– image operator = convolution

Graphics : http://www.hpc.msstate.edu/~zhanping/Research/FlowVis/LIC/LIC.htm

Vector Field White Noise Image LIC Image



How ? - image convolution

● Each output pixel p' is computed as a weighted sum of pixel neighbourhood of corresponding input pixel p– weighting / size of neighbourhood defined by kernel filter

Input pixels

Output pixels

FilterKernel



Example : image convolution

● Linear convolution applied to an image– linear kernel (causes blurring)



Effects of Convolution● convolution ‘blurs’ the pixels together

– amount and direction of blurring defined by kernel● perform convolution in the direction of the vector field

– use vector field to define (and modify) convolution kernel – produce the effect of motion blur in direction of vector field

● strong correlation along the vector field streamlines ● no correlation across the streamlines.



Principle of LIC

Input white noise. Streamlines in vector field

LIC result



Example : wind flow using LIC

Data: atmospheric wind data from UK Met. Office Visualisation : G. Watson (UoE)

Colour-mapped LIC



LIC : stated formallyp is the image domain

s is the parameter along the streamline, L is streamline length

F(p) is the input image

F’(p) is the output LIC image

P(s) is the position in the image of a point on the streamline

k(s) is the convolution kernelDenominator normalises the output pixel(i.e. maps it back into correct value range to be an output pixel)



LIC : streamline calculation● Constrain the image pixels to map 1-to-1 to the

vector field cells– for each vector field cell, the input white noise image has a

corresponding pixel

● Compute the streamline forwards and backwards in the vector field using variable-step Euler method.

● Compute the parametric endpoints of each line streamline segment that intersects a cell.



LIC : variable step Euler's method

P0

P1

P2

P3

Image and vector field cells.



LIC : approximating the kernel integral

P0

s1

s2

s3

Image and vector field cells

h i= ∫s i

si1

k s ds

Find parametric endpoints of line intersections

Between endpoints line is straight with constant valued F(p).

Evaluate using 1D summed area table



LIC : output image● Choice of L is important

– too small, not enough blurring (noise remains)– too large, miss small features

● Choice of Filter kernel– Average filter is simplest– Gaussian based kernel gives better localisation



What does the LIC show?● Constant length convolution kernel

– small scale flow features very clear– no visualisation of velocity magnitude from vectors

— can use colour-mapping instead

● Kernel length proportional to velocity magnitude– large scale flow features are clearer– poor visualisation of small scale features



LIC : 2D resultsVariable length Kernel Fixed length Kernel



Example : colour-mapped LIC

[Stalling / Hege ]

Zoom into an LIC image with colour mapping

Colourmap represents pressure



LIC : extension to 3D● LIC on uv parametric surfaces

Vector field on surface to be visualised

u

v

Perform LIC in uv parameter space

uv coordinates are the same as used in texture coordinates



LIC : 3D results



LIC : steady / unsteady flow● LIC : Steady Flow only (i.e. streamlines)

– animate : shift phase of a periodic convolution kernel[Cabral/Leedom '93]

● UFLIC : Unsteady Flow– Streaklines are calculated rather than streamlines– convolution takes time into account.

— Result of previous time step is used for input texture for next step

[Kao/Shen '97]



VTK : stream surfaces● StreamTube – vtkStreamLine object through vtkStreamTube filter

● StreamRibbon - vtkRibbonFilter (lines to ribbons)● StreamSurface - vtkStreamLine object through vtkRuledSurfaceFilter filter



Summary● Stream ribbons and surfaces:

– global visualisation of vector field and visualisation of local vector field variations

– methods have limitations● LIC

– steady flow visualisation using direct image synthessis

– convolution with kernel function– 3D & unsteady flow extensions

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