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2.1Vis_04
Data VisualizationData Visualization
Lecture 2Fundamental Concepts - Reference
ModelVisualization Techniques – Overview
Visualization Systems - Overview
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2.2Vis_04
A Simple ExampleA Simple Example
TIME (mins)
OXYGEN (%)
0 2 4 10 28 30 32
20.8 8.8 4.2 0.5 3.9 6.2 9.6
This table shows the observed oxygen levels inthe flue gas, when coal undergoes combustionin a furnace
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2.3Vis_04
Visualizing the Data - but is this what we want to
see?
Visualizing the Data - but is this what we want to
see?
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2.4Vis_04
Estimating behaviour between the data - but is
this believable?
Estimating behaviour between the data - but is
this believable?
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2.5Vis_04
Now it looks believable… but something is wrongNow it looks believable… but something is wrong
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2.6Vis_04
At least this is credible..At least this is credible..
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2.7Vis_04
What have we learnt?What have we learnt?
It is not only the data that we wish to visualize - it is also the bits inbetween!
The data are samples from some underlying ‘field’ which we wish to understand
First step is to create from the data a ‘best’ estimate of the underlying field - we shall call this a MODEL
This needs to be done with care and may need guidance from the scientist
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2.8Vis_04
Data EnrichmentData Enrichment
This process is sometimes called ‘data enrichment’ or ‘enhancement’
If data is sparse, but accurate, we INTERPOLATE to get sufficient data to create a meaningful representation of our model
If sparse, but in error, we may need to APPROXIMATE
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2.9Vis_04
The Visualization ProcessThe Visualization Process
Overall the Visualization Process can be divided into four logical operations:– DATA SELECTION: choose the portion
of data we want to analyse– DATA ENRICHMENT: interpolating, or
approximating raw data - effectively creating a model
– MAPPING: conversion of data into a geometric representation
– RENDERING: assigning visual properties to the geometrical objects (eg colour, texture) and creating an image
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2.10Vis_04
Back to the Simple Example
Back to the Simple Example
Data
Enrich
Map
Render
Interpolate to create model
Select a line graph as techniqueand create line segments fromenriched data
Draw line segments on display insuitable colour, line style and width
Select Extract part of data we are interested in
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2.11Vis_04
Classification of Mapping Techniques
Classification of Mapping Techniques
The mapping stage is where we decide which visualization technique to apply to our ‘enriched’ data
There are a bewildering range of these techniques - how do we know which to choose?
First step is to classify the data into sets and associate different techniques with different sets.
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2.12Vis_04
Back to the Simple Example
Back to the Simple Example
The underlying field is a function F(x) – F represents the oxygen level and is
the DEPENDENT variable– x represents the time and is the
INDEPENDENT variable It is a one dimensional scalar field
because– the independent variable x is 1D– the dependent variable F is a scalar
value
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2.13Vis_04
General Classification Scheme
General Classification Scheme
The underlying field can be regarded as a function of many variables: say
F(x)where F and x are both vectors:
F = (F1, F2, ... Fm)
x = (x1, x2, ... xn) The dimension is n The dependent variable can be
scalar (m=1) or vector (m>1)
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2.14Vis_04
A Simple NotationA Simple Notation
This leads to a simple classification of data as:
EnS/V
So the simple example is of type:
E1S
Flow within a volume can be classed as:
E3V3
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2.15Vis_04
ExerciseExercise
Can you give suitable techniques for the following classes:
ES1
ES2
ES3
EV33
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2.16Vis_04
Overview of Visualization Techniques
Overview of Visualization Techniques
Using the classification to organise the various visualization
techniques
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2.17Vis_04
ES1ES1
The humble graph!
How can we represent errors in the data?
A nice example of web-basedvisualization….
http://fx.sauder.ubc.ca/plot.html
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2.18Vis_04
ES2ES2
Here we see a contour map of wind speed over the USA (28-Sep-04)
What can you observe?
Can you use an ES
1 technique for this sort of data?
http://weather.unisys.com/surface/
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2.19Vis_04
ES3ES3
As dimension increases, it becomes harder to visualize on a 2D surface
Here we see a lobster within resin.. where the resin is represented as semi-transparent
Technique known as volume rendering
Image from D. Bartz and M. Meissner
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2.20Vis_04
ES3ES3
Corresponding to contours for ES
2, we can generate isosurfaces
What are the limitations of this approach compared with volume rendering? Image from D. Bartz and M. Meissner
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2.21Vis_04
EV22EV22
This is a flow field in two dimensions
Simple technique is to use arrows..
What are the strengths and weaknesses of this approach?
During the module, we will discover better techniques for this
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2.22Vis_04
EV33EV33
This is flow in a volume
Arrows become extremely cluttered
Here we are tracing the path of a particle through the volume
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2.23Vis_04
Visualization SystemsVisualization Systems
Showing how the map and render steps are realised in a visualization system
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2.24Vis_04
IRIS ExplorerIRIS Explorer