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Data VisualizationData Visualization

Lecture 2Fundamental Concepts - Reference

ModelVisualization Techniques – Overview

Visualization Systems - Overview

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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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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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Estimating behaviour between the data - but is

this believable?

Estimating behaviour between the data - but is

this believable?

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Now it looks believable… but something is wrongNow it looks believable… but something is wrong

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At least this is credible..At least this is credible..

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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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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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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

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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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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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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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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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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ExerciseExercise

Can you give suitable techniques for the following classes:

ES1

ES2

ES3

EV33

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Overview of Visualization Techniques

Overview of Visualization Techniques

Using the classification to organise the various visualization

techniques

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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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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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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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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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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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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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Visualization SystemsVisualization Systems

Showing how the map and render steps are realised in a visualization system

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IRIS ExplorerIRIS Explorer