2.1 Vis_04 Data Visualization Lecture 2 Fundamental Concepts - Reference Model Visualization Techniques – Overview Visualization Systems - Overview

2.2 Vis_04 A Simple Example TIME (mins) OXYGEN (%) This table shows the observed oxygen levels in the flue gas, when coal undergoes combustion in a furnace

2.3 Vis_04 Visualizing the Data - but is this what we want to see?

2.4 Vis_04 Estimating behaviour between the data - but is this believable?

2.5 Vis_04 Now it looks believable… but something is wrong

2.6 Vis_04 At least this is credible..

2.7 Vis_04 What have we learnt? n It is not only the data that we wish to visualize - it is also the bits inbetween! n The data are samples from some underlying ‘field’ which we wish to understand n First step is to create from the data a ‘best’ estimate of the underlying field - we shall call this a MODEL n This needs to be done with care and may need guidance from the scientist

2.8 Vis_04 Data Enrichment n This process is sometimes called ‘data enrichment’ or ‘enhancement’ n If data is sparse, but accurate, we INTERPOLATE to get sufficient data to create a meaningful representation of our model n If sparse, but in error, we may need to APPROXIMATE

2.9 Vis_04 The Visualization Process n 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

2.10 Vis_04 Back to the Simple Example Data EnrichMapRender Interpolate to create model Select a line graph as technique and create line segments from enriched data Draw line segments on display in suitable colour, line style and width Select Extract part of data we are interested in

2.11 Vis_04 Classification of Mapping Techniques n The mapping stage is where we decide which visualization technique to apply to our ‘enriched’ data n There are a bewildering range of these techniques - how do we know which to choose? n First step is to classify the data into sets and associate different techniques with different sets.

2.12 Vis_04 Back to the Simple Example n 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 n It is a one dimensional scalar field because – the independent variable x is 1D – the dependent variable F is a scalar value

2.13 Vis_04 General Classification Scheme n The underlying field can be regarded as a function of many variables: say F(x) where F and x are both vectors: F = (F 1, F 2,... F m ) x = (x 1, x 2,... x n ) n The dimension is n n The dependent variable can be scalar (m=1) or vector (m>1)

2.14 Vis_04 A Simple Notation n This leads to a simple classification of data as: E n S/V n So the simple example is of type: E 1 S n Flow within a volume can be classed as: E 3 V 3

2.15 Vis_04 Exercise n Can you give suitable techniques for the following classes: n E S 1 n E S 2 n E S 3 n E V 3 3

2.16 Vis_04 Overview of Visualization Techniques Using the classification to organise the various visualization techniques

2.17 Vis_04 ES1ES1 ES1ES1 n The humble graph! n How can we represent errors in the data? A nice example of web-based visualization….

2.18 Vis_04 ES2ES2 ES2ES2 n Here we see a contour map of wind speed over the USA (28-Sep-04) n What can you observe? n Can you use an E S 1 technique for this sort of data?

2.19 Vis_04 ES3ES3 ES3ES3 n As dimension increases, it becomes harder to visualize on a 2D surface n Here we see a lobster within resin.. where the resin is represented as semi-transparent n Technique known as volume rendering Image from D. Bartz and M. Meissner

2.20 Vis_04 ES3ES3 ES3ES3 n Corresponding to contours for E S 2, we can generate isosurfaces n What are the limitations of this approach compared with volume rendering? Image from D. Bartz and M. Meissner

2.21 Vis_04 E V2 2 n This is a flow field in two dimensions n Simple technique is to use arrows.. n What are the strengths and weaknesses of this approach? n During the module, we will discover better techniques for this

2.22 Vis_04 E V3 3 n This is flow in a volume n Arrows become extremely cluttered n Here we are tracing the path of a particle through the volume

2.23 Vis_04 Visualization Systems Showing how the map and render steps are realised in a visualization system

2.24 Vis_04 IRIS Explorer