COMP502101
This question paper consists
of 4 printed pages,
each of which is
identified by the Code
Number COMP502101
 UNIVERSITY OF LEEDS
School of Computing
January 2003
COMP5021: Data Visualization
Time allowed: 2 hours
Attempt THREE questions.
Question 1
a)
Consider the following simple 2D flow visualization problem. You are given the velocity V(x,y) at the four
corners of the unit square as follows:
V(0,0) = (1,1); V(1,0) = (3,1); V(1,1) = (1,2); V(0,1) = (2,1)
where we express the velocity as a vector of two components, the first giving the velocity component in the
x-direction, and the second the velocity component in the y-direction. Suppose a particle is released at time
t = 0 from seed point (0.7,0.0).
i.
Calculate an estimate of where the particle will travel to after a single time step of 0.1 seconds.
[3 marks]
ii.
State the two major sources of error in this calculation, and explain how these arise.
[2 marks]
iii.
Calculate an estimate of the velocity at the new position of the particle.
[5 marks]
b) For 3D flow visualization, discuss the difficulties in rendering particles and how these difficulties can be
overcome.
[4 marks]
c) Line Integral Convolution is a texture-based technique for 2D flow visualization over a surface.
i.
Describe how the texture effect is created.
[4 marks]
ii.
What is the effect of starting with a coarser initial texture?
[2 marks]
TURN OVER
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COMP502101
Question 2
a)
Isosurfacing and slicing are two approaches to the visualization of scalar 3D data. Each visualizes a
subset of the data. Contrast the methods by explaining how the subset is extracted.
[4 marks]
b) Volume rendering using ray casting is another technique for 3D scalar data defined on a regular,
rectilinear grid.
i.
A key step in volume rendering is calculating the light reflected from a sample point in the
volume. Describe three approaches available to an implementer of a volume rendering
algorithm in performing this calculation, given data values at the vertices of the cube within
which the sample point lies.
[6 marks]
ii.
For each approach, explain the advantages and disadvantages.
[6 marks]
c) The compositing step in ray casting is computationally expensive.
i.
What property of the compositing formula allows the computation to be parallelised?
[2 marks]
ii.
How does Maximum Intensity Projection (MIP) volume rendering reduce the computational
effort required?
[2 marks]
TURN OVER
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COMP502101
Question 3
In this question, you are asked to apply your knowledge of visualization gained during the module to a slightly
different scenario. In the lectures we assumed that the data we had to visualize were exact values. Now let us
suppose that each data value is supplied as an interval a<=f<=b –that is, the data value is greater than or equal to a
but less than or equal to b. We shall denote this interval by [a,b].
a)
Consider 1D scalar visualization where we are drawing a graph through a set of points – or rather now a set
of intervals.
i.
Suppose first there are two data points, x1 and x2, where the values are in the range [a1,b1]
and [a2,b2] respectively. Show that for any particular value of y1 in the range [a1,b1] and any
particular value of y2 in the range [a2,b2], the line joining (x1,y1) and (x2,y2) lies above the
line joining (x1,a1) and (x2,a2). You can either do this by a diagram using geometric
arguments, or do it algebraically.
[2 marks]
ii.
Thus show (by a diagram) how a line graph, using linear interpolation, can be extended to
visualize interval-defined data.
[2 marks]
b) For 2D scalar visualization, consider how contouring might be extended. As usual, it is sufficient to work
within a unit square with lower left corner at the origin (0,0), and to consider a contour level of zero.
Develop a technique for visualizing the zero ‘contour’ of interval-defined data - by ‘contour’ we mean the
set of all possible zero level contour lines that could be drawn, for different combinations of values from the
intervals at each vertex (this ‘contour’ will be an area). You can assume for the purposes of this question
that the contours of the bilinear interpolant to a set of four vertex values can be drawn exactly.
[HINT: It may help to draw the contour line corresponding to the lowest value at each vertex, and regard this as
dividing the unit square into areas where the value is greater than zero, and areas below zero. Do the same for
the highest value at each vertex.]
[12 marks]
c)
Briefly describe how the ‘contour’ technique could be extended to 3D scalar visualization using
isosurfacing.
[4 marks]
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COMP502101
Question 4
a)
Consider the following table of multivariate data showing the percentage of certain chemicals in a number of
separate samples:
Sample 1
Sample 2
Sample 3
Sample 4
Ozone
8
2
0
1
Nitric Oxide
10
9
12
11
Nitrous Oxide
5
15
20
10
Carbon Dioxide
6
10
11
10
Create two visualizations of this data using:
i.
parallel co-ordinates
ii.
star glyphs
[3 marks]
[3 marks]
In each case, take care with the drawings so that you show clearly the range of values of the variables, and
explain the order in which you have chosen to present the variables on the chart.
b) In Information Visualization, ‘focus + context’ is an important concept.
i.
Explain what is meant by the term and describe the benefits it affords – use an application to
illustrate your answer.
[4 marks]
ii.
Describe briefly two practical implementations of the technique.
[4 marks]
iii.
Suggest a ‘focus+context’ representation of the London underground map.
[3 marks]
c)
Describe the Rapid Serial Visual Processing (RSVP) technique for gaining a quick impression of a very
large data set, and suggest an application for which it could be useful.
[3 marks]
END
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