MM1CPM_CW2

COMPUTER PROGRAMMING - Coursework 2

Introduction:

This coursework is designed to help you revise your basic MATLAB knowledge

that you have gained in lectures 4-9. For each question you should write a script

that contains the answers. Save your scripts to disk with some sensible name for

example, the ffle containing the code for question one could be called Q1.m.

Once you have ffnished all the questions (or as many as you can manage), zip all

your scripts up into a single zip ffle and upload this to moodle. Name the zip ffle

using the following format Firstname_surname_studentid.zip. So for example my

In each .m ffle you generate, put on the ffrst line your name and e-mail address –

the markers will use this e-mail address to give you feedback. For questions

which require you to write English sentences just include these as comments

using the '%' character in a script ffle. Try to include comments in the script ffles

describing what the program is doing – you will get marks for this.

Finally, please remember this is individual work and not group work. Work

handed in must be entirely your own and not copied from anyone else. By all

means discuss the coursework with your friends BUT then go away and write the

programs yourself.

1Question 1 (10% of total mark): This question will

help you reinforce your basic computer knowledge.

Answer, by writing comments in a script ffle Q1.m:

a) Name the ffve fundamental components of a

computer which were covered in the lecture.

b) In no more than 10 words describe what each

component does.

c) Why does it take more time to get information from

a hard disk than from the computers main memory.

d) Give three examples of an embedded computer that

you use in your daily life.

Question 2 (10% of total mark): All computers store and transmit text as

American Standard Code for Information Interchange (ASCII) code. When you

start writing programs to interface to robots in your mechatronics courses you

will use ASCII code a lot to send commands to these robots. This question helps

you practice using ASCII code in MATLAB, make a new script called Q2.m and

answer the following questions:

a) Write a short program which asks the user to enter their name.

b) Make the program convert the text the user entered to ASCII numbers.

c) Using your program convert the

sentence 'Computers store all data as

numbers' to ASCII code. Save the

resulting list of numbers in Q2.m as a

comment.

Question 3 (10% of total mark):

This question lets you practice using

the sprintf and disp commands. Very

often when dealing with embedded

computers you won't have much

screen space to display information. It

is therefore important to be able to

carefully control text output.

Using one disp command and one

sprintf command make MATLAB print

out the poem on the right.

2

Oh! I have slipped the surly bonds of earth,

And danced the skies on laughter-silvered wings;

Sunward I've climbed, and joined the tumbling

mirth

Of sun-split clouds, --and done a hundred things

You have not dreamed of -- Wheeled and soared and

swung

High in the sunlit silence. Hov'ring there

I've chased the shouting wind along, and flung

My eager craft through footless halls of air...

Up, up the long, delirious, burning blue

I've topped the wind-swept heights with easy grace

Where never lark or even eagle flew --

And, while with silent lifting mind I've trod

The high untrespassed sanctity of space.

John Gillespie Magee, Jr

Figure 1: An Intel processor

chip seen from below. The

gold pins are the electrical

contacts used for getting

information in and out of the

chip.The poem should be formatted exactly the same way as I have formatted it,

including:

*Spaces between lines

*The author's name should be right aligned using tabs.

*All special characters should be printed.

Store your answer in Q3.m.

Question 4 (10% of total mark): This question lets you practice matrix

operations in MATLAB. Write a script to do the following and save it as Q4.m:

a) Generate the following matrices:

a=

[

0 0 1

0 1 0

0 0 1]

b=

[

1 0 0

0 1 0

1 0 0]

b) Add matrix a to matrix b and store the result in 'B'.

c) Subtract matrix a from matrix b, and store the result in 'C'

d) Perform a matrix multiplication of a by b.

e) Add four to each element of matrix a, and store the result in matrix e.

f) Generate a random matrix 10x10 between the values of -10 and 10 called Z

use surf to plot this matrix.

g) Calculate the determinant of matrix Z.

Question 5 (20% of total mark): This question is about basic image

processing, it will help you practice loops and 2D arrays. We are going to use

MATLAB to load in an image, then we are going to write an algorithm to adjust

the exposure. The algorithm we are going to write is used in digital cameras and

photo processing software. From moodle download the zip ffle CW2.zip, in this

ffle you will ffnd the jpg ffle museum_london.jpg, which is a picture of the natural

history museum in London. Extract this image to your home directory, then write

a script to do the following:

a) Load the image ffle using the imread command into an array 'a'. The imread

command works just like the load command, and will produce a 2D array of

numbers. Each element in the array represents the brightness of one pixel in the

image. The lower the number the darker the pixel, the higher the number the

brighter the pixel.

3b) Display the image using the command imshow(a), the image you see should

look like ffgure 2

c) Make two copies of the array 2D 'a', into variables 'L' (for light) and 'D' (for

dark).

d) The ffrst thing to do when working with a new array is to ffnd and store its

size. Calculate the size of the array 'a', using the size command and store the x

and y size in two variables x_len and y_len.

e) We now need to start writing our code to process the image. The ffrst step is

to write two nested for loops which will iterate over each pixel in the image. To

do this write one for loop that counts using x from 1 to the x_len. Now deffne a

second for loop inside the ffrst for loop which counts from 1 to y_len using y.

You have just made a nested for loop. There are more examples of how to do

nested loops in lecture 5. Now, by using the sprinf and disp commands within

the nested for loop, make the script display the following text for each pixel:

The brightness of pixel at ?,?? is ???.

where ? represents the x position, ?? represents the y position and ??? represents

the pixel brightness.

f) Now comment out the command printing each brightness value to the screen

(but don't delete them – otherwise you won't get the marks). We are now going

to make the image darker (less exposed). Within the nested for loops, multiply

each value stored at each position in array 'a' by 0.3 and store the result in the

same location in array 'D'. Now at the end of your script use imshow to display

the darker version of the image. If you issue the ffgure command before

imshow, matlab will display each ffgure in a new window. Compare the original

and less exposed images.

g) Now we are going to increase the exposure of the image by making it lighter.

Within the nested for loops, multiply each value stored, at each position in the

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Figure 2: The natural history museum in London.array 'a' by 1.5 and store the result in the same location in array 'L'. Display the

result in a new ffgure.

h) Often it is important to know how long a piece of code takes to run. MATLAB

has two built in functions to help you ffnd out how long code takes to run. These

are tic and toc functions. They work a bit like a stop watch, the tic command

starts a stop watch and toc stops the stop watch. When toc is called the time

elapsed is also printed out. Try putting tic at the beginning of your program and

toc at the end of your program. How long does it take your program to run?

Write the result as a comment in your program.

i) Now comment out the nested for loop with the '%' character so that it no

longer runs (but don't delete it – otherwise you won't get the marks), and replace

its functionality with matrix multiplication commands. How long does your

program now take to run – why is this?

Question 6 (20% of total mark): This question is designed to help you

practice writing simple functions.

a) Write a script to prompt the user for the height, width and breadth of a box.

The computer should then use the disp command and the sprintf command to

write the text:

Your box has dimensions width=??, height=??, length=??

Where ?? are replaced with the information the user entered.

b) Deffne a function called box_area which accepts three variables and returns

the area of the box.

c) Deffne another function called box_volume, which accepts three variables and

returns the volume of the box.

d) Use these functions to print the text:

The box has the area of xxx and volume of xxx.

e) Edit the script to ask the user for the units used in the measurements, then

adjust the text to read

The box has the area of xxx units_for_area and volume of xxx units_for_volume.

Where units_for_area and units_for_volume are replaced by the correct units.

Hint: You have to use %s*%s*%s, and %s*%s in the sprintf command to print the

correct units.

f) Edit the script so that if the user enters the dimensions height=5, width=30,

length=30 the program prints to the screen 'It's a pizza box!'

5Question 7 (20% of total mark): This example will

help you practice for loops, while loops and if

statements. In this question we are going to use

MATLAB to simulate randomly moving gas particles in

a box. To simplify the problem we are only going to

simulate a 2D gas in a 2D space. Please note: This

question is quite tricky and I don't expect everyone to

finish it, I have put it in because it's quite fun and will

challenge the people who find MATLAB easy. Try to

do as much as you can.

Generating a 2D box

a) Define a 2D array called 'a' of size 8x8 only

containing zeros, this array represents an empty 2D box containing no gas

particles. We are going to represent gas particles within the box by using the

number 1. Set the point at 3,3 to be equal to one, this represents one gas

particle at position 3,3.

b) Using the imagesc make your script display the 2D matrix 'a'. This command

works just like surf but only produces flat 2D images.

c) Just as you did in question 5 find out the size of the matrix 'a', and store its x

and y size in the variable 'x_len' and 'y_len'.

d) Again, just as you did in question 5, write two nested for loops which iterate

through all the x and y coordinates to the array 'a'. Use sprintf and disp to

output the following text for each point in the 2D array:

'At the value x=??, y=?? the value of a=??'

Where ?? are replaced by the current x value, y value and corresponding value of

a(y,x)

e) Place the disp command and the sprintf within an if statement, so that the

text is only printed when value at a(y,x) is equal to 1. Change the line of text to

read:

'A gas particle exists at x=??, y=??'

where, ?? is replaced by the actual x and y coordinate of the gas particle.

Moving the gas particle

f) Gas particles will randomly move within any space due to thermal energy. In

order to simulate this movement, we need to write some code to randomly move

the gas particle in our 2D matrix. Change your if statement you wrote above, so

that if your code finds a gas particle, it will choose a random number between 0

and 4, store this number in the variable r. Depending upon the number chosen

we are going to move our gas particle up (r==0), down (r==1), right (r==2) or

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Figure 3: Gas particles in a box.left (r==3). We therefore need the rand command to produce only whole

numbers, we can do this by using the floor command to round 'r' down to the

nearest whole number. Use the floor command to make sure only whole

numbers are randomly generated.

g) Write an if-elseif-elseif statement which will print the following text using the

disp command, depending upon the value of r generated:

Value of r Text to print

0 Moving particle up

1 Moving particle down

2 Moving particle right

3 Moving particle left

h) The above if-elseif-elseif tells us which direction we would like to move the

particle, but does not actually move the particle in the 2D array. In this next

section we will write the code to actually move the particle. Firstly, above the ifelseif

statement but still in the for loops, save the current value of x and y to

two variables called x_new, and y_new. Now comment out the disp commands

within the if-elseif-elseif statement and replace them with the following

commands:

0: y_new=y_new 1

1: y_new=y_new+1

2: x_new=x_new+1

3: x_new=x_new-1

This will generate a new random coordinate for the gas particle only one pixel

away from where it currently resides.

Hint: In the next few subsections, the script will start to produce a lot

of output to the screen, printing to the screen is very slow, to speed up

your code use the ; command at the end of lines.

i) The final job is to move the particle to the new coordinate we have generated.

Place these commands:

a(y,x)=0

a(y_new,x_new)=1

within the for loops but after the if-elseif-elseif statements to move the gas

particle by one step. Make sure the imagesc command comes after both for

loops, and run the program to see what happens to your particle.

-j) In order to make your particle continually move you need to place the two

nested for loops in a while loop. Make a while loop that runs 1000 times. The

code may run so fast that your 2D plot of the matrix will not update, if this

happens place the command pause(0.5) after the imagesc command. Your

particle should now randomly move in the box until it reaches the edge. Why

does the program crash when the gas particle reaches the edge of the box?

Write the reason for the crash at the top of the script.

k) To keep the particle within the box use four nested if statements to check if

the values of y_new,x_new are within the array. Rerun the code and see what

happens to the particle. Congratulations you have simulated a gas particle in a

box! Now, add four more particles to your box and let the simulation run. And

run the code, what is what is wrong with the simulation (place the answer at the

top of the script)?

l) To stop the gas particles destroying themselves when they meet, wrap the

code that moves the gas particle:

a(y_new,x_new)=1

a(y,x)=0

in an if statement, which will only execute if a(y_new,x_new)==0.

m) Increase the size of your box to 100 by 100, using two for loops generate a

square of 20x20 gas particles in the center of the box. Let the simulation run

and watch the gas particles spread out in the box.

n) We are now going to simulate a liquid evaporating from a surface. Comment

out the for loops you wrote in part 'n' – but don't delete them or you will loose

the marks. Using two for loops generate a layer of gas particles at the bottom of

your box 20 units deep, which spans the entire box. Let the simulation run and

watch the particles evaporate.

8Removing gas particles from the simulation (tricky)

o) Set the value at 4,4 in your matrix to 5. Edit your code so that if your particle

moves on to a data point with a value of 5, the gas particle is deleted. This could

represent a hole in your box though which gas escapes.

p) The problem with this simulation is that once the particles reach the top of our

box they become trapped. In reality the particles would continue moving away

from the surface forever. To prevent the particles becoming trapped in the box,

use a single for loop to set the top edge of the box to the value of 5. When a

particle reaches the top of the box it will now be deleted – thus simulating

particles escaping from the top of the box.

q) Now include the effect of gravity in the simulation, by making it more probable

that the particle will choose to move towards the bottom of the box than in any

other direction.

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Figure 4: Simulating evaperation. Your code should

produce something that looks like this.