First Courses Workshop
Day 4
Mark Guzdial
College of Computing
Georgia Institute of Technology
[email protected]
http://www.cc.gatech.edu/~mark.guzdial
http://www.georgiacomputes.org
Workshop Plan-Day 4

9-10:00 am: Introducing data structures (in Java) in a Media
Computation approach



10:00-10:15: Break
10:15-11:15: Linked lists and trees of pictures


MIDI notes, then linked lists of MIDI.
A "scene graph" as a first tree.
11:15-12:15: Simulations.

Using Turtles from the Wednesday lecture
 Creating the wildebeests and villagers: Making movies from simulations





12:15-1:15: Lunch
1:15-2:30: Tackling a homework assignment in Media Computation
with Java. Creating linked list music or Making a movie with sound
or Modifying a Simulation.
2:30-2:45: Break
2:45-3:15: Introducing Computing in an Engineering Context with
MATLAB
3:15-4:30: Tackling a homework assignment in MATLAB
Engineering Computing: Analyzing live Internet data
Multimedia CS2 in Java


Driving question:
“How did the
wildebeests
stampede in The
Lion King?”
Spring 2005: 31
students, 75%
female, 91%
success rate.
Connecting to the Wildebeests
It’s all about data structures
Syllabus

Introduction to Java and Media Computation
 Manipulating
turtles, images, MIDI, sampled sounds.
 Insertion and deletion (with shifting) of sampled
sounds (arrays).

Structuring Music
 Goal: A structure
for flexible music composition
 Put MIDI phrases into linked list nodes.

Use Weave and Repeat to create repeating motifs as found
in Western Music

At very end, create a two-branched list to start on trees.
Swan
Bells
Canon
Fur Elise
HW2: Create a collage, but must
use turtles
Syllabus (Continued)

Structuring Images





Using linearity in linked list to
represent ordering (e.g., left to right)
Using linearity in linked list to
represent layering (as in PowerPoint)
Mixing positioned and layered in one
structure, using abstract super
classes.
Structuring a scene in terms of
branches—introducing a scene graph
(first tree)
(We’ll see these slides as an
example later.)
Syllabus (Cont’d)

Structuring Sound
 Collecting
sampled
sounds into linked
lists and trees, as
with images.

But all traversals are
recursive.
 Use
different
traversals of same
tree to generate
different sounds.
 Replace a sound inplace
Original
Scale the children
Scale the next
Syllabus (cont’d)

Generalizing lists and
trees
 Create
an abstract class
“Linked List Node”
(LLNode) on top of the
sound and image class
hierarchies

Make all image and
sound examples work
the same
abstract LLNode
Knows next
Knows how to do
all basic list
operations
Syllabus (Cont’d)
JFrame

GUIs as trees



We introduce
construction of a Swing
frame as construction of
a tree.
Different layout
managers are then
different renderers of the
same tree.
Traditional (binary)
trees as a
specialization

Can we make trees that
are faster to search?
JPanel
JPanel
JLabel “This is panel1!”
JButton
“Make a
picture”
JButton “Make
a sound”
Syllabus (cont’d)

Lists that Loop
 Introduce
circular linked lists as a way of create
Mario-Brothers’ style cel animations.
 Introduce trees that loop as a way of introducing
graphs.
gal1rightface.jpg
gal1right2.jpg
gal1rightface.jpg
gal1right1.jpg
Syllabus (cont’d)

Introducing Simulations





Introduce continuous and discrete event simulations, and Normal
and uniform probability distributions
We do wolves and deer,
disease propagation,
political influence.
Create a set of classes for simulation, then re-write our
simulations for those classes.
Writing results to a file for later analysis
Finally, Making the Wildebeests and Villagers


Mapping from positions of our turtles to an animation frame.
Creating an animation from a simulation.
HW7: Simulate European emigration to
America


Students are
required to try
several different
scenarios, aiming for
historical accuracy.
Counts of
Europeans,
Americans, and intransit per year are
written to a file for
graphing in Excel
Syllabus (cont’d)

Introduction to Discrete Event Simulations
 Create
a discrete event simulation of trucks, factories,
salespeople, and markets.
 Use turtles to create an animated display.
 Now, the real focus is the simulation, and the
animation is just a mapping from the simulation.

Animation becomes yet another medium in which we can
review results, like data in an Excel spreadsheet, music, or
sound.
A selection of data structures

First, structuring music:
 Notes,
Phrases, Parts, and Scores as a nice example
of objects and modeling.

Then linked lists of images
 Is
it about layering (as in Photoshop) or positioning
(as in Lord of the Rings)?

Then trees of images
 A Scene
Graph
Telling DrJava where to find files
Parts of DrJava
List of
class
files that
you have
open
Text of
your
class file
(.java)
Where you
interact
with Java
An example with Music
> import jm.util.*;
> import jm.music.data.*;
> Note n1;
> n1 = new Note(60,0.5);
> // Create an eighth note at
C octave 4
• JMusic pieces
need to be
imported first to
use them.
An example with Music
> import jm.util.*;
> import jm.music.data.*;
> Note n1;
> n1 = new Note(60,0.5);
> // Create an eighth note at
C octave 4
• Declare a Note
variable.
An example with Music
> import jm.util.*;
> import jm.music.data.*;
> Note n1;
> n1 = new Note(60,0.5);
> // Create an eighth note at
C octave 4
Starting a line with // creates a
comment—ignored by Java
• Note instances
have nothing to do
with filenames.
• To create a note,
you need to know
which note, and a
duration
MIDI notes
Making more notes
> Note n2=new Note(64,0.5);
> View.notate(n1);
Error: No 'notate' method in
'jm.util.View' with arguments:
(jm.music.data.Note)
> Phrase phr = new Phrase();
> phr.addNote(n1);
> phr.addNote(n2);
> View.notate(phr);
-- Constructing MIDI file from'Untitled
Score'... Playing with JavaSound
... Completed MIDI playback -------
What’s going on here?
> Note n2=new Note(64,0.5);
> View.notate(n1);
Error: No 'notate' method in
'jm.util.View' with arguments:
(jm.music.data.Note)
• We’ll make another Note (at E4,
another eighth note)
• There is an object named View
that knows how to notate parts of
music, but not an individual note.
What’s going on here?
> Phrase phr = new Phrase();
> phr.addNote(n1);
> phr.addNote(n2);
> View.notate(phr);
-- Constructing MIDI file
from'Untitled Score'... Playing
with JavaSound ... Completed
MIDI playback --------
• We’ll create a new Phrase
instance and make a variable phr to
refer to it. (phr has to be declared
to be a Phrase.)
• Phrase instances know how to
addNote notes to them. These are
methods that take an argument—a
Note instance.
• The View object does know how
to notate an input Phrase instance.
It generates this cool window where
you see the notes and can play
them (or save them as MIDI.)
Playing a different Phrase
> Phrase nuphr = new
Phrase(0.0,JMC.FLUTE);
> nuphr.addNote(n2);
> nuphr.addNote(n1);
> View.notate(nuphr);
• We can specify when a phrase starts and with what
instrument.
• We can add notes (even the same notes!) in different
orders
Modeling Music

The JMusic package is really modeling music.
 Notes
have tones and durations.
 Musical Phrases are collections of notes.
 We can play (and View) a musical phrase.

A phrase doesn’t have to start when other phrases do, and a
phrase can have its own instrument.
Objects know things and can do
things
What instances
of this class
know
What instances
of this class can
do
Note
A musical note and a <Nothing we’ve seen
duration
yet>
Phrase
The notes in the
phrase
addNote(aNote)
Amazing
Grace
> AmazingGraceSong song1 =
new AmazingGraceSong();
> song1.fillMeUp();
> song1.showMe();
import jm.music.data.*;
import jm.JMC;
import jm.util.*;
import jm.music.tools.*;
public class AmazingGraceSong {
private Score myScore = new Score("Amazing Grace");
public void fillMeUp(){
myScore.setTimeSignature(3,4);
double[] phrase1data =
{JMC.G4, JMC.QN,
JMC.C5, JMC.HN, JMC.E5,JMC.EN, JMC.C5,JMC.EN,
JMC.E5,JMC.HN,JMC.D5,JMC.QN,
JMC.C5,JMC.HN,JMC.A4,JMC.QN,
JMC.G4,JMC.HN,JMC.G4,JMC.EN,JMC.A4,JMC.EN,
JMC.C5,JMC.HN,JMC.E5,JMC.EN,JMC.C5,JMC.EN,
JMC.E5,JMC.HN,JMC.D5,JMC.EN,JMC.E5,JMC.EN,
JMC.G5,JMC.DHN};
double[] phrase2data =
{JMC.G5,JMC.HN,JMC.E5,JMC.EN,JMC.G5,JMC.EN,
JMC.G5,JMC.HN,JMC.E5,JMC.EN,JMC.C5,JMC.EN,
JMC.E5,JMC.HN,JMC.D5,JMC.QN,
JMC.C5,JMC.HN,JMC.A4,JMC.QN,
JMC.G4,JMC.HN,JMC.G4,JMC.EN,JMC.A4,JMC.EN,
JMC.C5,JMC.HN,JMC.E5,JMC.EN,JMC.C5,JMC.EN,
JMC.E5,JMC.HN,JMC.D5,JMC.QN,
JMC.C5,JMC.DHN
};
Phrase myPhrase = new Phrase();
myPhrase.addNoteList(phrase1data);
myPhrase.addNoteList(phrase2data);
// create a new part and add the phrase to it
Part aPart = new Part("Parts",
JMC.FLUTE, 1);
aPart.addPhrase(myPhrase);
// add the part to the score
myScore.addPart(aPart);
};
public void showMe(){
Imports and some private data
import jm.music.data.*;
import jm.JMC;
import jm.util.*;
import jm.music.tools.*;
public class AmazingGraceSong {
private Score myScore = new Score("Amazing Grace");
 myScore is private instance data
Filling the
Score
Each array is note,
duration, note,
duration, note,
duration, etc.
I broke it roughly
into halves.
public void fillMeUp(){
myScore.setTimeSignature(3,4);
double[] phrase1data =
{JMC.G4, JMC.QN,
JMC.C5, JMC.HN, JMC.E5,JMC.EN, JMC.C5,JMC.EN,
JMC.E5,JMC.HN,JMC.D5,JMC.QN,
JMC.C5,JMC.HN,JMC.A4,JMC.QN,
JMC.G4,JMC.HN,JMC.G4,JMC.EN,JMC.A4,JMC.EN,
JMC.C5,JMC.HN,JMC.E5,JMC.EN,JMC.C5,JMC.EN,
JMC.E5,JMC.HN,JMC.D5,JMC.EN,JMC.E5,JMC.EN,
JMC.G5,JMC.DHN};
double[] phrase2data =
{JMC.G5,JMC.HN,JMC.E5,JMC.EN,JMC.G5,JMC.EN,
JMC.G5,JMC.HN,JMC.E5,JMC.EN,JMC.C5,JMC.EN,
JMC.E5,JMC.HN,JMC.D5,JMC.QN,
JMC.C5,JMC.HN,JMC.A4,JMC.QN,
JMC.G4,JMC.HN,JMC.G4,JMC.EN,JMC.A4,JMC.EN,
JMC.C5,JMC.HN,JMC.E5,JMC.EN,JMC.C5,JMC.EN,
JMC.E5,JMC.HN,JMC.D5,JMC.QN,
JMC.C5,JMC.DHN
};
Phrase myPhrase = new Phrase();
myPhrase.addNoteList(phrase1data);
myPhrase.addNoteList(phrase2data);
// create a new part and add the phrase to it
Part aPart = new Part("Parts",
JMC.FLUTE, 1);
aPart.addPhrase(myPhrase);
// add the part to the score
myScore.addPart(aPart);
};
Showing the Score
public void showMe(){
View.notate(myScore);
};
The Organization of JMusic
Objects
Score: timeSignature, tempo, &
Part: Instrument &
Part: Instrument &
Phrase: startingTime &
Note
(pitch,duration)
Note
(pitch,duration)
Note
(pitch,duration)
Phrase: startingTime &
Note
(pitch,duration)
Note
(pitch,duration)
Thought Experiment


How are they doing that?
How can there be any number of Notes in a
Phrase, Phrases in a Part, and Parts in a Score?
 (Hint:
They ain’t usin’ arrays!)
How do we explore composition
here?


We want to quickly and easily throw together
notes in different groupings and see how they
sound.
The current JMusic structure models music.
 Let’s
try to create a structure that models thinking
about music as bunches of riffs/SongElements that
we want to combine in different ways.
Then comes notes in arrays,
linked lists of segments of AmazingGrace,
then real and flexible linked lists…
Version 3:
SongNode and SongPhrase


SongNode instances will hold pieces (phrases)
from SongPhrase.
SongNode instances will be the nodes in the
linked list
 Each

one will know its next.
Ordering will encode the order in the Part.
 Each
one will get appended after the last.
Using SongNode and SongPhrase
Welcome to DrJava.
> import jm.JMC;
> SongNode node1 = new SongNode();
> node1.setPhrase(SongPhrase.riff1());
> SongNode node2 = new SongNode();
> node2.setPhrase(SongPhrase.riff2());
> SongNode node3 = new SongNode();
> node3.setPhrase(SongPhrase.riff1());
> node1.setNext(node2);
> node2.setNext(node3);
> node1.showFromMeOn(JMC.SAX);
All three SongNodes in one Part
How to think about it
node1
node2
myPhrase: riff1
myPhrase: riff2
next: node2
next: node3
node3
myPhrase: riff1
next: null
Declarations for SongNode
import jm.music.data.*;
import jm.JMC;
import jm.util.*;
import jm.music.tools.*;
public class SongNode {
/**
* the next SongNode in the list
SongNode’s know their
*/
Phrase and the next
private SongNode next;
node in the list
/**
* the Phrase containing the notes and durations associated with this node
*/
private Phrase myPhrase;
Constructor for SongNode
/**
* When we make a new element, the next part is empty,
and ours is a blank new part
*/
public SongNode(){
this.next = null;
this.myPhrase = new Phrase();
}
Setting the phrase
/**
* setPhrase takes a Phrase and makes it the one for this
node
* @param thisPhrase the phrase for this node
*/
public void setPhrase(Phrase thisPhrase){
this.myPhrase = thisPhrase;
}
Linked list methods
/**
* Creates a link between the current node and the input node
* @param nextOne the node to link to
*/
public void setNext(SongNode nextOne){
this.next = nextOne;
}
/**
* Provides public access to the next node.
* @return a SongNode instance (or null)
*/
public SongNode next(){
return this.next;
}
insertAfter
/**
* Insert the input SongNode AFTER this node,
* and make whatever node comes NEXT become the next of the input node.
* @param nextOne SongNode to insert after this one
*/
public void insertAfter(SongNode nextOne)
{
SongNode oldNext = this.next(); // Save its next
this.setNext(nextOne); // Insert the copy
nextOne.setNext(oldNext); // Make the copy point on to the rest
}
Using and tracing insertAfter()
> SongNode nodeA = new SongNode();
> SongNode nodeB = new SongNode();
> nodeA.setNext(nodeB);
> SongNode nodeC = new SongNode()
> nodeA.insertAfter(nodeC);
public void insertAfter(SongNode nextOne)
{
SongNode oldNext = this.next(); // Save
its next
this.setNext(nextOne); // Insert the copy
nextOne.setNext(oldNext); // Make the
copy point on to the rest
}
Traversing
the list
/**
* Collect all the notes from this node on
* in an part (then a score) and open it up for viewing.
* @param instrument MIDI instrument (program) to be used in playing this list
*/
public void showFromMeOn(int instrument){
// Make the Score that we'll assemble the elements into
// We'll set it up with a default time signature and tempo we like
// (Should probably make it possible to change these -- maybe with inputs?)
Score myScore = new Score("My Song");
myScore.setTimeSignature(3,4);
myScore.setTempo(120.0);
// Make the Part that we'll assemble things into
Part myPart = new Part(instrument);
// Make a new Phrase that will contain the notes from all the phrases
Phrase collector = new Phrase();
// Start from this element (this)
SongNode current = this;
// While we're not through...
while (current != null)
{
collector.addNoteList(current.getNotes());
// Now, move on to the next element
current = current.next();
};
// Now, construct the part and the score.
myPart.addPhrase(collector);
myScore.addPart(myPart);
// At the end, let's see it!
View.notate(myScore);
}
The Core of the Traversal
// Make a new Phrase that will contain the notes from all the phrases
Phrase collector = new Phrase();
// Start from this element (this)
SongNode current = this;
// While we're not through...
while (current != null)
{
collector.addNoteList(current.getNotes());
// Now, move on to the next element
current = current.next();
};
Then return what you collected
// Now, construct the part and the score.
myPart.addPhrase(collector);
myScore.addPart(myPart);
// At the end, let's see it!
View.notate(myScore);
}
getNotes() just pulls the notes back out
/**
* Accessor for the notes inside the node's phrase
* @return array of notes and durations inside the phrase
*/
private Note [] getNotes(){
return this.myPhrase.getNoteArray();
}
SongPhrase



SongPhrase is a collection of static methods.
We don’t ever need an instance of SongPhrase.
Instead, we use it to store methods that return
phrases.
 It’s
not very object-oriented, but it’s useful here.
SongPhrase.riff1()
import jm.music.data.*;
import jm.JMC;
import jm.util.*;
import jm.music.tools.*;
public class SongPhrase {
//Little Riff1
static public Phrase riff1() {
double[] phrasedata =
{JMC.G3,JMC.EN,JMC.B3,JMC.EN,JMC.C4,JMC.EN,JMC.D4,JMC.EN};
Phrase myPhrase = new Phrase();
myPhrase.addNoteList(phrasedata);
return myPhrase;
SongPhrase.riff2()
//Little Riff2
static public Phrase riff2() {
double[] phrasedata =
{JMC.D4,JMC.EN,JMC.C4,JMC.EN,JMC.E4,JMC.EN,JMC.G4,JMC.
EN};
Phrase myPhrase = new Phrase();
myPhrase.addNoteList(phrasedata);
return myPhrase;
}
Computing a phrase
//Larger Riff1
static public Phrase pattern1() {
double[] riff1data =
{JMC.G3,JMC.EN,JMC.B3,JMC.EN,JMC.C4,JMC.EN,JMC.D4,JMC.EN};
double[] riff2data =
{JMC.D4,JMC.EN,JMC.C4,JMC.EN,JMC.E4,JMC.EN,JMC.G4,JMC.EN};
Phrase myPhrase = new Phrase();
// 3 of riff1, 1 of riff2, and repeat all of it 3 times
for (int counter1 = 1; counter1 <= 3; counter1++)
{for (int counter2 = 1; counter2 <= 3; counter2++)
myPhrase.addNoteList(riff1data);
myPhrase.addNoteList(riff2data);
};
return myPhrase;
}
As long as it’s a phrase…

The way that we use SongNote and
SongPhrase, any method that returns a phrase
is perfectly valid SongPhrase method.
10 Random Notes
(Could be less random…)
/*
* 10 random notes
**/
static public Phrase random() {
Phrase ranPhrase = new Phrase();
Note n = null;
for (int i=0; i < 10; i++) {
n = new Note((int) (128*Math.random()),0.1);
ranPhrase.addNote(n);
}
return ranPhrase;
}
10 Slightly Less Random Notes
/*
* 10 random notes above middle C
**/
static public Phrase randomAboveC() {
Phrase ranPhrase = new Phrase();
Note n = null;
for (int i=0; i < 10; i++) {
n = new Note((int) (60+(5*Math.random())),0.25);
ranPhrase.addNote(n);
}
return ranPhrase;
}
Going beyond connecting nodes



So far, we’ve just created nodes and connected
them up.
What else can we do?
Well, music is about repetition and interleaving
of themes.
 Let’s
create those abilities for SongNodes.
Repeating a Phrase
Welcome to DrJava.
> SongNode node = new SongNode();
> node.setPhrase(SongPhrase.randomAboveC());
> SongNode node1 = new SongNode();
> node1.setPhrase(SongPhrase.riff1());
> node.repeatNext(node1,10);
> import jm.JMC;
> node.showFromMeOn(JMC.PIANO);
What it looks like
node
node1
node1
node1
…
Repeating
Note! What
happens to this’s
next? How
would you create
a looong repeat
chain of several
types of phrases
with this?
/**
* Repeat the input phrase for the number of times
specified.
* It always appends to the current node, NOT insert.
* @param nextOne node to be copied in to list
* @param count number of times to copy it in.
*/
public void repeatNext(SongNode nextOne,int count) {
SongNode current = this; // Start from here
SongNode copy; // Where we keep the current copy
for (int i=1; i <= count; i++)
{
copy = nextOne.copyNode(); // Make a copy
current.setNext(copy); // Set as next
current = copy; // Now append to copy
}
}
Really useful: Do this with people as
nodes!


We give people pieces of paper with “notes” on
them.
Nodes point to their “next”
Here’s making a copy
/**
* copyNode returns a copy of this node
* @return another song node with the same notes
*/
public SongNode copyNode(){
SongNode returnMe = new SongNode();
returnMe.setPhrase(this.getPhrase());
return returnMe;
}
Step 1:
public void repeatNext(SongNode nextOne,int count) {
SongNode current = this; // Start from here
SongNode copy; // Where we keep the current copy
node
node1
phrase:
10
random
notes
phrase:
riff1()
next: null
next: null
current
nextOne
Step 2:
copy = nextOne.copyNode(); // Make a copy
node
node1
phrase:
10
random
notes
phrase:
riff1()
phrase:
riff1()
next: null
next: null
next: null
current
copy
nextOne
Step 3:
current.setNext(copy); // Set as next
node
node1
phrase:
10
random
notes
phrase:
riff1()
phrase:
riff1()
next: null
next: null
next:
current
copy
nextOne
Step 4:
current = copy; // Now append to copy
node
node1
phrase:
10
random
notes
phrase:
riff1()
phrase:
riff1()
next: null
next: null
next:
current
copy
nextOne
Step 5 & 6:
copy = nextOne.copyNode(); // Make a copy
current.setNext(copy); // Set as next
node
node1
phrase:
10
random
notes
phrase:
riff1()
phrase:
riff1()
phrase:
riff1()
next:
next: null
next: null
next:
current
copy
nextOne
Step 7 (and so on):
current = copy; // Now append to copy
node
node1
phrase:
10
random
notes
phrase:
riff1()
phrase:
riff1()
phrase:
riff1()
next:
next: null
next: null
next:
current
copy
nextOne
What happens if the node already
points to something?




Consider repeatNext and how it inserts:
It simply sets the next value.
What if the node already had a next?
repeatNext will erase whatever used to come
next.
How can we fix it?
repeatNextInserting
/**
* Repeat the input phrase for the number of times specified.
* But do an insertion, to save the rest of the list.
* @param nextOne node to be copied into the list
* @param count number of times to copy it in.
**/
public void repeatNextInserting(SongNode nextOne, int count){
SongNode current = this; // Start from here
SongNode copy; // Where we keep the current copy
for (int i=1; i <= count; i++)
{
copy = nextOne.copyNode(); // Make a copy
current.insertAfter(copy); // INSERT after current
current = copy; // Now append to copy
}
}
Weaving
/**
* Weave the input phrase count times every skipAmount nodes
* @param nextOne node to be copied into the list
* @param count how many times to copy
* @param skipAmount how many nodes to skip per weave
*/
public void weave(SongNode nextOne, int count, int skipAmount)
{
SongNode current = this; // Start from here
SongNode copy; // Where we keep the one to be weaved in
SongNode oldNext; // Need this to insert properly
int skipped; // Number skipped currently
for (int i=1; i <= count; i++)
{
copy = nextOne.copyNode(); // Make a copy
Should we
break before
the last
insert (when
we get to the
end) or
after?
//Skip skipAmount nodes
skipped = 1;
while ((current.next() != null) && (skipped < skipAmount))
{
current = current.next();
skipped++;
};
oldNext = current.next(); // Save its next
current.insertAfter(copy); // Insert the copy after this one
current = oldNext; // Continue on with the rest
if (current.next() == null) // Did we actually get to the end early?
break; // Leave the loop
}
}
Creating a node to weave
> SongNode node2 = new SongNode();
> node2.setPhrase(SongPhrase.riff2());
> node2.showFromMeOn(JMC.PIANO);
Doing a weave
> node.weave(node2,4,2);
> node.showFromMeOn(JMC.PIANO);
Weave Results
Before:
After
Walking the Weave
public void weave(SongNode nextOne, int count, int
skipAmount)
{
SongNode current = this; // Start from here
SongNode copy; // Where we keep the one to be weaved in
SongNode oldNext; // Need this to insert properly
int skipped; // Number skipped currently
Skip forward
for (int i=1; i <= count; i++)
{
copy = nextOne.copyNode(); // Make a copy
//Skip skipAmount nodes
skipped = 1;
while ((current.next() != null) && (skipped < skipAmount))
{
current = current.next();
skipped++;
};
Then do an insert
if (current.next() == null) // Did we actually get to the end early?
break; // Leave the loop
oldNext = current.next(); // Save its next
current.insertAfter(copy); // Insert the copy after this one
current = oldNext; // Continue on with the rest
}
Shifting to Images

Now that we’ve introduced linked lists with MIDI,
we shift to images.
 Briefly,
two kinds of linked lists.
 Then scene graphs
Building a Scene

Computer graphics professionals work at two
levels:
 They
define individual characters and effects on
characters in terms of pixels.
 But then most of their work is in terms of the scene:
Combinations of images (characters, effects on
characters).

To describe scenes, they often use linked lists
and trees in order to assemble the pieces.
Version 1:
PositionedSceneElement
> FileChooser.setMediaPath("D:/cs1316/MediaSources/");
> PositionedSceneElement tree1 = new PositionedSceneElement(new
Picture(FileChooser.getMediaPath("tree-blue.jpg")));
> PositionedSceneElement tree2 = new PositionedSceneElement(new
Picture(FileChooser.getMediaPath("tree-blue.jpg")));
> PositionedSceneElement tree3 = new PositionedSceneElement(new
Picture(FileChooser.getMediaPath("tree-blue.jpg")));
> PositionedSceneElement doggy = new PositionedSceneElement(new
Picture(FileChooser.getMediaPath("dog-blue.jpg")));
> PositionedSceneElement house = new PositionedSceneElement(new
Picture(FileChooser.getMediaPath("house-blue.jpg")));
> Picture bg = new Picture(FileChooser.getMediaPath("jungle.jpg"));
> tree1.setNext(tree2); tree2.setNext(tree3); tree3.setNext(doggy);
doggy.setNext(house);
> tree1.drawFromMeOn(bg);
> bg.show();
In this example, using
chromakey to compose..just
for the fun of it.
What this looks like:
Slightly different ordering:
Put the doggy between tree2 and tree3
> tree3.setNext(house); tree2.setNext(doggy);
doggy.setNext(tree3);
> bg = new
Picture(FileChooser.getMediaPath("jungle.jpg"));
> tree1.drawFromMeOn(bg);
> bg.show();
Yes, we can put
multiple
statements in
one line.
Slightly different picture
Removing the doggy
> tree1.setNext(tree2);
tree2.setNext(tree3);
tree3.setNext(doggy);
doggy.setNext(house);
> tree1.remove(doggy);
> tree1.drawFromMeOn(bg);
Putting the mutt back
> bg = new
Picture(FileChooser.getMediaPa
th("jungle.jpg"));
> tree1.insertAfter(doggy);
> tree1.drawFromMeOn(bg);
Animation = (Changing a structure
+ rendering) * n



We can use what we just did to create
animation.
Rather than think about animation as “a series of
frames,”
Think about it as:
 Repeatedly:
 Change a data structure
 Render (draw while traversing) the data structure to create a
frame
AnimatedPositionedScene
public class AnimatedPositionedScene {
/**
* A FrameSequence for storing the frames
**/
FrameSequence frames;
/**
* We'll need to keep track
* of the elements of the scene
**/
PositionedSceneElement tree1, tree2, tree3, house, doggy, doggyflip;
Setting up
the animation
public void setUp(){
frames = new FrameSequence("D:/Temp/");
FileChooser.setMediaPath("D:/cs1316/mediasource
s/");
Picture p = null; // Use this to fill elements
p = new Picture(FileChooser.getMediaPath("treeblue.jpg"));
tree1 = new PositionedSceneElement(p);
p = new Picture(FileChooser.getMediaPath("treeblue.jpg"));
tree2 = new PositionedSceneElement(p);
p = new Picture(FileChooser.getMediaPath("treeblue.jpg"));
tree3 = new PositionedSceneElement(p);
p = new Picture(FileChooser.getMediaPath("houseblue.jpg"));
house = new PositionedSceneElement(p);
p = new Picture(FileChooser.getMediaPath("dogblue.jpg"));
doggy = new PositionedSceneElement(p);
doggyflip = new PositionedSceneElement(p.flip());
}
Render the first frame
public void make(){
frames.show();
// First frame
Picture bg = new
Picture(FileChooser.getMediaPath("jungle.jpg"));
tree1.setNext(doggy); doggy.setNext(tree2);
tree2.setNext(tree3);
tree3.setNext(house);
tree1.drawFromMeOn(bg);
frames.addFrame(bg);
Render the doggy moving right
// Dog moving right
bg = new Picture(FileChooser.getMediaPath("jungle.jpg"));
tree1.remove(doggy);
tree2.insertAfter(doggy);
tree1.drawFromMeOn(bg);
frames.addFrame(bg);
bg = new Picture(FileChooser.getMediaPath("jungle.jpg"));
tree1.remove(doggy);
tree3.insertAfter(doggy);
tree1.drawFromMeOn(bg);
frames.addFrame(bg);
bg = new Picture(FileChooser.getMediaPath("jungle.jpg"));
tree1.remove(doggy);
house.insertAfter(doggy);
tree1.drawFromMeOn(bg);
frames.addFrame(bg);
Moving left
//Dog moving left
bg = new Picture(FileChooser.getMediaPath("jungle.jpg"));
tree1.remove(doggy);
house.insertAfter(doggyflip);
tree1.drawFromMeOn(bg);
frames.addFrame(bg);
bg = new Picture(FileChooser.getMediaPath("jungle.jpg"));
tree1.remove(doggyflip);
tree3.insertAfter(doggyflip);
tree1.drawFromMeOn(bg);
frames.addFrame(bg);
bg = new Picture(FileChooser.getMediaPath("jungle.jpg"));
tree1.remove(doggyflip);
tree2.insertAfter(doggyflip);
tree1.drawFromMeOn(bg);
frames.addFrame(bg);
bg = new Picture(FileChooser.getMediaPath("jungle.jpg"));
tree1.remove(doggyflip);
tree1.insertAfter(doggyflip);
tree1.drawFromMeOn(bg);
frames.addFrame(bg);
}
Results
Version 2: Layering
> Picture bg = new Picture(400,400);
> LayeredSceneElement tree1 = new LayeredSceneElement(
new Picture(FileChooser.getMediaPath("tree-blue.jpg")),10,10);
> LayeredSceneElement tree2 = new LayeredSceneElement(
new Picture(FileChooser.getMediaPath("tree-blue.jpg")),100,10);
> LayeredSceneElement tree3 = new LayeredSceneElement(
new Picture(FileChooser.getMediaPath("tree-blue.jpg")),200,100);
> LayeredSceneElement house = new LayeredSceneElement(
new Picture(FileChooser.getMediaPath("house-blue.jpg")),175,175);
> LayeredSceneElement doggy = new LayeredSceneElement(
new Picture(FileChooser.getMediaPath("dog-blue.jpg")),150,325);
> tree1.setNext(tree2); tree2.setNext(tree3); tree3.setNext(doggy);
doggy.setNext(house);
> tree1.drawFromMeOn(bg);
> bg.show();
First version of Layered Scene
Reordering the layering
> house.setNext(doggy); doggy.setNext(tree3);
tree3.setNext(tree2); tree2.setNext(tree1);
> tree1.setNext(null);
Basically, we’re
> bg = new Picture(400,400); reversing the list
> house.drawFromMeOn(bg);
> bg.show();
Reordered (relayered) scene
Think about
what’s
involved in
creating a
method to
reverse() a
list…
What’s the difference?

If we were in PowerPoint or Visio, you’d say that
we changed the layering.
 “Bring
to front”
 “Send to back”
 “Bring forward”
 “Send backward”
These commands are
actually changing the
ordering of the layers in the
list of things to be redrawn.
• Change the ordering in the
list.
• Render the scene
• Now it’s a different layering!
Version 3: A List with Both


Problem 1: Why should we have only layered scene elements
or positioned scene elements?
Can we have both?

SURE! If each element knows how to draw itself!
 But they took different parameters!



Layered got their (x,y) passed in.
It works if we always pass in a turtle that’s set to the right place to draw
if it’s positioned (and let the layered ones do whatever they want!)
Problem 2: Why is there so much duplicated code?

Why do only layered elements know last() and add()?
Using Superclasses

What we really want is to define a class SceneElement



That knows most of being a picture element.
It would be an abstract class because we don’t actually mean to
ever create instances of THAT class.
Then create subclasses: SceneElementPositioned and
SceneElementLayered

We’d actually use these.
Class Structure
Abstract Class SceneElement
It knows its Picture myPic and
its next (SceneElement).
It knows how to get/set next,
to reverse() and insertAfter(),
and to drawFromMeOn().
It defines drawWith(turtle), but
leaves it for its subclasses do
complete.
An abstract
class defines
structure and
behavior that
subclasses
will inherit.
Class Structure
Abstract Class SceneElement
It knows its Picture myPic and its
next.
The subclasses
inherit data and
methods from
superclass.
It knows how to get/set next, to
reverse() and insertAfter(), and to
drawFromMeOn() and
drawWith(turtle)
We say that the
subclasses
extend the
superclass.
Class SceneElementLayered
Class SceneElementPositioned
It knows its position (x,y).
It knows how to drawWith(turtle)
It knows how to drawWith(turtle)
by moving to (x,y) then dropping.
Using the new structure
public class MultiElementScene {
public static void main(String[] args){
FileChooser.setMediaPath("D:/cs1316/mediasources/");
// We'll use this for filling the nodes
Picture p = null;
p = new Picture(FileChooser.getMediaPath("swan.jpg"));
SceneElement node1 = new SceneElementPositioned(p.scale(0.25));
p = new Picture(FileChooser.getMediaPath("horse.jpg"));
SceneElement node2 = new SceneElementPositioned(p.scale(0.25));
p = new Picture(FileChooser.getMediaPath("dog.jpg"));
SceneElement node3 = new SceneElementLayered(p.scale(0.5),10,50);
p = new Picture(FileChooser.getMediaPath("flower1.jpg"));
SceneElement node4 = new SceneElementLayered(p.scale(0.5),10,30);
p = new Picture(FileChooser.getMediaPath("graves.jpg"));
SceneElement node5 = new SceneElementPositioned(p.scale(0.25));
Rendering the scene
node1.setNext(node2); node2.setNext(node3);
node3.setNext(node4); node4.setNext(node5);
// Now, let's see it!
Picture bg = new Picture(600,600);
node1.drawFromMeOn(bg);
bg.show();
}
}
Rendered scene
New Version: Trees for defining
scenes

Not everything in a scene is a single list.



Is it the responsibility of the elements to know about
layering and position?


Think about a pack of fierce doggies, er, wolves attacking the
quiet village in the forest.
Real scenes cluster.
Is that the right place to put that know how?
How do we structure operations to perform to sets of
nodes?

For example, moving a set of them at once?
The Attack of the Nasty Wolvies
Closer…
Then the Hero Appears!
And the Wolvies retreat
What’s underlying this

This scene is described by a tree
 Each
picture is a BlueScreenNode in this tree.
 Groups of pictures are organized in HBranch or
VBranch (Horizontal or Vertical branches)
 The root of the tree is just a Branch.
 The branches are positioned using a MoveBranch.
Labeling the Pieces
Branch (root)
MoveBranch to
(10,50)
VBranch with
BlueScreenNode
wolves
MoveBranch to
(10,400)
MoveBranch to
(300,450)
HBranch with 3
BSN houses and a
HBranch with BSN
trees
VBranch with 3
BSN houses
It’s a Tree
Branch (root)
MoveBranch to
(10,50)
MoveBranch to
(10,400)
MoveBranch to
(300,450)
HBranch with 3
BSN houses and a
VBranch with
BlueScreenNode
wolves
HBranch with BSN
trees
VBranch with 3
BSN houses
The Class Structure

DrawableNode knows only next, but knows
how to do everything that our picture linked lists
do (insertAfter, remove, last, drawOn(picture)).
 Everything


else is a subclass of that.
PictNode knows it’s Picture myPict and knows
how to drawWith(turtle) (by dropping a picture)
BlueScreenNode doesn’t know new from
PictNode but knows how to drawWith(turtle) by
using bluescreen.
Branch Class Structure

Branch knows its children—a linked list of other
nodes to draw. It knows how to drawWith by:
 (1)
telling all its children to draw.
 (2) then telling all its children to draw.


A HBranch draws its children by spacing them
out horizontally.
A VBranch draws its children by spacing them
out vertically.
The Class Structure Diagram
Note: This is not
the same as the
scene (object)
structure!
DrawableNode
Knows: next
PictNode
Branch
Knows: myPict
Knows: children
Knows how to
drawWith
HBranch
VBranch
Knows how
to drawWith
horizontally
Knows how to
drawWith
vertically
BlueScreenNode
Knows how to
drawWith as
bluescreen
Using these Classes:
When doggies go bad!
public class WolfAttackMovie {
/**
* The root of the scene data structure
**/
Branch sceneRoot;
/**
* FrameSequence where the animation
* is created
**/
FrameSequence frames;
/**
* The nodes we need to track between methods
**/
MoveBranch wolfentry, wolfretreat, hero;
These are the nodes
that change during the
animation, so must be
available outside the
local method context
Setting up the pieces
/**
* Set up all the pieces of the tree.
**/
public void setUp(){
Picture wolf = new Picture(FileChooser.getMediaPath("dogblue.jpg"));
Picture house = new Picture(FileChooser.getMediaPath("houseblue.jpg"));
Picture tree = new Picture(FileChooser.getMediaPath("treeblue.jpg"));
Picture monster = new Picture(FileChooser.getMediaPath("monsterface3.jpg"));
Making a Forest
//Make the forest
MoveBranch forest = new MoveBranch(10,400); // forest
on the bottom
HBranch trees = new HBranch(50); // Spaced out 50
pixels between
BlueScreenNode treenode;
for (int i=0; i < 8; i++) // insert 8 trees
{treenode = new BlueScreenNode(tree.scale(0.5));
trees.addChild(treenode);}
forest.addChild(trees);
Make attacking wolves
// Make the cluster of attacking "wolves"
wolfentry = new MoveBranch(10,50); // starting position
VBranch wolves = new VBranch(20); // space out by 20 pixels
between
BlueScreenNode wolf1 = new BlueScreenNode(wolf.scale(0.5));
BlueScreenNode wolf2 = new BlueScreenNode(wolf.scale(0.5));
BlueScreenNode wolf3 = new BlueScreenNode(wolf.scale(0.5));
wolves.addChild(wolf1);wolves.addChild(wolf2);
wolves.addChild(wolf3);
wolfentry.addChild(wolves);
Make retreating wolves
// Make the cluster of retreating "wolves"
wolfretreat = new MoveBranch(400,50); // starting position
wolves = new VBranch(20); // space them out by 20 pixels between
wolf1 = new BlueScreenNode(wolf.scale(0.5).flip());
wolf2 = new BlueScreenNode(wolf.scale(0.5).flip());
wolf3 = new BlueScreenNode(wolf.scale(0.5).flip());
wolves.addChild(wolf1);wolves.addChild(wolf2);
wolves.addChild(wolf3);
wolfretreat.addChild(wolves);
It takes a Village…
// Make the village
MoveBranch village = new MoveBranch(300,450); // Village on bottom
HBranch hhouses = new HBranch(40); // Houses are 40 pixels apart
across
BlueScreenNode house1 = new BlueScreenNode(house.scale(0.25));
BlueScreenNode house2 = new BlueScreenNode(house.scale(0.25));
BlueScreenNode house3 = new BlueScreenNode(house.scale(0.25));
VBranch vhouses = new VBranch(-50); // Houses move UP, 50 pixels
apart
BlueScreenNode house4 = new BlueScreenNode(house.scale(0.25));
BlueScreenNode house5 = new BlueScreenNode(house.scale(0.25));
BlueScreenNode house6 = new BlueScreenNode(house.scale(0.25));
vhouses.addChild(house4); vhouses.addChild(house5);
vhouses.addChild(house6);
hhouses.addChild(house1); hhouses.addChild(house2);
hhouses.addChild(house3);
hhouses.addChild(vhouses); // Yes, a VBranch can be a child of an
HBranch!
village.addChild(hhouses);
Making the village’s hero
// Make the monster
hero = new MoveBranch(400,300);
BlueScreenNode heronode = new
BlueScreenNode(monster.scale(0.75).flip());
hero.addChild(heronode);
Assembling the Scene
//Assemble the base scene
sceneRoot = new Branch();
sceneRoot.addChild(forest);
sceneRoot.addChild(village);
sceneRoot.addChild(wolfentry);
}
Want the forest on top
of the village? Put the
village in BEFORE the
forest! Then it will get
rendered first
Where’s the wolfretreat and monster?
They’ll get inserted into the scene in
the middle of the movie
Trying out one scene:
Very important for testing!
/**
* Render just the first scene
**/
public void renderScene() {
Picture bg = new Picture(500,500);
sceneRoot.drawOn(bg);
bg.show();
}
Okay that works
Rendering the whole movie
/**
* Render the whole animation
**/
public void renderAnimation() {
frames = new FrameSequence("D:/Temp/");
frames.show();
Picture bg;
Wolvies attack! (for 25 frames)
// First, the nasty wolvies come closer to the poor village
// Cue the scary music
for (int i=0; i<25; i++)
{
// Render the frame
bg = new Picture(500,500);
Inch-by-inch, er, 5-pixels by 10
sceneRoot.drawOn(bg);
frames.addFrame(bg);
pixels, they creep closer.
// Tweak the data structure
wolfentry.moveTo(wolfentry.getXPos()+5,wolfentry.getYPos()+10);
}
Our hero arrives! (In frame 26)
// Now, our hero arrives!
this.root().addChild(hero);
// Render the frame
bg = new Picture(500,500);
sceneRoot.drawOn(bg);
frames.addFrame(bg);
Exit the threatening wolves,
enter the retreating wolves
// Remove the wolves entering, and insert the wolves
retreating
this.root().children.remove(wolfentry);
this.root().addChild(wolfretreat);
// Make sure that they retreat from the same place that
they were at
wolfretreat.moveTo(wolfentry.getXPos(),
wolfentry.getYPos());
// Render the frame
bg = new Picture(500,500);
sceneRoot.drawOn(bg);
frames.addFrame(bg);
The wolves retreat
(more quickly)
// Now, the cowardly wolves hightail it out of there!
// Cue the triumphant music
for (int i=0; i<10; i++)
{
// Render the frame
bg = new Picture(500,500);
sceneRoot.drawOn(bg);
frames.addFrame(bg);
// Tweak the data structure
wolfretreat.moveTo(wolfretreat.getXPos()-10,
wolfretreat.getYPos()-20);
}
}
Making the Movie
Welcome to DrJava.
> WolfAttackMovie wam = new WolfAttackMovie();
wam.setUp(); wam.renderScene();
> wam.renderAnimation();
There are no frames to show yet. When you add a frame it
will be shown
> wam.replay();
The Completed Movie
Homework Assignment!
 Option 1: Create linked list music
 Create music with at least five calls to repeatInserting or weave
 It must be at least 20 nodes long.
 Make one new riff yourself and use it.
 Draw the resultant sound structure
 Option 2: Make a movie—with sound!
 Use a scene graph for the visuals, and a linked list for the sound.
 Maybe play one node per frame?
 Can use play() for background sounds, blockingPlay() for foreground
sounds
 Only rule: During rendering, cannot create any new sounds.

 Must be in the linked list of sounds already.
Example: HW4 and HW6 at http://coweb.cc.gatech.edu/cs1316/458
Simulations

We build a simulation “from scratch”: Wolves
and deer
 Based
on Anne Fleury’s work about students avoiding
abstraction and preferring duplicating/explicit code.
 We’re trying to make it easier to understand, and then
introduce abstraction.

Then we build a simulation package that makes
it all easier.
Real programmers don’t make data
structures…often


Programmers almost never make arrays.
Most programmers don’t make linked lists or trees or
graphs, either!


Or hashtables/dictionaries, or heaps, or stacks and queues.
These core, general, abstract data structures are
typically provided in some form through libraries for the
language.

That’s true for both Python/Jython and Java.
Real programmers make
models…often

The basic processes of modeling is something
that every object-oriented programmer does all
the time.
 Aggregation:
connecting objects together through
references
 Generalization and Specialization

Learning how data structures work is
learning about modeling.
Real programmers make data
structures…sometimes

Sometimes you do make data structures.
 If
you need a specialized structure.
 If you want just the methods you want in the way that
you want them.

 If
For example, Java’s LinkedList has no insertAfter()!
you need it to work faster.
Real programmers make data
structures choices!


You choose between different data structures all the
time.
Often the choice is based on running time.


Arrays are faster than linked lists for some things (like
accessing element i),
while linked lists are faster for other things (like insertion
and deletion).
Sometimes the choice is for particular properties.



Use trees for clustering,
Use graphs for cycles,
Use hashtables for lookup by String, not index number
Building a Simulation Package

Let’s make it much easier to build simulations.



We’ll use Java’s data structures, rather than build our own.
We’ll create Simulation and Agent as a general simulation, so
that we only subclass them to create our specific simulations.
A classic “real programmer” challenge: Making code
designed to be reused (by us, but could be anyone) later.
WDSimulation with new package
DiseaseSimulation
PoliticalSimulation
Design of the Package
How we use the package

Subclass Simulation to define your general simulation.



Override the methods that you want to change.
Feel free to call super.method() to reuse the general
functionality.
Subclass Agent to define your simulation agents/actors.


Override the methods that you want to change.
Feel free to call super.method() to reuse the general
functionality.
What Simulation provides








getAgents(), add(), remove(): Manipulate the list of all
agents
setUp(): Open a world
openFile(): Write data to a file
openFrames(): Write frames to a FrameSequence
run(): Run the simulation—for a number of timesteps, tell
each agent to act()
endStep(): Print the timestep and write to the file.
lineForFile(): Define what to print to the file.
closeFile(): End the file writing
What Agent provides






setSpeed(), getSpeed(): Change/get speed
init(): Add to simulation agents list
die(): Make body red and remove from
simulation agents list
getClosest(): Get the closest agent from a list
within a range.
countInRange(): Count the agents within a range
that are on a list.
act(): By default, wander aimlessly
Redefining WDSimulation
WDSimulation
/**
* WDSimulation -- using the Simulation class
**/
public class WDSimulation extends Simulation {
/**
* Fill the world with wolves and deer
**/
public void setUp(){
// Let the world be set up
super.setUp();
// Just for storing the new deer and wolves
DeerAgent deer;
WolfAgent wolf;
We need setUp() to
define the world (let
super.setUp() do
that), then fill it with
our agents.
// create some deer
int numDeer = 20;
for (int i = 0; i < numDeer; i++)
{
deer = new DeerAgent(world,this);
}
// create some wolves
int numWolves = 5;
for (int i = 0; i < numWolves; i++)
{
wolf = new WolfAgent(world,this);
}
}
Writing out our counts in
WDSimulation
/**
* lineForFile -- write out number of wolves and deer
**/
public String lineForFile(){
// Get the size (an int), make it an Integer,
// in order to turn it into a string. (Whew!)
return (new Integer(DeerAgent.allDeer.size())).toString()+"/t"+
(new Integer(WolfAgent.allWolves.size())).toString();
}
It’s not easy to convert an integer (size() of
the list) to a string.
Defining our Deer
import java.awt.Color; // Color for colorizing
import java.util.LinkedList;
/**
* DeerAgent -- Deer as a subclass of Agent
**/
public class DeerAgent extends Agent {
/** class constant for the color */
private static final Color brown = new Color(116,64,35);
/** class constant for how far deer can smell */
private static final double SMELL_RANGE = 50;
/** Collection of all Deer */
public static LinkedList allDeer = new LinkedList();
Notice allDeer!
It’s a LinkedList—
for free!
It’s static—there’s
one list shared by
all instances of the
class. It’s the list
of all DeerAgents,
and there’s only
one of these lists.
DeerAgent initialization
/**
* Initialize, by adding to Deer list
**/
public void init(Simulation thisSim){
// Do the normal initializations
super.init(thisSim);
// Make it brown
setColor(brown);
// Add to list of Deer
allDeer.add(this);
}
DeerAgent’s way of dying
/**
* To die, do normal stuff, but
* also remove from deer list
**/
public void die(){
super.die();
allDeer.remove(this);
System.out.println("Deer left: "+allDeer.size());
}
DeerAgent’s
actions
/**
* How a DeerAgent acts
**/
public void act()
{
// get the closest wolf within the smell range
WolfAgent closeWolf = (WolfAgent)
getClosest(SMELL_RANGE,
WolfAgent.allWolves);
if (closeWolf != null) {
// Turn to face the wolf
this.turnToFace(closeWolf);
// Now directly in the opposite direction
this.turn(180);
// How far to run? How about half of current speed??
this.forward((int) (speed/2));
}
else {
// Run the normal act() -- wander aimlessly
super.act();
}
This is it folks!
It’s all that we have
to write to make
DeerAgents work!
}
Constructors
////////////////////////////// Constructors ////////////////////////
// Copy this section AS-IS into subclasses, but rename Agent to
// Your class.
/**
* Constructor that takes the model display (the original
* position will be randomly assigned)
* @param modelDisplayer thing that displays the model
* @param thisSim my simulation
*/
public DeerAgent (ModelDisplay modelDisplayer,Simulation thisSim)
{
super(randNumGen.nextInt(modelDisplayer.getWidth()),
randNumGen.nextInt(modelDisplayer.getHeight()),
modelDisplayer, thisSim);
}
/** Constructor that takes the x and y and a model
* display to draw it on
* @param x the starting x position
* @param y the starting y position
* @param modelDisplayer the thing that displays the model
* @param thisSim my simulation
*/
public DeerAgent (int x, int y, ModelDisplay modelDisplayer,
Simulation thisSim)
{
// let the parent constructor handle it
super(x,y,modelDisplayer,thisSim);
}
DON’T care about
this!
Copy it in as-is, and
make the names
match your class.
That’s it. Period.
WolfAgent
import java.awt.Color;
import java.util.LinkedList;
/**
* WolfAgent -- Wolf as a subclass of Agent
**/
public class WolfAgent extends Agent {
/** class constant for how far wolf can smell */
private static final double SMELL_RANGE = 50;
/** class constant for how close before wolf can attack */
private static final double ATTACK_RANGE = 30;
/** Collection of all Wolves */
public static LinkedList allWolves = new LinkedList();
WolfAgent initializations
/**
* Initialize, by adding to Wolf list
**/
public void init(Simulation thisSim){
// Do the normal initializations
super.init(thisSim);
// Make it brown
setColor(Color.gray);
// Add to list of Wolves
allWolves.add(this);
}
WolfAgent
act()
The same
constructors are
there, but let’s
ignore those.
/**
* Chase and eat the deer
**/
/**
* Method to act during a time step
* pick a random direction and move some random amount up to top speed
*/
public void act()
{
// get the closest deer within smelling range
DeerAgent closeDeer = (DeerAgent) getClosest(SMELL_RANGE,
DeerAgent.allDeer);
if (closeDeer != null)
{
// Turn torward deer
this.turnToFace(closeDeer);
// How much to move? How about minimum of maxSpeed
// or distance to deer?
this.forward((int) Math.min(speed,
closeDeer.getDistance(this.getXPos(),this.getYPos())));
}
// get the closest deer within the attack distance
closeDeer = (DeerAgent) getClosest(ATTACK_RANGE,
DeerAgent.allDeer);
if (closeDeer != null)
{
this.moveTo(closeDeer.getXPos(),
closeDeer.getYPos());
closeDeer.die();
}
else // Otherwise, wander aimlessly
{
super.act();
Running the WDSimulation
Welcome to DrJava.
> WDSimulation wd = new WDSimulation();
> wd.openFrames("D:/temp/"); // If you want an animation
> wd.openFile(“D:/cs1316/wds-data1.txt”); // If you want an output
file.
> wd.run();
If you just want to run it:
> WDSimulation wd = new WDSimulation();
> wd.run();
DiseaseSimulation
What happens in a
DiseaseSimulation



We create a bunch of PersonAgents.
One of them is sick.
While running:
 They
wander aimlessly.
 If a Person gets close (within 10? 20?) of an infected
person, that Person gets infected, too.
DiseaseSimulation
setUp() just creates 60
people, and the first one
becomes infected.
/**
* DiseaseSimulation -- using the Simulation class
**/
public class DiseaseSimulation extends Simulation {
/**
* Fill the world with 60 persons, one sick
**/
public void setUp(){
// Let the world be set up
//super.setUp();
// Or set it up with a smaller world
world = new World(300,300);
world.setAutoRepaint(false);
PersonAgent moi;
// 60 people
for (int num = 0; num < 60; num++) {
moi = new PersonAgent(world,this);
}
// Infect the first one
moi = (PersonAgent) getAgents().get(0);
moi.infect();
}
Deciding what to store in a file
/**
* lineForFile -- write out number of infected
**/
public String lineForFile(){
PersonAgent first;
first = (PersonAgent) agents.get(0);
return (new Integer(first.infected())).toString();
}
infected() is an instance method that
returns the number of infected
persons. It doesn’t matter which
person we ask it of, so we just grab
the first one.
Defining a PersonAgent
import java.awt.Color; // Color for colorizing
import java.util.LinkedList;
/**
* PersonAgent -- Person as a subclass of Agent
**/
public class PersonAgent extends Agent {
public boolean infection;
PersonAgent
initialization
/**
* Initialize, by setting color and making move fast
**/
public void init(Simulation thisSim){
// Do the normal initializations
super.init(thisSim);
// Make it lightGray
setColor(Color.lightGray);
// Don't need to see the trail
setPenDown(false);
// Start out uninfected
infection = false;
// Make the speed large
speed = 100;
}
PersonAgent act()
/**
* How a Person acts
**/
public void act()
{
// Is there a person within infection range of me?
PersonAgent closePerson = (PersonAgent) getClosest(10,
simulation.getAgents());
if (closePerson != null) {
// If this person is infected, and I'm not infected
if (closePerson.infection && !this.infection) {
// I become infected
this.infect();
}
}
// Run the normal act() -- wander aimlessly
super.act();
}
Getting sick
/**
* Become infected
**/
public void infect(){
this.infection = true;
this.setColor(Color.red);
// Print out count of number infected
System.out.println("Number infected: "+infected());
}
Counting the infected
/**
* Count infected
**/
public int infected() {
int count = 0;
LinkedList agents = simulation.getAgents();
PersonAgent check;
for (int i = 0; i<agents.size(); i++){
check = (PersonAgent) agents.get(i);
if (check.infection) {count++;}
}
We could have
added them to an
infected list and just
checked the size(),
too.
return count;
}
There are constructors
here, too, but we’re
ignoring them now.
Running a DiseaseSimulation
DiseaseSimulation ds2 = new
DiseaseSimulation();
ds2.openFile(“D:/cs1316/disease-fullsize.txt”);
ds2.run();
Comparing Small and Large Worlds
for Disease Propagation
public void setUp(){
// Let the world be set up
super.setUp();
// Or set it up with a smaller world
//world = new World(300,300);
//world.setAutoRepaint(false);
70
60
50
40
30
20
10
0
1
4
7 10 13 16 19 22 25 28 31 34 37 40 43 46 49
A common activity in this
class: Generate data for Excel
and analyze it there.
Small world DiseaseSimulation
public void setUp(){
// Let the world be set up
//super.setUp();
// Or set it up with a smaller world
world = new World(300,300);
world.setAutoRepaint(false);
70
60
50
40
30
20
10
0
1
4
7 10 13 16 19 22 25 28 31 34 37 40 43 46 49
PoliticalSimulation
How it works


There are two sets of PoliticalAgents: Red and Blue
Both wander aimlessly, but within constraints.



Blue is only to the right, red only to the left.
Overlap for 200 pixels in the middle.
If a Blue gets surrounded (argued down?) by more Red
supporters than Blue supporters, the Blue turns Red.
And vice-versa.
But there is a problem
with getting converted
mid-timestep!
Political
Simulation
/**
* PoliticalSimulation -- using the Simulation class
**/
public class PoliticalSimulation extends Simulation {
/**
* Fill the world with 60 persons
**/
public void setUp(){
// Let the world be set up
super.setUp();
PoliticalAgent moi;
// 60 people
for (int num = 0; num < 60; num++) {
moi = new PoliticalAgent(world,this);
// First 30 are red
if (num < 30) {
moi.politics = Color.red;
moi.moveTo(100,100);
PoliticalAgent.redParty.add(moi);
}
else {
moi.politics = Color.blue;
moi.moveTo(500,100);
PoliticalAgent.blueParty.add(moi);
}
moi.setColor(moi.politics);
} // for loop
Tracking the PoliticalSimulation
/**
* lineForFile -- write out number of each party
**/
public String lineForFile(){
return (new Integer(PoliticalAgent.redParty.size())).toString()+"\t"+
(new Integer(PoliticalAgent.blueParty.size())).toString();
}
/**
* EndStep, count the number of each
**/
public void endStep(int t){
super.endStep(t);
System.out.println("Red: "+PoliticalAgent.redParty.size()+" Blue: "+
PoliticalAgent.blueParty.size());
}
We’re
accessing here
the static
variables that
track the
redParty and
blueParty.
PoliticalAgent
import java.awt.Color; // Color for colorizing
import java.util.LinkedList;
/**
* PoliticalAgent -- Red or Blue Stater as a subclass of Agent
**/
public class PoliticalAgent extends Agent {
// Red or Blue
public Color politics;
public static LinkedList redParty = new LinkedList();
public static LinkedList blueParty = new LinkedList();
Initializing our PoliticalAgents
/**
* Initialize
**/
public void init(Simulation thisSim){
// Do the normal initializations
super.init(thisSim);
// Don't need to see the trail
setPenDown(false);
// Speed is 100
speed = 100;
}
Converting political preference
/**
* Set politics
**/
public void setPolitics(Color pref){
System.out.println("I am "+politics+" converting to "+pref);
if (pref == Color.red) {
blueParty.remove(this);
redParty.add(this);
this.politics = pref;}
else {
blueParty.add(this);
redParty.remove(this);
this.politics = pref;
}
this.setColor(pref);
}
PoliticalAgent act()
/**
* How a PoliticalAgent acts
**/
public void act()
{
// What are the number of blues and red near me?
int numBlue = countInRange(30,blueParty);
int numRed = countInRange(30,redParty);
if (politics==Color.red){
// If I'm red, and there are more blue than red near me, convert
if (numBlue > numRed){
setPolitics(Color.blue);}
}
if (politics==Color.blue){
// If I'm blue, and there are more red than blue near me, convert
if (numRed > numBlue) {
setPolitics(Color.red);}
}
PoliticalAgent act(), cont’d
// Run the normal act() -- wander aimlessly
super.act();
// But don't let them wander too far!
// Let them mix only in the middle
if (politics==Color.red) {
if (this.getXPos() > 400) { // Did I go too far right?
this.moveTo(200,this.getYPos());}
}
if (politics==Color.blue) {
if (this.getXPos() < 200) { // Did I go too far left?
this.moveTo(400,this.getYPos());}
}
}
How the Simulation Package works

There are lots of calls to this


This will call the instance’s method.



this.setUp(), for example.
Typically, the subclass!
If the subclass doesn’t have the method, it will inherit
the method from the superclass.
The subclass can still call the superclass version using
super.
Let’s trace the DiseaseSimulation
DiseaseSimulation ds2 = new DiseaseSimulation();
ds2.run();
Here’s how a
Simulation class
instance gets
constructed.
public Simulation() {
// By default, don't write to a file.
output = null;
// And there is no FrameSequence
frames = null;
}
ds2.run();
/**
* Run for a default of 50 steps
**/
public void run(){
this.run(50);
this.closeFile();
}
Both methods are in
Simulation
/**
* Ask all agents to run for the number of input
* steps
**/
public void run(int timeRange)
{
// A frame, if we're making an animation
Picture frame;
// For storing the current agent
Agent current = null;
// Set up the simulation
this.setUp();
Does ds2 have a setUp()
method?
this.setUp() in DiseaseSimulation
/**
* Fill the world with 60 persons, one sick
**/
public void setUp(){
// Let the world be set up
super.setUp();
PersonAgent moi;
// 60 people
for (int num = 0; num < 60; num++) {
moi = new PersonAgent(world,this);
}
// Infect the first one
moi = (PersonAgent) getAgents().get(0);
moi.infect();
}
public void setUp(){
// Set up the World
world = new World();
world.setAutoRepaint(false);
}
Back to Simulation
just for a moment, to
set up the world, then
back again.
Back to public void run(int
timeRange) in Simulation
// Set up the simulation
this.setUp();
// loop for a set number of timesteps
for (int t = 0; t < timeRange; t++)
{
// loop through all the agents, and have them
// act()
for (int index=0; index < agents.size(); index++) {
current = (Agent) agents.get(index);
current.act();
}
Do PersonAgents have act()’s?
You bet!
PersonAgent act() to Agent act()
public void act()
{
// Is there a person within infection range of me?
PersonAgent closePerson = (PersonAgent)
getClosest(20,
simulation.getAgents());
if (closePerson != null) {
// If this person is infected, and I'm not infected
if (closePerson.infection && !this.infection) {
// I become infected
this.infect();
}
}
// Run the normal act() -- wander aimlessly
super.act();
}
public void act()
{
// Default action: wander aimlessly
// if the random number is > prob of
NOT turning then turn
if (randNumGen.nextFloat() >
PROB_OF_STAY)
{
this.turn(randNumGen.nextInt(360));
}
// go forward some random amount
forward(randNumGen.nextInt(speed));
} // end act()
Finishing Simulation run()
// repaint the world to show the movement
world.repaint();
if (frames != null){
// Make a frame from the world, then
// add the frame to the sequence
frame = new Picture(world.getWidth(),world.getHeight());
world.drawOn(frame);
frames.addFrame(frame);
}
// Do the end of step processing
this.endStep(t);
// Wait for one second
//Thread.sleep(1000);
}
Hang on! Not done yet!
endStep() calls lineForFile() (in
DiseaseSimulation)
public void endStep(int t){
// Let's figure out where we stand...
System.out.println(">>> Timestep: "+t);
// If we have an open file, write the counts to it
if (output != null) {
// Try it
try{
output.write(lineForFile());
output.newLine();
} catch (Exception ex) {
System.out.println("Couldn't write the data!");
System.out.println(ex.getMessage());
// Make output null so that we don't keep trying
output = null;
}
}
} // endStep()
public String lineForFile(){
PersonAgent first;
first = (PersonAgent) agents.get(0);
return (new
Integer(first.infected())).toString();
}
How much do you have to know?

Do you have to know what Simulation run()
does? Or Agent act()?
 Not
in any detail!
 You need to know what it roughly does, so you can
decide if you need it via super

You need to know when your code will be called,
so that you can do what you need to, at the right
point in the simulation.
Finally! Making Wildebeests

We simply copy characters to frames wherever
the turtles are.
Story: The Curious Birds



The turtle-like curious bird things wander, slowly,
toward the mysterious egg.
As they get up close to it—it opens its eyes and
shows its fangs!
They scamper away while the monster shifts
around and looks to the left and right.
The Movie
“What’s the big deal?”




“Isn’t this darn similar to the wolves attacking the village
movie?”
Yes.
But we didn’t have to build a scene graph and define
every frame here.
We simply built a simulation and said “Go.”


Each time that we run this simulation, it’ll be slightly different.
We can have as many “takes” as we want, and tweak the rules
of behavior as we want.
A Mapping
We move Agents (turtles) in a
simulation
And once a timestep, we
map these to images and
draw them.
BirdSimulation
/**
* BirdSimulation
* A flock of 10 birds investigate a mysterious egg,
* which suddenly shows itself to be a monster!
**/
public class BirdSimulation extends Simulation {
public EggAgent egg; // We'll need to get this later in BirdAgent
FrameSequence myFrames; // Need a separate one from Simulations
Setting up the Simulation
/**
* Set up the world with 10 birds and the mysterious egg
**/
public void setUp(){
// Set up the world
super.setUp();
// We'll need frames for the animation
myFrames = new FrameSequence("D:/Temp/");
myFrames.show();
BirdAgent tweetie;
// 10 of 'em
for (int num = 0; num < 10; num++) {
tweetie = new BirdAgent(world,this);}
// And the egg
egg = new EggAgent(world,this);
}
Creating the Animation
public void endStep(int t) {
// Do the normal file processing (if any)
super.endStep(t);
// But now, make a 640x480 frame, and copy
// in pictures from all the agents
Picture frame = new Picture(640,480);
Agent drawMe = null;
for (int index=0; index<this.getAgents().size(); index++) {
drawMe = (Agent) this.getAgents().get(index);
drawMe.myPict.bluescreen(frame,drawMe.getXPos(),
drawMe.getYPos());
}
myFrames.addFrame(frame);
}
Explaining the key lines


We get our Agent
(BirdAgent or
EggAgent).
Get the picture myPict
then bluescreen it onto
the frame at the current
position of the agent’s
turtle.
drawMe = (Agent)
this.getAgents().get(index);
drawMe.myPict.bluescreen(frame,
drawMe.getXPos(),
drawMe.getYPos());
Getting the timestep

Since we want something to happen at certain
timesteps, we need act() to have the timestep.
 We
need Simulation to pass us the timestep.
 We need Agent’s act() to catch the timestep and
pass it on as no timestep, so that all the old
simulations continue to work.
Simulation change
// loop through all the agents, and have them
// act()
for (int index=0; index < agents.size(); index++) {
current = (Agent) agents.get(index);
current.act(t); // NEW -- pass in timestep
}
Addition to Agent
/**
* act() with a timestep
**/
public void act(int t){
// By default, don't act on it
this.act();
}
Think through why we
need this.
Simulation is now
calling act(timestep).
Our other simulations
don’t have act(int t)…
BirdAgent
/**
* BirdAgents use the bird character JPEGs
**/
public class BirdAgent extends Agent{
public static Picture bird1, bird2, bird3, bird4, bird5, bird6;
Why static? Would it work
without static? Yes, but
more resource intensive.
Setting up birds
/**
* Set up the birds
**/
Setting up a bunch of
public void init(Simulation thisSim){
static variables to hold the
if (bird1 == null) {
bird pictures
// Do we have the bird characters defined yet?
// CHANGE ME!
FileChooser.setMediaPath("D:/cs1316/MediaSources/");
bird1 = new Picture(FileChooser.getMediaPath("bird1.jpg"));
bird2 = new Picture(FileChooser.getMediaPath("bird2.jpg"));
bird3 = new Picture(FileChooser.getMediaPath("bird3.jpg"));
bird4 = new Picture(FileChooser.getMediaPath("bird4.jpg"));
bird5 = new Picture(FileChooser.getMediaPath("bird5.jpg"));
bird6 = new Picture(FileChooser.getMediaPath("bird6.jpg"));
}
Finishing BirdAgent init()
// Start out with myPict as bird1
myPict = bird1;
// Do the normal initializations
super.init(thisSim);
// Move all the birds to the far right corner
this.setPenDown(false);
this.moveTo(600,400);
// Set speed to relatively slow
this.setSpeed(40);
}
What Birds do
/**
* act(t) For first 20 steps, walk toward the egg,
* +/- 30 degrees.
* Then walk AWAY from the egg, and with MORE wandering (panic).
**/
public void act(int t){
// First, handle motion
if (t <= 20) {
// Tell it that this really is a BirdSimulation
BirdSimulation mySim = (BirdSimulation) simulation;
// which has an egg
this.turnToFace(mySim.egg);
this.turn(randNumGen.nextInt(60)-30);
forward(randNumGen.nextInt(speed));
} else {
// Run away!!
this.turnToFace(640,480); // Far right corner
this.turn(randNumGen.nextInt(80)-40);
forward(randNumGen.nextInt(speed));
}
What’s going on with this
math is getting +/-. 0 to
60, minus 30, gives you 30 to 30
Birds also change character look
(cell animation)
// Next, set a new character
int cell = randNumGen.nextInt(6)+1; // 0 to 5, + 1 => 1 to 6
switch (cell) {
case 1:
myPict = bird1; // this.drop(bird1);
break;
case 2:
myPict = bird2; //this.drop(bird2);
break;
case 3:
myPict = bird3; //this.drop(bird3);
break;
case 4:
myPict = bird4; //this.drop(bird4);
break;
case 5:
myPict = bird5; //this.drop(bird5);
break;
case 6:
myPict = bird6; //this.drop(bird6);
break;
} // end switch
} // end act
What’s this?
It’s called a
switch or case
statement.
Instead of 6 if’s,
we have one big
case.
Consider drop vs. chromakey?
Think about resources and
mapping to other media
Zooming in on the switch





We compute a random integer
between 1 and 6.
We announce that we’re going
to choose between options
(switch) depending on the value
of cell.
We identify each value we’re
checking with a case statement.
Java executes the one that
matches the switch.
Execution ends and jumps to
the end of the switch on break.
int cell =
randNumGen.nextInt(6)+1;
// 0 to 5, + 1 => 1 to 6
switch (cell) {
case 1:
myPict = bird1;
break;
case 2:
myPict = bird2;
break;
EggAgent
/**
* EggAgent -- big scary egg that sits there until t=15,
* then emerges as a monster!
**/
public class EggAgent extends Agent {
public static Picture egg1, egg2, egg3, egg4;
Init() for an EggAgent
/**
* To initialize, set it up as the Egg in the upper lefthand corner
**/
public void init(Simulation thisSim){
if (egg1 == null) { //Initialize
//CHANGE ME!
FileChooser.setMediaPath("D:/cs1316/MediaSources/");
egg1 = new Picture(FileChooser.getMediaPath("egg1.jpg"));
egg2 = new Picture(FileChooser.getMediaPath("egg2.jpg"));
egg3 = new Picture(FileChooser.getMediaPath("egg3.jpg"));
egg4 = new Picture(FileChooser.getMediaPath("egg4.jpg"));
}
// Start out as egg1
myPict = egg1;
Meet the Eggs
The rest of EggAgent init()
// Normal initialization
super.init(thisSim);
// Make the turtle disappear
//this.hide(); // Not really necessary
this.setPenDown(false);
// Move the egg up to the left hand corner
this.moveTo(10,10);
}
Eggs don’t move in act(int t)
/**
* To act, just drop the Egg for 15 steps,
* then be the eyes opened for five steps,
* then be the eyes switching back-and-forth
**/
public void act(int t) {
if (t < 19) {
myPict = egg1;}
//this.drop(egg1);}
if (t>19 && t<24) {
myPict = egg2;}
//this.drop(egg2);}
Even when they’re looking scary
if (t>23) {
int choose=randNumGen.nextInt(2);
if (choose == 1) {
myPict = egg3;}
//this.drop(egg3);}
else {
myPict = egg4;}
//this.drop(egg4);}
}
} // end act()
To Explore

Start the birds out all over the screen


Have the birds react to a state of the egg


For example: “egg.scary()==true”, so that we’re not tied to a
particular timestep (frame #)
Have the birds react to one another.
“I’m crowded, I’m going to move that way.”
Big idea! An animation is only one kind of representation
to make from a simulation.
 How about playing certain sounds or MIDI phrases from
different characters at different times?


So that we can see them wave, etc. better.
CS1 for Engineering in MATLAB


Syllabus
Sample lessons on getting started
Syllabus

Getting started with MATLAB











Introduction to Vectors, the main MATLAB data type
Conditionals, iteration, and functions
Cell arrays (mini-databases)
Structures
Problem solving
General arrays
Graphing (MATLAB does professional quality graphics)
Bodies of Rotation and Matrices
File I/O
Multimedia: Image and sound manipulation
Serious CS: Numerical methods, Big O, Sorting,
Queues, and Graphs
Objectives – the MATLAB User
Interface
■ How to use the Command window to explore single
commands interactively and how to recall earlier
commands to be repeated or changed
■ Where to examine the variables and files created in
MATLAB
■ How to view and edit data tables created in MATLAB
■ How MATLAB presents graphical data in separate
windows
■ How to create scripts to solve simple arithmetic problems
File menu
Close icon
The Default Window
Current
directory
Command window
Workspace window
Command history
Array Editor
New variable icon
If you don’t have MATLAB, Octave!
2.4 Scripts
Create a script derived from the Pythagorean theorem to compute
the hypotenuse of a right triangle:
H2 = A2 + B2
where A and B are the sides adjacent to the right angle, and H is
the hypotenuse opposite.
clear
clc
A = 3; % the first side of a triangle
B = 4; % the second side of a triangle
hypSq = A^2 + B^2; % the square of the
% hypotenuse
H = sqrt(hypSq) % the answer
Store these in your working directory to
access

cd W:/home/guzdial/Documents/
2.5 Engineering Example—Spacecraft
Launch
clear
clc
cmPerInch = 2.54; % general knowledge
inchesPerFt = 12; % general knowledge
metersPerCm = 1/100; % general knowledge
MetersPerFt = metersPerCm * cmPerInch * inchesPerFt;
startFt = 25000; % ft - given
startM = startFt * MetersPerFt;
g = 9.81; % m/sec^2
top = 100; % km - given
s = (top*1000) - startM; % m
initial_v = (2*g*s)^0.5 % the final answer
Passing in parameters, return values
function retval = avg (v)
if (isvector (v))
retval = sum (v) / length (v);
endif
endfunction
 Saved as avg.m
3.1 Concept: Using Built-in
Functions



In this chapter we will see the use of some of the functions built into
MATLAB.
At the end of each chapter that uses built-in functions, you will find a
summary table listing the function specifications.
For help on a specific function, you can type the following:
>> help <function name>

For example:
>> help sqrt
SQRT
Square root.
SQRT(X) is the square root of the elements of X.
Complex results are produced if X is not positive.
3.2 Concept: Data Collections
This section considers two very common ways to group data: in arrays
and in vectors.
Data Abstraction allows us to refer to groups of data collectively:
“all the temperature readings for May” or
 “all the purchases from Wal-Mart.”

We can not only move these items around as a group, but also perform
mathematical or logical operations on these groups, e.g.:

compute the average, maximum, or minimum temperatures for a month
A Homogeneous Collection is constrained to accept only items of the
same data type – in this case, they will all be numbers
3.3 MATLAB Vectors
Individual items in a vector are usually referred to as its elements.
Vector elements have two separate and distinct attributes that make
them unique in a specific vector:

their numerical value and
 their position in that vector.
For example, the individual number 66 is the third element in this
vector. Its value is 66 and its index is 3. There may be other items in the
vector with the value of 66, but no other item will be located in this
vector at position 3.
Vector Manipulation
We consider the following basic operations on
vectors:
 Creating
a Vector
 Determining the size of a Vector
 Extracting data from a vector by indexing
 Shortening a Vector
 Mathematical and logical operations on Vectors
Creating a Vector – Constant
Values

Entering the values directly, e.g.
A = [2, 5, 7, 1, 3]

Entering the values as a range of numbers e.g.,
B = 1:3:20

Using the linspace(...) function e.g.
C = linspace (0, 20, 11)

Using the functions zeros(1,n), ones(1,n), rand(1,n) and
randn(1,n) to create vectors filled with 0, 1, or random
values between 0 and 1
Size of Vectors and Arrays
MATLAB provides two functions to determine the
size of arrays in general (a vector is an array with
one row):
 the
function size(A) when applied to the array A
returns vector containing two quantities: the number
of rows and the number of columns
 The function length(A) returns the maximum value in
the size of an array; for a vector, this is its length.
Indexing a Vector


The process of extracting values from a vector,
or inserting values into a vector
Syntax:
 v(index)
returns the element(s) at the location(s)
specified by the vector index.
 v(index) = value replaces the elements at the
location(s) specified by the vector index.

The indexing vector may contain either
numerical or logical values
Indexing examples
octave:10> a =
[1,12,43,25,34]
a=
1 12 43 25 34
octave:14> a
a=
1 12 43 25 34
octave:16> a(1)
ans = 1
octave:17> a(a < 12)
ans = 1
octave:18> a < 20
ans =
1 1 0 0 0
octave:15> a<12
ans =
1 0 0 0 0
octave:19> a(a < 20)
ans =
1 12
Numerical Indexing



The indexing vector may be of any length
It should contain integer (non-fractional)
numbers
The values in the indexing vector are
constrained by the following rules:
For
reading elements, all index values must be
1 <= element <= length(vector)
For
replacing elements, all index values must be
1 <= element
Replacement Rules
Either:
1.
•
•
All dimensions of the blocks on either side of the replacement
instruction must be equal, or
There must be a single element on the RHS of the
replacement
If you replace beyond the end of the existing vector,
the vector length is automatically increased.
2.
•
•
Any element not specifically replaced remains unchanged.
Elements beyond the existing length not replaced are set to 0.
Replacement examples
octave:20> a(3)=567
a=
1 12 567 25 34
octave:21> a
a=
1 12 567 25 34
octave:22> a(a < 20) = [12,34]
a=
12 34 567 25 34
Logical Indexing



The indexing vector length must be less than or equal to
the original vector length
It must contain logical values (true or false)
Access to the vector elements is by their relative position
in the logical vector



When reading elements, only the elements corresponding to
true index values are returned
When replacing elements, the elements corresponding to true
index values are replaced
Beware – logical vectors in Matlab echo in the Command
window as 1 or 0, but they are not the same thing.
Shortening an Array



Never actually necessary. It is advisable to
extract what you want by indexing rather than
removing what you don’t want.
Can lead to logic problems when changing the
length of a vector
Accomplished by assigning the empty vector ([])
to elements of a vector, or to complete rows or
columns of an array.
Operating on Vectors
Three techniques extend directly from operations
on scalar values:
■ Arithmetic operations
■ Logical operations
■ Applying library functions
Two techniques are unique to arrays in general,
and to vectors in particular:
■ Concatenation
■ Slicing (generalized indexing)
Arithmetic operations
In the Command window, enter the following:
>> A = [2 5 7 1 3];
>> A + 5
ans =
7 10 12 6 8
>> A .* 2
ans =
4 10 14 2 6
>> B = -1:1:3
B =
-1 0 1 2 3
Arithmetic operations (continued)
>> A .* B % element-by-element multiplication
ans =
-2 0 7 2 9
>> A * B % matrix multiplication!!
??? Error using ==> mtimes
Inner matrix dimensions must agree.
>> C = [1 2 3]
C =
1 2 3
>> A .* C % A and C must have the same length
??? Error using ==> times
Matrix dimensions must agree.
Logical operations
>> A = [2
>> B = [0
>> A >= 5
ans =
0 1 1 0 0
>> A >= B
ans =
1 0 1 0 1
>> C = [1
>> A > C
??? Error
5 7 1 3];
6 5 3 2];
2 3]
using ==> gt
Matrix dimensions must agree.
Logical operations (continued)
>> A = [true true false false];
>> B = [true false true false];
>> A & B
ans =
1 0 0 0
>> A | B
ans =
1 1 1 0
>> C = [1 0 0]; % NOT a logical vector
>> A(C) % yes, you can index logical vectors, but ...
??? Subscript indices must either be real positive
integers or logicals.
A Footnote: the find function

Continuing the code above:
>> C = find(B)
ans =
[1 3]
The find(...) function consumes a logical vector and
returns the numerical indices of the elements of that
vector that are true.
 Example:
octave:23> a > 20
ans =
0 1 1 1 1
octave:24> c = find(a > 20)
c=
2 3 4 5

Applying library functions
All MATLAB functions accept vectors of numbers rather than single
values and return a vector of the same length.
Special Functions:
■ sum(v) and mean(v) consume a vector and return a number
■ min(v) and max(v) return two quantities: the minimum or
maximum value in a vector, plus the position in that vector
where that value occurred.
■ round(v), ceil(v), floor(v), and fix(v) remove the fractional
part of the numbers in a vector by conventional rounding, rounding up,
rounding down, and rounding toward zero, respectively.
Exercise: Make up a
vector and try all of
these on it!
Concatenation

MATLAB lets you construct a new vector by
concatenating other vectors:
 A = [B C D ... X Y Z]
where the individual items in the brackets may be any
vector defined as a constant or variable, and the length
of A will be the sum of the lengths of the individual
vectors.
 A = [1 2 3 42]
is a special case where all the component elements are
scalar quantities.
Concatenation Example
octave:27> a
a=
12 34 567 25 34
octave:28> b
b=
78.600 45.600 12.200
octave:29> c=[a b]
c=
12.000 34.000 567.000 25.000 34.000 78.600
45.600 12.200
Slicing (generalized indexing)


A(4) actually creates an anonymous 1 × 1 index vector,
4, and then using it to extract the specified element from
the array A.
In general,
B(<rangeB>) = A(<rangeA>)
where <rangeA> and <rangeB> are both index vectors, A is an
existing array, and B can be an existing array, a new array, or
absent altogether (giving B the name ans). The values in B at the
indices in <rangeB> are assigned the values of A from <rangeA> .
Rules for Slicing
■ Either the dimensions of <rangeB> must be equal
to the dimensions of <rangeA> or <rangeA> must be
of size 1
■ If B did not exist before this statement was
implemented, it is zero filled where assignments
were not explicitly made
■ If B did exist before this statement, the values
not directly assigned in <rangeB> remain
unchanged
Representing Mathematical Vectors


An unfortunate clash of names
Vectors in mathematics can be represented by Matlab
vectors





The first, second and third values being the x, y and z
components
Matlab vector addition and subtraction work as expected.
Matlab magnitude and scaling works as expected.
Dot product is just the sum of A .* B
Cross product has a Matlab function
Engineering Example—Forces and
Moments

So given a pair of forces A
and B acting at a point P,
find:
 The
resultant force, and
 The moment of that resultant
about the origin
Vector Solution
clear
clc
PA = [0 1 1]
PB = [1 1 0]
P = [2 1 1]
M = [4 0 1]
% find the resultant of PA and PB
PC = PA + PB
% find the unit vector in the direction of PC
mag = sqrt(sum(PC.^2))
unit_vector = PC/mag
% find the moment of the force PC about M
% this is the cross product of MP and PC
MP = P - M
moment = cross( MP, PC )
MATLAB Arrays
A Transposed Array
Array Manipulation
We consider the following basic operations on
vectors:
 Creating
an array
 Extracting data from an array by indexing
 Shortening an array
 Mathematical and logical operations on arrays
Creating an Array – Constant
Values


Entering the values directly, e.g.
A = [2, 5, 7; 1, 3, 42] the semicolon identifies
the next row, as would a new line in the
command
Using the functions zeros( rows, cols), ones(rows,
cols), rand(rows, cols) and randn(rows, cols) to
create vectors filled with 0, 1, or random values
between 0 and 1
octave:32> m = [1, 2, 3; 4, 5, 6]
m=
1 2 3
4 5 6
Indexing an Array


The process of extracting values from an array,
or inserting values into an array
Syntax:
 A(row,
col) returns the element(s) at the location(s)
specified by the array row and column indices.
 A(row, col) = value replaces the elements at the
location(s) specified by the array row and column
indices.

The indexing row and column vectors may
contain either numerical or logical values
Numerical Indexing



The indexing vectors may be of any length
It should contain integer (non-fractional)
numbers
The values in the indexing vectors are
constrained by the following rules:
For
reading elements, all index values must be
1 <= element <= length(array dimension)
For
replacing elements, all index values must be
1 <= element
Replacement Rules
Either:
1.
•
•
All dimensions of the blocks on either side of the replacement
instruction must be equal, or
There must be a single element on the RHS of the
replacement
If you replace beyond the end of any dimension of the
existing array, the size in that dimension is
automatically increased.
2.
•
•
Any element not specifically replaced remains unchanged.
Elements beyond the existing dimension length not replaced
are set to 0.
Logical Indexing



The indexing vector length must be less than or
equal to the original array dimension
It must contain logical values (true or false)
Access to the array elements is by their relative
position in the logical vectors


When reading elements, only the elements
corresponding to true index values are returned
When replacing elements, the elements
corresponding to true index values are replaced
Logical indexing in matrices example
octave:32> m = [1, 2, 3; 4, 5, 6]
m=
1 2 3
4 5 6
octave:34> m ( m<=4 ) = -1
m=
-1 -1 -1
-1 5 6
Operating on Arrays
Four techniques extend directly from operations on
vectors:
■ Arithmetic operations
■ Logical operations
■ Applying library functions
■ Slicing (generalized indexing)
The following deserves an additional word
because of the nature of arrays:
■ Concatenation
Array Concatenation

Array concatenation can be accomplished
horizontally or vertically:
R
= [A B C] succeeds as long as A, B and C have the
same number of rows; the columns in R will be the
sum of the columns in A, B and C.
 R = [A; B; C] succeeds as long as A, B and C have
the same number of columns; the rows in R will be
the sum of the rows in A, B and C.
Reshaping Arrays

Arrays are actually stored in column order in
Matlab. So internally, a 2 × 3 array is stored as
a column vector: A(1,1)
A(2,1)
A(1,2)
A(2,2)
A(1,3)
A(2,3)

Any n × m array can be reshaped into any p × q
array as long as n*m = p*q using the reshape
function.
3.6 Engineering Example—Computing
Soil Volume



Consider the example where you are given the
depth of soil from a survey in the form of a
rectangular array of soil depth.
You are also given the footprint of the
foundations of a building to be built on that site
and the depth of the foundation.
Compute the volume of soil to be removed.
Survey Data
Building Footprint
Solution
clear
clc
% soil depth data for each square produced
% by the survey
dpth = [8 8 9 8 8 8 8 8 7 8 7 7 7 7 8 8 8 7
8 8 8 8 8 8 8 7 7 7 7 7 8 7 8 8 8 7
. . .
9 8 8 7 7 8 7 7 7 7 8 8 9 9 9 8 7 8];
% estimated proportion of each square that should
% be excavated
area = [1 1 1 1 1 1 1 1 1 1 .3 0 0 0 0 0 0 0
. . .
0 0 0 0 0 0 .4 .8 .9 1 1 1 1 1 1 1 1 .6];
square_volume = dpth .* area;
total_soil = sum(sum(square_volume))
4.1 Concept: Code Blocks

A code block is a collection of zero or more MATLAB instructions
identified for one of two reasons:
you wish to execute them only under certain circumstances, or
2. You wish to repeat them a certain number of times
1.


Some languages identify code blocks by enclosing them in braces ({.
. .}); others identify them by the level of indentation of the text.
MATLAB uses the occurrence of key command words in the text to
define the extent of code blocks:


if, switch, while, for, case, otherwise, else,
elseif, end
Code blocks are identified with blue coloring by the MATLAB text
editor. They are not part of the code block, but they serve both


as instructions on what to do with the code block, and
as delimiters that define the extent of the code block.
4.2 Conditional Execution in
General

Basic conditional execution
requires two things:
 A logical
expression, and
 A code block


If the expression is true, the code
block is executed.
Otherwise, execution is resumed
at the instruction following the
code block
Compound conditionals

By introducing elseif and else, we allow for the possibility
of either conditional or unconditional execution when a
test returns false as illustrated.
4.3 if Statements

The general template for if statements is:
if <logical expression 1>
<code block 1>
elseif <logical expression 2>
<code block 2>
.
.
.
elseif <logical expression n>
<code block n>
else
<default code block>
end
General Observations


A logical expression is any statement that
returns a logical result.
If that result is a logical vector, v, the if statement
behaves as:
if all(v)

While indentation has no effect on the logical
flow, it helps to clarify the logical flow. The
MATLAB editor automatically creates suitable
indentation as you type.
4.4 switch Statements

The template for a switch statement is:
switch <parameter>
case <case specification 1>
<code block 1>
case <case specification 2>
<code block 2>
.
.
case <case specification n>
<code block n>
otherwise
<default code block>
end
General Observations




The switch statement is looking for the
parameter to have an exact match to one of the
cases.
One case specification may have multiple
values enclosed in braces( {…}).
The default case catches any values of the
parameter other than the specified cases.
The default case should trap bad parameter
values.
4.5 Iteration in General
Iteration allows controlled repetition of a code block.
Control statements at the beginning of the code block
specify the manner and extent of the repetition:


The for loop is designed to repeat its code block a fixed number
of times and largely automates the process of managing the
iteration.
The while loop is more flexible in character. Its code block can
be repeated a variable number of times. It is much more of a
“do-it-yourself” iteration kit.
4.6 for Loops
The template for a for loop is:
for <variable> = <vector>
<code block>
end
The for loop automatically sets
the value of the variable to each
element of the vector in turn and
executes the code block with that
value.
4.7 while Loops
The code block will be repeated
as long as the logical expression
returns true.
The while loop template is:
<initialization>
while <logical expression>
<code block>
% must make some changes
% to enable the loop to terminate
end
4.8 Engineering Example—
Computing Liquid Levels
Give a tank as shown, how do
you calculate the volume of
liquid? The answer of course is “it
depends on h.”
If h <= r, do one calculation;
otherwise if h < (H-r) do a second;
Otherwise if h <= H, do a third;
Otherwise there is an error!
The Solution
if h < r
v = (1/3)*pi*h.^2.*(3*r-h);
elseif h < H-r
v = (2/3)*pi*r^3 + pi*r^2*(h-r);
elseif h <= H
v = (4/3)*pi*r^3 + pi*r^2*(H-2*r) ...
- (1/3)*pi*(H-h)^2*(3*r-H+h);
else
disp(‘liquid level too high’)
continue
end
fprintf( ...
'rad %0.2f ht %0.2f level %0.2f vol %0.2f\n', ...
r, H, h, v);
5.1 Concept: Abstraction
Procedural abstraction permits a code block that solves a
particular sub-problem to be packaged and applied to
different data inputs.



analogous to the concept of data abstraction where individual
data items are gathered to form a collection.
We have already used a number of built-in procedural
abstractions in the form of functions.
They allow us to apply a code block about which we know
nothing to data that we provide.
5.1 Concept: Encapsulation
Encapsulation is the concept of putting a wrapper
around a collection that you wish to protect from
outside influence.
Functions encapsulate the code they contain in
two ways:
 the
variables declared within the function are not
visible from elsewhere, and
 the function’s ability to change the values of variables
(otherwise known as causing side effects) is restricted
to its own code body.
5.2 Black Box View of a Function


are the formal parameters – the names given to the
incoming data inside the function.
<item 1...n> are the actual parameters provided to the function by
its caller.
<param 1...n>


They may have names different from the formal parameter names
They are correlated to the formal parameter names by their position
5.3 MATLAB Implementation
The template for defining a function is:
function <return info> <function name> (<parameters>)
<documentation>
<code body> % must return the results



The function code must be stored in a file whose
name is the name of the function.
Functions return data to the caller by assigning
values to the return variable(s)
MATLAB throws an error if a function does not
make assignments to all the return variables.
5.4 Engineering Example—Measuring a
Solid Object



We need to compute the volume and wetted area of this
object.
This requires one function that computes the volume and
wetted area of a cylinder
We have a range of disk heights for which we require
this information.
Solution

The function stored in cylinder.m
function [area, volume] =
% function to compute the
% usage: [area, volume] =
base = pi .* radius.^2;
volume = base .* height;
area = 2 * pi * radius .*

cylinder(height, radius)
area and volume of a cylinder
cylinder(height, radius)
height + 2 * base;
The test script
clear
clc
h = 1:5; % set a range of disk thicknesses
R = 25;
r = 3;
[Area Vol] = cylinder(h, R) % dimensions of large disk
[area vol] = cylinder(h, r) % dimensions of the hole
% compute remaining volume
Vol = Vol - 8*vol
Area = Area + 8*(area - 2*2*pi*r.^2)
Background
Two relationships between characters and numbers
1. Individual characters have an internal numerical
representation: The shapes we see in windows are created
by a character generator.
2. Strings of characters represent numerical values:



Numerical values are stored in MATLAB in a special, internal
representation for efficient numerical computation.
Whenever we need to see the value of a number, the internal
representation is converted into a character string representing its
value in a form we can read.
Similarly, to enter numerical values, we create a character string and
have it converted to the internal representation
Concept: Mapping
Mapping defines a relationship between two entities. e.g.
the idea that the function f(x) = x2 defines the mapping
between the value of x and the value
of f(x).
We will apply that concept to the process of translating a
character (like ‘A’) from its graphical form to a numerical
internal code. Character mapping allows each individual
graphic character to be uniquely represented by a
numerical value.
Concept: Casting
Casting is the process of changing the way a language views a piece
of data without actually changing the data value.
Under normal circumstances, a language like MATLAB automatically
presents a set of data in the “right” form.
However, there are times when we wish to force the language to treat a
data item in a specific way; we might want to view the underlying
numerical representation as a number rather that as a character, in
which case we have to cast the variable containing the character to a
numerical data type.
MATLAB implements casting as a function with the name of the data
type expected. In essence, these functions implement the mapping
from one character representation to another.
MATLAB Implementation of Casting
>> uint8('A') % uint8 is an integer data type
% with values 0 - 255
ans = 65
>> char(100) % char is the character class
ans = d
>> char([97 98 99 100 101])
ans = abcde
>> double('fred')
ans = 102 114 101 100
>> fred = 'Fred'
fred = Fred
>> next = fred + 1
next = 71 115 102 101
>> a = uint8(fred)
a = 70 114 101 100
>> name = char(a + 1)
name = Gsfe
String Operations

Since strings are internally represented as
vectors of numbers, all the normal vector
operations apply:
 Arithmetic
and logical operations
 Concatenation
 Shortening
 Indexing
 Slicing
Conversion from Numbers to Strings
Use the following built-in MATLAB functions for a simple
conversion of a single number, x, to its string
representation:


int2str(x) if you want it displayed as an integer value
num2str(x, n) to see the decimal parts; the parameter n
represents the number of decimal places required—if not
specified, its default value is 3
sprintf(…) provides finer-grained format control


Its first parameter is a format control string that defines how
the resulting string should be formatted.
A variable number of value parameters follow the format string,
providing data items as necessary to satisfy the formatting.
Format Control in sprintf(…)


Characters in the format string are copied to the result string.
Special behavior is introduced by two special characters:

'%' introduces a conversion specification:






%d (integer),
%f (real),
%g (general),
%c (character) and
%s(string).
Each conversion requires a value parameter in the sprintf(…) call.
A number may be placed immediately after the % character to specify the
minimum number of characters in the conversion. The %f and %g
conversions can include '.n' to indicate the number of decimal places
required.
'\' introduces escape characters for format control. The most common:


\n (new line) and
\t (tab).
Conversion from Strings to
Numbers:input(…)


When possible, allow input(...) to do the conversion.
The function input(str) presents the string parameter to the user in the
Command window and waits for the user to type some characters and
the Enter key, all of which are echoed in the Command window. Then
it converts the input string according to the following rules. If the string
begins with:


a numerical character, MATLAB converts the string to a number
An alpabetic character, MATLAB constructs a variable name and looks
for its definition
 an open bracket, '[', an array is constructed
 the single quote character, MATLAB creates a string
 If a format error occurs, MATLAB repeats the prompt.

This behavior can be modified if 's' is provided as the second
parameter to input(…), in which case the complete input character
sequence is saved as a string regardless of content.
Conversion from Strings to Numbers:
sscanf




In its simplest form, CV = sscanf(str, fmt) scans the string str and converts
each data item according to the conversion specifications in the format string
fmt.
Each item discovered in str produces a new row on the result array, CV, a
column vector.
If you convert strings this way, each character in the string becomes a
separate numerical result in the output vector.
MATLAB allows you to substitute thecharacter '*' for the conversion size
parameter to suppress any strings in the input string. For example:
str = 'are 4.700 1.321 4.800000'
B = sscanf( str, '%*s %f %f %f')
B =
4.7000
1.3210
4.8000
Miscellaneous Character String
Operations


disp(…) shows the contents of a variable in the
Command Window
fprintf(…) formats data for the Command Window exactly
as sprintf does to produce a string.
String Comparison


Strings may be compared as vectors; however, they must then obey vector
comparison rules
strcmp(…) and strcmpi(…) compare strings of any length.
>> 'abcd' == 'abcd'
ans = 1 1 1 1
>> 'abcd' == 'abcde'
??? Error using ==> eq
Array dimensions must match for binary array op.
>> strcmp('abcd', 'abcde')
ans = 0
>> strcmp('abcd', 'abcd')
ans = 1
>> 'abc' == 'a'
ans = 1 0 0
>> strcmpi('ABcd', 'abcd')
ans = 1
6.5 Arrays of Strings

Character string arrays can be constructed by
either of the following:
 As
a vertical vector of strings, all of which must be the
same length
 By using a special version of the char(…) cast
function that accepts a variable number of strings with
different lengths, pads them with blanks to make all
rows the same length, and stores them in an array of
characters
Engineering Example—Encryption

Encryption is the process of somehow changing a
message in the form of a string of characters so that it




can be understood at its destination, but
is unintelligible to a third party who does not have access to the
original encryption scheme.
Early encryption schemes involved shifting characters in
the alphabet either by a constant amount or according to
a one-time message pad.
However, these schemes are relatively easily cracked by
examining letter frequencies.
Our Approach



We will use a scheme that makes use of the MATLAB
random number generator to create a random character
shift unique to each occurrence of characters in a
message, so that letter frequency cannot be used to
determine the encryption technique.
At the destination, as long as the random number
generator is seeded with an agreed value, the message
can be reconstructed by shifting back the message
characters.
A few minor modifications wrap the characters on the
alphabet to remain within the set of printable letters.
The Solution - encryption
%%% encryption section
% seed the random generator to a known state
rand('state', 123456)
loch = 33;
hich = 126;
range = hich+1-loch;
rn = floor( range * rand(1, length(txt) ) );
change = (txt>=loch) & (txt<=hich);
enc = txt;
enc(change) = enc(change) + rn(change);
enc(enc > hich) = enc(enc > hich) - range;
disp('encrypted text')
encrypt = char(enc);
The Solution - decryption
%% good decryption
% seed the random generator to the same state
rand('state', 123456);
rn = floor( range * rand(1, length(txt) ) );
change = (encrypt>=loch) & (encrypt <= hich)
dec = encrypt;
dec(change) = dec(change) - rn(change) + range;
dec(dec > hich) = dec(dec > hich) - range;
disp('good decrypt');
decrypt = char(dec)
String Functions
num2str(a,n) Converts a number to its numerical
representation with n decimal places
disp(...) Displays matrix or text
fprintf(...) Prints formatted information
input(...) Prompts the user to enter a value
sscanf(...) Formats input conversion
sprintf(...) Formats a string result
strcmp(s1, s2) Compares two strings; returns true if equal
strcmpi(s1, s2) Compares two strings without regard to
case; returns true if equal
11.1 Plotting in General



The fundamental container for plotting is a
MATLAB figure
Simple plot of x versus y: plot(x, y)
Plot enhancements
 axis,
colormap, grid on, hold on, legend, shading, text,
title, view, xlabel, ylabel, zlabel

Use subplot(r, c, n) for multiple plots on one
figure
1-301
Exercise: Try this simple graph
octave:38> x=0:0.05:10*pi;
octave:39> y=exp(-1.*x).*sin(x);
octave:40> plot(x,y)
Don’t forget the semi-colons!
Plot Enhancements
1.
2.
3.
4.
5.
clf
x = -2*pi:.05:2*pi;
subplot(2,3,1)
plot(x, sin(x))
title('1 - sin(x)');
6. subplot(2,3,2)
7. plot(x, cos(x))
8. title('2 - cos(x)');
9. subplot(2,3,3)
10. plot(x, tan(x))
11. title('3 - tan(x)');
12. subplot(2,3,4)
13. plot(x, x.^2)
14. title('4 - x^2');
15. subplot(2,3,5)
16. plot(x, sqrt(x))
17. title('5 - sqrt(x)');
18. subplot(2,3,6)
19. plot(x, exp(x))
20. title('4 - e^x');
1-303
11.2 2-D Plotting

Basic function for 2-D plots: plot(x, y, str)
x
and y are vectors of the same length
 str specifies optional line color & style control

Plot options
 subplot,

axis, hold on, title
Parametric plotting
 Allows
the variables on each axis to be dependent on
a separate, independent variable
1-304
Multiple 2-D Plots
1-305
Special 2-D Effects
% Code for the first three plots
1. clear
2. clc
3. close all
4. x = linspace(0, 2*pi);
5. subplot(2, 3, 1)
6. plot(x, sin(x))
7. axis([0 2*pi -0.5 0.5])
8. title('Changing Data Range on an
Axis')
9. subplot(2, 3, 2)
10. plot(x, sin(x))
11. hold on
12. plot(x, cos(x))
13. axis tight
14. title('Multiple Plots with hold on')
15.
16.
17.
18.
19.
20.
subplot(2, 3, 3)
plot(x, sin(x), 'ó')
hold on
plot(x, cos(x), 'r:')
axis tight
title('Multiple Plots with hold on')
1-306
Transforming a Circle to an Airfoil
1-307
11.3 3-D Plotting


2-D plots in MATLAB are actually 3-D plots (select
the Rotate 3D icon on the tool bar)
Linear 3-D Plots
 Extend
2-D plots by adding a set of z values
 Use plot3(x, y, z, str)

Linear Parametric 3-D Plots
 Allow
variables on each axis to be dependent on a
separate, independent variable

Other plot capabilities

bar3(x, y), barh3(x, y), pie3(y)
1-308
Exercise: Try this simple 3-D plot
octave:38> x=0:0.05:10*pi;
octave:39> y=exp(-1.*x).*sin(x);
octave:41> z=cos(x);
octave:46> plot3(x,y,z)
3-D View of a 2-D Plot
1-310
3-D Line plots
1-311
Parametric Line Plots
1-312
11.4 Surface Plots


Production of images based on mapping a 2-D
surface  create a plaid
Basic capabilities
 meshgrid(x,
y): compute mappings for the 3-D
coordinates
 mesh(xx, yy, zz): plots the surface as white facets
outlined by colored lines
 surf(xx, yy, zz): plots the surface as colored facets
outlined by black lines
1-313
Exercise: Try this Surface Example
facets = 120; len = 2; radius = 1;
thr = linspace(0,2*pi,facets);
xr = [0 len];
[x th] = meshgrid(xr, thr );
y = radius * cos(th);
z = radius * sin(th);
surf(x,y,z);
Designing a Cube Surface plot
1-315
Cube Surfaces
1-316
Simple Surface Plot
1-317
Compound Surface Plot
1-318
Using External Illumination
1-319
Designing a Cylinder Plot
1-320
Cylinder Plot
1-321
Sphere Plot
1-322
Bodies of Rotation

Created by rotating a linear curve about a
specified axis
 i.e.

Rotate z = f(x) about the x-axis
y

rotate z = f(x) about the x or z axes (not y)
= r cos(θ), z = r sin(θ)
Rotate z = f(x) about the z-axis
x
= r cos(θ), y = r sin(θ)
1-323
Rotating About the X Axis
1-324
Rotating About the Z Axis
1-325
Bodies of Rotation
1-326
Rotating Arbitrary Shapes
1-327
General Rotation Techniques
Rotating about an Arbitrary Axis
• Calculate the matrix that will place your
axis of rotation along the x-axis
• Transform x and z with that rotation
• Rotate the results about the x-axis
• Invert the transformation on the resulting
surface
1-328
A Solid Disk
1-329
A Klein Bottle
1-330
Reading Excel Data
MATLAB actually has
very nice csvread
and csvwrite.
Octave…doesn’t
octave:51> help csv2cell
csv2cell is the dynamically-linked function from the file
/usr/lib/octave/site/oct/api-v13/i686-pc-cygwin/octave-forge/csv2cell.oct
-- Function File: C = csv2cell (FILE)
-- Function File: C = csv2cell (FILE, SEP)
-- Function File: C = csv2cell (FILE, SEP, PROT)
Read a CSV (Comma Separated Values) file and convert it into a
cell. SEP changes the character used to separate two fields. By
default, two fields are expected to be separated by a coma (`,').
PROT changes the character used to protect a string. By default
it's a double quote (`"').
Reading into Cells
octave:61> cells=csv2cell("Names.csv")
cells =
{
[1,1] = Name
[2,1] = Mark
[3,1] = Barb
[4,1] = Matthew
[5,1] = Katherine
[6,1] = Jennifer
[1,2] = Gender
[2,2] = 1
[3,2] = 2
[4,2] = 1
[5,2] = 2
[6,2] = 2
[1,3] = Age
[2,3] = 44
[3,3] = 45
[4,3] = 15
[5,3] = 12
[6,3] = 9
}
Another way to read Excel Data
octave:60> help dlmread
dlmread is the dynamically-linked function from the file
/usr/lib/octave/site/oct/api-v13/i686-pc-cygwin/octave-forge/dlmread.oct
-- Loadable Function: DATA = dlmread (FILE)
-- Loadable Function: DATA = dlmread (FILE,SEP)
-- Loadable Function: DATA = dlmread (FILE,SEP,R0,C0)
-- Loadable Function: DATA = dlmread (FILE,SEP,RANGE)
Read the matrix DATA from a text file The RANGE parameter must
be
a 4 element vector containing the upper left and lower right
corner [R0,C0,R1,C1] The lowest index value is zero.
Using dlmread
octave:62> data = dlmread("Names.csv",",")
data =
NA 0.00000 0.00000 0.00000
0.00000 1.00000 44.00000 0.00000
0.00000 2.00000 45.00000 0.00000
0.00000 1.00000 15.00000 0.00000
0.00000 2.00000 12.00000 0.00000
0.00000 2.00000 9.00000 0.00000
How do we get just the data we want?
octave:79> [rows cols] = size(data)
rows = 6
cols = 4
octave:80> col3 = [zeros(rows,1) zeros(rows,1) ones(rows,1)
zeros(rows,1)]
col3 =
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
Can’t use 0’s and 1’s –
must be true/false
octave:88> col3==1
ans =
0 0 1 0
0 0 1 0
0 0 1 0
0 0 1 0
0 0 1 0
0 0 1 0
octave:89> index = col3==1
index =
0 0 1 0
0 0 1 0
0 0 1 0
0 0 1 0
0 0 1 0
0 0 1 0
octave:90> data(index)
ans =
0
44
45
15
12
9
But that first row is just from the
header!
octave:93> ages(2:1:rows)
ans =
44
45
15
12
9
Exercise

Study the
world!
 Country
 Country
code
 Year (2004)
 Population in
thousands
 Exchange rate
with US$
 Per capita
GDP
Getting you started
octave:95> pops=dlmread("pops2004.csv",",");
octave:96> [rows,cols]=size(pops)
rows = 189
cols = 11
octave:97> col4=[zeros(rows,1) zeros(rows,1)
zeros(rows,1), ones(rows,1) zeros(rows,1) zeros(rows,1)
zeros(rows,1) zeros(rows,1) zeros(rows,1) zeros(rows,1)
zeros(rows,1)];
Alternatively:
popdata = pops(col4==1);
col4 = popdata(:,4)
octave:99> x=1:1:rows;
octave:100> plot(x,popdata)
Country populations in 2004
Exercise Questions




If you sort the data (hint: “help sort”), what does
the curve of world populations look like? Are all
populations equally likely?
How about the curve of exchange rates or per
capita GDP?
What’s the highest CGDP? What’s the lowest?
What’s the highest exchange rate? What’s the
lowest?
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ACM SIGCSE 2003: Multimedia Construction Projects