motivation the interactive tools: drawing commands interactive figure manipulation

Motivation

The interactive tools: Drawing commands Interactive figure manipulation

The programmer point of view: Introduction to objects and their handles Invoking and manipulating graphics objects

The interactive tools

>> x = -5:0.05:5; % [-5 -4.95 …….4.95 5]>> y = sin(x.^2);>> plot(x,y)

The axes is contained within the figure.

A figure may have more than one axes.

The plot is contained within the axes.

An axes may have more than one plot.

>> y2= 1./(1+exp(-x));>> holdCurrent plot held>> plot(x,y2,'color','k','lineStyle','-.')

>> y2= 1./(1+exp(-x));>> holdCurrent plot held>> plot(x,y2,'color','k','lineStyle','-.')

Property-name, property value pair

dash-dot line-.

dotted line:

dashed line--

solid line (default)

-Line StyleSpecifier

six-pointed star (hexagram)hfive-pointed star (pentagram)p

triangle pointing left<triangle pointing right >

triangle pointing downward vtriangle pointing upward^

diamonddsquarescrossxpoint.

asterisk*circleo

Plus sign+ Marker typeSpecifier

whitew

blackk

yellowy

magentam

cyanc

blueb

greeng

Redr

ColorSpecifier

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10Alternative format:>> x=[1 2.3 4 10 3 11.3];>> y=[3.2 5 2 7.4 3 9.4];>> p2=plot(x,y,'or:’);

Alternative format:>> x=[1 2.3 4 10 3 11.3];>> y=[3.2 5 2 7.4 3 9.4];>> p2=plot(x,y,'or:’);

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Marker Color LineStyle

There are more alternative formats Use MATLAB help.Consult the property inspector.

Specialized 2D plots• Bars• Histograpms• Stair• Stem • Scatter• Error bars• Area• Pie charts• contour

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10Vertical bar graph

-10 0 10 200

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4000histogram with 20 bins

-2 0 20

0.1

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0.4Stair graph

-2 0 2-10

-5

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10stem

0 0.5 10

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1Scatter plot

0 5 10-50

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50

100Errorbars

0.2 0.4 0.6 0.8-10

-5

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5Ploting functions with fplot

x

f(x)

cos(30*x)/x

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25Area plot

47%

5%14%

2%

33%

Pie chart

Specialized 3D plots

• plot3• mesh• surf

Use MATLAB help and demos.

The programmer’s point of view:

Graphic Objects

Handles

Properties

Graphic Object(figure, axes, text, line etc.)

handle

Graphic Object(figure, axes, text, line etc.)

handle

properties

Many objects may exist simultaneously

We use the handles to pick an object and manipulate it.

An object may have more than one handle

Objects may contain other objects

• Everything inside a figure window is a graphic object

• The figure window itself is a graphic object

• All plots in MATLAB are made of graphic objects

• All graphic objects have properties that control the way they look and behave

• Graphic object: any element as defined by the set of its properties

that constitute part of a figure

>>t = -pi:0.05:pi; >>x = cos(3*t)*1./(1+exp(-t)); >>y = sin(3*t)*1./(1+exp(-t));

>>p = plot(x,y)

p=

158.0055

A handle

Objects The plot The axes The figure?

Handlesp is the plots handle??

>>set(p,'color','r')>>set(p,'lineWidth',4)

handle


property names


How would I know what properties does the plot have?

property values

>> get(p) Color: [1 0 0] EraseMode: 'normal' LineStyle: '-' LineWidth: 4 Marker: 'none' MarkerSize: 6 MarkerEdgeColor: 'auto' MarkerFaceColor: 'none' XData: [1x126 double] YData: [1x126 double] ZData: [1x0 double] BeingDeleted: 'off' ButtonDownFcn: [] Children: [0x1 double] Clipping: 'on' CreateFcn: [] DeleteFcn: [] BusyAction: 'queue' HandleVisibility: 'on' HitTest: 'on' Interruptible: 'on' Selected: 'off' SelectionHighlight: 'on' Tag: '' Type: 'line' UIContextMenu: [] UserData: [] Visible: 'on' Parent: 157.0059 DisplayName: '' XDataMode: 'manual' XDataSource: '' YDataSource: '' ZDataSource: ''

>>p_parent=get(p,'parent')

p_parent=

157.0059

handle

property name


p_parent=

157.0059

property value


p_parent=

157.0059


p_parent=

157.0059

p_parent is a handle.

Of what?

>> get(p_parent,'type')

ans =

axes

>> get(p_parent,'children')???ans =

158.0063>> pans = 158.0063

>>set(p_parent,'xcolor','b'); >>set(p_parent,'ycolor','b');

What about the title?

>>title=get(p_parent,'title')title=

163.0059 >>get(title,'type')

ans= text

>>set(p_parent,'xcolor','b'); >>set(p_parent,'ycolor','b');

What about the title?

>>title=get(p_parent,'title')title=

163.0059 >>get(title,'type')

ans= text>> set(title,'string','Spiral')>> set(title,'color','b')

Lets add another line

Ooooops…

>> x1 = -cos(3*t)*1./(1+exp(-t)); >>y1 = -sin(3*t)*1./(1+exp(-t));

>> plot(x1,y1)

>>lines = get(p_parent,'children')lines=

204.0061 158.0063

>>blue=lines(1)blue=

204.0061>> set(blue,'lineWidth',4)

Alternatively:

>>findobj('color','b')

ans=

204.0061

Who is the title’s parent?

Who are the title’s children?

Who is the axes` parent?

Who is the figure’ parent?

Graph Objects PhylogenyGraph Objects Phylogeny

This hierarchy is based on the interdependency of objects. A line can only be plotted inside an Axes. A figure contains Axes and so on.


parent


children

…in the beginning there is only the root object….

Hello, I am the root object

Although I am the root I always got a 0 as my

handle

I know and control many important things… Type

get(0) to see all my properties

What is the difference between a handle and “simple variable”?

>>a = [1 2 3 4 5]; >>b = a; >>b(3)=9

b=

1 2 9 4 5

>>a

a=

1 2 3 4 5

>>get(title,'String')

ans=

Spiral

>>ttt = title; >>set(ttt,'string','Red wide spiral')

>>get(title,'String')

ans=

Red wide spiral

handle

right_handle = handle

The subplot command

•Present simultaneously several pieces of information that when displayed on a single plot may confuse the reader

•Display and image and quantification

•Let’s see an example

x=linspace(0,3,500);plot(x,1./(x-1).^2+3./(x-2).^2)grid on

%Change zoomingylim([0 50])

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>>x=linspace(0,3,500);>>a(1)=subplot(1,2,1);%1 rows, 2 cols use first axis>>plot(x,1./(x-1).^2+3./(x-2).^2)>>a(2)=subplot(1,2,2 );%1 rows, 2 cols use second axis>>plot(x,1./(x-1).^2+3./(x-2).^2)>>ylim([0 50])>>set(a,'XGrid','on','YGrid','on')

The general synopsis of subplot is subplot (n,m,p) where• n is the number of rows • m is the number of columns• p identifies the specific subplot. Starting from the top left axes and counting across rows

How to use the subplot command

>>subplot(1,2,2)

MATLAB has an text interpreter named TEX very similar to LATEX. • format mathematical expressions and Greek letters to display

nicely both in the screen and in printed material • we use a backslash “\” followed by either a symbol identifier,

or a string modifier• We can limit the extent of string formatting by placing the

string inside curly braces {…}• To create the following formatted string

f()=sin()• We write:

{\itf(\tetha)}=sin{\it(\tetha)}

A little more elaborated example:

The most useful string modifiers are:\it changes text to italics\rm changes text to normal^ superscript_ underscript

Bar plots

• bar and barh create vertical and horizontal bar graph respectively

• When you use bar(Y) where Y is a matrix, rows are treated as groups.

• Use bar(x,Y) to center the bars at the places specified by x

10 20 300

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>>x=[10,20,30];>>y=[5 3 10 2 7 10 3 7 10 10 2 2];>>bar(x,y)>>title('Vertical bar graph');

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>>bar(x,y,'stacked')

Histograms• Use hist(X,[bins]) to create an histogram (one

per column of X)• By default the count of the data is done in 10

bins• You can change this by passing a second

argument to hist– Scalar => tells the number of bins– Vector => tell the center of each bin

Y(:,1)=randn(10000,1);Y(:,2)=randn(10000,1)+10;hist(Y,20)title('histogram with 20 bins');

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3500histogram with 20 bins

Value

Cou

nt

• As we saw hist plots the count (i.e. the number of elements in each category)

• What if we want to plot the frequencies instead?

• Use [n,x]=hist(X,[bins]) – n will hold the # of elements of each bin– x will hold the center value of each bin

>> [n,x]=hist(Y,20)

>> freqN=n./repmat(sum(n),length(n),1)

% freqN=n/10000

>> bar (x,freqN)

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Value

Fre

quen

cy

Stair plots

• Commonly used in digital signal processing and statistical analysis

• When we sample data at a given rate, we have no information about what is going on between two consecutive samples

>> x=-2:0.1:2;>> y=normpdf([-2:0.1:2],0,1);>> stairs(x,y)>> title('Stair graph')

-2 -1.5 -1 -0.5 0 0.5 1 1.5 20.05

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0.4Stair graph

Error bars

• Error bars can be added to plots with the help of the errorbar function.

• The synopsis of this function is errorbar(x,y,l,u,[formatting string])

• x,y,l,u are all vertors of the same size• draws a marker on the point specified by the

x,y and add bars of the size [ y+u(i) y-l(i)]

0 1 2 3 4 5 6 7 8 9 10 11-80

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>> x=1:10;>> y=2*x+5;>> noise=rand(1,1)*x.^2;>> errorbar(x,y,noise,'ok:')>> xlim([0 11])>> title('Errorbars')

Pie charts

• among the less recommend though common • use a lot of graphics to represent very low

data density • Still, if you want to use them it is easily

done

• pie(x,[outline]):– x is a vector with the value of each data– Outline is a vector of 1s and 0s the same size of

x that states which pie slices should be outlined (1) or held together (0)

>> x=[10 1 3 0.5 7]>> outline=x>5; % = [1 0 0 0 1]>> pie(x,outline)>> title('Pie chart')

47%

5%

14%

2%

33%

Pie chart

motivation the interactive tools: drawing commands interactive figure manipulation

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