Lecture4: Plotting Lecture4: Plotting 1 Plotting in MATLAB 2D - - PowerPoint PPT Presentation

Lecture4: Plotting

Lecture4: Plotting 1

Plotting in MATLAB 2D Plots

Plotting Scalar functions

Plot f (x) = x2 on [−2π, 2π].

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Define a discrete set of values uniformly distributed on the domain of f .

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Evaluate f at each point in the discrete domain.

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Plot!

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%step 1 : define discrete domain

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x=linspace(-2*pi,2*pi,100);

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%step2: Evaluate each element of the vector x

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%component-wise as:

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yvals = x.ˆ2;

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%step 3: call plot with an option to specify line width

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plot(x,yvals,'LineWidth',3);

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title('$y=xˆ2$ \quad ($n=100$)', 'Interpreter','latex')

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xlabel('x'); ylabel('y');

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Plotting in MATLAB 2D Plots

Plotting Scalar functions

Plot of f (x) = x2 on [−2π, 2π].

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Plotting in MATLAB 2D Plots

Plotting Scalar functions: axis tight

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%step 1 : define discrete domain

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x=linspace(-2*pi,2*pi,100);

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%step2: Evaluate each element of the vector x

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%component-wise as:

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yvals = x.ˆ2;

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%step 3: call plot with an option to specify line width

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plot(x,yvals,'LineWidth',3);

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title('$y=xˆ2$ \quad ($n=100$)', 'Interpreter','latex')

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xlabel('x') ylabel('y')

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axis tight;

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Plotting in MATLAB 2D Plots

Plotting Scalar function: axis tight

Plot of f (x) = x2 on [−2π, 2π].

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Plotting in MATLAB 2D Plots

Caution

It is important to choose a large enough number of sample points in the domain. If n is too small, e.g. n = 10, the quality of the plots is poor.

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Plotting in MATLAB 2D Plots

Multiple plots

Plot y1 = sin(x), y2 = 2cos(x), y3 = 3cos(2x) on the same axis

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y1 = sin(x);

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y2 = 2*cos(x);

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y3 = 3*cos(2*x);

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%pass the "domain" and "range" for each function to plot

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plot(x,y1,x,y2,x,y3,'LineWidth',2)

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title('Mutiple plots')

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xlabel('x')

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ylabel('y')

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%add legend

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legend('sin(x)','2cos(x)','3cos(2x)')

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axis tight

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Plotting in MATLAB 2D Plots

Multiple plots

Plot of y1 = sin(x) y2 = 2cos(x) y3 = 3cos(2x)

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Plotting in MATLAB 2D Plots

Multiple plots: hold function

Plot of y1 = sin(x) y2 = 2cos(x) y3 = 3cos(2x)

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y1 = sin(x);

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y2 = 2*cos(x);

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y3 = 3*cos(2*x);

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plot(x,y1,'LineWidth',2) %plot 1

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hold on % retains the current axis and to add more plots

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plot(x,y2,'LineWidth',2) % plot 2

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plot(x,y3,'LineWidth',2) % plot 3

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title('Mutiple plots')

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xlabel('x')

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ylabel('y')

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%add legend with option to specify its location

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legend('sin(x)','2cos(x)','3cos(2x)', ... 'Location','SouthWest')

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%make the plot box fit tightly around the data

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axis tight

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hold off

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Plotting in MATLAB 2D Plots

Multiple plots

Plot of y1 = sin(x) y2 = 2cos(x) y3 = 3cos(2x)

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Plotting in MATLAB 2D Plots

Customizing plots

2D Plot options 1

y1 = sin(x);

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y2 = 2*cos(x);

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y3 = 3*cos(2*x);

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plot(x,y1,'rv','LineWidth',2) % red triangles (no line)

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hold on % retains the current axis and to add more plots

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plot(x,y2,'g--*','LineWidth',2) % plot 2: green dashed + *

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plot(x,y3,'b:d','LineWidth',2) %plot 3: blue dotted + ... diamond

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title('Mutiple plots')

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xlabel('x')

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ylabel('y')

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%add legend with option to specify its location

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legend('sin(x)','2cos(x)','3cos(2x)', ... 'Location','SouthWest')

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%make the plot box fit tightly around the data

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axis tight;

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hold off

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Plotting in MATLAB 2D Plots

Multiple plots - customized

Plot of y1 = sin(x) y2 = 2cos(x) y3 = 3cos(2x)

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Plotting in MATLAB 2D Plots

subplot - creates array of plots

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x=linspace(-5*pi,5*pi,200);

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% Evaluate your functions on x

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y1 = sin(x); y2 = 2*sin(x); y3 = sin(x/2); y4 = sin(2*x);

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% We want to plot 4 functions on a 2 by 2 grid

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subplot(2,2,1) % subplot 1

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plot(x,y1)

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title('Subplot 1: sin(x)');

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subplot(2,2,2)

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plot(x,y2,'g') % subplot2

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title('Subplot 2: 2sin(x)');

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subplot(2,2,3) % subplot 3

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plot(x,y3,'k')

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title('Subplot 3: sin(x/2)');

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subplot(2,2,4) %subplot 4

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plot(x,y4,'r')

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title('Subplot 4: 2sin(2x)');

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Plotting in MATLAB 2D Plots

subplot - creates array of plots

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Plotting in MATLAB 2D Plots

subplot - axis properties

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ax1=subplot(2,2,1) % subplot 1

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plot(x,y1)

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title('Subplot 1: sin(x)');

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ax2=subplot(2,2,2)

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plot(x,y2,'g') % subplot2

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title('Subplot 2: 2sin(x)');

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ax3=subplot(2,2,3) % subplot 3

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plot(x,y3,'k')

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title('Subplot 3: sin(x/2)');

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ax4=subplot(2,2,4) %subplot 4

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plot(x,y4,'r')

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title('Subplot 4: 2sin(2x)');

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%I can then spacify common axis properties

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axis([ax1 ax2 ax3 ax4], [-5*pi, 5*pi, -2, 2])

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Plotting in MATLAB 2D Plots

subplot - axis properties

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Plotting in MATLAB 2D Plots

Other plots

Parametric plot: x = 5cos(t), y = 3sin(t), t ∈ [0, 2π].

1

t = linspace(0,2*pi);

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x = 5*cos(t);

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y = 3*sin(t);

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plot(x,y,'LineWidth',2)

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xlabel('x')

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ylabel('y')

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title('Parametric plot');

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axis equal % same length for the units along axis

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axis([-6 6 -6 6])

Polar curves of the from r, θ - use polarplot(theta, r).

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Plotting in MATLAB 2D Plots

Parametric plot

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Plotting in MATLAB 2D Plots

Parmateric plot - customize axis properties

axis properties 1

t = linspace(0,2*pi);

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x = 5*cos(t);

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y = 3*sin(t);

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ax=gca; % returns current axis

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plot(x,y,'LineWidth',2)

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xlabel('x')

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ylabel('y')

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title('Parametric plot');

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axis equal % use the same length for the data units ... along each axis

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axis([-6 6 -6 6])

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%set other axis properties

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ax.FontSize =15;

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ax.LineWidth =2;

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ax.XTick =-6:2:6;

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ax.YTick = -6:2:6;

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ax.XMinorTick='on';

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ax.YMinorTick='on';

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Plotting in MATLAB 2D Plots

Parametric plot

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Plotting in MATLAB 3D Plots

Vector functions and Space curves

A vector-valued function or vector function is a function whose domain is the set of real numbers and whose range is a set of vectors. If we let t be in the domain and f (t), g(t) and h(t) be scalar functions, we can write a vector valued function r(t) = f (t), g(t), h(t) = f (t)i + g(t)j + h(t)k Suppose that f , g and h are continuous real-valued functions on an interval I. The set C of all points (x, y, z) where x = f (t) y = g(t)z = h(t) and t varies on I is called a space curve.

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Plotting in MATLAB 3D Plots

Space curve

Example x = t cos t, y = t, z = t sin t, t ∈ [0, 10π]

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t =linspace(0,10*pi,1000);

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%define x, y, z (component-wise)

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x= t.*cos(t);

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y= t;

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z = t.*sin(t);

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plot3(x,y,z,'LineWidth',2);

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xlabel('x'),ylabel('y'),zlabel('z')

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title('Space curve');

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grid on

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Plotting in MATLAB 3D Plots

Space curve

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Plotting in MATLAB 3D Plots

Plotting surfaces (z = f (x, y))

Step 1: Define two vectors containing the x and y coordinates of the discrete domain. Step 2: Create the 2D grid coordinates X and Y using mesh grid [X,Y] = meshgrid(x,y). Step 3: Evaluate z = f (x, y) at all points on the mesh grid. Step 4: Plot the surface using mesh or surf.

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Plotting in MATLAB 3D Plots

meshgrid

1 >

> x=1:4

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x =

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1 2 3 4

4 >

> y=2:6

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y =

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2 3 4 5 6

7 >

> [X,Y]=meshgrid(x,y)

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X =

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1 2 3 4

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1 2 3 4

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1 2 3 4

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1 2 3 4

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1 2 3 4

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Y =

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2 2 2 2

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3 3 3 3

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4 4 4 4

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5 5 5 5

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6 6 6 6

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Plotting in MATLAB 3D Plots

2D domain

>>plot(X,Y,'r*')

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Plotting in MATLAB 3D Plots

Plot a plane z = x + y

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x=1:4;

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y=2:6;

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[X,Y]=meshgrid(x,y); %create discrete domain

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Z =X+Y; % evaluate f(x,y)

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mesh(X,Y,Z); %plot

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title('z=x+y');

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xlabel('x')

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ylabel('y')

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zlabel('z')

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Plotting in MATLAB 3D Plots

f (x, y) = x + y

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Plotting in MATLAB 3D Plots

f (x, y) = sin(x) − sin(y)

1

[X,Y]=meshgrid(linspace(-10,10,200)); %create square grid

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Z = sin(X)-sin(Y); % evaluate z

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surf(X,Y,Z); %plot

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Plotting in MATLAB 3D Plots

f (x, y) = sin(x) − sin(y) axis equal

1

[X,Y]=meshgrid(linspace(-10,10,200)); %create square grid

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Z = sin(X)-sin(Y); % evaluate z

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surf(X,Y,Z); %plot

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axis equal

This gives a better perception of the 3D plot

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Plotting in MATLAB 3D Plots

surf vs mesh

surf - turns face coloring on by default and uses black edges mesh - turns off face coloring and uses colored edges

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Plotting in MATLAB 3D Plots

f (x, y) = sin(x) − sin(y) mesh

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[X,Y]=meshgrid(linspace(-10,10,200)); %create square grid

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Z = sin(X)-sin(Y); % evaluate z

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mesh(X,Y,Z); %plot

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axis equal

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Plotting in MATLAB 3D Plots

Other 3D plots - [X,Y,Z] = sphere(N)

Recall that (x − a)2 + (y − b)2 + (z − c)2 = r2 is the equation of a sphere of radius r with centre (a, b, c).

1 >

> help sphere

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sphere Generate sphere.

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[X,Y,Z] = sphere(N) generates three (N+1)-by-(N+1)

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matrices so that SURF(X,Y,Z) produces a unit sphere.

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[X,Y,Z] = sphere uses N = 20.

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Plotting in MATLAB 3D Plots

>>sphere (default)

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Plotting in MATLAB 3D Plots

>>sphere(10)

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Plotting in MATLAB 3D Plots

>>sphere(50)

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Plotting in MATLAB 3D Plots

Transformations

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[X,Y,Z] = sphere(50); % sphere r=1, center = origin

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r=0.5;

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%scale the radius

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new X = 0.5*X; new Y = 0.5*Y; new Z = 0.5*Z;

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%plot 1

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%sphere of r=0.5

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surf(new X,new Y,new Z);

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hold on

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title('Transformations');

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xlabel('x'),ylabel('y'),zlabel('z')

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%plot 2

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%move sphere 3 units to the right in the x direction

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surf(new X+3,new Y, new Z);

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axis equal

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% move sphere 1.5 units in x and 1 unit in the z

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surf(new X+1.5,new Y, new Z +1);

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hold off

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Plotting in MATLAB 3D Plots

Transformations

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Plotting in MATLAB 3D Plots

Other 3D plots - [X,Y,Z] = cylinder(R,N)

Forms unit cylinder based on the radius specified at equally spaced points along the unit height in R and N points around the circumference

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Plotting in MATLAB 3D Plots

>>cylinder (default)

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Plotting in MATLAB 3D Plots

>>cylinder(0.5,50)

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Plotting in MATLAB 3D Plots

>>cylinder(0:10,50)

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Plotting in MATLAB 3D Plots

>>cylinder((0:10).ˆ2,100)

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Plotting in MATLAB 3D Plots

General plotting tips

Use clf between plots to clear any axis settings. Always include axis labels that have, when appropriate, units. When using hold on, you should only use it after the first plot command has been issued. Always remember to call hold off Always include appropriate titles. Use different styles for multiple lines on the same plots.

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