Matlab Graphics

Matlab Graphics

S. Awad, Ph.D.M. Corless, M.S.E.E.E.C.E. DepartmentUniversity of Michigan-Dearborn

Introduction to Matlab:

3D Graphics

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MATLAB Graphics:U of M-Dearborn ECE DepartmentIntroduction to MATLAB and its Toolboxes

3D Graphics

3D Graphics Topics Creating Mesh and Surface Plots Viewing a Pseudocolor Matrix Creating Contour Plots Adding a Color-Bar Interpolating 3D Data

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3D Graphics

Mesh and Surface Plots

Given a function f(x,y) of two variables:

22

),( yxexyxf

Assume that:» x=[-1:0.2:1]; y=[-1:0.2:1];

We can plot the function z as a mesh or surface plot

)( 22

),( yxxeyxfz

Useful for displaying functions of 2 variables or to visualize large matrices

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3D Graphics

Calculating xx

Height = Length of y

15.005.01 x

Row = Vector x

15.005.01

11111

xx

15.0005.115.0005.115.0005.115.0005.115.0005.1

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3D Graphics

Generating xx in Matlab» x=[-1:0.5:1];» xx=ones(length(x),1)*x

xx =

-1.0000 -0.5000 0 0.5000 1.0000 -1.0000 -0.5000 0 0.5000 1.0000 -1.0000 -0.5000 0 0.5000 1.0000 -1.0000 -0.5000 0 0.5000 1.0000 -1.0000 -0.5000 0 0.5000 1.0000

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3D Graphics

Calculating yy

Length = Length of y

15.005.01 y

11111

15.005.01

yy

111115.05.05.05.05.0000005.05.05.05.05.011111

Column = y Transpose

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3D Graphics

Generating yy in Matlab» y=[-1:0.5:1];» yy=y'*ones(1,length(y))

yy =

-1.0000 -1.0000 -1.0000 -1.0000 -1.0000 -0.5000 -0.5000 -0.5000 -0.5000 -0.5000 0 0 0 0 0 0.5000 0.5000 0.5000 0.5000 0.5000 1.0000 1.0000 1.0000 1.0000 1.0000

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3D Graphics

Find xx & yy Using Meshgrid» [xx,yy] = meshgrid(x,y)xx = -1.0000 -0.5000 0 0.5000 1.0000 -1.0000 -0.5000 0 0.5000 1.0000 -1.0000 -0.5000 0 0.5000 1.0000 -1.0000 -0.5000 0 0.5000 1.0000 -1.0000 -0.5000 0 0.5000 1.0000yy = -1.0000 -1.0000 -1.0000 -1.0000 -1.0000 -0.5000 -0.5000 -0.5000 -0.5000 -0.5000 0 0 0 0 0 0.5000 0.5000 0.5000 0.5000 0.5000 1.0000 1.0000 1.0000 1.0000 1.0000

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3D Graphics

Find z Find z using element by element computations

» z=xx.*exp(-xx.^2-yy.^2)

z =

-0.1353 -0.1433 0 0.1433 0.1353 -0.2865 -0.3033 0 0.3033 0.2865 -0.3679 -0.3894 0 0.3894 0.3679 -0.2865 -0.3033 0 0.3033 0.2865 -0.1353 -0.1433 0 0.1433 0.1353

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3D Graphics

Mesh Plot z» mesh(x,y,z)

Finer increments of x and y will smooth the surface

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3D Graphics

Create a new mesh plotcomplete with labels

Mesh for a Larger x & y

» x =[-2:0.2:2];» y =[-2:0.2:2];» [xx,yy]=meshgrid(x,y);» z=xx.*exp(-xx.^2-yy.^2);» mesh(x,y,z)» title('Larger Mesh');» xlabel('X Data');» ylabel('Y Data');» zlabel('z=xx.*exp(-xx.^2-yy.^2)');

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3D Graphics

Plots the colored parametric surface where color is proportional to surface height

Surface Plot of z» surf(x,y,z)

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3D Graphics

The values of the elements specify the color in each cell of the plot

pseudocolor or "checkerboard" plot of matrix

Pcolor» pcolor(x,y,z)

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3D Graphics

Contour Plots contour plot of

matrix where z contains heights above a plane

Number of Contour Lines

» contour(x,y,z,16);» title('Contour');

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3D Graphics

Displaying Contour Heights To write the values

identifying the heights:

» cs=contour(x,y,z,16);» clabel(cs);» title('Contour Heights');

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3D Graphics

Meshc Contour Plots meshc is same as

mesh except that a contour plot is drawn beneath the mesh

Only works for surfaces defined on a rectangular grid

» meshc(x,y,z)

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3D Graphics

Adding a Colorbar

colorbar adds a vertical line (color scale) to show the contour plots

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3D Graphics

3D Interpolation Rough or scattered data can be interpolated using mesh

The original data is plotted as a mesh by:

» x=[-3:3]; y=[1:5];» [xx, yy]=meshgrid(x,y);» z= xx + yy;» mesh(x,y,z);» title('Original Mesh Grid');» xlabel('X Data'); ylabel('y Data');» zlabel('z = xx + yy');

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3D Graphics

Mesh of Rough Data Original Course Surface where:

x = [-3:3]y = [1:5]z = xx+yy

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3D Graphics

Interpolation of Data The original mesh from the data is can be improved by

creating interpolated values using griddata:

» xi=[-3:0.5:4]; % Interpolated x axis» yi=[ 0:0.2:5]; % Interpolated y axis» [xxi,yyi]=meshgrid(xi,yi);» % zi = interpolated values» zi=griddata(xx,yy,z,xxi,yyi);» mesh(xxi,yyi,zi); % Better surface» title('Interpolated Mesh Grid');» xlabel('X Data'); ylabel('y Data');» zlabel('z = xx + yy');

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3D Graphics

3D Interpolation Plot Interpolated Smooth Surface where:

xi = [-3:0.5:4] yi = [ 0:0.2:5]

Matlab Graphics

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