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ENGG1801_Engineering Computing_2013 summer course_lecture_9_2_1pp

Lecture 9-2

3-D Surface Plotting

Semester 1, 2012

School of Information Technologies

The University of Sydney, Australia

https://www.doczj.com/doc/4a9717545.html,.au/~engg1801

engg1801help@https://www.doczj.com/doc/4a9717545.html,.au

Jason Chan

j.chan@https://www.doczj.com/doc/4a9717545.html,.au

ENGG1801 Engineering Computing 1

Day Date (Jan 2013)Lecture topics Assessment

1Fri 4Introduction, Part 1: Excel–Basics

2Sat 5Functions, Plotting, Solving equations, File I/O

Sun 6---

3Mon 7Matrix algebra Lab Exam 1 (10%) [9-10am] 4Tue 8Part 2: Matlab–Basics, If statements, Arrays

5Wed 9Loops

6Thu 10Functions (1)

7Fri 11Functions (2)

8Sat 12Text & File I/O, Character strings Lab Exam 2 (15%) [9-11am] Sun 13---

9Mon 142-D and 3-D plotting, Surface plots

10Tue 15Creating movies from matrices, Matrix algebra

11Wed 16Matrix algebra, Interpolation and curve fitting

12Thu 17Polynomial regression, Images

13Fri 18Help for the Final Exam Lab Exam 3 (25%) [9-11am] Sat 19 –Sun 20---

Exam Mon 21---Final Exam (50%)

ENGG1801 Engineering Computing

?Surface plotting

–How to draw shapes and surfaces in 3-D

ENGG1801 Engineering Computing

?We can plot z = x 2+ y 2

ENGG1801 Engineering Computing

mesh()only shows the connecting lines -3

-2

-10

-2

51015x

z = x 2 + y 2

-3

-2

-10

-2

1015

z = x 2 + y 2

surf()shows the faces of the surfaces

% Set the x and y values

x = -3:3;

y = x;

% Create a matrix, 'xx', which contains the x

% values for all the points on the x-y plane

% (similar for 'yy')

[xx,yy] = meshgrid(x,y);

% Calculate the corresponding z values for each of % the (x,y) points on the x-y plane

zz = xx.^2 + yy.^2;

% Continued on next slide...

ENGG1801 Engineering Computing

% ... continued from previous slide

% Plot the mesh given the x, y and z values mesh(xx,yy,zz);

% Set the axes so that they reach only to the % limits of the values axis tight;

% Add labels

title('z = x^2 + y^2');xlabel('x');ylabel('y');zlabel('z');

ENGG1801 Engineering Computing

-3

-2

-10

-2

51015

z = x 2 + y 2

?Instead of mesh(), we can use the surf()function to plot a surface

% Plot the surface given the % x, y and z values surf(xx,yy,zz);

ENGG1801 Engineering Computing

-3

-2

-10

-2

51015

z = x 2 + y 2

?We can also plot one after the other on the same figure using pause:

% Plot the mesh

mesh(xx,yy,zz);

% Wait until the user presses something

pause;

% Now, overwrite the mesh and plot the

% surface on the same figure

surf(xx,yy,zz);

ENGG1801 Engineering Computing

?meshgrid()creates 2 matrices with the values of x and y for each point on the x-y plane

–It takes 2 arrays x and y and returns 2

matrices xx and yy

–The rows of xx are copies of x

–The columns of yy are copies of y

ENGG1801 Engineering Computing

>> x = -3:1:3

x = -3 -2 -1 0 1 2 3 >> y = x;

>> [xx,yy] = meshgrid(x,y)

xx = -3 -2 -1 0 1 2 3

-3 -2 -1 0 1 2 3-3 -2 -1 0 1 2 3-3 -2 -1 0 1 2 3-3 -2 -1 0 1 2 3-3 -2 -1 0 1 2 3-3 -2 -1 0 1 2 3yy = -3 -3 -3 -3 -3 -3 -3

-2 -2 -2 -2 -2 -2 -2-1 -1 -1 -1 -1 -1 -10 0 0 0 0 0 01 1 1 1 1 1 12 2 2 2 2 2 23 3 3 3 3 3 3

ENGG1801 Engineering Computing

-3

-2

-10

-2

z = x 2 + y 2

1) Use meshgrid()to generate matrices of repeated rows of x and columns of y over the domain of the function

2)Calculate z = f(x,y)

3)Call either mesh()or surf()that accepts the x-y grid and z values to produce the plot

ENGG1801 Engineering Computing

[xx,yy] = meshgrid(x,y);mesh(xx,yy,zz)surf(xx,yy,zz)zz = xx.^2 + yy.^2;

?Matlab as 13 in-built colormaps ?User-defined colormaps can also be created ?The default is Jet

ENGG1801 Engineering Computing

-3

-2

-10

-2

510

15x

z = x 2 + y 2

-3

-2

-10

-2

15x

z = x 2 + y 2

-3

-2

-10

-2

z = x 2 + y 2

colormap bone colormap cool

colormap autumn

?Plot part of the top half of a sphere, defined by the equation:

x2+ y2+ z2= r2

where r is the radius

–Vary x and y from -1 to 1 with a step of 0.01

–Set the radius of the sphere r to 3

–The surface should be colored in gray shades –Name the plot “hemisphere” and label axes

ENGG1801 Engineering Computing

% Define r, x and y values

r = 3;

x = -1:0.01:1;

y = x;

% Create the x-y grid

[xx yy] = meshgrid(x, y);

% Calculate the z values using the x-y

% grid

zz = sqrt(r.^2 -xx.^2 -yy.^2)

ENGG1801 Engineering Computing

% Use grey shades for the surface colormap bone

% Generate the surface plot surf(xx,yy,zz) % Add a title and % labels

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

title('Hemisphere');

ENGG1801 Engineering Computing

?We can smooth the surface with:shading interp

ENGG1801 Engineering Computing

?Given 2 files:

atlanta.txt–coordinates of streets of Atlanta

ttimes.txt–travel times to the city centre

from different parts of Atlanta

?Visualize these datasets

ENGG1801 Engineering Computing

?Here are the first few lines of atlanta.txt

53423.00 53343.00 -84546100.00 33988160.00 -84556050.00 33993620.00 1.00 3025.00

54528.00 53351.00 -84546080.00 33988480.00 -84558400.00 33995480.00 1.00 3025.00

130081.00 128176.00 -84243880.00 33780010.00 -84249980.00 33800840.00 1.00 3025.00

130105.00 128192.00 -84243590.00 33780060.00 -84249740.00 33800840.00 1.00 3025.00

58150.00 71086.00 -84509920.00 33944340.00 -84517200.00 33958190.00 1.00 3025.00

58190.00 71102.00 -84510420.00 33944930.00 -84516490.00 33957280.00 1.00 3025.00

166861.00 168241.00 -84252840.00 33895840.00 -84247360.00 33899290.00 1.00 66.00

168241.00 169968.00 -84247360.00 33899290.00 -84240250.00 33903630.00 1.00 71.00

169968.00 169984.00 -84240250.00 33903630.00 -84216090.00 33911010.00 1.00 64.00

169984.00 173303.00 -84216090.00 33911010.00 -84203990.00 33913990.00 1.00 70.00?Each row corresponds to a street ?Columns 1, 2 and 8 are irrelevant ?Columns 3 and 4: the x and y coordinates of the beginning of the street