gibson:teaching:fall-2014:math445:lab6

Important matlab commands: **linspace, meshgrid, pcolor, surf, contour, surfc, contourf, quiver, mesh, load, subplot, pcolor, shading**.

Skim the Matlab documentation for `linspace, meshgrid,`

and `pcolor`

. Create a 2D mesh from −π to π with 30 points in both the *x* and *y* directions. Then for each position in the mesh let *z = cos(x) sin(y)*. Use `pcolor,`

`axis equal,`

and `axis tight`

to generate this figure:

But don't you hate those ugly black lines? You can get rid of them with the `shading`

command. Use `subplot`

and the `shading`

command to generate this figure:

Create a 2D mesh from −π to π with 20 points in both the `x`

and `y`

directions, let `z = cos(x) sin(y)`

pointwise, and then recreate this figure using the `surf`

and `colorbar`

commands.

Create a 2D mesh from −10 to 10 with 100 points in both the `x`

and `y`

directions,
let and `z = 5 sin(r)/r`

. Then recreate Figure 4 using the `surf`

and `shading`

commands.

Attribution: based on Prof. Mark Lyon's “Advanced Graphics” lab for Math 445, which was adapted from an Octave demo.

Create a 2D mesh from −π to π with 100 points in both the x and y directions and
then recreate Figure 5, using the functions `z = cos(x/2) cos(y/2)`

, `z = sin(x) cos(y/2),`

`z = cos(x/2) sin(y)`

, and `z = sin(x) sin(y)`

.

Enter the following code into a script ﬁle, save the ﬁgure produced as a '.jpg' or '.png' image, and include it with your project. What does the image produce? What is the role of the 'C' variable?

[phi,theta] = meshgrid(linspace(0,2*pi,100)); X=(cos(phi) + 3) .* cos(theta); Y=(cos(phi) + 3) .* sin(theta); Z=sin(phi); C=sin(3*theta); surf(X,Y,Z,C) shading interp

Draw a Klein bottle in Matlab. Feel free to search the web, but understand whatever you use.

Attribution: This lab is adapted from Prof.Mark Lyon's Math 445 Advanced Graphics lab, which is adapted from Octave demos at http://yapso.sourceforge.net/demo/demo.html.

gibson/teaching/fall-2014/math445/lab6.txt · Last modified: 2014/11/17 13:12 by gibson