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====== Math 445 Lab 6: 3D graphics ======

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


===== Problem 1: pcolor, meshgrid, shading, subplot =====

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:

{{:gibson:teaching:fall-2012:math445:a.png?nolink&500|}}

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:

{{:gibson:teaching:fall-2012:math445:lab10-fig2.png?nolink&500|}}


===== Problem 2: surf ===== 


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.


{{:gibson:teaching:fall-2012:math445:lab10-fig3.png?400|}}



===== Problem 3: surf in the shade ===== 


Create a 2D mesh from −10 to 10 with 100 points in both the ''x'' and ''y'' directions,
let $r = \sqrt{x^2 + y^2}$ and  ''%%z = 5 sin(r)/r%%''. Then recreate Figure 4 using the ''surf'' and ''shading'' commands.

{{:gibson:teaching:fall-2012:math445:lab10-fig4.png?500|}}

Attribution: based on Prof. Mark Lyon's "Advanced Graphics" lab for Math 445, which was adapted from an [[http://yapso.sourceforge.net/demo/demo.html | Octave demo]].


===== Problem 4: surf 'n' subplot  ===== 

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)''.

{{:gibson:teaching:fall-2012:math445:lab10-fig5.png?500|}}

===== Problem 5: mystery plot =====


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? 

<code>
[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
</code>

===== Bonus =====
 
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]].
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