# (Solved Homework): Surface Plots Sketch the surface defined by the following using surf(): z = f(x, y) = cos(x^2 + y^2) on D = {(x, y): |x| lesstha…

MATLAB

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Surface Plots Sketch the surface defined by the following using surf(): z = f(x, y) = cos(x^2 + y^2) on D = {(x, y): |x| lessthanorequalto 2, |y| lessthanorequalto 2} Sketch the surface defined by the following parametric equations using mesh(). [x = 2 [1 – e^u/6 pi] cos u cos^2 (v/2) y = 2 [-1 + e^u/6 pi sin u cos^2 (v/2) z = 1 – e^u/3 pi – sin v + e^u/6 pi sin v] where 0 lessthanorequalto u lessthanorequalto 6 pi and 0 lessthanorequalto v lessthanorequalto 2 pi. Begin by creating the vectors for u and v. Use enough points so that each of your plots has a “smooth” appearance. Label the plots appropriately. Use the view(AZ, EL) command to change the plot viewpoint. AZ is the azimuth or horizontal rotation and EL is the vertical elevation (both in degrees). Azimuth revolves about the z-axis, with positive values indicating counter-clockwise rotation of the viewpoint. Positive values of elevation correspond to moving above the object: negative values move below. To animate the object rotation implement two nested loops to sweep through the AZ and EL parameters. The AZ in should be the inner loop but you are allowed to choose the number of revolutions and loop step.

[x,y] = meshgrid([-2:.1:2]);
Z = cos(-x.^2-y.^2);
colorbar

Output:

2)

[u] = 0:6*pi/200:6*pi;
[v] = 0:2*pi/200:2*pi;
[u v]=meshgrid(u,v);
x=[];
y=[];
z=[];
x=2*(1-exp(u/(6*pi))).*cos(u).*(cos(v/2)).^2;
y=2*(-1+exp(u/(6*pi))).*sin(u).*(cos(v/2)).^2;
z = 1-exp(u./3*pi)-sin(v)+exp(u./6*pi).*sin(v);
mesh(x,y,z)
xlabel(‘X Axis ‘)
ylabel(‘Y Axis ‘)
zlabel(‘Z Axis ‘)

output:

3)

mesh(x,y,z)
xlabel(‘X Axis ‘)
ylabel(‘Y Axis ‘)
zlabel(‘Z Axis ‘)
prompt = ‘What is the value az? ‘;
az = input(prompt)
prompt = ‘What is the value el? ‘;
el = input(prompt)
view(az, el);

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