Question

2.9. Derive a parametric equation for the surface of the quarter cone shown below, using the surface of revolution. Plot the surface using Matlab. Note that Po (0,-1,0) Po [0,-1,0], P[1,0,0] Submit the following: a. Detailed parametric equations that describe the surface; b. Matlab script and screen capture of the surface plotted in Matlab.

Answer 1

a) We define x=0 to 1

We define t=$\pi$ to $\pi/2$

We grid x and t as X and T

The Y and Z grid values are defined by

$Y=(1-X)cos(T)$

$Z=(1-X)sin(T)$

b) The Matlab script is given below:

x=linspace(0,1,101);
t=linspace(pi,pi/2,101);
[X,T]=meshgrid(x,t)
Y=(1-X).*cos(T);
Z=(1-X).*sin(T);
mesh(X,Y,Z)
xlabel('x')
ylabel('y')
zlabel('z')

The screenshot is given below:

07 0.3 OA -06 0.9 07 0.5 04 аз 01

The workspace screenshot is given below:

Command Window >> x-linspace (0,1,101) t-linspace (pi,pi/2,101) X, T]-meshgrid (x,t); Y= (1-X) . *cos (T) ; z= (1-X) . *sin (T) ; mesh (X,Y, Z) xlabel('x') ylabel ('y zlabel('z') x >