Question

Derive a parametric equation for the surface of the quarter cone, using the following: P. R(0,0,1) P T (1,0,0) (i) Surface of revolution. Plot the surface using Matlab, and (ii) Sweep surface. Note that Po= [0,0,1], P1 = [1,0,0]. Submit the following: (i) Detailed equations that describe the surface of revolution and sweep surface; (ii) Matlab scripts and screen captures of the surface plotted in Matlab.

Answer 1

first define z = 0 to 1 with a linear space of 100 values.

then define theta i.e t = 0 to pi/2 with a linear space of 100 values.

then X and Y grid values are computed by using

Parametric equations as follows:

X = (1 - Z)*cos(T)

Y = (1 - Z)*sin(T)

Code for this problem :

z = linspace(0,1,100);
t = linspace(0,pi/2,100);
[Z,T] = meshgrid(z,t);
X = (1-Z).*cos(T);
Y = (1-Z).*sin(T);
surf(X,Y,Z)
xlabel('x')
ylabel('y')
zlabel('z')

Images for the code and OUTPUT :

x + NO IIIIIIIII HomeworkLib123.m x HomeworkLib1234.m X HomeworkLib1212. m z = linspace (0,1,100); t = linspace(0, pi/2,100); [2,T] = meshgrid(z,t); X = (1-2).*cos(T); Y = (1-2).*sin (T); surf (X,Y,Z) xlabel('x') ylabel('y') zlabel('2'

- O X Figure 1 File Edit View a Insert Tools Desktop Window A. Help E O ........ 1 0.5 i 0.2 0.4 0.6 0.8 1

Let me know if you have any doubts in the comment section.

Thank You