Problem 3: Please solve using matlab

Do a 3D surface function. You can make a sphere, cylinder, cone - or a sheet. You may not call sphere/cylinder for this problem.

Extra credit:

Do a super quadric instead: https://en.wikipedia.org/wiki/Superquadrics

Deliverables:

1. Function to map s,t to x,y,z (in a function file)

2. Script to create grid of points, call surface, and plot surface

3. Picture of your surface

Step by Step Instructions:

1. Create a function file that takes in u,v and returns X,Y,Z

a) Sphere/cylinder/cone: Use the equation (google it)

b) Sheet: I did the equation below; but you can make up your own

..... X = u²

..... Y = v² + u

..... Z = 1/(uv + 3)

2. Use meshgrid to create your U,V 2D array of u,v values

a) Sphere/cylinder/cone: usually has one of u,v going from -pi to pi, the other going from -pi/2 to pi/2 (or sometimes 0 to pi). Make sure the grid is the right-way round

..... If you get half a sphere or a double sphere you may need to swap u and v

b) Sheet: I did -1 to 1 for u, -2 to 2 for v

3. Call your function with your U and V 2D arrays

4. Plot using surf

5. Extra credit:

a) This would be a really good time to use a struct to carry around the parameters for your superquadric

b) You will need two auxiliary functions, f and g, in addition to the main function

..... You will need the function sign(x) to write f and g

c) If A = B = C = 1,and r = s = t = 2 then you get a sphere. See comment above about u and v in meshgrid above if you are, eg, getting half a surface

d) Title your plot with your ABC and rst values

Self-check: Sphere or sheet

ADG 1.010 L0 rat 202020 Example extra credit 8o