Plotting 3d parametric equations in Matlab

[froderick]

Homework Statement

The goal of this exercise is to plot parametric equations so that the image looks like the Agnolotti Pasta shell given in the link below.

http://www.nytimes.com/interactive/2012/01/10/science/20120110_pasta.html?ref=science.

Homework Equations

The relevant equations for the Agnolotti Pasta shell are given in the link

http://www.nytimes.com/interactive/2012/01/10/science/20120110_pasta.html?ref=science.

The Attempt at a Solution

I get a completely messed up image with my code below. I am not sure what I am missing to dimensionalize the figure. Any help with how to approach this problem would be greatly appreciated! I feel like I am miles away from what this looks like

i = linspace(0,60);
j = linspace(0,60);
z1 = (10.*sin(i.*pi./120).^5 + i./400.*sin(3.*j.*pi./10)).*cos(19.*j.*pi/2000 +0.03.*pi);
z2 = (10.*sin(i.*pi./120) + i./400.*sin(3.*j.*pi./10)).*cos(19.*j.*pi/2000 +0.03.*pi);
z3 = 5.*cos(i.*pi./120).^5.*sin(j.*pi./100) - 5.*sin(j.*pi./100).*cos(i.*pi./120).^200;

plot3(i,j,z1);
hold on
plot3(i,j,z2);
plot3(i,j,z3);
hold off;

 

[KataKoniK]

First, it is important to clarify the goal of this exercise. Are you trying to plot parametric equations for the Agnolotti Pasta shell or are you trying to create a code that will generate an image of the pasta shell? Depending on the goal, the approach and equations used may differ.

Assuming the goal is to plot parametric equations, the first step would be to understand the equations given in the link and how they relate to the shape of the pasta shell. From the link, we can see that the shape of the pasta shell is created by three equations, each representing a different part of the shell. These equations involve sine and cosine functions, which are used to create the curves and ridges of the shell.

Next, it is important to consider the range of values for the variables in the equations. In this case, the variables i and j represent the x and y coordinates, respectively, and are given a range of 0 to 60. This means that the plot will cover a square area with a side length of 60 units.

Based on this information, the code provided in the forum post is not correct. The first issue is that the z1, z2, and z3 equations are not using the correct range for the variables. They should be using linspace(0,60) instead of linspace(0,1). Additionally, the equations used in the code are not the same as the ones given in the link.

A possible solution for plotting the parametric equations for the pasta shell could be:

i = linspace(0,60);
j = linspace(0,60);
z1 = (10.*sin(i.*pi./120).^5 + i./400.*sin(3.*j.*pi./10)).*cos(19.*j.*pi/2000 +0.03.*pi);
z2 = (10.*sin(i.*pi./120) + i./400.*sin(3.*j.*pi./10)).*cos(19.*j.*pi/2000 +0.03.*pi);
z3 = 5.*cos(i.*pi./120).^5.*sin(j.*pi./100) - 5.*sin(j.*pi./100).*cos(i.*pi./120).^2;

figure
plot3(z1,z2,z3)
xlabel('x')
ylabel('y')
zlabel('z')
title('Parametric Equations for Agnolotti Pasta Shell')