matlab 3d mesh and line plotting

Question

I need help plotting a spiral helix on a cone. For the helix:

x = tsin(6t)
y = tcos(6t)
z = t/3

...and this helix lies on the cone:

z = sqrt(x^2+y^2)/3

I need to plot the mesh plot of the cone and the 3D line plot of the helix on the same chart.

Answer 1

I think you want a surface plot of the cone first. Try

[X Y] = meshgrid(-1:.01:1);
Z = sqrt(X.^2 + Y.^2)/3;

Then, plot this surface with the surf function, and set some sort of shading and transparency

surf(X,Y,Z), caxis([-1 1]), shading flat, alpha(.5);

This should make a cone shape (you can play with the colors).

Now for the helix, define the vectors as you did

t = 0:.01:1;
x = t.*cos(6*t);
y = t.*sin(6*t);
z = t/3;

Then do

hold on;

This makes it so any other plotting you do will appear on the same figure.

Then finally,

plot3(x,y,z);