CODEWITHSUNDEEP
matlabmathgeometry
hhh
hhh

Reputation: 52840

Projecting Conical Helix on Cone in Matlab?

enter image description here enter image description here

Suppose you have f(x)=x-floor(x).

enter image description here

By this, you can generate the grooves by gluing the top side and the bottom side together and then squeezing the left to zero -- now you have a conical helix: the line spins around the cone until it hits the bottom. You already have one form of the equations for the conical helix namely x=a*cos(a); y=a*sin(a); z=a. Now like here:

How can you project the conical helix on the cone in Matlab?

Upvotes: 0

Views: 2766

Answers (1)

bla
bla

Reputation: 26069

I'd approach your problem without using plot3, instead I'd use meshgrid and sinc. Note that sinc is a matlab built in functions that just do sin(x)./x, for example:

enter image description here

So in 1-D, if I understand you correctly you want to "project" sinc(x) on sqrt(x.^2). The problem with your question is that you mention projection with the dot product, but a dot product reduces the dimensionality, so a dot product of two vectors gives a scalar, and of two 2D surfaces - a vector, so I don't understand what you mean. From the 2-D plot you added I interpreted the question as to "dress" one function with the other, like in addition...

Here's the implementation:

N=64;
[x y]=meshgrid(linspace(-3*pi,3*pi,N),linspace(-3*pi,3*pi,N));
t=sqrt(x.^2+y.^2);
f=t+2*sinc(t);

subplot(1,2,1)
mesh(x,y,f) ;      axis vis3d

subplot(1,2,2)
mesh(x,y,f)
view(0,0) ;  axis square
colormap bone

enter image description here

The factor 2 in the sinc was placed for better visualization of the fluctuations of the sinc.

Upvotes: 4

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