How to change the centre of one face of a cone

Im trying to design a cone where the centre for one of the faces is offset from the centre of the other face, as in the picture

This is the code I've done for a basic cone with two faces. Thanks

[x,y,z]=cylinder([0,10,5,0],100);

z([1,2],:)=0

z([3,4],:)=75;

hm=surf(x,y,z);

axis equal;

direction=[1,0,0];

rotate(hm,direction,90)

Answer 1

[Star Strider]

Try this:

a = linspace(0, 2*pi);
ra = 1;
rb = 5;
apex = [rb*cos(a); ra*cos(a)];
base = [rb*sin(a)+rb; ra*sin(a)+ra];
h = 10;
z = [h*ones(size(a)); zeros(size(a))];

figure(1)
surf((apex), (base), z)
axis equal
shading interp
view(80,30)

[Jonathan Bird]

Thanks again, please could you explain what the function does in words?

[Star Strider]

As always, my pleasure.

This works similarly to the cylinder function. It creates two (2x100) matrices, ‘base’ and ‘apex’, consisting of x-coordinates for ‘base’, and y-coordinates for ‘apex’. It then relies on surf to do the requisite plotting. The ‘+rb’ and ‘+ra’ offsets in ‘base’ get the ‘y’ alignments correct, to produce the ‘straight’ side of the cone. The ‘z’ matrix describes the height.

It is straightforward to plot a cone, since all that is necessary is to create one circle with a greater radius than the other. However ‘tilting’ and ‘distorting’ it to get the shape you want requires offsetting the centres so that one side of the cone has the same coordinates, creating the ‘straight’ side. (This is based on my understanding of how surf and the related plots work.)

[Jonathan Bird]

If apex is y values and base x values why don't we do surf((base),(apex),z) as we normally do surf(x,y,z)? Please could you also try to explain what the matrix z would look like, I'm guessing its also 2x100 with the value of h in the first row and zeros in the second row? Thanks

[Star Strider]

You can certainly rename them and then switch their order in the surf call. Note that ‘apex’ and ‘base’ are each (2x100) matrices. The x-coordinates are cos values, and the y-coordinates are sin values, each forming a different circle. The exact order doesn’t matter, so long as the two circles get drawn. The z-coordinate (another (2x100) matrix) displaces them in the third dimension, forming the cone.

And you’re correct about the structure of z. If you want the z-coordinates to be different, use this:

z = [h1*ones(size(a)); h2*ones(size(a))];

That will plot one circle at ‘h1’ and the other at ‘h2’, forming the cone between those values.