Points which are inside a cone

Hello all, I have a query , I have a cone and I know its R and H . I also know the outer points of the cone .How I can get all points which lie inside the cone and describes the cone . thank you

[John D'Errico]

There are infinitely many points inside a cone, or any non-degenerate volume.

[yogesh jain]

Ya , those are many . But some of them which can tend to make a solid cone . I know the starting and ending points of the cone . thank you

Answer 1

[Walter Roberson]

http://uk.mathworks.com/matlabcentral/answers/257208-how-to-get-points-inside-a-cone#comment_325438

[yogesh jain]

Thank you very much Mr. Roberson and sorry I did not check your previous answer .

[yogesh jain]

And what if I want to get inside points of cone according to its starting and ending points ?

[Walter Roberson]

What does it mean for a cone to have a starting point?

[yogesh jain]

hello , starting point is where I want to place the circular part and ending point is where the conical section will end .

[Walter Roberson]

The easiest way is to do the generalized rotation that you already said was too complicated; however if you are willing to constrain the orientations then there might be an easier way.

[yogesh jain]

yes , you are right . but the code u provided is for general cone . How we can alter that for rotated and shifted cone ? is my question . Thank you .

[Walter Roberson]

This code here is for the very specific case of a cone whose tip is at x = 0 and y = 0 and for which the center of the base is at (0,0,0) . To extend this to rotated and shifted cones can require the whole power of that link from earlier that worked out rotations in 3 space along an arbitrary center. Perhaps I could work out an easier way... but it is 04:40 in the morning here and I am not going to think about it until after I sleep and you have described exactly which axes of rotations are permitted for your situation. Remember, any cone anywhere in space could be described as having only been rotated and shifted. For example in your earlier question about cylinders you talked about it being rotated only around z: does that hold true for this as well? Rotate around z and then translate?

[yogesh jain]

I am really very grateful towards your all considerations . Yes , the cone also permitted to rotate around z-dir . according to the rotation and point input by user I am placing the cone so it might be having random parameters (dependent on x,y,z and az-el only) . as I already told parameters of cone are R and H only . thank you

[yogesh jain]

But if you really have any algorithm for getting inner points for cone which has starting and ending points please share that with me . thank you

[Walter Roberson]

When an object is symmetric around one axis, then rotating around the axis produces a result identical to the original. Therefor your "dependent on x,y,z and az-el only" is really describing a cone at an arbitrary location and orientation in space, not a restricted case at all.

[yogesh jain]

yes sir , that is true . But when I am rotating the points around any of the axis it is not showing them precisely . I used these -

 r=5 ; h=20;
x1=2 ; x2 =20 ; y1=3 ; y2 =3 ; z1=12; z2 = 12;
xvec = floor(-r+x1):ceil(r+x1);
yvec = xvec;
hvec = 0:ceil(h);
[X, Y, H] = ndgrid(xvec, yvec,0:floor(h));
r_at_H = r * (1 - H/h);
is_in_cone = abs(X) <= r & abs(Y) <= r & H <= h & sqrt(X.^2+Y.^2) <= r_at_H;
Xc = X(is_in_cone);
Yc = Y(is_in_cone);
Hc = H(is_in_cone);
Xc1=Xc+20.3;
Yc1=Yc+10.5;
Hc1=Hc+12.7;

 A(:,1)=Xc1;
A(:,2)=Yc1;
A(:,3)=Hc1;
B=ceil(A);

 theta=45;
rad=degtorad(theta);
C=B*[1,0,0 ; 0,cos(rad),sin(rad) ; 0,sin(rad),cos(rad)];         % X-plane
Xc2=C(:,1);
Yc2=C(:,2);
Hc2=C(:,3);
pointsize = 20;
scatter3(Xc2,Yc2,Hc2, pointsize, 'filled');

Thank you