Generating random points within a solid from 3D CAD model.

Hello,

I am trying to generate 100 random point within the solid vase (attached .gif file) ; NOT inside the hollow region, but the closed volume of the solid only.

How can I do this work on matlab?

Well, I can make the solid file as a set of points on the surface of the vase.

Thanks.

Answer 1

[Roger Stafford]

Let an x,y,z coordinate system be located with the origin on, and the z-axis along, the central axis of your vase. Let R be a sufficiently large radius and zL and zU be lower and upper bounds of a solid circular cylinder that will completely enclose your vase. Then generate a large number, N, say, N = 10000, of random points that lie within this solid cylinder and from them select 100 that are also within the vase.

Here is how to generate the N points with coordinates (x,y,z) within the solid cylinder:

t = 2*pi*rand(N,1);
r = R*sqrt(rand(N,1));
x = r.*cos(t);
y = r.*sin(t);
z = (zU-zL)*rand(N,1)+zL;

Now select from among these N points, the first 100 of them that lie within the vase. I assume you are able to do this with the parameters defined by your CAD model.

[Jeongho Sohn]

Thanks,

you solved it by approaching parametric math.

But I want rather general method.

Say, the vase cannot be expressed in simple parametric equation (irregular shape), then how can you make a set of points ?

[Roger Stafford]

It is absolutely essential that you have a method that either can directly generate a point randomly within your volume or else detect whether or not a random point generated in a simpler enclosing volume does in fact lie within the given volume. There is no way out of doing that, however irregular your volume may be. Such a determination is not necessarily the result of only a single expression but could require many such tests. Somehow the detailed shape of your volume has to enter into the action.