Represent shape as particles

Question

Input: Triangles which make up an arbitrary shape. Each triangle is represented by 3 3D points.

Output: A set of particles which fills up the inside of the object (see image).

I have read the description made by GPU-Gems, and tried to implement the proposed solution that don't make the computations on the GPU. I have tried to take each triangle one at a time and see if they intersect with lines, and if so store the z-value which I later used to generate particles. This gave bad results, and in theory it is possible for a line to intersect with a lone point which would cause a bug.

Can anyone tell me how to easily on the CPU side create a set of particles that represent a shape? Where the shape is defined as a set of triangles.

I prefer a solution that is simple and works well rather than an efficient solution that can have bugs.

Edit: I re-checked my code, and I found that I was not sorting the z-value arrays correctly like I thought I did, after fixing this I got a good result! If anyone still wants to answer this question that is ok, but I consider my problem to be solved now.

Answer 1

Solution: Check for the minimum x,y,z value for all points. Add these values multiplied by (-1) to all points in order to guarantee that all points are not negative. Then take the largest point and subtract with the minimum point (max and minimum x y z) in order to get a cube-like bound for the object.

Then divide this cube by an arbitrary size constant representing the radius of each particle. Now you should have a 2D array for z-values, such that for any x, y position you can quickly store z-values that you find intersecting lines.

For each triangle in the mesh, check all possible that have a large or small enough x-y value for intersections with a line going through the whole cube. If there is an intersection, save the z-value in the x-y array for z-values.

Lastly loop through each possible z-values in the imaginary cube and check if it has an odd number of z-value hits before the current z-value. If that is the case, then we know that there is a particle here. Don't forget to add the minimum x,y,z values that we added in the beginning in order to make the particles have the correct positions again.