1 Using Voxelization and Ray-Tracing to Identify Wall Thinness of ...

and less 'boxy' the more polygons are used to render the object. We see 3D content creators usingvast numbers of polygons as is, and the numbers of polygons used will only continue to grow.Therefore, when performing computations on 3D models now and in the future, dealing with theenormous memory costs is the biggest challenge. Indeed, one might need a specialized datastructure in order to handle all the data, such as an octree.145. OctreesVoxelization, to reiterate, is a representation of a geometric shape as a set of voxels, or cubes. Itis natural when approaching voxelization to think only of the smallest voxel-cubes used in theprocess. After all, the smallest voxels are what determines the accuracy of the final voxelization;as size is reduced, the more 'true' the voxelization becomes. With this in mind, one (poor)implementation of a voxelization algorithm would be to first make a flat list of every minimallysizedvoxel needed to represent the final model. Given a flat list, one could then evaluate whichvoxels contain triangle geometry by performing a triangle-voxel intersection test for everyavailable triangle against every available minimally-sized voxel.Calculating the algorithmic cost of such an operation shows us just how computationallyexpensive that would be. Where M is the number of minimally-sized voxels and N is the numberof triangles in the triangle mesh, our intersection tests would be O(M*N). Note that M isdependent upon the size of the input model. One calculates the number of minimally-sizedvoxels needed to represent the model by first taking the bounds of the model and calculatingmodel width, height, and depth. Then the maximum number of minimally-sized voxels possiblyneeded is equal to (model width/smallest voxel size)*(model height/smallest voxel size)*(modeldepth/ smallest voxel size). As the size of the model increases and the size of the smallest voxelsdecreases, M grows exponentially.Memory costs for storing all the triangle intersection data with this method are evenworse – one might call them prohibitively expensive. Best case, of course, would be a modeldesigned purposely with the intent to minimize the number of triangle-voxel intersections. Evenin that case, each triangle is bound to intersect at least a few minimally-sized voxels. Conversely,the worst case would be for every triangle to intersect with a very large number of voxels.Imagine, for instance, some model that is composed out of hundreds of thousands of very largetriangles, ones that are practically the same width as the model they describe. It might be difficultto model such an object, since it would necessitate a very convoluted structure, but it could bedone. This intersection data would be crippling. Triangles of such size would intersect tens ofthousands of minimally-sized voxels, each of which would need to remember that fact for theray-tracing step to follow. A situation would arise where each of the hundreds of thousands ofvoxels was remembering each of the thousands of triangles which intersected it! In other words,