The Persistence of Vision Raytracer (POVRay).
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FS#240  Object for efficient automatic periodic pavement
Opened by Simon (infoised)  Friday, 02 March 2012, 10:54 GMT
Last edited by William F Pokorny (wfpokorny)  Monday, 23 January 2017, 12:15 GMT

Details
Whenever some object is to be periodically repeated in some kind of grid, you can achieve this with macros, but it even if object references are implemented in the future, wrapper with its own transformation matrix still takes space and bookkeeping b) is not infinite annoying when making infinite planar tiling with arbitrary objects like an approximate water surface or tiling with real bricks or anything that needs to extend to horizon c) is not optimized for periodicity
I think it can be very efficiently implemented as an object that takes a finite object argument (like CSG functions) and can be periodic in either 1D,2D or (possibly dangeorous?) 3D with specified period. In each dimension, the number of repetitions can be any integer or even infinity (or max_int). Something like All the code needs to do is raytrace in the current unit cell and if the ray passes uninterrupted, pass it through the neighbouring unit cell (which means trace a translated ray through the same object). The object itself would just feel an additional clipping box, everything else would work seamlessly. In case of infinite column of transparent object, max_trace stops the infinite loop anyway. This is just a suggestion, I realize this is more of a longterm change but it is quite easy to implement and would simplify a large number of projects. 
Complications arise if the tiling is "sparse", i.e. when the repeated objects don't completely fill the space. Imagine e.g. an infinite stack of donuts, with the camera inside: A ray going straight along the axis of the stack would never hit any of the objects, and therefore would result in an infinite number of intersection tests unless we find a smart solution to this.
Original poster seems to assume a space filling with a orthogonal grid (classical cubic packing, or with grid_separation, rather Cuboid http://en.wikipedia.org/wiki/Cuboid).
It might be considered that the filling is going to be done in 3D, infinity in all directions.(you could bound/intersect with a smaller containers if you do not need such infinity).
Let's assume it's done with perfect unitsidedcube.
As the ray does not turn, it should be simple to use modulo arithmetic to reduce the number of cubes to study... alas, that approach fails as soon as the ratio between the vector components are not rational. When they are in a rational ratio (remember, we got 3 of them:x,y&z; the ratio between the 3 couples must be rational to have repetition), it's fine. But as soon as one ratio is not in Q (ergo, any irrational ratio, in R instead of Q) it will never repeat. (sqrt(2), pi, ... all of them are not in Q.); In fact Q is discontinuous, whereas R is continuous... most of the time, you will be in R and not in Q.
So give up on finding a trick if you really want infinity of repeating object.
On the opposite way, we could give up on true infinity and just compress the repetition (in 3D) as a single object containing the repeated object and the parameter of the repetition, a bit like is done for area light. It will trade memory for cpu, as the generic bounding tree will be smashed by the gridobject, until the implementation is smarter than testing all possible objects (instead of shifting the object, shifting the ray source...)
About other space filling, the grid might be slanted (nonorthogonal cristal), done with a transform. The same transform can be used to manage the dimension of the cuboid (grid_separation) (applying its inverse to the object)
It might also be another pattern than a cuboidgrid: dense sphere filling has 2 fillings: ABA and ABCA patterns of hexagonalycentered spheres.
Also, other patterns of crystallography might be considered... if one really want to cover the idea.
(Summary: give up infinity, and it might be possible)
@Grimbert nice analysis, I understand that infinity brings a lot of problems.
True infinity is not needed anyway because things become very small at the horizon. The user will use large numbers at his own risk, much like with everything else. Without the infinity, the number of intersection tests is no larger than with the manual tiling. In any case, such a solution would enable much larger systems than manual tiling, as the parse time and memory consumption are independent of the grid size.
The grid object can have its own large bounding box. The internal raytracing handled by this object may be even faster than in the case of manually inserted objects. We know there is no overlapping and that all the cells are of the same size. The selection of visited cells does not even require a tree search, just a direct calculation of indices (something similar to Bresenham's line algorithm, only it has to visit all the cells touched by the ray).
The most general case to consider is a parallelopiped (slanted brick), all periodic packings (even ABCA hexagonal and others) are covered by this if a larger unit cell is used.
Now tracked on github as issue #214.