A specific, representative algorithm-finding problem that was derived from traditions in Ùzje.
A collection of cuboids \(C_1, C_2, \ldots, C_i\) all have the same dimensions \(x, y, z\). On the one of the largest faces in terms of surface area, there are several areas coloured red, and the rest are coloured green. All areas are bounded by Jordan curves, so there is a clear sense of what’s inside and what’s outside. The other faces of the cuboids are not coloured.
Your task is to, for any collection of such cuboids, arrange them in regular 3D Euclidean space such that no red area is completely visible from a given angle while maximising the amount of green area visible from that angle.
This is a very general problem and there are many parameters that would have to be fixed for any particular algorithm. For instance, the simple Mound of Rivals problem sets \(z = 1, x = 10, y = 16\), with a single red area on each cuboid a being a rectangle with sides parallel to the rectangle of the cuboid and with corners at \((2.5, 4)\) and \((7.5, 12)\).
A simplification of the problem is to set \(z = 0\), so that the cuboids become rectangles.
