Our thought experiment here is that we want to project some figures in a wall using a centralized light and some material to block the light at the wanted parts.
If you want to screen lets say 4 different schemes then you probably need to contruct four different object that block the light in the appropriate places. Our plan is to explore how much one could save if we had the ability to put one object in front of the other and change their relative position with a construction as shown below. We used SketchUp for the sketches of this section.
We tried to understand what is the proccess that we could do in order to decided which lines have to appear and which lines shouldn't.
The first attempt was to do some randomized greedy algorithm but this never gaved satisfying results. For this reason we developed a more sofisticated algorithm. Our algorithm, after the appropriate discretization, expresses the problem as a linear program whose solution gives the importance of every line to appear in the picture. The importance is expressed an number in the interval [0, 1]. Now one simple way to decide which lines to actually draw is to draw the lines with importance greater than 1/2. This gives satisfying results but especially the final rounding proccedure can be made in a better way.