# Choosing a shape

As stated in this previous post, we have to compare different PCB dispositions to avoid blind spots. We soon came to realization that we would not be able to get rid of blind spots with our design, but it is possible to study the different ideas we came up with in order to mitigate this issue.

That’s why we created a python program that can simulate :

• blind spots created by PCBs hiding each other
• the variations of brightness due to the fact that LEDs can be seen at an angle (which is what created the dark center zone in CyL3D, which we are trying to get rid of)

## Stairs : an iteration over CyL3D’s design

To avoid the issue of a dark zone due to all LEDs facing the observer at an angle in the center zone, an idea was to make sure that all LEDs were not facing the same direction. There came the stairs idea:

After modelling this idea in python we get:

As you can see, there are a lot of deadzones, particularly in the central viewing axis.

Imagine a configuration with one vertical PCB with LEDs on both sides, facing the radial direction. Wait, don’t. I modeled it so you don’t have to :

This creates a 2D cylindrical POV display, with dark zones on the sides, which is in our opinion much better than a center dark zone. To create a 3D POV display, we “only” need to add concentric cylinders. The question is now: how serious is the problem of PCBs hiding each other and how to avoid it.

## Spiraling down the rabbit hole

The idea of spirals seems natural. PCBs can laid out with an angular offset when compared to the adjacent PCB. For balancing reason, we alternate the PCBs with a central symmetry in order to create a double spiral.

The major issue is that the adjacent PCBs tend to hide each other in large portions of space, due to the fact that they are aligned and closed to each other. We can also notice that the resulting shape is far from being symmetric (which is expected with a spiral).

## Some arithmetics

In order to shake things up a little more, we can keep the idea of a constant angular offset, but with a twist.

Let us take a circle split in n angular positions. If you choose a starting point and then jump from position to positions by skipping k positions, you will reach all positions if, and only if, n and k are coprime. This gives us a more evenly spread disposition.

For the sake of convenience, and because it is a nice name, we shall name this configuration “modulo forest”.

Deadzones tend to be much more spread out, which seems more acceptable. Further investigation has to be done in order to choose a definitive shape.