Lean Trees

Trees with thin trunks are problematic for a voxel engine. The reason is aliasing. When the tree is far away you still see its crown, but the trunk may have disappeared entirely because of the voxel resolution cannot hold such a thin feature anymore.

I was not ready to give up on skinny trees. They are abundant in colder climates, definitively a must-have for the engine. After some kicking and screaming, I managed to get it done:

Let's see how.

This problem is linked to the sampling theorem and Nyquist frequencies. In a nutshell what this means is you can only reconstruct some information if your sampling frequency is at least twice of the information's frequency. If that sounds weird to you, you are not alone. As it turns out, we live in a freaky reality. Things, regardless of them being real or virtual, have frequencies sort of baked into them and their arrangements. In this particular case the virtual tree trunks had frequencies that were higher than the voxel frequency used to represent them. These trunks would just disappear.

As long as you use a discrete method, like pixels or voxels, to represent a continuous reality you are guaranteed to suffer from these aliasing issues. In the case of pixels, we solved this problem by just throwing lots of memory and processing power to it. With voxels, the hardware is still far from being there.

So this limitation will be there for a while. We better learn it well. Once you think about it, you see the limit is not really how thin a feature can be, but how close two thin features can be. If your voxel size is 1 meter, you can still do a golf ball with them. What you cannot do is have another golf ball next to it, unless you place it at 2 meters.

Maybe this image will help explain it better:

This image is a 2D representation of voxels, which are 3D, so you will need to extrapolate a little bit. The eight squares are voxels. The two red dots are two balls. Each voxel measures "d", which for the sake of argument we will make equal to one meter. We can engage voxels 1, 2, 3 and 4 to represent the first ball. This is how we can achieve a feature inside these voxels that is much smaller than "d". In fact, it could be really small, near zero.

So even huge voxels could encode a tiny feature. The real limit is how close the next feature can appear. In the image you see we cannot use voxels 2, 5, 4 and 7 to add another ball there. This is because voxels 2 and 4 area already engaged into expressing the first ball. So the closest ball can be placed two voxels away, using voxels 5, 6, 7 and 8. The distance between the two balls cannot be less than two meters, that is 2 times "d". This is the sampling theorem rearing its ugly head again.

But this was the key to my solution. Because of how forests are, I did not need two thin trees one immediately next to another after all. I just needed the thin trunks to align with the largest voxels that would still need to display the trunk. This involved shifting the tree a clever amount, which was never too much to disrupt the distribution of trees in the forest.

If you look at the forest screenshot again, you will see some fairly thin trunks in the distance. These trunks are an order of magnitude thinner than  the voxels used to represent them.