Mango, Sequoia, Baobab

At some point I was wondering if Space Colonization was all I needed for creating trees. Since the method was so simple, I always had my doubts. Could it be used to produce trees beyond the classic examples you see in the method's description?

I set out to define different tree classes, all using the same algorithm, just different parameters. Here are the results (click on the image to get a higher resolution):

In this post I will introduce the main parameters I used. As you will see, most of them control how the initial points for the colonization are seeded in space, the rest is colonization magic.

First there is the crown's envelope. The envelope starts from an ellipsoid. The class defines vertical and horizontal radii for the ellipsoid. In the next image you can see this large ellipsoid noted as (a):

A portion of this ellipsoid may be empty. This is noted as (c). This section may be quite large for some classes  like the baobab. The class also determines a proportion between the height of the trunk (b) and the size of the ellipsoid (a).

As points are randomly created inside the crown volume, the odds for a point to be added depend on another parameter: the "crown density". This parameter goes from zero to one. If it is close to zero, most points end up in the surface of the ellipsoid. If it is close to one, they are distributed evenly inside the ellipsoid.

The following image illustrates this effect:

Not all trees have this kind of elliptical crown. Many appear to have a number of smaller crowns, often showing some gaps in-between.

I wanted to have a simple definition for the class so I immediately ruled out any verbose approach. I realized that if I inserted the colonization tree points in an R-Tree and the clump the points on each node, it would naturally compact some areas of the crown. The clumps could also be shifted vertically to mimic the stratification you see in some trees.

I added two main parameters to control the clumping of the crown. One for the radius of the clumps, the second for how strongly the points will be pulled towards each other within the same clump. Then I added a third parameter: a probability that an entire clump may be removed. When an entire clump goes away it creates a natural gap in the crown.

The baobab class uses this to achieve the distinct look of its crown. The clumps appear as ellipsoids, noted as (d):

You probably remember Leonardo's observation about tree branching. For two branches splitting from one main branch, it stated that the cross-section areas of the two branches would add up to the area of the main branch. Something like:

Where a, b and c are the branch diameters as noted in the image.

Well, maybe Leo never went to Africa. The pipe model holds for trees that only care about moving stuff up and down. In some dryer places, trees also store water. This makes the trunks and some of the branches fatter. To account for this I added another parameter that controls the exponent of this equation. By default it is 2 which applies to most trees, but it opens many interesting possibilities as the fat baobad model above shows.

And that's it. There are some other parameters controlling the roots and venation, but they are quite similar to the ones I described above. One interesting addition to the algorithm is that now it produces very visible large veins along the trunk and main branches. I will cover this in a future post.

If you can think of a tree that cannot be represented by these parameters, just drop a comment here and point to the tree. I will try to reproduce it.