As you can see, not all seed values will produce equally believable and attractive trees; the
centre tree in particular looks rather lopsided. As the actual shape of any given
tree is formed from a complex interrelationship between all three of the categories listed
two
paragraphs back, you will often find that you need to experiment with a variety of different
values to obtain the effect you're looking for.
Angles of the Splits
This brings us to the second category - the allowable angles of the splits. This
is a fairly complex category, and tends to have the biggest effect on the shape of the tree. There
is a maximum and minimum angle setting for each of the three major axises (X, Y and Z). There is a
multiplier that can be used to increment or decrease these angles as the limbs branch. And there is
the previously mentioned PlusMinus variable, used to control the change of
direction of the terminal split of each section. To understand how these variables work, you'll
need to understand how the utility creates the tree.
To begin with, the file uses a series of random numbers to follow a hypothetical splitting from the
trunk thrugh a limb, a bough, and a branch, finally reaching the cluster of twigs that will be
attached to that branch. It then begins assembling this structure in reverse, from the twigs
back down to the trunk, re-splitting out to the twig level as necessary. You could simulate this
decision-making process with a die; roll it once to determine how many limbs there will be. Roll
it again to decide how many boughs the first limb will have; and again for how many branches the first
bough will have. And a final time to determine how many twigs that branch will bear. Draw this many
twigs and the branch they're attached to, then roll again to figure out how many twigs there are on the
next branch over (or if there's only the one branch, how many branches on the next bough). The following
diagram illustrates this decision-making process - the brighter parts have been "drawn in", the dimmer
one are the ones yet to come:
When "drawing" the tree sections, the file begins by creating a section so that it is running in the
+Y direction with it's base at the origin. It is then rotated around the X-axis to move it off of
the vertical, by an angle which falls between stated MinXDeg and MaxXDeg values - these
values can be any number, but realistically speaking you'll probably find you get the best result with
values falling somewhere between 10 and 90 degrees, that are at least 10 degrees apart but not more than
30 or 40. The tree shown to the left illustrates a tree with small minimum and maximum angles; the
tree to the right shows one with large angles.
The section is next rotated around the Y-axis, again by an angle with MinYDeg and
MaxYDeg values, which determines it's orientation about it's parent section.
Unless you want to achieve a "windswept" or bonsai-like appearance, you should leave these values
with a minimum of 0 and a maximum of 360. Allowance has been made for an additional rotation
around the Z-axis, but it is strickly optional and you can get along just fine with both MinZDeg
and MaxZDeg left at 0. Finally, the section is translated in the +Y direction by a distance
that leaves it somewhere along the length of its parent section, which at this point has not yet
been created. Once the necessary number of sections (and any relevant sub-sections) have been
created, they are unioned together with the parent section, which then itself goes through the
rotations, translation, and union described already.
One interesting and usefull tip should be brought up at this point. Because of the way in which
it is used to calculate the range of values
(rotate x*((rand(SD1)*(PlusMinus*2))-PlusMinus)) you can force the terminal branches
to always bend in the negative direction by specifying a negative PlusMinus value;
please be aware that if you do so, it's maximum angle is as a result three times the size of the
value actually used. This -PlusMinus method can be used to created "droopy" trees like
the one shown to the left.
The second exception is that all limbs (initial splits off the trunk) are always allowed a full 360 degrees of freedom
for their rotation around the trunk, as otherwise you get some EXTREMELY odd-looking and unbalanced
trees if you start changing the MinYDeg and MaxYDeg from their defaults of 0 and 360
(they look wierd enough even with this caveat, see the interestingly odd example at the right).
If you are actually aiming for an unusual, windswept, or bonsai-like appearance, then this is something
you'll probably want to play around with. It's also one of the few times the ability to do Z-rotations
may be useful.
Returning to all the MinXDeg, MaxXDeg, and so on variables, you may find that you'd
like to do a tree whose branchs curve either more or less towards the tips. To allow for this,
there are an additional three axis-specific variables - IncXDeg, IncYDeg, and
IncZDeg. These allow you to specify an additional few degrees of angle to be added on to
the initial minimum and maximum values. For example, suppose you want to increase your X rotation.
Your initial values are MinXDeg=35 and MaxXDeg=55, and you specify a IncXDeg of 10.
The tree will look like that shown to the left, and the actual values used for the minimum and
maximum X angles at each of the levels will be as follows:
- Limb from Trunk = 35 to 55 degrees
- Bough from Limb = 45 to 65 degrees
- Branch from Bough = 55 to 75 degrees
- Twig from Branch = 65 to 85 degrees
You can, of course, also use this value
to make the allowable angles smaller, by simply stating a negative value for it - the tree
to the right is an example of this. And, of course, you can use the IncYDeg and
IncZDeg on the other two axis if you're experimenting with values other than the defaults
for these two rotations.
Just as a reminder, here's our
original example tree again.
Except for the addition of the
fruit, all of the trees you've
seen so far have only had the
variables under discussion at
the moment changed from this
original definition.
How Many and How Big?
Number of Splits
The third tree is very bushy - lots and lots and lots of twigs and leaves and fruit. There is,
however, a better way to achieve this same result; if you look at a tree, you'll notice that
it usually has more twigs on a branch than branches on a bough and so on. To simulate this, there
is a multiplier for the MaxSplits variable called IncSplits. When in use (ie., set at
values higher than one) it will be used to multiply the maximum number of splits - and it "compounds",
so be careful when setting it; as a little math will show you, even quite small increases to it can
increase your maximum number of splits (and resultant number of objects) dramatically. For
example, with our original MaxSplits value of 4, the highest possible number of twigs is 4 to the
fourth power (not the fifth power, as even though there are five levels, the first, the trunk, is limited
to having only one object):
4*4*4*4 =256 twigs
And the maximum number of objects in the tree (not counting leaves, fruit, or flowers, which tend to
make up the bulk of the tree) is:
1+4+(4*4)+(4*4*4)+(4*4*4*4) = 341 objects
Of course, the random number generator would have to get a result of "4" every single time to get
this many twigs.
Suppose we set the IncSplits to 1.25? Now
the number of possible splits at each level will be increased by a factor based on this value
(converted to an integer as you can't have a fraction of a split).
It would change our equations to read as follows:
4 * INT(4*1.25) * INT(4*(1.25*1.25)) * INT(4*(1.25*1.25*1.25)) = 840 twigs
1+4+(4*5)+(4*5*6)+(4*5*6*7) = 985 objects
Or, to put it another way, our trunk can still only have up to 4 limbs, but our branches can now have
up to seven twigs. This tree is shown to the left. This, by the way, is the kind of place where
being able to increase the spread (angle) of the splits as your approach the tips can come in
very useful, as otherwise you end up having a tree with lots of leaves and twigs all crammed into a
fairly small volume. The tree to the right illustrates the combined use of IncSplits and
IncXDeg.
Size of Objects Being Split
The overall size of the tree is based on the variables BaseLen and LengthInc.
The former variable is used for several purposes - it is the length of a twig, the radius of
the base of the trunk of the tree, and the scaling factor used to scale the leaves and
fruit to fit the size of the tree. It's default value is 1. To easily scale your tree
up or down in size (thereby avoiding later rescaling an object that may be built of thousands, or
even hundreds of thousands of objects), scale this variable.
LengthInc is yet another multiplier - this one is used to determine how much longer a branch is
than a twig, a bough is than a branch, a limb is than a bough, and the trunk is than a limb. You can make
a compact, chunky tree by setting it to just a little over 1 (see left) or an elongated airy tree by
making it closer to 2 (see right). You'll get very elongated trees if you go beyond 2 - and even
2 is pushing it.
And now it's time to explain just what objects are being used in the creation of the tree. Overall, it's
an assemblage of cones, with spheres to smooth the joins. These spheres can be turned on or off using the
BallJoint variable, or restricted to only working up to a specific level of detail in the tree
by setting BallLevels equal to any value from 1 to 5. DON'T bother using 5 (or even 4, really)
unless you're rendering an extreme close-up view of the tree; it'll basically double the number of objects
making up the tree (exclusive of whatever's stuck to the twigs), as every section would then be made of a
sphere-and-cone instead of just a cone. If the tree is in the distance, then you can probably get away with
turning BallJoint off altogether.
Leaves, Fruits, Flowers and Finishes
Unless you're doing an early spring or late fall scene, you'll probably want to have leaves on your tree,
and possibly fruit or flowers as well. There are a number of pre-defined shapes you can use for these, or
you can use your own user-defined shape. There is also an assortment of pre-defined textures available
for the leaves, fruit, flowers, and bark of the tree.
In addition, there's also several variables that affect the
placement and orientation of these objects. These are as follows:
To begin with, I'd better
take a second to define some terms; the trees are created using random numbers and
five nested loops, resulting in five levels of structure - these can be thought of as the
trunk, limbs, boughs, branches, and twigs, and will be referred to by these terms
in the rest of the document. When limbs branch off of trunks and boughs off of limbs and
so on, I'll be referring to that as "splits" so as not to get it confused with the other
meaning of "branch". The twigs are the only part of the tree
that have leaves, fruits, or flowers; the remainder of the structure is bare. Also, fruits
and flowers only appear at the tips of the twigs. This can be seen in the image to the left,
where I've turned on "fruit" and made the color of the fruit be a very bright red. To make
it easier to see where the twig tips are (and how many of them there are), I'll leave the
"fruit" option enabled for the remaining examples.
