NOVEMBER POETRY
Simplified generator of maple leaves
Tools: Rhinoceros, Grasshopper, Python
Autumn is a perfect time to behold a variety of shapes and colors. When the leaves turn gold and red I can’t help myself but pick them up. This time instead of admiration I decided to take a closer look at them…
To begin with, I chose a maple leaf as a target.
It is clear that before reverse engineering something it is necessary to answer the questions of what it is and how it is unique.
Since the leaf shapes are extremely diverse and cannot be analyzed in their entirety at once, the material should be divided into parts. Lucky for me it is well studied and that means it is classified. Correct classification is one of the first steps in the description.
Most of the leaf classifications are concentrated on the 3 properties: leaf shape (blade), venation, and margin (edge contour). As we will see later these properties are interconnected and related to each other in a strong manner.
SHAPE
Leaf shapes can be simple or compound. Simple leaves can also be lobed.
VENATION
In the terms of the structure I will simplify all venation systems to 3 types. The arrangement can be more complicated but the logic is the same.
MARGIN
The edges of the leaves are very diverse, it is important for us that in the case of a non-entire edge, there could be smooth continuous lines and the picks.
Shape, size, and structure usually reflect adaptability to certain environmental conditions.
PTYXIS
There is another important property that I am not taking into consideration today. Leaves are growing structures. It is true for some species that before they come out of the bud their blades are folded in a certain way. This folding condition is called ptyxis. Note that the main veins in such leaves correspond to the creases formed by a fold.
The folding subject is deeply connected to the structure of the blade geometry. It is a huge topic that deserves a particular study and surely a separate post. Maybe one day I will get there but for now, let me bring you back to our maples.
Here is the scan of a leaf with its main characteristics.
STRUCTURE / SHAPE
Let’s start with the primary veins. To define their directions imagine that the leaf is a flat polygon – so that – the Vertices of such polygon are the End Points of the primary veins with only one Start Point. If we assume that the angle between the veins is approximately the same, then we can get the vertices by using a circle. Move the Circle to adjust the directions.
These lines define the future mains veins. I strongly advise to sort the end points to keep the order.
I remove the line at 6 o’clock to save the space for a petiole.
To create an outline sort and connect the End Points.
My leaf has only 5 Primary Veins so I got rid of some points in the lower part of the blade.
MARGIN
Use KANGAROO plugin to create a pointed contour using the End Points of the veins :
VENATION
Besides the Primary and Secondary veins which form the shape of the leaf, the surface itself is filled with tiny little veins running from the big ones to small.
This pattern can be created with help of the Voronoi diagram or Voronoi groups component in this case.
You will find bellow the whole GH script that I used.
Resources:
- Adam Runions, Miltos Tsiantis, Przemyslaw Prusinkiewicz “A common developmental program can produce diverse leaf shapes”
- Etienne Couturier, Sylvain Courrech Du Pont, Stéphane Douady “The filling law: A general framework for leaf folding and its consequences on leaf shape diversity”