We discussed in our post Generating 3D Models the script I wrote to generate the 3D model of our phyllotactic sculpture. In this script, I start by generating a polyhedron made up of quadrilaterals arranged in a phyllotactic pattern:

Then, my script takes as input a 3D model of a petal and copies it on each quadrilateral:

One problem with this method is each quadrilateral is different, which means I had to slightly deform each petal to fir the quadrilateral's shape. Figuring the exact 3D transformation to accomplish this seemed a little too time consuming so I used lattices in blender, which are a way to deform objects according to a 3D grid. It turns out the result is not perfectly clean, and leaves small gaps between petals:

We also noticed the petals on John Edmark's model are not all identical: they all have slightly different orientations, and therefore appear to slowly rotate on themselves when animated.

Using identical petals leads to a much less interesting animation. These two problems led me to abandon this method of generating petals, and procedurally generate them instead.

In order to do this, I chose to use NURBS, which are a way to generate smooth surfaces using a 2D grid. This is also what John Edmark used to generate his petals.

Reproducing the petals will likely take some time, so for now I only generate simplified petals. Manually modelling the petals with NURBS surface wouldn't be that hard, but generating them within a script from a quadrilateral given in input, and being able to control their orientation is a whole other story...

Controlling the orientation of this simplified petal is quite simple : I only have to move around the upper polygon.

This new method allowed me to generate a clean model of our sculpture, with a nice rotating effect on each petal:

I'll probably attempt to model more complex petals during the winter vacations, so stay tuned for that !

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