In this first workshop session, we will perform simple statistical operations in a *nonlinear* shape space: the set of polygons up to similarities.

The main references on the subject are:

*Shape manifolds, procrustean metrics, and complex projective spaces*(1984);*Statistical shape analysis, with applications in R*(1998,2016);*Functional and Shape Data Analysis*(2016);

which are respectively Kendall's landmark paper, a classic handbook by Dryden and Mardia and a recent handbook by Srivastava and Klassen.

In [1]:

```
%matplotlib inline
import matplotlib.pyplot as plt
import plotly
# run at the start of every notebook
plotly.offline.init_notebook_mode()
# Mandatory imports...
import numpy as np
from numpy import random
import torch
from torch import tensor
from torch.nn import Parameter
# Custom modules:
from kendall_triangles import KendallTriangles # Fancy visualization
from model import Model # Optimization blackbox
from display import plot # Simple plotting routine for triangles
# Finally, emulate complex numbers with pairs of floats:
from torch_complex import rot, normalize, herm, angle, mod2, mod
```