Nicolas Rougier - 1 year ago 102
Python Question

# Multiple individual 2d rotation at once

I've a set of (n) geometrical shapes that are defined by a fixed number (p) of 2D points. Those shapes are independent but for efficiency reason, I stored time in a single numpy array. Scaling or translating those shapes are easy, but I would like to rotate them and I'm not sure how to do that. I suspect

`np.tensordot`
is my friend but I can't find the way to properly use it.

``````n = 100 # Number of shape
p = 4   # Points per shape
P = np.random.uniform(0, 1, (n, p, 2))

# Scaling
S = 0.5*np.ones(n)
P *= S

# Translating
T = np.random.uniform(0, 1, (n, 1, 2))
P += T

# Rotating
A = np.random.uniform(0, 2*np.pi, n)
cosA, sinA = np.cos(A), np.sin(A)

R = np.empty((n,2,2))
R[:,0,0] = cosA
R[:,1,0] = sinA
R[:,0,1] = -sinA
R[:,1,1] = cosA

np.tensordot(P, R, axes=???)
``````

It seems you are keeping the first axis between the two arrays - `P` and `R` aligned and `sum-reducing` one each off the remaining axes from the input arrays. So, we can use `np.einsum` as it will allow us the axis-alignment criteria.
You are using the last axis from `P` for the sum-reduction. Now, depending on which axis of `R` you are losing with `sum-reduction` for the rotation calculation, one of these should do the job -
``````np.einsum('ijk,ilk->ijl',P,R) # Using last dim of R for sum-reduction