H-Signature

A C++ or Python Library for computing the h-signature as defined in [1].

What is the H-signature? In the simplest case, it tells you whether two closed 3D curves are linked, or unlinked. The figure below shows some examples.

In the general case, the H-signature is computed between one closed curve $\tau$ and a skeleton of closed curves $S=\{S_1,\dots,S_m\}$. In code, each curve is a matrix of [3xN] (C++) or [Nx3] (Python) where N is the number of points in the curve. The H-signature is a vector (ordered list) of integers, where each element correspond to the h-signature of $\tau$ with respect to one curve in $S$.

Installation

For python:

pip install h-signature

For C++:

# The only option we offer is building from source with cmake 
git clone git@github.com:UM-ARM-Lab/h-signature.git
cd h-signature
mkdir build
# The only dependency is Eigen3
sudo apt install libeigen3-dev
# Build and run tests
cd build
cmake ..
make
ctest

API

There is only one function!

# Python with numpy
from h_signature.h_signature_np import get_h_signature
# Tau is an [Nx3] numpy array and skeleton is a dict of [3xN] numpy arrays
h_sig = get_h_signature(tau, skeleton)
print(h_sig)

// C++ with Eigen
#include <h_signature/h_signature.hpp>
// The above header has these typedefs
// typedef Eigen::Matrix3Xd Loop;
// typedef std::map<std::string, Eigen::Matrix3Xd> Skeleton;

// And this is the function, that's it! 
HSignature get_h_signature(Loop const &loop, Skeleton const & skeleton);

Citation