ReePy

ReePy is a Reeb graph construction library containing accelerated algorithms for constructing Reeb graphs for multiple data modalities.

Currently supported classes include:

• A top level ReebGraph implementation for any data

• An implementation for trajectories of fixed length

• An implementation for trajectories with thresholded distances as a connectivity metric

Planned features which still need to be integrated:

• A GPU accelerated implementation for graph analysis

• An implementation for mesh analysis

Installation

You can install ReePy using uv from the GitHub. ReePy should work with other Python package managers as well.

uv add git+https://github.com/UCSB-VRL/ReePy.git

Philosophy

Reeb graphs capture the evolution of connected components over a series of level sets. For any Reeb graph in ReePy, we must define level which is a function that maps a point from the input modality to a number (either integer or floating point). To define what a connected component is, we must define connectivity which, given a collection of points, returns True if they are connected and False if they are not. Finally, we must define continuity, which given two points, returns True if one "evolves" from another. In the trajectory context, continuity would return True if the two points are consecutive in the same trajectory.

For example, for Sequential Reeb Graphs, you might use the following definitions:

import itertools
import math
from reepy import ReebGraph

# each point p is (traj_index, sequence_index, x, y)
epsilon = 1 

level = lambda p: p[1]
connectivity = lambda pts: all(math.dist(p[2:], q[2:]) <= epsilon for p, q in itertools.combinations(pts, 2))
continuity = lambda p, q: p[0] == q[0] and abs(p[1] - q[1]) == 1

graph = ReebGraph(level=level, connectivity=connectivity, continuity=continuity)

Once a ReebGraph is defined, you can add data using the ReebGraph.add(self, data) method, which incrementally constructs the Reeb graph. You may observe that ReebGraph construction times scale exponentially with the number of points added, which may make using the base class impractical for your data. For this reason, we have modality-specific accelerated ReebGraph implementations, each of which make assumptions about the structure of the data. However, they still will define connectivity, continuity and level so an equivalent graph can be computed (and verified) against the base class.