update readme to reflect new changes

README.md

@@ -1,10 +1,16 @@
 # `ect`: A python package for computing the Euler Characteristic Transform
 
-Python computation tools for computing the Euler Characteristic Transform of embedded graphs. 
+Python computation tools for computing the Euler Characteristic Transform of embedded complexes. 
 
 ## Description
 
-Right now, the content includes stuff for doing ECT on graphs embedded in 2D. Eventually the goal is to get voxel versions, higher dimensional simplicial complexes, etc in here.
+The package provides fast tools for computing the Euler Characteristic Transform (ECT) on embedded cell complexes in any ambient dimension. You build a complex (vertices, edges, and optional higher‑dimensional cells), choose a set of directions and thresholds, and compute either the exact ECT or its smoothed/differentiable variants. Results come back as NumPy arrays with metadata, plotting helpers, and distance utilities, making it straightforward to visualize transforms and compare shapes. The core is implemented with NumPy and Numba, with optional validation of geometric and structural constraints when constructing complexes.
+
+- `EmbeddedComplex`: convert point clouds into complexes with vertices, edges, and higher‑dimensional cells with embedded coordinates.
+- `ECT`, `SECT`, `DECT` : ECT calculations along with the smooth and differentiable variants over sampled directions and transforms.
+- `Directions`: uniform, random, or custom directions (angles in 2D; vectors in any dimension)
+- Results as `ECTResult`: behaves like a NumPy array, with plotting and distance helpers
+- Optional geometric/structural validation when building complexes
 
 For more information on the ECT, see:
 
@@ -17,16 +23,12 @@ For more information on the ECT, see:
 - The documentation is available at: [munchlab.github.io/ect](https://munchlab.github.io/ect/)
 - A tutorial jupyter notebook can be found [here](https://munchlab.github.io/ect/notebooks/Tutorial-EmbeddedComplex.html)
 
-### Dependencies
-
-- `networkx`
-- `numpy`
-- `matplotlib`
-- `numba`
 
 ### Installing
 
-The package can be installed using pip:
+Requires Python 3.10+.
+
+Install from PyPI:
 
 ```{bash}
 pip install ect
@@ -40,6 +42,28 @@ cd ect
 pip install .
 ```
 
+### Quickstart
+
+Compute an ECT for a simple embedded triangle and plot it.
+
+```python
+from ect import ECT, EmbeddedComplex
+
+G = EmbeddedComplex()
+G.add_node("a", [0.0, 0.0])
+G.add_node("b", [1.0, 0.0])
+G.add_node("c", [0.5, 0.8])
+G.add_edge("a", "b")
+G.add_edge("b", "c")
+G.add_edge("c", "a")
+
+ect = ECT(num_dirs=32, num_thresh=128)
+result = ect.calculate(G)
+result.plot()
+```
+
+
+
 ## Authors
 
 This code was written by [Liz Munch](https://elizabethmunch.com/) along with her research group and collaborators. People who have contributed to `ect` include: