Add sage code

lib/tutte_embedding.py

@@ -0,0 +1,57 @@
+"""Module for performing tutte embeddings"""
+from typing import Iterable, cast, Any
+from sage.all import vector, Graph, cos, pi, sin # type: ignore
+
+
+def create_tutte_embedding(
+    graph: Graph,
+    outer_face: list[Any],
+    max_iter: int=50,
+    set_pos: bool = True) -> dict[Any, Any]:
+    """
+    Performs a tutte force embedding with a prescribed outer face on
+    a given sage graph.
+
+    For a description on tutte embeddings, see the video [here](\
+    https://www.youtube.com/watch?v=mEzPPMhR8XE).
+    """
+    radius = 1000
+    pos: dict[Any, Any] = {}
+    num_outer_points = len(outer_face)
+    for i, v in enumerate(outer_face):
+        pos[v] = (
+            radius * cos((i / num_outer_points) * 2 * pi),
+            radius * sin((i / num_outer_points) * 2 * pi)
+        )
+
+    # start off setting all other points to (0, 0)
+    num_inner_points = cast(int, graph.order()) - num_outer_points
+
+    for i, v in enumerate(cast(Iterable[Any], graph.vertices())): # type: ignore
+        if v in pos:
+            continue
+        pos[v] = (
+            radius/3 * cos((i / num_inner_points) * 2 * pi),
+            radius/3 * sin((i / num_inner_points) * 2 * pi)
+        )
+
+    i = 0
+    while i < max_iter:
+        for v in cast(Iterable[Any], graph.vertices()): # type: ignore
+            if v in outer_face:
+                continue
+            neighbors = cast(list[Any], graph.neighbors(v)) # type: ignore
+            deg = len(neighbors)
+            x_desired = sum(map(lambda n: pos[n][0], neighbors)) / deg
+            y_desired = sum(map(lambda n: pos[n][1], neighbors)) / deg
+            pos[v] = tuple(
+                vector(pos[v]) - vector([  # type: ignore
+                    pos[v][0] - x_desired, pos[v][1] - y_desired
+                ])
+            )
+        i += 1
+
+    if set_pos:
+        graph.set_pos(pos) # type: ignore
+
+    return pos