Implement, test find_intersection helper

src/outset/_auxlib/find_intersection_.py

@@ -0,0 +1,41 @@
+import math
+import typing
+
+
+def find_intersection(
+    p1: typing.Tuple[float, float],
+    p2: typing.Tuple[float, float],
+    p3: typing.Tuple[float, float],
+    p4: typing.Tuple[float, float],
+) -> typing.Tuple[float, float]:
+    """Finds the intersection of two lines (p1 to p2 and p3 to p4).
+
+    Points are represented a tuple of (x, y).
+
+    Returns
+    -------
+    Tuple[float, float]
+        The intersection point, (x, y).
+
+        If lines do not intersect or are underspecified, result is (nan, nan).
+    """
+
+    # Unpack points
+    x1, y1 = p1
+    x2, y2 = p2
+    x3, y3 = p3
+    x4, y4 = p4
+
+    denominator = (x1 - x2) * (y3 - y4) - (y1 - y2) * (x3 - x4)
+    if denominator == 0:
+        return (math.nan, math.nan)
+
+    # adapted from https://stackoverflow.com/a/51127674
+    px = (
+        (x1 * y2 - y1 * x2) * (x3 - x4) - (x1 - x2) * (x3 * y4 - y3 * x4)
+    ) / denominator
+    py = (
+        (x1 * y2 - y1 * x2) * (y3 - y4) - (y1 - y2) * (x3 * y4 - y3 * x4)
+    ) / denominator
+
+    return (px, py)

tests/test_auxlib/test_find_intersection.py

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+import math
+
+from outset._auxlib.find_intersection_ import find_intersection
+
+
+def test_intersection_typical():
+    # Test a typical case where two lines intersect
+    assert find_intersection((0, 0), (1, 1), (0, 1), (1, 0)) == (0.5, 0.5)
+
+
+def test_intersection_parallel():
+    # Test a case where two lines are parallel and don't intersect
+    assert math.isnan(find_intersection((0, 0), (1, 1), (0, 1), (1, 2))[0])
+    assert math.isnan(find_intersection((0, 0), (1, 1), (0, 1), (1, 2))[1])
+
+
+def test_intersection_collinear():
+    # Test a case where two lines are collinear
+    assert math.isnan(find_intersection((0, 0), (1, 1), (2, 2), (3, 3))[0])
+    assert math.isnan(find_intersection((0, 0), (1, 1), (2, 2), (3, 3))[1])
+
+
+def test_intersection_points_underspecified():
+    # Test a case where lines are underspecified (e.g., points are identical)
+    assert math.isnan(find_intersection((0, 0), (0, 0), (1, 1), (1, 1))[0])
+    assert math.isnan(find_intersection((0, 0), (0, 0), (1, 1), (1, 1))[1])