Rework distance calculation

src/data_morph/shapes/bases/line_collection.py

@@ -23,11 +23,12 @@ class LineCollection(Shape):
     """
 
     def __init__(self, *lines: Iterable[Iterable[Number]]) -> None:
-        # check that lines that have the same starting and ending points raise an error
+        # check that lines with the same starting and ending points raise an error
         for line in lines:
             start, end = line
             if np.allclose(start, end):
                 raise ValueError(f'Line {line} has the same start and end point')
+
         self.lines = np.array(lines)
         """Iterable[Iterable[numbers.Number]]: An iterable
         of two (x, y) pairs representing the endpoints of a line."""
@@ -57,28 +58,41 @@ def distance(self, x: Number, y: Number) -> float:
 
         .. _this Stack Overflow answer: https://stackoverflow.com/a/58781995
         """
-        p = np.array([x, y])
-
-        a = self.lines[:, 0, :]
-        b = self.lines[:, 1, :]
-
-        d_ba = b - a
-        d = np.divide(d_ba, (np.hypot(d_ba[:, 0], d_ba[:, 1]).reshape(-1, 1)))
-
-        # signed parallel distance components
-        # rowwise dot products of 2D vectors
-        s = np.multiply(a - p, d).sum(axis=1)
-        t = np.multiply(p - b, d).sum(axis=1)
-
-        # clamped parallel distance
-        h = np.maximum.reduce([s, t, np.zeros(len(s))])
-
-        # perpendicular distance component
-        # rowwise cross products of 2D vectors
-        d_pa = p - a
-        c = d_pa[:, 0] * d[:, 1] - d_pa[:, 1] * d[:, 0]
-
-        return np.min(np.hypot(h, c))
+        point = np.array([x, y])
+
+        start_points = self.lines[:, 0, :]
+        end_points = self.lines[:, 1, :]
+
+        tangent_vector = end_points - start_points
+        normalized_tangent_vectors = np.divide(
+            tangent_vector,
+            np.hypot(tangent_vector[:, 0], tangent_vector[:, 1]).reshape(-1, 1),
+        )
+
+        # row-wise dot products of 2D vectors
+        signed_parallel_distance_start = np.multiply(
+            start_points - point, normalized_tangent_vectors
+        ).sum(axis=1)
+        signed_parallel_distance_end = np.multiply(
+            point - end_points, normalized_tangent_vectors
+        ).sum(axis=1)
+
+        clamped_parallel_distance = np.maximum.reduce(
+            [
+                signed_parallel_distance_start,
+                signed_parallel_distance_end,
+                np.zeros(signed_parallel_distance_start.shape[0]),
+            ]
+        )
+
+        # row-wise cross products of 2D vectors
+        perpendicular_distance_component = np.cross(
+            point - start_points, normalized_tangent_vectors
+        )
+
+        return np.min(
+            np.hypot(clamped_parallel_distance, perpendicular_distance_component)
+        )
 
     @plot_with_custom_style
     def plot(self, ax: Axes = None) -> Axes: