feat: add DistanceMap (#1142)

* feat: add DistanceMap

* feat: add DistanceMap test

* feat: add DistanceMap doc

* feat: DistanceMap doc update

* feat: DistanceMap update

Mapping/DistanceMap/distance_map.py

@@ -0,0 +1,151 @@
+"""
+Distance Map
+
+author: Wang Zheng (@Aglargil)
+
+Ref:
+
+- [Distance Map]
+(https://cs.brown.edu/people/pfelzens/papers/dt-final.pdf)
+"""
+
+import numpy as np
+import matplotlib.pyplot as plt
+
+INF = 1e20
+ENABLE_PLOT = True
+
+
+def compute_sdf(obstacles):
+    """
+    Compute the signed distance field (SDF) from a boolean field.
+
+    Parameters
+    ----------
+    obstacles : array_like
+        A 2D boolean array where '1' represents obstacles and '0' represents free space.
+
+    Returns
+    -------
+    array_like
+        A 2D array representing the signed distance field, where positive values indicate distance
+        to the nearest obstacle, and negative values indicate distance to the nearest free space.
+    """
+    a = compute_udf(obstacles)
+    b = compute_udf(obstacles == 0)
+    return a - b
+
+
+def compute_udf(obstacles):
+    """
+    Compute the unsigned distance field (UDF) from a boolean field.
+
+    Parameters
+    ----------
+    obstacles : array_like
+        A 2D boolean array where '1' represents obstacles and '0' represents free space.
+
+    Returns
+    -------
+    array_like
+        A 2D array of distances from the nearest obstacle, with the same dimensions as `bool_field`.
+    """
+    edt = obstacles.copy()
+    if not np.all(np.isin(edt, [0, 1])):
+        raise ValueError("Input array should only contain 0 and 1")
+    edt = np.where(edt == 0, INF, edt)
+    edt = np.where(edt == 1, 0, edt)
+    for row in range(len(edt)):
+        dt(edt[row])
+    edt = edt.T
+    for row in range(len(edt)):
+        dt(edt[row])
+    edt = edt.T
+    return np.sqrt(edt)
+
+
+def dt(d):
+    """
+    Compute 1D distance transform under the squared Euclidean distance
+
+    Parameters
+    ----------
+    d : array_like
+        Input array containing the distances.
+
+    Returns:
+    --------
+    d : array_like
+        The transformed array with computed distances.
+    """
+    v = np.zeros(len(d) + 1)
+    z = np.zeros(len(d) + 1)
+    k = 0
+    v[0] = 0
+    z[0] = -INF
+    z[1] = INF
+    for q in range(1, len(d)):
+        s = ((d[q] + q * q) - (d[int(v[k])] + v[k] * v[k])) / (2 * q - 2 * v[k])
+        while s <= z[k]:
+            k = k - 1
+            s = ((d[q] + q * q) - (d[int(v[k])] + v[k] * v[k])) / (2 * q - 2 * v[k])
+        k = k + 1
+        v[k] = q
+        z[k] = s
+        z[k + 1] = INF
+    k = 0
+    for q in range(len(d)):
+        while z[k + 1] < q:
+            k = k + 1
+        dx = q - v[k]
+        d[q] = dx * dx + d[int(v[k])]
+
+
+def main():
+    obstacles = np.array(
+        [
+            [1, 0, 0, 0, 0],
+            [0, 1, 1, 1, 0],
+            [0, 1, 1, 1, 0],
+            [0, 0, 1, 1, 0],
+            [0, 0, 1, 0, 0],
+            [0, 0, 0, 0, 0],
+            [0, 0, 0, 0, 0],
+            [0, 0, 0, 0, 0],
+            [0, 0, 1, 0, 0],
+            [0, 0, 0, 0, 0],
+            [0, 0, 0, 0, 0],
+        ]
+    )
+
+    # Compute the signed distance field
+    sdf = compute_sdf(obstacles)
+    udf = compute_udf(obstacles)
+
+    if ENABLE_PLOT:
+        _, (ax1, ax2, ax3) = plt.subplots(1, 3, figsize=(15, 5))
+
+        obstacles_plot = ax1.imshow(obstacles, cmap="binary")
+        ax1.set_title("Obstacles")
+        ax1.set_xlabel("x")
+        ax1.set_ylabel("y")
+        plt.colorbar(obstacles_plot, ax=ax1)
+
+        udf_plot = ax2.imshow(udf, cmap="viridis")
+        ax2.set_title("Unsigned Distance Field")
+        ax2.set_xlabel("x")
+        ax2.set_ylabel("y")
+        plt.colorbar(udf_plot, ax=ax2)
+
+        sdf_plot = ax3.imshow(sdf, cmap="RdBu")
+        ax3.set_title("Signed Distance Field")
+        ax3.set_xlabel("x")
+        ax3.set_ylabel("y")
+        plt.colorbar(sdf_plot, ax=ax3)
+
+        plt.tight_layout()
+        plt.show()
+
+
+if __name__ == "__main__":
+    main()