Fixed database typo and removed unnecessary class identifier.

venv/Lib/site-packages/skimage/measure/_polygon.py

@@ -0,0 +1,168 @@
+import numpy as np
+from scipy import signal
+
+
+def approximate_polygon(coords, tolerance):
+    """Approximate a polygonal chain with the specified tolerance.
+
+    It is based on the Douglas-Peucker algorithm.
+
+    Note that the approximated polygon is always within the convex hull of the
+    original polygon.
+
+    Parameters
+    ----------
+    coords : (N, 2) array
+        Coordinate array.
+    tolerance : float
+        Maximum distance from original points of polygon to approximated
+        polygonal chain. If tolerance is 0, the original coordinate array
+        is returned.
+
+    Returns
+    -------
+    coords : (M, 2) array
+        Approximated polygonal chain where M <= N.
+
+    References
+    ----------
+    .. [1] https://en.wikipedia.org/wiki/Ramer-Douglas-Peucker_algorithm
+    """
+    if tolerance <= 0:
+        return coords
+
+    chain = np.zeros(coords.shape[0], 'bool')
+    # pre-allocate distance array for all points
+    dists = np.zeros(coords.shape[0])
+    chain[0] = True
+    chain[-1] = True
+    pos_stack = [(0, chain.shape[0] - 1)]
+    end_of_chain = False
+
+    while not end_of_chain:
+        start, end = pos_stack.pop()
+        # determine properties of current line segment
+        r0, c0 = coords[start, :]
+        r1, c1 = coords[end, :]
+        dr = r1 - r0
+        dc = c1 - c0
+        segment_angle = - np.arctan2(dr, dc)
+        segment_dist = c0 * np.sin(segment_angle) + r0 * np.cos(segment_angle)
+
+        # select points in-between line segment
+        segment_coords = coords[start + 1:end, :]
+        segment_dists = dists[start + 1:end]
+
+        # check whether to take perpendicular or euclidean distance with
+        # inner product of vectors
+
+        # vectors from points -> start and end
+        dr0 = segment_coords[:, 0] - r0
+        dc0 = segment_coords[:, 1] - c0
+        dr1 = segment_coords[:, 0] - r1
+        dc1 = segment_coords[:, 1] - c1
+        # vectors points -> start and end projected on start -> end vector
+        projected_lengths0 = dr0 * dr + dc0 * dc
+        projected_lengths1 = - dr1 * dr - dc1 * dc
+        perp = np.logical_and(projected_lengths0 > 0,
+                              projected_lengths1 > 0)
+        eucl = np.logical_not(perp)
+        segment_dists[perp] = np.abs(
+            segment_coords[perp, 0] * np.cos(segment_angle)
+            + segment_coords[perp, 1] * np.sin(segment_angle)
+            - segment_dist
+        )
+        segment_dists[eucl] = np.minimum(
+            # distance to start point
+            np.sqrt(dc0[eucl] ** 2 + dr0[eucl] ** 2),
+            # distance to end point
+            np.sqrt(dc1[eucl] ** 2 + dr1[eucl] ** 2)
+        )
+
+        if np.any(segment_dists > tolerance):
+            # select point with maximum distance to line
+            new_end = start + np.argmax(segment_dists) + 1
+            pos_stack.append((new_end, end))
+            pos_stack.append((start, new_end))
+            chain[new_end] = True
+
+        if len(pos_stack) == 0:
+            end_of_chain = True
+
+    return coords[chain, :]
+
+
+# B-Spline subdivision
+_SUBDIVISION_MASKS = {
+    # degree: (mask_even, mask_odd)
+    #         extracted from (degree + 2)th row of Pascal's triangle
+    1: ([1, 1], [1, 1]),
+    2: ([3, 1], [1, 3]),
+    3: ([1, 6, 1], [0, 4, 4]),
+    4: ([5, 10, 1], [1, 10, 5]),
+    5: ([1, 15, 15, 1], [0, 6, 20, 6]),
+    6: ([7, 35, 21, 1], [1, 21, 35, 7]),
+    7: ([1, 28, 70, 28, 1], [0, 8, 56, 56, 8]),
+}
+
+
+def subdivide_polygon(coords, degree=2, preserve_ends=False):
+    """Subdivision of polygonal curves using B-Splines.
+
+    Note that the resulting curve is always within the convex hull of the
+    original polygon. Circular polygons stay closed after subdivision.
+
+    Parameters
+    ----------
+    coords : (N, 2) array
+        Coordinate array.
+    degree : {1, 2, 3, 4, 5, 6, 7}, optional
+        Degree of B-Spline. Default is 2.
+    preserve_ends : bool, optional
+        Preserve first and last coordinate of non-circular polygon. Default is
+        False.
+
+    Returns
+    -------
+    coords : (M, 2) array
+        Subdivided coordinate array.
+
+    References
+    ----------
+    .. [1] http://mrl.nyu.edu/publications/subdiv-course2000/coursenotes00.pdf
+    """
+    if degree not in _SUBDIVISION_MASKS:
+        raise ValueError("Invalid B-Spline degree. Only degree 1 - 7 is "
+                         "supported.")
+
+    circular = np.all(coords[0, :] == coords[-1, :])
+
+    method = 'valid'
+    if circular:
+        # remove last coordinate because of wrapping
+        coords = coords[:-1, :]
+        # circular convolution by wrapping boundaries
+        method = 'same'
+
+    mask_even, mask_odd = _SUBDIVISION_MASKS[degree]
+    # divide by total weight
+    mask_even = np.array(mask_even, np.float) / (2 ** degree)
+    mask_odd = np.array(mask_odd, np.float) / (2 ** degree)
+
+    even = signal.convolve2d(coords.T, np.atleast_2d(mask_even), mode=method,
+                             boundary='wrap')
+    odd = signal.convolve2d(coords.T, np.atleast_2d(mask_odd), mode=method,
+                            boundary='wrap')
+
+    out = np.zeros((even.shape[1] + odd.shape[1], 2))
+    out[1::2] = even.T
+    out[::2] = odd.T
+
+    if circular:
+        # close polygon
+        out = np.vstack([out, out[0, :]])
+
+    if preserve_ends and not circular:
+        out = np.vstack([coords[0, :], out, coords[-1, :]])
+
+    return out