# Authors: see git history # # Copyright (c) 2010 Authors # Licensed under the GNU GPL version 3.0 or later. See the file LICENSE for details. import math from shapely.geometry import LineString, LinearRing, MultiLineString, Polygon, MultiPolygon, MultiPoint, GeometryCollection from shapely.geometry import Point as ShapelyPoint from scipy.interpolate import splprep, splev import numpy as np def cut(line, distance, normalized=False): """ Cuts a LineString in two at a distance from its starting point. This is an example in the Shapely documentation. """ if normalized: distance *= line.length if distance <= 0.0: return [None, line] elif distance >= line.length: return [line, None] coords = list(ShapelyPoint(p) for p in line.coords) traveled = 0 last_point = coords[0] for i, p in enumerate(coords[1:], 1): traveled += p.distance(last_point) last_point = p if traveled == distance: return [ LineString(coords[:i + 1]), LineString(coords[i:])] if traveled > distance: cp = line.interpolate(distance) return [ LineString(coords[:i] + [(cp.x, cp.y)]), LineString([(cp.x, cp.y)] + coords[i:])] def cut_multiple(line, distances, normalized=False): """Cut a LineString at multiple distances along that line. Always returns a list of N + 1 members, where N is the number of distances provided. Some members of the list may be None, indicating an empty segment. This can happen if one of the distances is at the start or end of the line, or if duplicate distances are provided. Returns: a list of LineStrings or None values""" distances = list(sorted(distances)) segments = [line] distance_so_far = 0 nones = [] for distance in distances: segment = segments.pop() before, after = cut(segment, distance - distance_so_far, normalized) segments.append(before) if after is None: nones.append(after) else: if before is not None: distance_so_far += before.length segments.append(after) segments.extend(nones) return segments def roll_linear_ring(ring, distance, normalized=False): """Make a linear ring start at a different point. Example: A B C D E F G A -> D E F G A B C Same linear ring, different ordering of the coordinates. """ if not isinstance(ring, LinearRing): # In case they handed us a LineString ring = LinearRing(ring) pieces = cut(LinearRing(ring), distance, normalized=False) if None in pieces: # We cut exactly at the start or end. return ring # The first and last point in a linear ring are duplicated, so we omit one # copy return LinearRing(pieces[1].coords[:] + pieces[0].coords[1:]) def reverse_line_string(line_string): return LineString(line_string.coords[::-1]) def ensure_multi_line_string(thing): """Given either a MultiLineString or a single LineString, return a MultiLineString""" if isinstance(thing, LineString): return MultiLineString([thing]) else: return thing def ensure_geometry_collection(thing): """Given either some kind of geometry or a GeometryCollection, return a GeometryCollection""" if isinstance(thing, (MultiLineString, MultiPolygon, MultiPoint)): return GeometryCollection(thing.geoms) elif isinstance(thing, GeometryCollection): return thing else: return GeometryCollection([thing]) def ensure_multi_polygon(thing): """Given either a MultiPolygon or a single Polygon, return a MultiPolygon""" if isinstance(thing, Polygon): return MultiPolygon([thing]) else: return thing def cut_path(points, length): """Return a subsection of at the start of the path that is length units long. Given a path denoted by a set of points, walk along it until we've travelled the specified length and return a new path up to that point. If the original path isn't that long, just return it as is. """ if len(points) < 2: return points path = LineString(points) subpath, rest = cut(path, length) return [Point(*point) for point in subpath.coords] def _remove_duplicate_coordinates(coords_array): """Remove consecutive duplicate points from an array. Arguments: coords_array -- numpy.array Returns: a numpy.array of coordinates, minus consecutive duplicates """ differences = np.diff(coords_array, axis=0) zero_differences = np.isclose(differences, 0) keepers = np.r_[True, np.any(zero_differences == False, axis=1)] # noqa: E712 return coords_array[keepers] def smooth_path(path, smoothness=100.0): """Smooth a path of coordinates. Arguments: path -- an iterable of coordinate tuples or Points smoothness -- float, how much smoothing to apply. Bigger numbers smooth more. Returns: A list of Points. """ # splprep blows up on duplicated consecutive points with "Invalid inputs" coords = _remove_duplicate_coordinates(np.array(path)) num_points = len(coords) # splprep's s parameter seems to depend on the number of points you pass # as per the docs, so let's normalize it. s = round(smoothness / 100 * num_points) # .T transposes the array (for some reason splprep expects # [[x1, x2, ...], [y1, y2, ...]] tck, fp, ier, msg = splprep(coords.T, s=s, nest=-1, full_output=1) if ier > 0: from ..debug import debug debug.log(f"error {ier} smoothing path: {msg}") return path # Evaluate the spline curve at many points along its length to produce the # smoothed point list. 2 * num_points seems to be a good number, but it # does produce a lot of points. smoothed_x_values, smoothed_y_values = splev(np.linspace(0, 1, num_points * 2), tck[0]) coords = np.array([smoothed_x_values, smoothed_y_values]).T return [Point(x, y) for x, y in coords] class Point: def __init__(self, x: float, y: float): self.x = x self.y = y @classmethod def from_shapely_point(cls, point): return cls(point.x, point.y) @classmethod def from_tuple(cls, point): return cls(point[0], point[1]) def __json__(self): return vars(self) def __add__(self, other): return self.__class__(self.x + other.x, self.y + other.y) def __sub__(self, other): return self.__class__(self.x - other.x, self.y - other.y) def mul(self, scalar): return self.__class__(self.x * scalar, self.y * scalar) def __mul__(self, other): if isinstance(other, Point): # dot product return self.x * other.x + self.y * other.y elif isinstance(other, (int, float)): return self.__class__(self.x * other, self.y * other) else: raise ValueError("cannot multiply %s by %s" % (type(self), type(other))) def __neg__(self): return self * -1 def __rmul__(self, other): if isinstance(other, (int, float)): return self.__mul__(other) else: raise ValueError("cannot multiply %s by %s" % (type(self), type(other))) def __truediv__(self, other): if isinstance(other, (int, float)): return self * (1.0 / other) else: raise ValueError("cannot divide %s by %s" % (type(self), type(other))) def __eq__(self, other): return self.x == other.x and self.y == other.y def __repr__(self): return "%s(%s,%s)" % (type(self), self.x, self.y) def length(self): return math.sqrt(math.pow(self.x, 2.0) + math.pow(self.y, 2.0)) def distance(self, other): return (other - self).length() def unit(self): return self.mul(1.0 / self.length()) def angle(self): return math.atan2(self.y, self.x) def rotate_left(self): return self.__class__(-self.y, self.x) def rotate(self, angle): return self.__class__(self.x * math.cos(angle) - self.y * math.sin(angle), self.y * math.cos(angle) + self.x * math.sin(angle)) def as_int(self): return self.__class__(int(round(self.x)), int(round(self.y))) def as_tuple(self): return (self.x, self.y) def __getitem__(self, item): return self.as_tuple()[item] def __len__(self): return 2 def __str__(self): return "({0:.3f}, {1:.3f})".format(self.x, self.y) def line_string_to_point_list(line_string): return [Point(*point) for point in line_string.coords]