""" Polygon filling algorithm. """ # Licensed under a 3-clause BSD style license - see LICENSE.rst # NOTE: Algorithm description can be found, e.g., here: # http://www.cs.rit.edu/~icss571/filling/how_to.html # http://www.cs.uic.edu/~jbell/CourseNotes/ComputerGraphics/PolygonFilling.html import abc from collections import OrderedDict import numpy as np __all__ = ['Region', 'Edge', 'Polygon'] _INTERSECT_ATOL = 1e2 * np.finfo(float).eps class Region: """ Base class for regions. Parameters ---------- rid : int or str region ID coordinate_frame : `~gwcs.coordinate_frames.CoordinateFrame` Coordinate frame in which the region is defined. """ def __init__(self, rid, coordinate_frame): self._coordinate_system = coordinate_frame self._rid = rid @abc.abstractmethod def __contains__(self, px): """ Determines if a pixel is within a region. Parameters ---------- px : tuple[float, float] A pixel coordinate (x, y) Returns ------- True or False Subclasses must define this method. """ @abc.abstractmethod def scan(self, mask): """ Sets mask values to region id for all pixels within the region. Subclasses must define this method. Parameters ---------- mask : ndarray An array with the shape of the mask to be uised in `~gwcs.selector.RegionsSelector`. Returns ------- mask : ndarray An array where the value of the elements is the region ID. Pixels which are not included in any region are marked with 0 or "". """ class Polygon(Region): """ Represents a 2D polygon region with multiple vertices. Parameters ---------- rid : str polygon id vertices : list of (x,y) tuples or lists The list is ordered in such a way that when traversed in a counterclockwise direction, the enclosed area is the polygon. The last vertex must coincide with the first vertex, minimum 4 vertices are needed to define a triangle coord_frame : str or `~gwcs.coordinate_frames.CoordinateFrame` Coordinate frame in which the polygon is defined. """ def __init__(self, rid, vertices, coord_system="Cartesian"): if len(vertices) < 4: raise ValueError("Expected vertices to be a list of minimum 4 tuples (x,y)") super().__init__(rid, coord_system) # self._shiftx & self._shifty are introduced to shift the bottom-left # corner of the polygon's bounding box to (0,0) as a (hopefully # temporary) workaround to a limitation of the original code that the # polygon must be completely contained in the image. It seems that the # code works fine if we make sure that the bottom-left corner of the # polygon's bounding box has non-negative coordinates. self._shiftx = 0 self._shifty = 0 for vertex in vertices: x, y = vertex if x < self._shiftx: self._shiftx = x if y < self._shifty: self._shifty = y v = [(i - self._shiftx, j - self._shifty) for i, j in vertices] # convert to integer coordinates: self._vertices = np.asarray(list(map(_round_vertex, v))) self._shiftx = int(round(self._shiftx)) self._shifty = int(round(self._shifty)) self._bbox = self._get_bounding_box() self._scan_line_range = list( range(self._bbox[1], self._bbox[3] + self._bbox[1] + 1) ) # constructs a Global Edge Table (GET) in bbox coordinates self._GET = self._construct_ordered_GET() def _get_bounding_box(self): x = self._vertices[:, 0].min() y = self._vertices[:, 1].min() w = self._vertices[:, 0].max() - x h = self._vertices[:, 1].max() - y return (x, y, w, h) def _construct_ordered_GET(self): """ Construct a Global Edge Table (GET) The GET is an OrderedDict. Keys are scan line numbers, ordered from bbox.ymin to bbox.ymax, where bbox is the bounding box of the polygon. Values are lists of edges for which edge.ymin==scan_line_number. Returns ------- GET: OrderedDict {scan_line: [edge1, edge2]} """ # edges is a list of Edge objects which define a polygon # with these vertices edges = self.get_edges() GET = OrderedDict.fromkeys(self._scan_line_range) ymin = np.asarray([e._ymin for e in edges]) for i in self._scan_line_range: ymin_ind = (ymin == i).nonzero()[0] # a hack for incomplete filling .any() fails if 0 is in ymin_ind # if ymin_ind.any(): (yminindlen,) = ymin_ind.shape if yminindlen: GET[i] = [edges[ymin_ind[0]]] for j in ymin_ind[1:]: GET[i].append(edges[j]) return GET def get_edges(self): """ Create a list of Edge objects from vertices """ return [ Edge(name=f"E{i - 1}", start=self._vertices[i - 1], stop=self._vertices[i]) for i in range(1, len(self._vertices)) ] def scan(self, data): """ This is the main function which scans the polygon and creates the mask Parameters ---------- data : array the mask array it has all zeros initially, elements within a region are set to the region's ID Algorithm: - Set the Global Edge Table (GET) - Set y to be the smallest y coordinate that has an entry in GET - Initialize the Active Edge Table (AET) to be empty - For each scan line: 1. Add edges from GET to AET for which ymin==y 2. Remove edges from AET fro which ymax==y 3. Compute the intersection of the current scan line with all edges in the AET 4. Sort on X of intersection point 5. Set elements between pairs of X in the AET to the Edge's ID """ # TODO: # 1. This algorithm does not mark pixels in the top row and left most # column. Pad the initial pixel description on top and left with 1 px # to prevent this. # 2. Currently it uses # intersection of the scan line with edges. If # this is too slow it should use the 1/m increment (replace 3 above) # (or the increment should be removed from the GET entry). # see comments in the __init__ function for the reason of introducing # polygon shifts (self._shiftx & self._shifty). Here we need to shift # it back. (ny, nx) = data.shape y = np.min(list(self._GET.keys())) AET = [] scline = self._scan_line_range[-1] while y <= scline: if y < scline: AET = self.update_AET(y, AET) if self._bbox[2] <= 0: y += 1 continue scan_line = Edge( "scan_line", start=[self._bbox[0], y], stop=[self._bbox[0] + self._bbox[2], y], ) x = [ int(np.ceil(e.compute_AET_entry(scan_line)[1])) for e in AET if e is not None ] xnew = np.sort(x) ysh = y + self._shifty if ysh < 0 or ysh >= ny: y += 1 continue for i, j in zip(xnew[::2], xnew[1::2]): xstart = max(0, i + self._shiftx) xend = min(j + self._shiftx, nx - 1) data[ysh][xstart : xend + 1] = self._rid y += 1 return data def update_AET(self, y, AET): """ Update the Active Edge Table (AET) Add edges from GET to AET for which ymin of the edge is equal to the y of the scan line. Remove edges from AET for which ymax of the edge is equal to y of the scan line. """ edge_cont = self._GET[y] if edge_cont is not None: for edge in edge_cont: if edge._start[1] != edge._stop[1] and edge._ymin == y: AET.append(edge) for edge in AET[::-1]: if edge is not None: if edge._ymax == y: AET.remove(edge) return AET def __contains__(self, px): """even-odd algorithm or something else better should be used""" return ( px[0] >= self._bbox[0] and px[0] <= self._bbox[0] + self._bbox[2] and px[1] >= self._bbox[1] and px[1] <= self._bbox[1] + self._bbox[3] ) class Edge: """ Edge representation. An edge has a "start" and "stop" (x,y) vertices and an entry in the GET table of a polygon. The GET entry is a list of these values: [ymax, x_at_ymin, delta_x/delta_y] """ def __init__(self, name=None, start=None, stop=None, next=None): # noqa: A002 self._start = None if start is not None: self._start = np.asarray(start) self._name = name self._stop = stop if stop is not None: self._stop = np.asarray(stop) self._next = next if self._stop is not None and self._start is not None: if self._start[1] < self._stop[1]: self._ymin = self._start[1] self._yminx = self._start[0] else: self._ymin = self._stop[1] self._yminx = self._stop[0] self._ymax = max(self._start[1], self._stop[1]) self._xmin = min(self._start[0], self._stop[0]) self._xmax = max(self._start[0], self._stop[1]) else: self._ymin = None self._yminx = None self._ymax = None self._xmin = None self._xmax = None self.GET_entry = self.compute_GET_entry() @property def ymin(self): return self._ymin @property def start(self): return self._start @property def stop(self): return self._stop @property def ymax(self): return self._ymax def compute_GET_entry(self): """ Compute the entry in the Global Edge Table [ymax, x@ymin, 1/m] """ if self._start is None: entry = None else: earr = np.asarray([self._start, self._stop]) if np.diff(earr[:, 1]).item() == 0: return None else: entry = [ self._ymax, self._yminx, (np.diff(earr[:, 0]) / np.diff(earr[:, 1])).item(), None, ] return entry def compute_AET_entry(self, edge): """ Compute the entry for an edge in the current Active Edge Table [ymax, x_intersect, 1/m] note: currently 1/m is not used """ x = self.intersection(edge)[0] return [self._ymax, x, self.GET_entry[2]] def __repr__(self): fmt = "" if self._name is not None: fmt += self._name next_edge = self.next while next_edge is not None: fmt += "-->" fmt += next_edge._name next_edge = next_edge.next return fmt @property def next(self): # noqa: A003 return self._next @next.setter def next(self, edge): # noqa: A003 if self._name is None: self._name = edge._name self._stop = edge._stop self._start = edge._start self._next = edge.next else: self._next = edge def intersection(self, edge): u = self._stop - self._start v = edge._stop - edge._start w = self._start - edge._start D = _det(u, v) if abs(D) < _INTERSECT_ATOL: return np.array(self._start) return _det(v, w) / D * u + self._start def is_parallel(self, edge): u = self._stop - self._start v = edge._stop - edge._start return np.allclose(_det(u, v), 0, rtol=0, atol=_INTERSECT_ATOL) def _det(u, v): """ Find the determinant of the matrix formed by the vectors u and v Note: Originally this was computed using a numpy "2D" cross product, however, this functionality has been deprecated and slated for removal. Note: This is marginally faster than using `np.linalg.det([u, v])` by ~10ms during empirical testing """ return u[0] * v[1] - u[1] * v[0] def _round_vertex(v): x, y = v return (int(round(x)), int(round(y)))