# Source code for jwst.skymatch.region

```"""
Polygon filling algorithm.

"""
# Original author: Nadezhda Dencheva
#
# modifications by Mihai Cara: removed functionality not needed for the
# skymatch algorithm and modified the code to be able to work with polygons
# that have vertices with negative coordinates. Polygon vertices are now
# *internally* (to region.py) rounded to integers so that Polygon will not
# crash when input vertices are floats. Fixed a bug in _construct_ordered_GET
# that was causing varying polygon filling for different ordering of the
# vertices. Finally, modified the algorithm to fill the right-most pixels
# as well as top-most row of the polygon.
#
# 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
#
from collections import OrderedDict
import numpy as np

__all__ = ['Region', 'Edge', 'Polygon']
__author__ = 'Nadezhda Dencheva, Mihai Cara'

class ValidationError(Exception):
def __init__(self, message):
self._message = message

def __str__(self):
return self._message

[docs]class Region():
"""
Base class for regions.

Parameters
-------------
rid : int or string
region ID
coordinate_system : astropy.wcs.CoordinateSystem instance or a string
in the context of WCS this would be an instance of wcs.CoordinateSysem
"""

def __init__(self, rid, coordinate_system):
self._coordinate_system = coordinate_system
self._rid = rid

def __contains__(self, x, y):
"""
Determines if a pixel is within a region.

Parameters
----------
x, y : float
x , y values of a pixel

Returns
-------
True or False

Subclasses must define this method.
"""
raise NotImplementedError("__contains__")

[docs]    def scan(self, mask):
"""
Sets mask values to region id for all pixels within the region.
Subclasses must define this method.

Parameters
----------
a byte array with the shape of the observation to be used as a mask

Returns
-------
mask : array where the value of the elements is the region ID or 0 (for
pixels which are not included in any region).
"""
raise NotImplementedError("scan")

[docs]class Polygon(Region):
"""
Represents a 2D polygon region with multiple vertices

Parameters
----------
rid : string
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_system : string
coordinate system

"""

def __init__(self, rid, vertices, coord_system="Cartesian"):
assert len(vertices) >= 4, ("Expected vertices to be "
"a list of minimum 4 tuples (x,y)")
super(Polygon, self).__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, self._bbox + self._bbox + 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()
# 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]]
for j in ymin_ind[1:]:
GET[i].append(edges[j])
return GET

[docs]    def get_edges(self):
"""
Create a list of Edge objects from vertices
"""
edges = []
for i in range(1, len(self._vertices)):
name = 'E' + str(i - 1)
edges.append(Edge(name=name, start=self._vertices[i - 1], stop=self._vertices[i]))
return edges

[docs]    def scan(self, data):
"""
This is the main function which scans the polygon and creates the mask

Parameters
----------
data : 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 <= 0:
y += 1
continue

scan_line = Edge('scan_line', start=[self._bbox, y],
stop=[self._bbox + self._bbox, y])
x = [int(np.ceil(e.compute_AET_entry(scan_line))) 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

[docs]    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 != edge._stop 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 smth else better should be used"""
# minx = self._vertices[:,0].min()
# maxx = self._vertices[:,0].max()
# miny = self._vertices[:,1].min()
# maxy = self._vertices[:,1].max()
return px >= self._bbox and px <= self._bbox + self._bbox and \
px >= self._bbox and px <= self._bbox + self._bbox

[docs]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):
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 < self._stop:
self._ymin = self._start
self._yminx = self._start
else:
self._ymin = self._stop
self._yminx = self._stop
self._ymax = max(self._start, self._stop)
self._xmin = min(self._start, self._stop)
self._xmax = max(self._start, self._stop)
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

[docs]    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

[docs]    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)
return [self._ymax, x, self.GET_entry]

def __repr__(self):
fmt = ""
if self._name is not None:
fmt += self._name
next = self.next
while next is not None:
fmt += "-->"
fmt += next._name
next = next.next
return fmt

@property
def next(self):
return self._next

@next.setter
def next(self, edge):
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

[docs]    def intersection(self, edge):
u = self._stop - self._start
v = edge._stop - edge._start
w = self._start - edge._start
D = np.cross(u, v)

if np.allclose(np.cross(u, v), 0, rtol=0,
atol=1e2 * np.finfo(float).eps):
return np.array(self._start)

return np.cross(v, w) / D * u + self._start

[docs]    def is_parallel(self, edge):
u = self._stop - self._start
v = edge._stop - edge._start
return np.allclose(np.cross(u, v), 0, rtol=0,
atol=1e2 * np.finfo(float).eps)

def _round_vertex(v):
x, y = v
return int(round(x)), int(round(y))
```