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September 24, 2014 15:05
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Part of io_vector SVG import script for Blender
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# ##### BEGIN GPL LICENSE BLOCK ##### | |
# | |
# This program is free software; you can redistribute it and/or | |
# modify it under the terms of the GNU General Public License | |
# as published by the Free Software Foundation; either version 2 | |
# of the License, or (at your option) any later version. | |
# | |
# This program is distributed in the hope that it will be useful, | |
# but WITHOUT ANY WARRANTY; without even the implied warranty of | |
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the | |
# GNU General Public License for more details. | |
# | |
# You should have received a copy of the GNU General Public License | |
# along with this program; if not, write to the Free Software Foundation, | |
# Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. | |
# | |
# ##### END GPL LICENSE BLOCK ##### | |
# <pep8 compliant> | |
"""Convert an Art object to a list of PolyArea objects. | |
""" | |
__author__ = "howard.trickey@gmail.com" | |
import math | |
from . import geom | |
from . import vecfile | |
import itertools | |
class ConvertOptions(object): | |
"""Contains options used to control art to poly conversion. | |
Attributes: | |
subdiv_kind: int - one of a few 'enum' strings: | |
'UNIFORM' - all curves subdivided the same amount | |
'ADAPTIVE' - curves subdivided until flat enough | |
'EVEN' - curves subdivided to make segments of uniform length | |
smoothness: int - controls smoothness of curve conversion: | |
usage depends on subdiv_kind: | |
'UNIFORM': number of times to subdivide | |
'ADAPTIVE': if subdivide a quarter circle bezier this many times, | |
then that is the definition of 'flat enough' | |
'EVEN': proportional to 1/uniform-length-of-segments | |
(so higher numbers mean shorter segments) | |
filled_only: bool - look only at filled faces | |
combine_paths: bool - use union of all subpaths to find | |
boundaries and holes instead of just looking for compound | |
paths in the input file | |
ignore_white: bool - ignore white-filled paths (background, probably) | |
""" | |
def __init__(self): | |
self.subdiv_kind = "UNIFORM" | |
self.smoothness = 1 | |
self.filled_only = True | |
self.combine_paths = False | |
self.ignore_white = True | |
def ArtToPolyAreas(art, options): | |
"""Convert Art object to PolyAreas. | |
Each filled Path in the Art object will produce zero | |
or more PolyAreas. If options.filled_only is False, then stroked paths | |
produce PolyAreas too. | |
If options.ignore_white is True, we assume that white is the background | |
color and not intended to produce polyareas (for example, sometimes there | |
is a filled background rectangle for the entire page). | |
If options.combine_paths is True, use the union of all subpaths of all | |
Paths to look for outer boundaries and holes, else just look insdie each | |
Path separately. | |
Args: | |
art: geom.Art - contains Paths to convert | |
options: ConvertOptions | |
Returns: | |
geom.PolyAreas | |
""" | |
ans = geom.PolyAreas() | |
paths_to_convert = art.paths | |
if options.filled_only: | |
paths_to_convert = [p for p in paths_to_convert if p.filled] | |
if options.ignore_white: | |
paths_to_convert = [p for p in paths_to_convert \ | |
if p.fillpaint != geom.white_paint] | |
# TODO: look for dup paths (both filled and stroked) and dedup | |
# TODO (perhaps): look for a 'background rectangle' and remove | |
if options.subdiv_kind == "EVEN": | |
_SetEvenLength(options, paths_to_convert) | |
if options.combine_paths: | |
combinedpath = geom.Path() | |
combinedpath.subpaths = _flatten([p.subpaths \ | |
for p in paths_to_convert]) | |
areas = PathToPolyAreas(combinedpath, options, ans.points) | |
else: | |
areas = _flatten([PathToPolyAreas(p, options, ans.points) \ | |
for p in paths_to_convert]) | |
ans.polyareas.extend(areas) | |
return ans | |
def PathToPolyAreas(path, options, points): | |
"""Convert Path object to list of PolyArea, sharing points. | |
Like ArtToPolyAreas, but for a single Path in Art. | |
Usually only one PolyArea will be in the returned list, | |
but there may be zero if the path has zero area, | |
and there may be more than one if it contains | |
non-overlapping polygons. | |
(TODO: or if it self-crosses) | |
Args: | |
path: geom.Path - the path to convert | |
options: ConvertOptions | |
points: geom.Points - use this shared points for all areas | |
Returns: | |
list of geom.PolyArea | |
""" | |
subpolyareas = [ | |
_SubpathToPolyArea(sp, options, points, path.fillpaint.color) \ | |
for sp in path.subpaths] | |
subpolyareas = [pa for pa in subpolyareas if len(pa.poly) > 0] | |
return CombineSimplePolyAreas(subpolyareas) | |
def CombineSimplePolyAreas(subpolyareas): | |
"""Combine PolyAreas without holes into ones that may have holes. | |
Take the poly's in each argument PolyArea and find those that | |
are contained in others, so returning a list of PolyAreas that may | |
contain holes. | |
The argument PolyAreas may be reused an modified in forming | |
the result. | |
Args: | |
subpolyareas: list of geom.PolyArea | |
Returns: | |
list of geom.PolyArea | |
""" | |
n = len(subpolyareas) | |
areas = [geom.SignedArea(pa.poly, pa.points) for pa in subpolyareas] | |
lens = list(map(lambda x: len(x.poly), subpolyareas)) | |
cls = dict() | |
for i in range(n): | |
for j in range(n): | |
cls[(i, j)] = _ClassifyPathPairs(subpolyareas[i], subpolyareas[j]) | |
# calculate set cont where (i,j) is in cont if | |
# subpolyareas[i] contains subpolyareas[j] | |
cont = set() | |
for i in range(n): | |
for j in range(n): | |
if i != j and _Contains(i, j, areas, lens, cls): | |
cont.add((i, j)) | |
# now make real PolyAreas, with holes assigned | |
polyareas = [] | |
assigned = set() | |
count = 0 | |
while len(assigned) < n and count < n: | |
for i in range(n): | |
if i in assigned: | |
continue | |
if _IsBoundary(i, n, cont, assigned): | |
# have a new boundary area, i | |
assigned.add(i) | |
holes = _GetHoles(i, n, cont, assigned) | |
pa = subpolyareas[i] | |
for j in holes: | |
pa.AddHole(subpolyareas[j]) | |
polyareas.append(pa) | |
count += 1 | |
if len(assigned) < n: | |
# shouldn't happen | |
print("Whoops, PathToPolyAreas didn't assign all") | |
return polyareas | |
def _SubpathToPolyArea(subpath, options, points, color=(0.0, 0.0, 0.0)): | |
"""Return a PolyArea representing a single subpath. | |
Converts curved segments into approximating line | |
segments. | |
For 'EVEN' subdiv_kind, divides lines too. | |
Ignores zero-length or near zero-length segments. | |
Ensures that face is CCW-oriented. | |
Use the data field of the PolyArea to hold the filling color. | |
Args: | |
subpath: geom.Subpath - the subpath to convert | |
options: ConvertOptions | |
points: geom.Points - used this shared Points for area | |
color: (float, float, float) - rgb of filling color | |
Returns: | |
geom.PolyArea | |
""" | |
face = [] | |
prev = None | |
ans = geom.PolyArea() | |
ans.points = points | |
ans.data = color | |
for seg in subpath.segments: | |
(ty, start, end) = seg[0:3] | |
if not prev or prev != start: | |
face.append(start) | |
if ty == "L": | |
if options.subdiv_kind == "EVEN": | |
lines = _EvenLineDivide(start, end, options) | |
face.extend(lines[1:]) | |
else: | |
face.append(end) | |
prev = end | |
elif ty == "B": | |
approx = Bezier3Approx([start, seg[3], seg[4], end], options) | |
# first point of approx should be current end of face | |
face.extend(approx[1:]) | |
prev = end | |
elif ty == "Q": | |
print("unimplemented segment type Q") | |
elif ty == "A": | |
approx = ArcApprox(start, end, seg[3], seg[4], seg[5], seg[6], | |
options) | |
face.extend(approx[1:]) | |
prev = end | |
else: | |
print("unexpected segment type", ty) | |
# now make a cleaned face in a new PolyArea | |
# with no two successive points approximately equal | |
if len(face) <= 2: | |
# degenerate face, return an empty PolyArea | |
return ans | |
previndex = -1 | |
for i in range(0, len(face)): | |
point = face[i] | |
newindex = ans.points.AddPoint(point) | |
if newindex == previndex or \ | |
i == len(face) - 1 and newindex == ans.poly[0]: | |
continue | |
ans.poly.append(newindex) | |
previndex = newindex | |
# make sure that face is CCW oriented | |
if geom.SignedArea(ans.poly, ans.points) < 0.0: | |
ans.poly.reverse() | |
return ans | |
def Bezier3Approx(cps, options): | |
"""Compute a polygonal approximation to a cubic bezier segment. | |
Args: | |
cps: list of 4 coord tuples - | |
(start, control point 1, control point 2, end) | |
options: ConvertOptions | |
Returns: | |
list of tuples (coordinates) for straight line approximation of the | |
bezier | |
""" | |
if options.subdiv_kind == "EVEN": | |
return _EvenBezier3Approx(cps, options) | |
else: | |
return _SubdivideBezier3Approx(cps, options, 0) | |
def _SetEvenLength(options, paths): | |
"""Use the bounding box of paths to set even_length in options. | |
We want the option.smoothness parameter to control the length | |
of segments that we will try to divide Bezier curves into when | |
using the EVEN method. More smoothness -> shorter length. | |
But the user should think of this in terms of the overall dimensions | |
of their diagram, not in absolute terms. | |
Let's say that smoothness==0 means the length should 1/4 the | |
size of the longest size of the bounding box, and, for general | |
smoothness: | |
longest_side_length | |
even_length = ------------------- | |
4 * (smoothness+1) | |
Args: | |
options: ConvertOptions | |
paths: list of geom.Path | |
Side effects: | |
Sets options.even_length according to above formula | |
""" | |
minx = 1e10 | |
maxx = -1e10 | |
miny = 1e10 | |
maxy = -1e10 | |
for p in paths: | |
for sp in p.subpaths: | |
for seg in sp.segments: | |
endi = 3 if seg[0] == 'A' else len(seg) | |
for (x, y) in seg[1:endi]: | |
minx = min(minx, x) | |
maxx = max(maxx, x) | |
miny = min(miny, y) | |
maxy = max(maxy, y) | |
longest_side_length = max(maxx - minx, maxy - miny) | |
if longest_side_length <= 0: | |
longest_side_length = 1.0 | |
options.even_length = longest_side_length / \ | |
(4.0 * (options.smoothness + 1)) | |
def _EvenBezier3Approx(cps, options): | |
"""Use even segment lengths to approximate a cubic bezier segment. | |
Args: | |
cps: list of 4 coord tuples - | |
(start, control point 1, control point 2, end) | |
options: ConvertOptions | |
Returns: | |
list of tuples (coordinates) for straight line approximation of the | |
bezier | |
""" | |
# This could be made better by recursing a couple of times | |
# but the average of the control polygon and chord length is a good | |
# first order approximation. | |
arc_length = 0.5 * (geom.VecLen(geom.VecSub(cps[3], cps[0])) + \ | |
0.5 * (geom.VecLen(geom.VecSub(cps[1], cps[0])) + \ | |
geom.VecLen(geom.VecSub(cps[2], cps[1])) + \ | |
geom.VecLen(geom.VecSub(cps[3], cps[2])))) | |
# make sure segment lengths are at least as short as even_length | |
numsegs = math.ceil(arc_length / options.even_length) | |
# unless smoothness is zero, make sure Beziers split at least once | |
if options.smoothness > 0 and numsegs == 1: | |
numsegs = 2 | |
ans = [cps[0]] | |
for i in range(1, numsegs): | |
t = i * (1.0 / numsegs) | |
pt = _BezierEval(cps, t) | |
ans.append(pt) | |
ans.append(cps[3]) | |
return ans | |
def _BezierEval(cps, t): | |
"""Evaluate a cubic Bezier at parameter t. | |
Args: | |
cps: list of 4 coord tuples - | |
(start, control point 1, control point 2, end) | |
t: float - parameter (0 -> start, 1 -> end) | |
Returns: | |
tuple (coordinates) of point at parameter t along the curve | |
""" | |
b1 = _Bez3step(cps, 1, t) | |
b2 = _Bez3step(b1, 2, t) | |
b3 = _Bez3step(b2, 3, t) | |
return b3[0] | |
def _EvenLineDivide(start, end, options): | |
"""Like _EvenBezier3Approx, but for line segments. | |
Args: | |
start: tuple - coords of start point | |
end: tuple - coords of end point | |
options: ConvertOptions | |
Returns: | |
list of tuples (coordinates) for pieces of lines. | |
""" | |
line_length = geom.VecLen(geom.VecSub(end, start)) | |
numsegs = math.ceil(line_length / options.even_length) | |
ans = [start] | |
for i in range(1, numsegs): | |
t = i * (1.0 / numsegs) | |
pt = _LinInterp(start, end, t) | |
ans.append(pt) | |
ans.append(end) | |
return ans | |
def _LinInterp(a, b, t): | |
"""Return the point that is t of the way from a to b. | |
Args: | |
a: tuple - coords of start point | |
b: tuple - coords of end point | |
t: float - interpolation parameter | |
Returns: | |
tuple (coordinates) | |
""" | |
n = len(a) # dimension of coordinates | |
ans = [0.0] * n | |
for i in range(n): | |
ans[i] = (1.0 - t) * a[i] + t * b[i] | |
return tuple(ans) | |
# These ratios chosen so that a 4-bezier approximation | |
# to a circle gets subdivided 0, 1, 2, etc. times | |
# when using 'adaptive'. | |
adaptive_ratios = [1.2286, 1.0531, 1.0136, 1.0124, 1.0030, 1.0007] | |
def _SubdivideBezier3Approx(cps, options, recurse_count): | |
"""Use successive bisection to approximate a cubic bezier segment. | |
Args: | |
cps: list of 4 coord tuples - | |
(start, control point 1, control point 2, end) | |
options: ConvertOptions | |
recurse_count: int - how deep have we recursed so far | |
Returns: | |
list of tuples (coordinates) for straight line approximation of | |
the bezier | |
""" | |
(vs, _, _, ve) = b0 = cps | |
subdivide_num = options.smoothness | |
adaptive = (options.subdiv_kind == "ADAPTIVE") | |
if recurse_count >= subdivide_num and not adaptive: | |
return [vs, ve] | |
alpha = 0.5 | |
b1 = _Bez3step(b0, 1, alpha) | |
b2 = _Bez3step(b1, 2, alpha) | |
b3 = _Bez3step(b2, 3, alpha) | |
if adaptive: | |
straightlen = geom.VecLen(geom.VecSub(ve, vs)) | |
if straightlen < geom.DISTTOL: | |
return [vs, ve] | |
approxcurvelen = \ | |
geom.VecLen(geom.VecSub(cps[1], cps[0])) + \ | |
geom.VecLen(geom.VecSub(cps[2], cps[1])) + \ | |
geom.VecLen(geom.VecSub(cps[3], cps[2])) | |
ratio = approxcurvelen / straightlen | |
if subdivide_num < 0: | |
subdivide_num = 0 | |
elif subdivide_num >= len(adaptive_ratios): | |
subdivide_num = len(adaptive_ratios) - 1 | |
aratio = adaptive_ratios[subdivide_num] | |
if ratio <= aratio: | |
return [vs, ve] | |
else: | |
if subdivide_num - recurse_count == 1: | |
# recursive case would do this too, but optimize a bit | |
return [vs, b3[0], ve] | |
left = [b0[0], b1[0], b2[0], b3[0]] | |
right = [b3[0], b2[1], b1[2], b0[3]] | |
ansleft = _SubdivideBezier3Approx(left, options, recurse_count + 1) | |
ansright = _SubdivideBezier3Approx(right, options, recurse_count + 1) | |
# ansleft ends with b3[0] and ansright starts with it | |
return ansleft + ansright[1:] | |
def _Bez3step(b, r, alpha): | |
"""Cubic bezier step r for interpolating at parameter alpha. | |
Steps 1, 2, 3 are applied in succession to the 4 points | |
representing a bezier segment, making a triangular arrangement | |
of interpolating the previous step's output, so that after | |
step 3 we have the point that is at parameter alpha of the segment. | |
The left-half control points will be on the left side of the triangle | |
and the right-half control points will be on the right side of the | |
triangle. | |
Args: | |
b: list of tuples (coordinates), of length 5-r | |
r: int - step number (0=orig points and cps) | |
alpha: float - value in range 0..1 where want to divide at | |
Returns: | |
list of length 4-r, of vertex coordinates, giving linear interpolations | |
at parameter alpha between successive pairs of points in b | |
""" | |
ans = [] | |
n = len(b[0]) # dimension of coordinates | |
beta = 1 - alpha | |
for i in range(0, 4 - r): | |
# find c, alpha of the way from b[i] to b[i+1] | |
t = [0.0] * n | |
for d in range(n): | |
t[d] = b[i][d] * beta + b[i + 1][d] * alpha | |
ans.append(tuple(t)) | |
return ans | |
def ArcApprox(start, end, rad, xrot, large_arc, ccw, options): | |
"""Approximate an elliptical arc with line segments, according to options. | |
Implementation follows notes in F.6 of SVG spec. | |
Args: | |
start: (float, float) - starting point | |
end: (float, float) - ending point | |
rad: (float, float) - x-radius, y-radius | |
xrot: float - angle of rotation from x-axis, in degrees | |
large_arc: bool - should we take a larger arc? | |
ccw: bool - does arc proceed counter-clockwise? | |
options: ConvertOptions | |
Returns: | |
list of tuples (coordinates) for straight line approximation of arc | |
""" | |
if start == end: | |
return [start] | |
(rx, ry) = rad | |
if rx == 0.0 or ry == 0.0: | |
# treat same as line | |
if options.subdiv_kind == "EVEN": | |
return _EvenLineDivide(start, end, options) | |
else: | |
return [start, end] | |
rx = abs(rx) | |
ry = abs(ry) | |
(x1, y1) = start | |
(x2, y2) = end | |
# Convert to center parameterization. | |
# Primed coords: origin at midpoint of (start, end) | |
# followed by rotaiton to line up coord axes with ellipse axes | |
x1p = (x1 - x2) / 2.0 | |
y1p = (y1 - y2) / 2.0 | |
phi = xrot * math.pi / 180.0 | |
cos_phi = math.cos(phi) | |
sin_phi = math.sin(phi) | |
(x1p, y1p) = (cos_phi * x1p + sin_phi * y1p, \ | |
-sin_phi * x1p + cos_phi * y1p) | |
# perhaps scale up rx, ry to make ellipse achievable | |
lam = (x1p ** 2) / rx ** 2 + (y1p ** 2) / ry ** 2 | |
if lam > 1.0: | |
slam = math.sqrt(lam) | |
rx *= slam | |
ry *= slam | |
cf2 = (rx ** 2 * ry ** 2 - rx ** 2 * y1p ** 2 - ry ** 2 * x1p ** 2) / \ | |
(rx ** 2 * y1p ** 2 + ry ** 2 * x1p ** 2) | |
if cf2 <= 0.0: | |
cfactor = 0.0 | |
else: | |
cfactor = math.sqrt(cf2) | |
if large_arc == ccw: | |
cfactor = -cfactor | |
cxp = cfactor * rx * y1p / ry | |
cyp = -cfactor * ry * x1p / rx | |
cx = cos_phi * cxp - sin_phi * cyp + (x1 + x2) / 2.0 | |
cy = sin_phi * cxp + cos_phi * cyp + (y1 + y2) / 2.0 | |
theta1 = _Angle((1.0, 0.0), ((x1p - cxp) / rx, (y1p - cyp) / ry)) | |
delta_theta = _Angle(((x1p - cxp) / rx, (y1p - cyp) / ry), | |
((-x1p - cxp) / rx, (-y1p - cyp) / ry)) | |
if not ccw and delta_theta > 0.0: | |
delta_theta -= 2 * math.pi | |
elif ccw and delta_theta < 0.0: | |
delta_theta += 2 * math.pi | |
if abs(delta_theta) < 1e-5: | |
# shouldn't happen | |
return [start, end] | |
# Now arc is: | |
# (x, y) = M * col(rx * cos theta, ry * sin theta) + col(cx, cy) | |
# where theta goes from theta1 to theta1 + delta_theta | |
# and M is rotation matrix for phi | |
# Let's ignore the fact that the axes may have different lengths | |
# and just divide delta_theta into the right number of segments | |
# to satisfy the smoothness options. | |
if options.subdiv_kind == "EVEN": | |
# arc_length = pi*d * fraction of circle represented by delta_theta | |
arc_length = abs(delta_theta * (rx + ry) / 2.0) | |
numsegs = math.ceil(arc_length / options.even_length) | |
else: | |
# for smoothness 0, have 1 segment per quarter circle | |
# and double for each smoothness increment after that | |
numsegs = (2 ** options.smoothness) * \ | |
math.ceil(abs(delta_theta) / (math.pi * 2.0)) | |
theta_incr = delta_theta / numsegs | |
ans = start | |
theta = theta1 | |
endtheta = theta1 + delta_theta | |
ans = [start] | |
# end condition should be theta ~== endtheta but also | |
# should be no more than numsegs iters | |
for i in range(numsegs): | |
theta = theta + theta_incr | |
if abs(theta - endtheta) < 1e-5: | |
break | |
cos_theta = math.cos(theta) | |
sin_theta = math.sin(theta) | |
x = cos_phi * rx * cos_theta - sin_phi * ry * sin_theta + cx | |
y = sin_phi * rx * cos_theta + cos_phi * ry * sin_theta + cy | |
ans.append((x, y)) | |
ans.append(end) | |
return ans | |
def _Angle(u, v): | |
"""Return angle between two vectors. | |
Args: | |
u: (float, float) | |
v: (float, float) | |
Returns: | |
float - angle in radians between u and v, where | |
it is +/- depending on sign of ux * vy - uy * vx | |
""" | |
(ux, uy) = u | |
(vx, vy) = v | |
costheta = (ux * vx + uy * vy) / \ | |
(math.sqrt(ux ** 2 + uy ** 2) * math.sqrt(vx ** 2 + vy ** 2)) | |
if costheta > 1.0: | |
costheta = 1.0 | |
if costheta < -1.0: | |
costheta = -1.0 | |
theta = math.acos(costheta) | |
if ux * vy - uy * vx < 0.0: | |
theta = -theta | |
return theta | |
def _ClassifyPathPairs(a, b): | |
"""Classify vertices of path b with respect to path a. | |
Args: | |
a: geom.PolyArea - the test outer face (ignoring holes) | |
b: geom.PolyArea - the test inner face (ignoring holes) | |
Returns: | |
(int, int) - first is #verts of b inside a, second is #verts of b on a | |
""" | |
num_in = 0 | |
num_on = 0 | |
for v in b.poly: | |
vp = b.points.pos[v] | |
k = geom.PointInside(vp, a.poly, a.points) | |
if k > 0: | |
num_in += 1 | |
elif k == 0: | |
num_on += 1 | |
return (num_in, num_on) | |
def _Contains(i, j, areas, lens, cls): | |
"""Return True if path i contains majority of vertices of path j. | |
Args: | |
i: index of supposed containing path | |
j: index of supposed contained path | |
areas: list of floats - areas of all the paths | |
lens: list of ints - lenths of each of the paths | |
cls: dict - maps pairs to result of _ClassifyPathPairs | |
Returns: | |
bool - True if path i contains at least 55% of j's vertices | |
""" | |
if i == j: | |
return False | |
(jinsidei, joni) = cls[(i, j)] | |
if jinsidei == 0 or joni == lens[j] or \ | |
float(jinsidei) / float(lens[j]) < 0.55: | |
return False | |
else: | |
(insidej, _) = cls[(j, i)] | |
if float(insidej) / float(lens[i]) > 0.55: | |
return areas[i] > areas[j] # tie breaker | |
else: | |
return True | |
def _IsBoundary(i, n, cont, assigned): | |
"""Is path i a boundary, given current assignment? | |
Args: | |
i: int - index of a path to test for boundary possiblity | |
n: int - total number of paths | |
cont: dict - maps path pairs (i,j) to _Contains(i,j,...) result | |
assigned: set of int - which paths are already assigned | |
Returns: | |
bool - True if there is no unassigned j, j!=i, such that | |
path j contains path i | |
""" | |
for j in range(0, n): | |
if j == i or j in assigned: | |
continue | |
if (j, i) in cont: | |
return False | |
return True | |
def _GetHoles(i, n, cont, assigned): | |
"""Find holes for path i: i.e., unassigned paths directly inside it. | |
Directly inside means there is not some other unassigned path k | |
such that path such that path i contains k and path k contains j. | |
(If such a k is already assigned, then its islands have been assigned too.) | |
Args: | |
i: int - index of a boundary path | |
n: int - total number of paths | |
cont: dict - maps path pairs (i,j) to _Contains(i,j,...) result | |
assigned: set of int - which paths are already assigned | |
Returns: | |
list of int - indices of paths that are islands | |
Side Effect: | |
Adds island indices to assigned set. | |
""" | |
isls = [] | |
for j in range(0, n): | |
if j in assigned: | |
continue # catches i==j too, since i is assigned by now | |
if (i, j) in cont: | |
directly = True | |
for k in range(0, n): | |
if k == j or k in assigned: | |
continue | |
if (i, k) in cont and (k, j) in cont: | |
directly = False | |
break | |
if directly: | |
isls.append(j) | |
assigned.add(j) | |
return isls | |
def _flatten(l): | |
"""Return a flattened shallow list. | |
Args: | |
l : list of lists | |
Returns: | |
list - concatenation of sublists of l | |
""" | |
return list(itertools.chain.from_iterable(l)) |
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