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# <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))