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"""
This is a collection of utilities used by the ``svglib`` code module.
"""
import re
from math import acos, ceil, copysign, cos, degrees, fabs, hypot, radians, sin, sqrt
from reportlab.graphics.shapes import mmult, rotate, translate, transformPoint
def split_floats(op, min_num, value):
"""Split `value`, a list of numbers as a string, to a list of float numbers.
Also optionally insert a `l` or `L` operation depending on the operation
and the length of values.
Example: with op='m' and value='10,20 30,40,' the returned value will be
['m', [10.0, 20.0], 'l', [30.0, 40.0]]
"""
floats = [float(seq) for seq in re.findall(r'(-?\d*\.?\d*(?:[eE][+-]?\d+)?)', value) if seq]
res = []
for i in range(0, len(floats), min_num):
if i > 0 and op in {'m', 'M'}:
op = 'l' if op == 'm' else 'L'
res.extend([op, floats[i:i + min_num]])
return res
def split_arc_values(op, value):
float_re = r'(-?\d*\.?\d*(?:[eE][+-]?\d+)?)'
flag_re = r'([1|0])'
# 3 numb, 2 flags, 1 coord pair
a_seq_re = r'[\s,]*'.join([
float_re, float_re, float_re, flag_re, flag_re, float_re, float_re
]) + r'[\s,]*'
res = []
for seq in re.finditer(a_seq_re, value.strip()):
res.extend([op, [float(num) for num in seq.groups()]])
return res
def normalise_svg_path(attr):
"""Normalise SVG path.
This basically introduces operator codes for multi-argument
parameters. Also, it fixes sequences of consecutive M or m
operators to MLLL... and mlll... operators. It adds an empty
list as argument for Z and z only in order to make the resul-
ting list easier to iterate over.
E.g. "M 10 20, M 20 20, L 30 40, 40 40, Z"
-> ['M', [10, 20], 'L', [20, 20], 'L', [30, 40], 'L', [40, 40], 'Z', []]
"""
# operator codes mapped to the minimum number of expected arguments
ops = {
'A': 7, 'a': 7,
'Q': 4, 'q': 4, 'T': 2, 't': 2, 'S': 4, 's': 4,
'M': 2, 'L': 2, 'm': 2, 'l': 2, 'H': 1, 'V': 1,
'h': 1, 'v': 1, 'C': 6, 'c': 6, 'Z': 0, 'z': 0,
}
op_keys = ops.keys()
# do some preprocessing
result = []
groups = re.split('([achlmqstvz])', attr.strip(), flags=re.I)
op = None
for item in groups:
if item.strip() == '':
continue
if item in op_keys:
# fix sequences of M to one M plus a sequence of L operators,
# same for m and l.
if item == 'M' and item == op:
op = 'L'
elif item == 'm' and item == op:
op = 'l'
else:
op = item
if ops[op] == 0: # Z, z
result.extend([op, []])
else:
if op.lower() == 'a':
result.extend(split_arc_values(op, item))
else:
result.extend(split_floats(op, ops[op], item))
op = result[-2] # Remember last op
return result
def convert_quadratic_to_cubic_path(q0, q1, q2):
"""
Convert a quadratic Bezier curve through q0, q1, q2 to a cubic one.
"""
c0 = q0
c1 = (q0[0] + 2 / 3 * (q1[0] - q0[0]), q0[1] + 2 / 3 * (q1[1] - q0[1]))
c2 = (c1[0] + 1 / 3 * (q2[0] - q0[0]), c1[1] + 1 / 3 * (q2[1] - q0[1]))
c3 = q2
return c0, c1, c2, c3
# ***********************************************
# Helper functions for elliptical arc conversion.
# ***********************************************
def vector_angle(u, v):
d = hypot(*u) * hypot(*v)
if d == 0:
return 0
c = (u[0] * v[0] + u[1] * v[1]) / d
if c < -1:
c = -1
elif c > 1:
c = 1
s = u[0] * v[1] - u[1] * v[0]
return degrees(copysign(acos(c), s))
def end_point_to_center_parameters(x1, y1, x2, y2, fA, fS, rx, ry, phi=0):
'''
See http://www.w3.org/TR/SVG/implnote.html#ArcImplementationNotes F.6.5
note that we reduce phi to zero outside this routine
'''
rx = fabs(rx)
ry = fabs(ry)
# step 1
if phi:
phi_rad = radians(phi)
sin_phi = sin(phi_rad)
cos_phi = cos(phi_rad)
tx = 0.5 * (x1 - x2)
ty = 0.5 * (y1 - y2)
x1d = cos_phi * tx - sin_phi * ty
y1d = sin_phi * tx + cos_phi * ty
else:
x1d = 0.5 * (x1 - x2)
y1d = 0.5 * (y1 - y2)
# step 2
# we need to calculate
# (rx*rx*ry*ry-rx*rx*y1d*y1d-ry*ry*x1d*x1d)
# -----------------------------------------
# (rx*rx*y1d*y1d+ry*ry*x1d*x1d)
#
# that is equivalent to
#
# rx*rx*ry*ry
# = ----------------------------- - 1
# (rx*rx*y1d*y1d+ry*ry*x1d*x1d)
#
# 1
# = -------------------------------- - 1
# x1d*x1d/(rx*rx) + y1d*y1d/(ry*ry)
#
# = 1/r - 1
#
# it turns out r is what they recommend checking
# for the negative radicand case
r = x1d * x1d / (rx * rx) + y1d * y1d / (ry * ry)
if r > 1:
rr = sqrt(r)
rx *= rr
ry *= rr
r = x1d * x1d / (rx * rx) + y1d * y1d / (ry * ry)
r = 1 / r - 1
elif r != 0:
r = 1 / r - 1
if -1e-10 < r < 0:
r = 0
r = sqrt(r)
if fA == fS:
r = -r
cxd = (r * rx * y1d) / ry
cyd = -(r * ry * x1d) / rx
# step 3
if phi:
cx = cos_phi * cxd - sin_phi * cyd + 0.5 * (x1 + x2)
cy = sin_phi * cxd + cos_phi * cyd + 0.5 * (y1 + y2)
else:
cx = cxd + 0.5 * (x1 + x2)
cy = cyd + 0.5 * (y1 + y2)
# step 4
theta1 = vector_angle((1, 0), ((x1d - cxd) / rx, (y1d - cyd) / ry))
dtheta = vector_angle(
((x1d - cxd) / rx, (y1d - cyd) / ry),
((-x1d - cxd) / rx, (-y1d - cyd) / ry)
) % 360
if fS == 0 and dtheta > 0:
dtheta -= 360
elif fS == 1 and dtheta < 0:
dtheta += 360
return cx, cy, rx, ry, -theta1, -dtheta
def bezier_arc_from_centre(cx, cy, rx, ry, start_ang=0, extent=90):
if abs(extent) <= 90:
nfrag = 1
frag_angle = extent
else:
nfrag = ceil(abs(extent) / 90)
frag_angle = extent / nfrag
if frag_angle == 0:
return []
frag_rad = radians(frag_angle)
half_rad = frag_rad * 0.5
kappa = abs(4 / 3 * (1 - cos(half_rad)) / sin(half_rad))
if frag_angle < 0:
kappa = -kappa
point_list = []
theta1 = radians(start_ang)
start_rad = theta1 + frag_rad
c1 = cos(theta1)
s1 = sin(theta1)
for i in range(nfrag):
c0 = c1
s0 = s1
theta1 = start_rad + i * frag_rad
c1 = cos(theta1)
s1 = sin(theta1)
point_list.append((cx + rx * c0,
cy - ry * s0,
cx + rx * (c0 - kappa * s0),
cy - ry * (s0 + kappa * c0),
cx + rx * (c1 + kappa * s1),
cy - ry * (s1 - kappa * c1),
cx + rx * c1,
cy - ry * s1))
return point_list
def bezier_arc_from_end_points(x1, y1, rx, ry, phi, fA, fS, x2, y2):
if (x1 == x2 and y1 == y2):
# From https://www.w3.org/TR/SVG/implnote.html#ArcImplementationNotes:
# If the endpoints (x1, y1) and (x2, y2) are identical, then this is
# equivalent to omitting the elliptical arc segment entirely.
return []
if phi:
# Our box bezier arcs can't handle rotations directly
# move to a well known point, eliminate phi and transform the other point
mx = mmult(rotate(-phi), translate(-x1, -y1))
tx2, ty2 = transformPoint(mx, (x2, y2))
# Convert to box form in unrotated coords
cx, cy, rx, ry, start_ang, extent = end_point_to_center_parameters(
0, 0, tx2, ty2, fA, fS, rx, ry
)
bp = bezier_arc_from_centre(cx, cy, rx, ry, start_ang, extent)
# Re-rotate by the desired angle and add back the translation
mx = mmult(translate(x1, y1), rotate(phi))
res = []
for x1, y1, x2, y2, x3, y3, x4, y4 in bp:
res.append(
transformPoint(mx, (x1, y1)) + transformPoint(mx, (x2, y2)) +
transformPoint(mx, (x3, y3)) + transformPoint(mx, (x4, y4))
)
return res
else:
cx, cy, rx, ry, start_ang, extent = end_point_to_center_parameters(
x1, y1, x2, y2, fA, fS, rx, ry
)
return bezier_arc_from_centre(cx, cy, rx, ry, start_ang, extent)
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