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Vector_to_Coordinate.py
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Vector_to_Coordinate.py
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import re
import math
"""
Sources for approximation of arc to bezier curve:
1.) https://www.spaceroots.org/documents/ellipse/elliptical-arc.pdf
2.) https://www.joecridge.me/content/pdf/bezier-arcs.pdf
Source code for converting arc to bezier curves:
1.) https://github.com/fontello/svgpath
"""
# Class that contains methods for converting vector shape into set of
# coordinates
class analysis_methods():
def __init__(self, parent, res=False, err=False, decimal=5):
self._parent = parent
if not res:
self.RESOLUTION = 1
else:
self.RESOLUTION = res
if not err:
self.RESOLUTION_ERR = 0.01
else:
self.RESOLUTION_ERR = err
self.FLOAT_DECIMAL_PNTS = decimal
VALID_ARGUMENTS = [
["cx", "cy", "r"], # circle
["cx", "cy", "rx", "ry"], # ellipse
["x1", "y1", "x2", "y2"], # line
["d"], # path
[], # polygon | same as polyline
["points"], # polyline
["x", "y", "width", "height"], # rect
]
@staticmethod
def check_args(const, args):
for i in analysis_methods.VALID_ARGUMENTS[const]:
if i not in args:
raise ValueError("Invalid SVG element arguments (0)")
elif args[i] == "":
raise ValueError("Empty SVG element argument")
@staticmethod
def float_args(const, args):
for i in analysis_methods.VALID_ARGUMENTS[const]:
args[i] = float(args[i])
if i not in args:
raise ValueError("Invalid SVG element arguments (1)")
elif args[i] == "":
raise ValueError("Empty SVG element argument")
else:
args[i] = float(args[i])
@staticmethod
def dist(x1, y1, x2, y2):
return math.sqrt(math.pow(x2 - x1, 2) + math.pow(y2 - y1, 2))
def circle(self, args):
const = 0
analysis_methods.float_args(const, args)
iv = float(self.RESOLUTION) / args["r"]
deg = 0
point_array = [[]]
while deg < 2 * math.pi:
point_array[0].append(
[math.cos(deg) * args["r"] + args["cx"], math.sin(deg) * args["r"] + args["cy"]])
deg += iv
return point_array
@staticmethod
def ellipse_coord(a, b, x):
return math.sqrt(
(math.pow(
float(a) *
b,
2) -
math.pow(
float(b) *
x,
2)) /
math.pow(
a,
2))
def approx_ellipse(self, n1, n2, a, b, xi, yi):
xx = xi - (n2 + n1) / 2.0
yx = self.ellipse_coord(a, b, xx)
dist = self.dist(xi, yi, xx, yx)
if math.fabs(dist - self.RESOLUTION) / \
self.RESOLUTION <= self.RESOLUTION_ERR: # condition
return [xx, yx]
else:
if dist > self.RESOLUTION:
n2 = (n2 + n1) / 2.0
else:
n1 = (n2 + n1) / 2.0
return self.approx_ellipse(n1, n2, a, b, xi, yi)
def ellipse(self, args):
const = 1
analysis_methods.float_args(const, args)
xi = args["rx"] / 2.0
point_arr = [[xi, 0]]
while point_arr[-1][0] > 0:
pnt = self.approx_ellipse(0,
self.RESOLUTION,
args["rx"] / 2.0,
args["ry"] / 2.0,
point_arr[-1][0],
point_arr[-1][1])
point_arr.append(pnt)
point_arr[-1] = [0, args["ry"] / 2] # Quadrant 1 of ellipse
l = len(point_arr) - 1
i = l
while i >= 0: # Flip quadrant 1 over y-axis
if i != l:
point_arr.append([point_arr[i][0] * -1, point_arr[i][1]])
i -= 1
l = len(point_arr) - 1
i = l
while i >= 0: # Flip quadrant 1 over x-axis
if i != l and i != 0:
point_arr.append([point_arr[i][0] + args["cx"],
point_arr[i][1] * -1 + args["cy"]])
point_arr[i][0] += args["cx"]
point_arr[i][1] += args["cy"]
i -= 1
return [point_arr]
@staticmethod
def line(args):
const = 2
analysis_methods.check_args(const, args)
return [[
[float(args["x1"]), float(args["y1"])],
[float(args["x2"]), float(args["y2"])],
]]
@staticmethod
def path_break_args(arg):
ret = re.findall("([-]?[0-9]+[\.]?[0-9]*)[^-0-9]*", arg)
i = 0
for x in ret:
ret[i] = float(ret[i])
i += 1
return ret
@staticmethod
def calc_cubic_bezier(t, arg, w):
Ax = ((1 - t) * w[0]) + (t * arg[0])
Ay = ((1 - t) * w[1]) + (t * arg[1])
Bx = ((1 - t) * arg[0]) + (t * arg[2])
By = ((1 - t) * arg[1]) + (t * arg[3])
Cx = ((1 - t) * arg[2]) + (t * arg[4])
Cy = ((1 - t) * arg[3]) + (t * arg[5])
Dx = ((1 - t) * Ax) + (t * Bx)
Dy = ((1 - t) * Ay) + (t * By)
Ex = ((1 - t) * Bx) + (t * Cx)
Ey = ((1 - t) * By) + (t * Cy)
return [((1 - t) * Dx) + (t * Ex), ((1 - t) * Dy) + (t * Ey)]
@staticmethod
def calc_quadratic_bezier(t, arg, w):
x = (w[0] - 2 * arg[0] + arg[2]) * math.pow(t, 2) + \
(2 * arg[0] - 2 * w[0]) * t + w[0]
y = (w[1] - 2 * arg[1] + arg[3]) * math.pow(t, 2) + \
(2 * arg[1] - 2 * w[1]) * t + w[1]
return [x, y]
def approx_bezier(self, type, t1, t2, arg, x, y, xi, yi, res=False):
if not res:
res = self.RESOLUTION_ERR
coord = getattr(self, "calc_" + type +
"_bezier")((t2 + t1) / 2.0, arg, [xi, yi])
dist = self.dist(x, y, coord[0], coord[1])
if t2 == 1 and dist < self.RESOLUTION:
return [1, [arg[-2], arg[-1]]]
if math.fabs(dist - self.RESOLUTION) / \
self.RESOLUTION <= res: # condition
return [(t2 + t1) / 2.0, coord]
else:
if dist > self.RESOLUTION:
t2 = (t2 + t1) / 2.0
else:
t1 = (t2 + t1) / 2.0
return self.approx_bezier(type, t1, t2, arg, x, y, xi, yi, res)
def generate_bezier(self, w, arg, first_coordinate):
# Algorithm Backup: Approximate all points
t = 0
dist = 0
last_coordinate = [w[-1][0], w[-1][1]]
while t == 0 or dist > self.RESOLUTION:
approximation = self.approx_bezier(
"cubic",
t,
1,
arg,
last_coordinate[0],
last_coordinate[1],
first_coordinate[0],
first_coordinate[1])
t = approximation[0]
last_coordinate = approximation[1]
w.append(approximation[1])
dist = self.dist(
arg[4],
arg[5],
approximation[1][0],
approximation[1][1])
w.append([arg[4], arg[5]])
# Algorithm 2: Use approximation from first interval to extrapolate
# approximation = self.approx_bezier("cubic", 0, 1, arg, w[-1][0], w[-1][1], w[-1][0], w[-1][1])[0]
# dist = 0
# i = 1
# while i == 1 or dist > self.RESOLUTION:
# new_coordinate = self.calc_cubic_bezier(i * approximation, arg, first_coordinate)
# dist = self.dist(arg[4], arg[5], new_coordinate[0], new_coordinate[1])
# w.append(new_coordinate)
# i += 1
# w.append([arg[4], arg[5]])
@staticmethod
def unit_vector_angle(ux, uy, vx, vy):
sign = -1 if (ux * vy - uy * vx < 0) else 1
dot = ux * vx + uy * vy
if dot > 1.0:
dot = 1.0
if dot < -1.0:
dot = -1.0
return sign * math.acos(dot)
@staticmethod
def get_arc_center(x1, y1, x2, y2, fa, fs, rx, ry, sin_phi, cos_phi):
TAU = math.pi * 2.0
x1p = cos_phi * (x1 - x2) / 2.0 + sin_phi * (y1 - y2) / 2.0
y1p = -sin_phi * (x1 - x2) / 2.0 + cos_phi * (y1 - y2) / 2.0
rx_sq = rx * rx
ry_sq = ry * ry
x1p_sq = x1p * x1p
y1p_sq = y1p * y1p
radicant = (rx_sq * ry_sq) - (rx_sq * y1p_sq) - (ry_sq * x1p_sq)
if (radicant < 0):
radicant = 0
radicant /= (rx_sq * y1p_sq) + (ry_sq * x1p_sq)
radicant = math.sqrt(radicant) * (-1 if fa == fs else 1)
cxp = radicant * rx / ry * y1p
cyp = radicant * -ry / rx * x1p
cx = cos_phi * cxp - sin_phi * cyp + (x1 + x2) / 2
cy = sin_phi * cxp + cos_phi * cyp + (y1 + y2) / 2
v1x = (x1p - cxp) / rx
v1y = (y1p - cyp) / ry
v2x = (-x1p - cxp) / rx
v2y = (-y1p - cyp) / ry
theta1 = analysis_methods.unit_vector_angle(1, 0, v1x, v1y)
delta_theta = analysis_methods.unit_vector_angle(v1x, v1y, v2x, v2y)
if (fs == False and delta_theta > 0):
delta_theta -= TAU
if (fs and delta_theta < 0):
delta_theta += TAU
return [cx, cy, theta1, delta_theta]
@staticmethod
def approximate_unit_arc(theta1, delta_theta):
alpha = 4.0 / 3.0 * math.tan(delta_theta / 4.0)
x1 = math.cos(theta1)
y1 = math.sin(theta1)
x2 = math.cos(theta1 + delta_theta)
y2 = math.sin(theta1 + delta_theta)
return [
x1,
y1,
x1 - y1 * alpha,
y1 + x1 * alpha,
x2 + y2 * alpha,
y2 - x2 * alpha,
x2,
y2]
@staticmethod
def arc_to_bezier(x1, y1, x2, y2, fa, fs, rx, ry, phi):
TAU = math.pi * 2.0
sin_phi = math.sin(phi * TAU / 360)
cos_phi = math.cos(phi * TAU / 360)
x1p = cos_phi * (x1 - x2) / 2 + sin_phi * (y1 - y2) / 2
y1p = -sin_phi * (x1 - x2) / 2 + cos_phi * (y1 - y2) / 2
if (x1p == 0 and y1p == 0) or (rx == 0 or ry == 0):
return []
rx = math.fabs(rx)
ry = math.fabs(ry)
y = (x1p * x1p) / (rx * rx) + (y1p * y1p) / (ry * ry)
if (y > 1):
rx *= math.sqrt(y)
ry *= math.sqrt(y)
cc = analysis_methods.get_arc_center(
x1, y1, x2, y2, fa, fs, rx, ry, sin_phi, cos_phi)
result = []
theta1 = cc[2]
delta_theta = cc[3]
segments = max([int(math.ceil(math.fabs(delta_theta) / (TAU / 4))), 1])
delta_theta /= segments
for i in range(0, segments):
result.append(
analysis_methods.approximate_unit_arc(
theta1, delta_theta))
theta1 += delta_theta
return_arr = []
for curve in result:
for i in range(0, len(curve), 2):
x = curve[i]
y = curve[i + 1]
x *= rx
y *= ry
xp = cos_phi * x - sin_phi * y
yp = sin_phi * x + cos_phi * y
curve[i] = xp + cc[0]
curve[i + 1] = yp + cc[1]
return_arr.append(curve)
return return_arr
def convert_rel(self, rel, arg, w):
if rel:
rel = False
i = 0
for c in arg:
if i % 2 == 0: # x-axis
arg[i] += w[-1][0]
else: # y-axis
arg[i] += w[-1][1]
i += 1
def path(self, args):
const = 3
analysis_methods.check_args(const, args)
_args = re.findall("(([MLHVCSQTAZmlhvcsqtaz])[-0-9, \.]*)", args["d"])
array = []
w = False
last_command = False
index = -1
skip_flag = False
for x in _args:
index += 1
x = list(x)
rel = False
if not x[1].isupper():
x[1] = x[1].upper()
rel = True
arg = analysis_methods.path_break_args(x[0][1:])
if x[1] == "M":
if not w:
w = []
elif len(w) > 0:
array.append(w)
w = []
if len(arg) % 2 != 0:
raise ValueError("Invalid 'M' value in path SVG element")
else:
if len(arg) == 2:
if not rel or len(array) == 0 or len(array[-1]) == 0:
w.append([arg[0], arg[1]])
else:
w.append([arg[0] + array[-1][-1][0],
arg[1] + array[-1][-1][1]])
else:
cmd = "m" if rel else "M"
_args.insert(index +
1, [cmd +
" " +
" ".join([str('{:.' +
str(self.FLOAT_DECIMAL_PNTS) +
'f}').format(n) for n in arg[0:2]]), cmd])
cmd = "l" if rel else "L"
for u in range(2, len(arg), 2):
_args.insert(index +
1 +
u /
2, [cmd +
" " +
" ".join([str('{:.' +
str(self.FLOAT_DECIMAL_PNTS) +
'f}').format(n) for n in arg[u:u +
2]]), cmd])
elif x[1] == "Z" and w:
w_len = len(w)
if w_len >= 3:
w.append(w[0])
array.append(w)
w = []
else:
if not w:
w = []
w.append([0.0, 0.0])
elif len(w) == 0:
w.append(arr[-1][-1])
if x[1] == "H":
if len(arg) != 1:
raise ValueError(
"Invalid 'H' value in path SVG element")
else:
if not rel:
w.append([arg[0], w[-1][1]])
else:
w.append([w[-1][0] + arg[0], w[-1][1]])
elif x[1] == "V":
if len(arg) != 1:
raise ValueError(
"Invalid 'V' value in path SVG element")
else:
if not rel:
w.append([w[-1][0], arg[0]])
else:
w.append([w[-1][0], w[-1][1] + arg[0]])
elif x[1] == "A":
if len(arg) != 7:
raise ValueError(
"Invalid 'A' value in path SVG element")
else:
if rel:
arg[5] += w[-1][0]
arg[6] += w[-1][1]
arg[3] = True if arg[3] == 1 else False
arg[4] = True if arg[4] == 1 else False
bezier_approximations = self.arc_to_bezier(
w[-1][0], w[-1][1], arg[5], arg[6], arg[3], arg[4], arg[0], arg[1], arg[2])
cmd = "M " + (str("%." + str(self.FLOAT_DECIMAL_PNTS) + "f") % w[-1][0]) + " " + (
str("%." + str(self.FLOAT_DECIMAL_PNTS) + "f") % w[-1][1]) + " "
for b in bezier_approximations:
b = [str("%." +
str(self.FLOAT_DECIMAL_PNTS) +
"f") %
number for number in b]
cmd += "C " + " ".join(b[2:]) + " "
w.extend(self.path({"d": cmd})[0][1:])
else:
if x[1] == "C" or x[1] == "S":
if ((len(arg) < 6 or len(arg) % 6 != 0) and x[1] == "C") or (
(len(arg) < 4 or len(arg) % 4 != 0) and x[1] == "S"):
raise ValueError(
"Invalid 'C/S' value in path SVG element")
else:
if x[1] == "S":
if len(arg) > 4:
skip_flag = True
temp = "S"
temp = temp if not rel else temp.lower()
for u in range(0, len(arg), 4):
_args.insert(index +
1 +
u /
4, [temp +
" " +
" ".join([str('{:.' +
str(self.FLOAT_DECIMAL_PNTS) +
'f}').format(n) for n in arg[u:u +
4]]), temp])
else:
self.convert_rel(rel, arg, w)
if last_command[0] != "C":
x[1] = "Q"
else:
x1 = w[-1][0] * 2 - last_command[1][2]
y1 = w[-1][1] * 2 - last_command[1][3]
arg = [x1, y1] + arg
x[1] = "C"
if x[1] == "C":
if len(arg) > 6:
skip_flag = True
temp = "C"
temp = temp if not rel else temp.lower()
for u in range(0, len(arg), 6):
_args.insert(index +
1 +
u /
6, [temp +
" " +
" ".join([str('{:.' +
str(self.FLOAT_DECIMAL_PNTS) +
'f}').format(n) for n in arg[u:u +
6]]), temp])
else:
self.convert_rel(rel, arg, w)
first_coordinate = [w[-1][0], w[-1][1]]
self.generate_bezier(
w, arg, first_coordinate)
if x[1] == "Q" or x[1] == "T":
if ((len(arg) < 4 or len(arg) % 4 != 0) and x[1] == "Q") or (
(len(arg) < 2 or len(arg) % 2 != 0) and x[1] == "T"):
raise ValueError(
"Invalid 'Q' value in path SVG element")
else:
if x[1] == "T":
if len(arg) > 2:
skip_flag = True
temp = "T"
temp = temp if not rel else temp.lower()
for u in range(0, len(arg), 2):
_args.insert(index +
1 +
u /
2, [temp +
" " +
" ".join([str('{:.' +
str(self.FLOAT_DECIMAL_PNTS) +
'f}').format(n) for n in arg[u:u +
2]]), temp])
else:
self.convert_rel(rel, arg, w)
if last_command[0] != "Q":
x[1] = "L"
else:
x1 = w[-1][0] * 2 - last_command[1][0]
y1 = w[-1][1] * 2 - last_command[1][1]
arg = [x1, y1] + arg
x[1] = "Q"
if x[1] == "Q":
if len(arg) > 4:
skip_flag = True
temp = "Q"
temp = temp if not rel else temp.lower()
for u in range(0, len(arg), 4):
_args.insert(index +
1 +
u /
4, [temp +
" " +
" ".join([str('{:.' +
str(self.FLOAT_DECIMAL_PNTS) +
'f}').format(n) for n in arg[u:u +
4]]), temp])
else:
self.convert_rel(rel, arg, w)
first_coordinate = [w[-1][0], w[-1][1]]
# Algorithm Backup: Approximate all points
t = 0
dist = 0
last_coordinate = [w[-1][0], w[-1][1]]
while t == 0 or dist > self.RESOLUTION:
approximation = self.approx_bezier(
"quadratic",
t,
1,
arg,
last_coordinate[0],
last_coordinate[1],
first_coordinate[0],
first_coordinate[1])
t = approximation[0]
last_coordinate = approximation[1]
w.append(approximation[1])
dist = self.dist(
arg[2], arg[3], approximation[1][0], approximation[1][1])
w.append([arg[2], arg[3]])
# Algorithm 2: Use approximation from first interval to extrapolate
# approximation = self.approx_bezier("quadratic", 0, 1, arg, w[-1][0], w[-1][1], w[-1][0], w[-1][1])[0]
# dist = 0
# i = 1
# while i == 1 or dist > self.RESOLUTION:
# new_coordinate = self.calc_quadratic_bezier(i * approximation, arg, first_coordinate)
# dist = self.dist(arg[2], arg[3], new_coordinate[0], new_coordinate[1])
# w.append(new_coordinate)
# i += 1
# w.append([arg[2], arg[3]])
if x[1] == "L":
if len(arg) > 2 and len(arg) % 2 == 0:
cmd = "l" if rel else "L"
_args.insert(index +
1, [cmd +
" " +
" ".join([str('{:.' +
str(self.FLOAT_DECIMAL_PNTS) +
'f}').format(n) for n in arg[0:2]]), cmd])
cmd = "l" if rel else "L"
for u in range(2, len(arg), 2):
_args.insert(index +
1 +
u /
2, [cmd +
" " +
" ".join([str('{:.' +
str(self.FLOAT_DECIMAL_PNTS) +
'f}').format(n) for n in arg[u:u +
2]]), cmd])
elif len(arg) != 2:
raise ValueError(
"Invalid 'L' value in path SVG element")
else:
self.convert_rel(rel, arg, w)
w.append([arg[0], arg[1]])
if not skip_flag:
last_command = [x[1], arg]
if w and len(w) > 0:
array.append(w)
return array
@staticmethod
def polygon(args):
const = 4
point_arr = analysis_methods.polyline(args)
point_arr.append(point_arr[0])
return [point_arr]
@staticmethod
def polyline(args):
const = 5
analysis_methods.check_args(const, args)
_args = args["points"]
preg = re.compile(
"^([ ]*([-]?[0-9]+[\.]?[0-9]*,[-]?[0-9]+[\.]?[0-9]*)[ ]*)*$")
if not preg.search(_args):
raise ValueError("Invalid polyline SVG element argument value")
point_arr = re.findall("([0-9]+[\.]?[0-9]*,[0-9]+[\.]?[0-9]*)", _args)
i = 0
for x in point_arr:
j = x.find(",")
point_arr[i] = [float(x[0:j]), float(x[j + 1:])]
i += 1
return [point_arr]
@staticmethod
def rect(args):
const = 6
analysis_methods.check_args(const, args)
_args = [args["x"], args["y"], args["width"], args["height"]]
preg = re.compile("^[-]?[0-9]+[\.]?[0-9]*$")
i = 0
for x in _args:
if(not preg.match(x)):
raise ValueError("Invalid rect SVG element argument value")
else:
_args[i] = float(x)
i += 1
return [[
[_args[0], _args[1]],
[_args[0] + _args[2], _args[1]],
[_args[0] + _args[2], _args[1] + _args[3]],
[_args[0], _args[1] + _args[3]],
[_args[0], _args[1]]
]]