FreeCAD / src /Mod /Draft /SVGPath.py
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# SPDX-License-Identifier: LGPL-2.1-or-later
import re
import math
from FreeCAD import Vector, Matrix
from DraftVecUtils import equals, isNull, angle
from draftutils.utils import svg_precision
from draftutils.messages import _err, _msg, _wrn
from Part import (
Arc,
BezierCurve,
BSplineCurve,
Ellipse,
Face,
LineSegment,
Shape,
Edge,
Wire,
Compound,
OCCError,
)
def _tolerance(precision):
return 10 ** (-precision)
def _arc_end_to_center(lastvec, currentvec, rx, ry, x_rotation=0.0, correction=False):
"""Calculate the possible centers for an arc in endpoint parameterization.
Calculate (positive and negative) possible centers for an arc given in
``endpoint parametrization``.
See http://www.w3.org/TR/SVG/implnote.html#ArcImplementationNotes
the sweepflag is interpreted as: sweepflag <==> arc is travelled clockwise
Parameters
----------
lastvec : Base::Vector3
First point of the arc.
currentvec : Base::Vector3
End point (current) of the arc.
rx : float
Radius of the ellipse, semi-major axis in the X direction.
ry : float
Radius of the ellipse, semi-minor axis in the Y direction.
x_rotation : float
Default is 0. Rotation around the Z axis, in radians (CCW).
correction : bool, optional
Default is `False`. If it is `True`, the radii will be scaled
by a factor.
Returns
-------
list, (float, float)
A tuple that consists of one list, and a tuple of radii.
[(positive), (negative)], (rx, ry)
The first element of the list is the positive tuple,
the second is the negative tuple.
[(Base::Vector3, float, float),
(Base::Vector3, float, float)], (float, float)
Types
[(vcenter+, angle1+, angledelta+),
(vcenter-, angle1-, angledelta-)], (rx, ry)
The first element of the list is the positive tuple,
consisting of center, angle, and angle increment;
the second element is the negative tuple.
"""
# scalefacsign = 1 if (largeflag != sweepflag) else -1
rx = float(rx)
ry = float(ry)
v0 = lastvec.sub(currentvec)
v0.multiply(0.5)
m1 = Matrix()
m1.rotateZ(-x_rotation) # eq. 5.1
v1 = m1.multiply(v0)
if correction:
eparam = v1.x**2 / rx**2 + v1.y**2 / ry**2
if eparam > 1:
eproot = math.sqrt(eparam)
rx = eproot * rx
ry = eproot * ry
denom = rx**2 * v1.y**2 + ry**2 * v1.x**2
numer = rx**2 * ry**2 - denom
results = []
# If the division is very small, set the scaling factor to zero,
# otherwise try to calculate it by taking the square root
if abs(numer / denom) < 1.0e-7:
scalefacpos = 0
else:
try:
scalefacpos = math.sqrt(numer / denom)
except ValueError:
_msg("sqrt({0}/{1})".format(numer, denom))
scalefacpos = 0
# Calculate two values because the square root may be positive or negative
for scalefacsign in (1, -1):
scalefac = scalefacpos * scalefacsign
# Step2 eq. 5.2
vcx1 = Vector(v1.y * rx / ry, -v1.x * ry / rx, 0).multiply(scalefac)
m2 = Matrix()
m2.rotateZ(x_rotation)
centeroff = currentvec.add(lastvec)
centeroff.multiply(0.5)
vcenter = m2.multiply(vcx1).add(centeroff) # Step3 eq. 5.3
# angle1 = Vector(1, 0, 0).getAngle(Vector((v1.x - vcx1.x)/rx,
# (v1.y - vcx1.y)/ry,
# 0)) # eq. 5.5
# angledelta = Vector((v1.x - vcx1.x)/rx,
# (v1.y - vcx1.y)/ry,
# 0).getAngle(Vector((-v1.x - vcx1.x)/rx,
# (-v1.y - vcx1.y)/ry,
# 0)) # eq. 5.6
# we need the right sign for the angle
angle1 = angle(
Vector(1, 0, 0), Vector((v1.x - vcx1.x) / rx, (v1.y - vcx1.y) / ry, 0)
) # eq. 5.5
angledelta = angle(
Vector((v1.x - vcx1.x) / rx, (v1.y - vcx1.y) / ry, 0),
Vector((-v1.x - vcx1.x) / rx, (-v1.y - vcx1.y) / ry, 0),
) # eq. 5.6
results.append((vcenter, angle1, angledelta))
if rx < 0 or ry < 0:
_wrn("Warning: 'rx' or 'ry' is negative, check the SVG file")
return results, (rx, ry)
def _arc_center_to_end(center, rx, ry, angle1, angledelta, xrotation=0.0):
"""Calculate start and end points, and flags of an arc.
Calculate start and end points, and flags of an arc given in
``center parametrization``.
See http://www.w3.org/TR/SVG/implnote.html#ArcImplementationNotes
Parameters
----------
center : Base::Vector3
Coordinates of the center of the ellipse.
rx : float
Radius of the ellipse, semi-major axis in the X direction
ry : float
Radius of the ellipse, semi-minor axis in the Y direction
angle1 : float
Initial angle in radians
angledelta : float
Additional angle in radians
xrotation : float, optional
Default 0. Rotation around the Z axis
Returns
-------
v1, v2, largerc, sweep
Tuple indicating the end points of the arc, and two boolean values
indicating whether the arc is less than 180 degrees or not,
and whether the angledelta is negative.
"""
vr1 = Vector(rx * math.cos(angle1), ry * math.sin(angle1), 0)
vr2 = Vector(rx * math.cos(angle1 + angledelta), ry * math.sin(angle1 + angledelta), 0)
mxrot = Matrix()
mxrot.rotateZ(xrotation)
v1 = mxrot.multiply(vr1).add(center)
v2 = mxrot.multiply(vr2).add(center)
fa = ((abs(angledelta) / math.pi) % 2) > 1 # < 180 deg
fs = angledelta < 0
return v1, v2, fa, fs
def _approx_bspline(
curve: BezierCurve,
num: int = 10,
tol: float = 1e-7,
) -> BSplineCurve | BezierCurve:
_p0, d0 = curve.getD1(curve.FirstParameter)
_p1, d1 = curve.getD1(curve.LastParameter)
if (d0.Length < tol) or (d1.Length < tol):
tan1 = curve.tangent(curve.FirstParameter)[0]
tan2 = curve.tangent(curve.LastParameter)[0]
pts = curve.discretize(num)
bs = BSplineCurve()
try:
bs.interpolate(Points=pts, InitialTangent=tan1, FinalTangent=tan2)
return bs
except OCCError:
pass
return curve
def _make_wire(path: list[Edge], precision: int, checkclosed: bool = False, donttry: bool = False):
"""Try to make a wire out of the list of edges.
If the wire functions fail or the wire is not closed,
if required the TopoShapeCompoundPy::connectEdgesToWires()
function is used.
Parameters
----------
path : list[Edge]
A collection of edges
checkclosed : bool, optional
Default is `False`.
donttry : bool, optional
Default is `False`. If it's `True` it won't try to check
for a closed path.
Returns
-------
Part::Wire
A wire created from the ordered edges.
Part::Compound
A compound made of the edges, but unable to form a wire.
"""
if not donttry:
try:
sh = Wire(path)
# sh = Wire(path)
isok = (not checkclosed) or sh.isClosed()
if len(sh.Edges) != len(path):
isok = False
# BRep_API: command not done
except OCCError:
isok = False
if donttry or not isok:
# Code from wmayer forum p15549 to fix the tolerance problem
# original tolerance = 0.00001
comp = Compound(path)
_sh = comp.connectEdgesToWires(False, _tolerance(precision))
sh = _sh.Wires[0]
if len(sh.Edges) != len(path):
_wrn("Unable to form a wire. Resort to a Compound of Edges.")
sh = comp
return sh
class FaceTreeNode:
"""
Building Block of a tree structure holding one-closed-wire faces
sorted after their enclosure of each other.
This class only works with faces that have exactly one closed wire
"""
face: Face
children: list
name: str
def __init__(self, face=None, name="root"):
super().__init__()
self.face = face
self.name = name
self.children = []
def insert(self, face, name):
"""
takes a single-wire named face, and inserts it into the tree
depending on its enclosure in/of already added faces.
Parameters
----------
face : Face
single closed wire face to be added to the tree
name : str
face identifier
"""
for node in self.children:
if node.face.Area > face.Area:
# new face could be encompassed
if (
face.distToShape(node.face)[0] == 0.0
and face.Wires[0].distToShape(node.face.Wires[0])[0] != 0.0
):
# it is encompassed - enter next tree layer
node.insert(face, name)
return
else:
# new face could encompass
if (
node.face.distToShape(face)[0] == 0.0
and node.face.Wires[0].distToShape(face.Wires[0])[0] != 0.0
):
# it does encompass the current child nodes face
# create new node from face
new = FaceTreeNode(face, name)
# swap the new one with the child node
self.children.remove(node)
self.children.append(new)
# add former child node as child to the new node
new.children.append(node)
return
# the face is not encompassing and is not encompassed (from) any
# other face, we add it as new child
new = FaceTreeNode(face, name)
self.children.append(new)
def makeCuts(self):
"""
recursively traverse the tree and cuts all faces in even
numbered tree levels with their direct childrens faces.
Additionally the tree is shrunk by removing the odd numbered
tree levels.
"""
result = self.face
if not result:
for node in self.children:
node.makeCuts()
else:
new_children = []
for node in self.children:
result = result.cut(node.face)
for subnode in node.children:
subnode.makeCuts()
new_children.append(subnode)
self.children = new_children
self.face = result
def flatten(self):
"""creates a flattened list of face-name tuples from the facetree
content
"""
result = []
result.append((self.name, self.face))
for node in self.children:
result.extend(node.flatten())
return result
class SvgPathElement:
path: list[dict]
def __init__(self, precision: int, interpol_pts: int, origin: Vector = Vector(0, 0, 0)):
self.precision = precision
self.interpol_pts = interpol_pts
self.path = [{"type": "start", "last_v": origin}]
def add_move(self, x: float, y: float, relative: bool) -> None:
if relative:
last_v = self.path[-1]["last_v"].add(Vector(x, -y, 0))
else:
last_v = Vector(x, -y, 0)
# if we're at the beginning of a wire we overwrite the start vector
if self.path[-1]["type"] == "start":
self.path[-1]["last_v"] = last_v
else:
self.path.append({"type": "start", "last_v": last_v})
def add_lines(self, coords: list[float], relative: bool) -> None:
last_v = self.path[-1]["last_v"]
for x, y in zip(coords[0::2], coords[1::2]):
if relative:
last_v = last_v.add(Vector(x, -y, 0))
else:
last_v = Vector(x, -y, 0)
self.path.append({"type": "line", "last_v": last_v})
def add_horizontals(self, x_coords: list[float], relative: bool) -> None:
last_v = self.path[-1]["last_v"]
for x in x_coords:
if relative:
last_v = Vector(x + last_v.x, last_v.y, 0)
else:
last_v = Vector(x, last_v.y, 0)
self.path.append({"type": "line", "last_v": last_v})
def add_verticals(self, y_coords: list[float], relative: bool) -> None:
last_v = self.path[-1]["last_v"]
if relative:
for y in y_coords:
last_v = Vector(last_v.x, last_v.y - y, 0)
self.path.append({"type": "line", "last_v": last_v})
else:
for y in y_coords:
last_v = Vector(last_v.x, -y, 0)
self.path.append({"type": "line", "last_v": last_v})
def add_arcs(self, args: list[float], relative: bool) -> None:
p_iter = zip(
args[0::7],
args[1::7],
args[2::7],
args[3::7],
args[4::7],
args[5::7],
args[6::7],
strict=False,
)
for rx, ry, x_rotation, large_flag, sweep_flag, x, y in p_iter:
# support for large-arc and x-rotation is missing
if relative:
last_v = self.path[-1]["last_v"].add(Vector(x, -y, 0))
else:
last_v = Vector(x, -y, 0)
self.path.append(
{
"type": "arc",
"rx": rx,
"ry": ry,
"x_rotation": x_rotation,
"large_flag": large_flag != 0,
"sweep_flag": sweep_flag != 0,
"last_v": last_v,
}
)
def add_cubic_beziers(self, args: list[float], relative: bool, smooth: bool) -> None:
last_v = self.path[-1]["last_v"]
if smooth:
p_iter = list(
zip(
args[2::4],
args[3::4],
args[0::4],
args[1::4],
args[2::4],
args[3::4],
strict=False,
)
)
else:
p_iter = list(
zip(
args[0::6],
args[1::6],
args[2::6],
args[3::6],
args[4::6],
args[5::6],
strict=False,
)
)
for p1x, p1y, p2x, p2y, x, y in p_iter:
if smooth:
if self.path[-1]["type"] == "cbezier":
pole1 = last_v.sub(self.path[-1]["pole2"]).add(last_v)
else:
pole1 = last_v
else:
if relative:
pole1 = last_v.add(Vector(p1x, -p1y, 0))
else:
pole1 = Vector(p1x, -p1y, 0)
if relative:
pole2 = last_v.add(Vector(p2x, -p2y, 0))
last_v = last_v.add(Vector(x, -y, 0))
else:
pole2 = Vector(p2x, -p2y, 0)
last_v = Vector(x, -y, 0)
self.path.append({"type": "cbezier", "pole1": pole1, "pole2": pole2, "last_v": last_v})
def add_quadratic_beziers(self, args: list[float], relative: bool, smooth: bool):
last_v = self.path[-1]["last_v"]
if smooth:
p_iter = list(zip(args[1::2], args[1::2], args[0::2], args[1::2], strict=False))
else:
p_iter = list(zip(args[0::4], args[1::4], args[2::4], args[3::4], strict=False))
for px, py, x, y in p_iter:
if smooth:
if self.path[-1]["type"] == "qbezier":
pole = last_v.sub(self.path[-1]["pole"]).add(last_v)
else:
pole = last_v
else:
if relative:
pole = last_v.add(Vector(px, -py, 0))
else:
pole = Vector(px, -py, 0)
if relative:
last_v = last_v.add(Vector(x, -y, 0))
else:
last_v = Vector(x, -y, 0)
self.path.append({"type": "qbezier", "pole": pole, "last_v": last_v})
def add_close(self):
last_v = self.path[-1]["last_v"]
first_v = self.__get_last_start()
if not equals(last_v, first_v, self.precision):
self.path.append({"type": "line", "last_v": first_v})
# assume that a close command finalizes a subpath
self.path.append({"type": "start", "last_v": first_v})
def __get_last_start(self) -> Vector:
"""
Return the startpoint of the last SubPath.
"""
for pds in reversed(self.path):
if pds["type"] == "start":
return pds["last_v"]
return Vector(0, 0, 0)
def __correct_last_v(self, pds: dict, last_v: Vector) -> None:
"""
Correct the endpoint of the given path dataset to the
given vector and move possibly associated members accordingly.
"""
delta = last_v.sub(pds["last_v"])
# we won't move last_v if it's already correct or if the delta
# is substantially greater than what rounding errors could accumulate,
# so we assume the path is intended to be open.
if delta.x == 0 and delta.y == 0 and delta.z == 0 or not isNull(delta, self.precision):
return
# for cbeziers we also relocate the second pole
if pds["type"] == "cbezier":
pds["pole2"] = pds["pole2"].add(delta)
# for qbeziers we also relocate the pole by half of the delta
elif pds["type"] == "qbezier":
pds["pole"] = pds["pole"].add(delta.scale(0.5, 0.5, 0))
# all data types have last_v
pds["last_v"] = last_v
def correct_endpoints(self):
"""
Correct the endpoints of all subpaths and move possibly
associated members accordingly.
"""
start = None
last = None
for pds in self.path:
if pds["type"] == "start":
if start:
# there is already a start
if last:
# and there are edges behind us.
# we correct the last to the start vector
self.__correct_last_v(last, start["last_v"])
last = None
start = pds
continue
last = pds
if start and last and start != last:
self.__correct_last_v(last, start["last_v"])
def create_edges(self) -> list[list[Edge]]:
"""
Creates shapes from prepared path datasets and returns them in an
ordered list of lists of edges, where each 1st order list entry
represents a single continuous (and probably closed) sub-path.
"""
result = []
edges = None
last_v = Vector(0, 0, 0)
for pds in self.path:
next_v = pds["last_v"]
match pds["type"]:
case "start":
if edges and len(edges) > 0:
result.append(edges)
edges = []
case "line":
if equals(last_v, next_v, self.precision):
# line segment too short, skip it
next_v = last_v
else:
edges.append(LineSegment(last_v, next_v).toShape())
case "arc":
rx = pds["rx"]
ry = pds["ry"]
x_rotation = pds["x_rotation"]
large_flag = pds["large_flag"]
sweep_flag = pds["sweep_flag"]
# Calculate the possible centers for an arc
# in 'endpoint parameterization'.
_x_rot = math.radians(-x_rotation)
(solution, (rx, ry)) = _arc_end_to_center(
last_v, next_v, rx, ry, _x_rot, correction=True
)
# Choose one of the two solutions
neg_sol = large_flag != sweep_flag
v_center, angle1, angle_delta = solution[neg_sol]
if ry > rx:
rx, ry = ry, rx
swap_axis = True
else:
swap_axis = False
e1 = Ellipse(v_center, rx, ry)
if sweep_flag:
angle1 = angle1 + angle_delta
angle_delta = -angle_delta
d90 = math.radians(90)
e1a = Arc(e1, angle1 - swap_axis * d90, angle1 + angle_delta - swap_axis * d90)
seg = e1a.toShape()
if swap_axis:
seg.rotate(v_center, Vector(0, 0, 1), 90)
_tol = _tolerance(self.precision)
if abs(x_rotation) > _tol:
seg.rotate(v_center, Vector(0, 0, 1), -x_rotation)
if sweep_flag:
seg.reverse()
edges.append(seg)
case "cbezier":
pole1 = pds["pole1"]
pole2 = pds["pole2"]
_tol = _tolerance(self.precision + 2)
_d1 = pole1.distanceToLine(last_v, next_v)
_d2 = pole2.distanceToLine(last_v, next_v)
if _d1 < _tol and _d2 < _tol:
# poles and endpoints are all on a line
if equals(last_v, next_v, self.precision):
# in this case we don't accept (nearly) zero
# distance between start and end (skip it).
next_v = last_v
else:
seg = LineSegment(last_v, next_v).toShape()
edges.append(seg)
else:
b = BezierCurve()
b.setPoles([last_v, pole1, pole2, next_v])
seg = _approx_bspline(b, self.interpol_pts).toShape()
edges.append(seg)
case "qbezier":
if equals(last_v, next_v, self.precision):
# segment too small - skipping.
next_v = last_v
else:
pole = pds["pole"]
_tol = _tolerance(self.precision + 2)
_distance = pole.distanceToLine(last_v, next_v)
if _distance < _tol:
# pole is on the line
_seg = LineSegment(last_v, next_v)
seg = _seg.toShape()
else:
b = BezierCurve()
b.setPoles([last_v, pole, next_v])
seg = _approx_bspline(b, self.interpol_pts).toShape()
edges.append(seg)
case _:
_msg("Illegal path_data type. {}".format(pds["type"]))
return []
last_v = next_v
if not edges is None and len(edges) > 0:
result.append(edges)
return result
class SvgPathParser:
"""Parse SVG path data and create FreeCAD Shapes."""
commands: list[tuple]
pointsre: re.Pattern
data: dict
shapes: list[list[Shape]]
faces: FaceTreeNode
name: str
def __init__(self, data, name):
super().__init__()
"""Evaluate path data and initialize."""
_op = "([mMlLhHvVaAcCqQsStTzZ])"
_op2 = "([^mMlLhHvVaAcCqQsStTzZ]*)"
_command = "\\s*?" + _op + "\\s*?" + _op2 + "\\s*?"
pathcommandsre = re.compile(_command, re.DOTALL)
_num = "[-+]?[0-9]*\\.?[0-9]+"
_exp = "([eE][-+]?[0-9]+)?"
_arg = "(" + _num + _exp + ")"
self.commands = pathcommandsre.findall(" ".join(data["d"]))
self.argsre = re.compile(_arg, re.DOTALL)
self.data = data
self.paths = []
self.shapes = []
self.faces = None
self.name = name
def parse(self):
"""
Creates lists of SvgPathElements from raw svg path
data. It's supposed to be called direct after SvgPath Object
creation.
"""
path = SvgPathElement(svg_precision(), 10)
self.paths = []
for d, argsstr in self.commands:
relative = d.islower()
_args = self.argsre.findall(argsstr.replace(",", " "))
args = [float(number) for number, exponent in _args]
if d in "Mm":
path.add_move(args.pop(0), args.pop(0), relative)
if d in "LlMm":
path.add_lines(args, relative)
elif d in "Hh":
path.add_horizontals(args, relative)
elif d in "Vv":
path.add_verticals(args, relative)
elif d in "Aa":
path.add_arcs(args, relative)
elif d in "Cc":
path.add_cubic_beziers(args, relative, False)
elif d in "Ss":
path.add_cubic_beziers(args, relative, True)
elif d in "Qq":
path.add_quadratic_beziers(args, relative, False)
elif d in "Tt":
path.add_quadratic_beziers(args, relative, True)
elif d in "Zz":
path.add_close()
path.correct_endpoints()
self.shapes = path.create_edges()
def create_faces(self, fill=True, add_wire_for_invalid_face=False):
"""
Generate Faces from lists of Shapes.
If shapes form a closed wire and the fill Attribute is set, we
generate a closed Face. Otherwise we treat the shape as pure wire.
Parameters
----------
fill : Object/bool
if True or not None Faces are generated from closed shapes.
"""
precision = svg_precision()
cnt = -1
openShapes = []
self.faces = FaceTreeNode()
for sh in self.shapes:
cnt += 1
add_wire = True
wr = _make_wire(sh, precision, checkclosed=True)
wrcpy = wr.copy()
wire_reason = ""
if cnt > 0:
face_name = self.name + "_" + str(cnt)
else:
face_name = self.name
if not fill:
wire_reason = " no-fill"
if not wr.Wires[0].isClosed():
wire_reason += " open Wire"
if fill and wr.Wires[0].isClosed():
try:
face = Face(wr)
if not face.isValid():
add_wire = add_wire_for_invalid_face
wire_reason = " invalid Face"
if face.fix(1e-6, 0, 1):
res = "succeed"
else:
res = "fail"
_wrn(
"Invalid Face '{}' created. Attempt to fix - {}ed.".format(
face_name, res
)
)
else:
add_wire = False
if not (face.Area < 10 * (_tolerance(precision) ** 2)):
self.faces.insert(face, face_name)
except:
_wrn(
"Failed to make a shape from '{}'. ".format(face_name)
+ "This Path will be discarded."
)
if add_wire:
if wrcpy.Length > _tolerance(precision):
_msg("Adding wire for '{}' - reason: {}.".format(face_name, wire_reason))
openShapes.append((face_name + "_w", wrcpy))
self.shapes = openShapes
def doCuts(self):
"""Exposes the FaceTreeNode.makeCuts function of the tree containing
closed wire faces.
This function is called after creating closed Faces with
'createFaces' in order to hollow faces encompassing others.
"""
self.faces.makeCuts()
def getShapeList(self):
"""Returns the resulting list of tuples containing name and face of
each created element.
"""
result = self.faces.flatten()
result.extend(self.shapes)
return result