# 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