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# ***************************************************************************
# * *
# * Copyright (c) 2017 Yorik van Havre <yorik@uncreated.net> *
# * *
# * This file is part of FreeCAD. *
# * *
# * FreeCAD is free software: you can redistribute it and/or modify it *
# * under the terms of the GNU Lesser General Public License as *
# * published by the Free Software Foundation, either version 2.1 of the *
# * License, or (at your option) any later version. *
# * *
# * FreeCAD is distributed in the hope that it will be useful, but *
# * WITHOUT ANY WARRANTY; without even the implied warranty of *
# * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU *
# * Lesser General Public License for more details. *
# * *
# * You should have received a copy of the GNU Lesser General Public *
# * License along with FreeCAD. If not, see *
# * <https://www.gnu.org/licenses/>. *
# * *
# ***************************************************************************
import math
from datetime import datetime
import FreeCAD
import DraftGeomUtils
import DraftVecUtils
import Part
import WorkingPlane
# This is roughly based on the no-fit polygon algorithm, used in
# SvgNest: https://github.com/Jack000/SVGnest
# Wikihouse plugin: https://github.com/tav/wikihouse-plugin/blob/master/wikihouse.rb
TOLERANCE = 0.0001 # smaller than this, two points are considered equal
DISCRETIZE = 4 # the number of segments in which arcs must be subdivided
ROTATIONS = [0, 90, 180, 270] # the possible rotations to try
class Nester:
def __init__(self, container=None, shapes=None):
"""Nester([container,shapes]): Creates a nester object with a container
shape and a list of other shapes to nest into it. Container and
shapes must be Part.Faces.
Typical workflow:
n = Nester() # creates the nester
n.addContainer(object) # adds a doc object as the container
n.addObjects(objects) # adds a list of doc objects as shapes
n.run() # runs the nesting
n.show() # creates a preview (compound) of the results
n.apply() # applies transformations to the original objects
Defaults (can be changed):
Nester.TOLERANCE = 0.0001
Nester.DISCRETIZE = 4
Nester.ROTATIONS = [0,90,180,270]
"""
self.objects = None
self.container = container
self.shapes = shapes
self.results = [] # storage for the different results
self.indexedFaces = None
self.running = True
self.progress = 0
self.setCounter = None # optionally define a setCounter(value) function where value is a %
def addObjects(self, objects):
"""addObjects(objects): adds FreeCAD DocumentObjects to the nester"""
if not isinstance(objects, list):
objects = [objects]
if not self.objects:
self.objects = {}
if not self.shapes:
self.shapes = []
for obj in objects:
if hasattr(obj, "Shape"):
h = obj.Shape.hashCode()
if not h in self.objects:
self.objects[h] = obj
self.shapes.append(obj.Shape)
def addContainer(self, container):
"""addContainer(object): adds a FreeCAD DocumentObject as the container"""
if hasattr(container, "Shape"):
self.container = container.Shape
def clear(self):
"""clear(): Removes all objects and shape from the nester"""
self.objects = None
self.shapes = None
def stop(self):
"""stop((): stops the computation"""
self.running = False
def update(self):
"""update(): internal function to verify if computation can
go on"""
if self.setCounter:
self.setCounter(self.progress)
if FreeCAD.GuiUp:
from PySide import QtGui
QtGui.QApplication.processEvents()
if not self.running:
return False
return True
def run(self):
"""run(): Runs a nesting operation. Returns a list of lists of
shapes, each primary list being one filled container, or None
if the operation failed."""
# reset abort mechanism and variables
self.running = True
self.progress = 0
starttime = datetime.now()
# general conformity tests
print("Executing conformity tests… ", end="")
if not self.container:
print("Empty container. Aborting.")
return
if not self.shapes:
print("Empty shapes. Aborting.")
return
if not isinstance(self.container, Part.Face):
print("Container is not a face. Aborting.")
return
normal = self.container.normalAt(0, 0)
for s in self.shapes:
if not self.update():
return
if len(s.Faces) != 1:
print("One of the shapes does not contain exactly one face. Aborting.")
return
# check if all faces correctly oriented (same normal)
if s.Faces[0].normalAt(0, 0).getAngle(normal) > TOLERANCE:
# let pass faces with inverted normal
if s.Faces[0].normalAt(0, 0).getAngle(normal) - math.pi > TOLERANCE:
print(
"One of the face does not have the same orientation as the container. Aborting."
)
return
# TODO
# allow one to use a non-rectangular container
# manage margins/paddings
# allow one to prevent or force specific rotations for a piece
# LONG-TERM TODO
# add genetic algo to swap pieces, and check if the result is better
# track progresses
step = 100.0 / (len(self.shapes) * len(ROTATIONS))
# store hashCode together with the face so we can change the order
# and still identify the original face, so we can calculate a transform afterwards
self.indexedfaces = [[shape.hashCode(), shape] for shape in self.shapes]
# build a clean copy so we don't touch the original
faces = list(self.indexedfaces)
# replace shapes by their face
faces = [[f[0], f[1].Faces[0]] for f in faces]
# order by area
faces = sorted(faces, key=lambda face: face[1].Area)
# discretize non-linear edges and remove holes
nfaces = []
for face in faces:
if not self.update():
return
nedges = []
allLines = True
for edge in face[1].OuterWire.OrderedEdges:
if isinstance(edge.Curve, (Part.LineSegment, Part.Line)):
nedges.append(edge)
else:
allLines = False
last = edge.Vertexes[0].Point
for i in range(DISCRETIZE):
s = float(i + 1) / DISCRETIZE
par = edge.FirstParameter + (edge.LastParameter - edge.FirstParameter) * s
new = edge.valueAt(par)
nedges.append(Part.LineSegment(last, new).toShape())
last = new
f = Part.Face(Part.Wire(nedges))
if not f.isValid():
if allLines:
print("Invalid face found in set. Aborting.")
else:
print("Face distretizing failed. Aborting.")
return
nfaces.append([face[0], f])
faces = nfaces
# container for sheets with a first, empty sheet
sheets = [[]]
print("Everything OK (", datetime.now() - starttime, ")")
# main loop
facenumber = 1
facesnumber = len(faces)
# print("Vertices per face:",[len(face[1].Vertexes) for face in faces])
while faces:
print(
"Placing piece",
facenumber,
"/",
facesnumber,
"Area:",
FreeCAD.Units.Quantity(faces[-1][1].Area, FreeCAD.Units.Area).getUserPreferred()[0],
": ",
end="",
)
face = faces.pop()
boc = self.container.BoundBox
# this stores the available solutions for each rotation of a piece
# contains [sheetnumber,face,xlength] lists,
# face being [hascode,transformed face] and xlength
# the X size of all boundboxes of placed pieces
available = []
# this stores the possible positions on a blank
# sheet, in case we need to create a new one
initials = []
# this checks if the piece don't fit in the container
unfit = True
for rotation in ROTATIONS:
if not self.update():
return
self.progress += step
print(rotation, ", ", end="")
hashcode = face[0]
rotface = face[1].copy()
if rotation:
rotface.rotate(rotface.CenterOfMass, normal, rotation)
bof = rotface.BoundBox
rotverts = self.order(rotface)
# for i,v in enumerate(rotverts):
# Draft.makeText([str(i)],point=v)
basepoint = rotverts[0] # leftmost point of the rotated face
basecorner = boc.getPoint(0) # lower left corner of the container
# See if the piece fits in the container dimensions
if (bof.XLength < boc.XLength) and (bof.YLength < boc.YLength):
unfit = False
# Get the fit polygon of the container
# that is, the polygon inside which basepoint can
# circulate, and the face still be fully inside the container
v1 = basecorner.add(basepoint.sub(bof.getPoint(0)))
v2 = v1.add(FreeCAD.Vector(0, boc.YLength - bof.YLength, 0))
v3 = v2.add(FreeCAD.Vector(boc.XLength - bof.XLength, 0, 0))
v4 = v3.add(FreeCAD.Vector(0, -(boc.YLength - bof.YLength), 0))
binpol = Part.Face(Part.makePolygon([v1, v2, v3, v4, v1]))
initials.append([binpol, [hashcode, rotface], basepoint])
# check for available space on each existing sheet
for sheetnumber, sheet in enumerate(sheets):
# Get the no-fit polygon for each already placed face in
# current sheet. That is, a polygon in which basepoint
# cannot be, if we want our face to not overlap with the
# placed face.
# To do this, we "circulate" the face around the placed face
if not self.update():
return
nofitpol = []
for placed in sheet:
pts = []
for placedvert in self.order(placed[1], right=True):
fpts = []
for i, rotvert in enumerate(rotverts):
if not self.update():
return
facecopy = rotface.copy()
facecopy.translate(placedvert.sub(rotvert))
# test if all the points of the face are outside the
# placed face (except the base point, which is coincident)
outside = True
faceverts = self.order(facecopy)
for vert in faceverts:
if (vert.sub(placedvert)).Length > TOLERANCE:
if placed[1].isInside(vert, TOLERANCE, True):
outside = False
break
# also need to test for edge intersection, because even
# if all vertices are outside, the pieces could still
# overlap
if outside:
for e1 in facecopy.OuterWire.Edges:
for e2 in placed[1].OuterWire.Edges:
if not self.update():
return
if True:
# Draft code (SLOW)
p = DraftGeomUtils.findIntersection(e1, e2)
if p:
p = p[0]
p1 = e1.Vertexes[0].Point
p2 = e1.Vertexes[1].Point
p3 = e2.Vertexes[0].Point
p4 = e2.Vertexes[1].Point
if (
(p.sub(p1).Length > TOLERANCE)
and (p.sub(p2).Length > TOLERANCE)
and (p.sub(p3).Length > TOLERANCE)
and (p.sub(p4).Length > TOLERANCE)
):
outside = False
break
else:
# alt code: using distToShape (EVEN SLOWER!)
p = e1.distToShape(e2)
if p:
if p[0] < TOLERANCE:
# allow vertex-to-vertex intersection
if (p[2][0][0] != "Vertex") or (
p[2][0][3] != "Vertex"
):
outside = False
break
if outside:
fpts.append([faceverts[0], i])
# Draft.makeText([str(i)],point=faceverts[0])
# reorder available solutions around a same point if needed
# ensure they are in the correct order
idxs = [p[1] for p in fpts]
if (0 in idxs) and (len(faceverts) - 1 in idxs):
slicepoint = len(fpts)
last = len(faceverts)
for p in reversed(fpts):
if p[1] == last - 1:
slicepoint -= 1
last -= 1
else:
break
fpts = fpts[slicepoint:] + fpts[:slicepoint]
# print(fpts)
pts.extend(fpts)
# create the polygon
if len(pts) < 3:
print("Error calculating a no-fit polygon. Aborting.")
return
pts = [p[0] for p in pts]
pol = Part.Face(Part.makePolygon(pts + [pts[0]]))
if not pol.isValid():
# fix overlapping edges
overlap = True
while overlap:
overlap = False
for i in range(len(pol.OuterWire.Edges) - 1):
if not self.update():
return
v1 = DraftGeomUtils.vec(pol.OuterWire.OrderedEdges[i])
v2 = DraftGeomUtils.vec(pol.OuterWire.OrderedEdges[i + 1])
if abs(v1.getAngle(v2) - math.pi) <= TOLERANCE:
overlap = True
ne = Part.LineSegment(
pol.OuterWire.OrderedEdges[i].Vertexes[0].Point,
pol.OuterWire.OrderedEdges[i + 1].Vertexes[-1].Point,
).toShape()
pol = Part.Face(
Part.Wire(
pol.OuterWire.OrderedEdges[:i]
+ [ne]
+ pol.OuterWire.OrderedEdges[i + 2 :]
)
)
break
if not pol.isValid():
# trying basic OCC fix
pol.fix(0, 0, 0)
if pol.isValid():
if pol.ShapeType == "Face":
pol = Part.Face(pol.OuterWire) # discard possible inner holes
elif pol.Faces:
# several faces after the fix, keep the biggest one
a = 0
ff = None
for f in pol.Faces:
if f.Area > a:
a = f.Area
ff = f
if ff:
pol = ff
else:
print("Unable to fix invalid no-fit polygon. Aborting.")
Part.show(pol)
return
if not pol.isValid():
# none of the fixes worked. Epic fail.
print("Invalid no-fit polygon. Aborting.")
Part.show(pol.OuterWire)
for p in sheet:
Part.show(p[1])
Part.show(facecopy)
# for i,p in enumerate(faceverts):
# Draft.makeText([str(i)],point=p)
return
if pol.isValid():
nofitpol.append(pol)
# Part.show(pol)
# Union all the no-fit pols into one
if len(nofitpol) == 1:
nofitpol = nofitpol[0]
elif len(nofitpol) > 1:
b = nofitpol.pop()
for n in nofitpol:
if not self.update():
return
b = b.fuse(n)
nofitpol = b
# remove internal edges (discard edges shared by 2 faces)
lut = {}
for f in fitpol.Faces:
for e in f.Edges:
h = e.hashCode()
if h in lut:
lut[h].append(e)
else:
lut[h] = [e]
edges = [e[0] for e in lut.values() if len(e) == 1]
try:
pol = Part.Face(Part.Wire(edges))
except Exception:
# above method can fail sometimes. Try a slower method
w = DraftGeomUtils.findWires(edges)
if len(w) == 1:
if w[0].isClosed():
try:
pol = Part.Face(w[0])
except Exception:
print("Error merging polygons. Aborting.")
try:
Part.show(Part.Wire(edges))
except Exception:
for e in edges:
Part.show(e)
return
# subtract the no-fit polygon from the container's fit polygon
# we then have the zone where the face can be placed
if nofitpol:
fitpol = binpol.cut(nofitpol)
else:
fitpol = binpol.copy()
# check that we have some space on this sheet
if (fitpol.Area > 0) and fitpol.Vertexes:
# order the fitpol vertexes by smallest X
# and try to place the piece, making sure it doesn't
# intersect with already placed pieces
fitverts = sorted([v.Point for v in fitpol.Vertexes], key=lambda v: v.x)
for p in fitverts:
if not self.update():
return
trface = rotface.copy()
trface.translate(p.sub(basepoint))
ok = True
for placed in sheet:
if ok:
for vert in trface.Vertexes:
if placed[1].isInside(vert.Point, TOLERANCE, False):
ok = False
break
if ok:
for e1 in trface.OuterWire.Edges:
for e2 in placed[1].OuterWire.Edges:
p = DraftGeomUtils.findIntersection(e1, e2)
if p:
p = p[0]
p1 = e1.Vertexes[0].Point
p2 = e1.Vertexes[1].Point
p3 = e2.Vertexes[0].Point
p4 = e2.Vertexes[1].Point
if (
(p.sub(p1).Length > TOLERANCE)
and (p.sub(p2).Length > TOLERANCE)
and (p.sub(p3).Length > TOLERANCE)
and (p.sub(p4).Length > TOLERANCE)
):
ok = False
break
if not ok:
break
if ok:
rotface = trface
break
else:
print("Could not determine location on sheet. Aborting.")
return
# check the X space occupied by this solution
bb = rotface.BoundBox
for placed in sheet:
bb.add(placed[1].BoundBox)
available.append([sheetnumber, [hashcode, rotface], bb.XMax, fitpol])
if unfit:
print("One face does not fit in the container. Aborting.")
return
if available:
# order by smallest X size and take the first one
available = sorted(available, key=lambda sol: sol[2])
print("Adding piece to sheet", available[0][0] + 1)
sheets[available[0][0]].append(available[0][1])
# Part.show(available[0][3])
else:
# adding to the leftmost vertex of the binpol
sheet = []
print("Creating new sheet, adding piece to sheet", len(sheets))
# order initial positions by smallest X size
initials = sorted(initials, key=lambda sol: sol[1][1].BoundBox.XLength)
hashcode = initials[0][1][0]
face = initials[0][1][1]
# order binpol vertexes by X coord
verts = sorted([v.Point for v in initials[0][0].Vertexes], key=lambda v: v.x)
face.translate(verts[0].sub(initials[0][2]))
sheet.append([hashcode, face])
sheets.append(sheet)
facenumber += 1
print("Run time:", datetime.now() - starttime)
self.results.append(sheets)
return sheets
def order(self, face, right=False):
"""order(face,[right]): returns a list of vertices
ordered clockwise. The first vertex will be the
lefmost one, unless right is True, in which case the
first vertex will be the rightmost one"""
verts = [v.Point for v in face.OuterWire.OrderedVertexes]
# flatten the polygon on the XY plane
wp = WorkingPlane.PlaneBase()
wp.align_to_point_and_axis(face.CenterOfMass, face.normalAt(0, 0))
pverts = []
for v in verts:
vx = DraftVecUtils.project(v, wp.u)
lx = vx.Length
if vx.getAngle(wp.u) > 1:
lx = -lx
vy = DraftVecUtils.project(v, wp.v)
ly = vy.Length
if vy.getAngle(wp.v) > 1:
ly = -ly
pverts.append(FreeCAD.Vector(lx, ly, 0))
pverts.append(pverts[0])
# https://stackoverflow.com/questions/1165647/how-to-determine-if-a-list-of-polygon-points-are-in-clockwise-order
s = 0
for i in range(len(pverts) - 1):
s += (pverts[i + 1].x - pverts[i].x) * (pverts[i + 1].y + pverts[i].y)
if s < 0:
verts.reverse()
elif s == 0:
print("error computing winding direction")
return
return verts
def show(self, result=None):
"""show([result]): creates shapes in the document, showing
the given result (list of sheets) or the last result if
none is provided"""
if not result:
result = []
if self.results:
result = self.results[-1]
offset = FreeCAD.Vector(0, 0, 0)
feats = []
for sheet in result:
shapes = [self.container.OuterWire]
shapes.extend([face[1] for face in sheet])
comp = Part.makeCompound(shapes)
comp.translate(offset)
o = FreeCAD.ActiveDocument.addObject("Part::Feature", "Nest")
o.Shape = comp
feats.append(o)
offset = offset.add(FreeCAD.Vector(1.1 * self.container.BoundBox.XLength, 0, 0))
FreeCAD.ActiveDocument.recompute()
return feats
def getPlacements(self, result=None):
"""getPlacements([result]): returns a dictionary of hashCode:Placement
pairs from the given result or the last computed result if none
is given. The Placement contains a translation vector and a rotation
to be given to the final object."""
if not self.indexedfaces:
print("error: shapes were not indexed. Use run() first")
return
if not result:
result = []
if self.results:
result = self.results[-1]
d = {}
offset = FreeCAD.Vector(0, 0, 0)
for sheet in result:
for face in sheet:
orig = None
for pair in self.indexedfaces:
if pair[0] == face[0]:
orig = pair[1]
if not orig:
print("error: hashCode mismatch between original and transformed face")
return
shape = face[1]
if offset.Length:
shape.translate(offset)
deltav = shape.Faces[0].CenterOfMass.sub(orig.Faces[0].CenterOfMass)
rot = FreeCAD.Rotation(
orig.Vertexes[0].Point.sub(orig.Faces[0].CenterOfMass),
shape.Vertexes[0].Point.sub(shape.Faces[0].CenterOfMass),
)
pla = FreeCAD.Placement(deltav, rot)
d[face[0]] = pla
offset = offset.add(FreeCAD.Vector(1.1 * self.container.BoundBox.XLength, 0, 0))
return d
def apply(self, result=None):
"""apply([result]): Applies the computed placements of the given
result, or the last computed result if none is given, to the
document objects given to the nester via addObjects() before
running."""
if not self.objects:
print("objects list is empty")
return
p = self.getPlacements(result)
if p:
for key, pla in p.items():
if key in self.objects:
sh = self.objects[key].Shape.copy()
sh.translate(pla.Base)
sh.rotate(
sh.Faces[0].CenterOfMass,
pla.Rotation.Axis,
math.degrees(pla.Rotation.Angle),
)
self.objects[key].Placement = sh.Placement
else:
print("error: hashCode mismatch with original object")
def test():
"runs a test with selected shapes, container selected last"
import FreeCADGui
sel = FreeCADGui.Selection.getSelection()
if sel:
container = sel.pop().Shape
shapes = [o.Shape for o in sel]
n = Nester(container, shapes)
result = n.run()
if result:
n.show()
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