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Nesting algo for FreeCAD
# -*- coding: utf-8 -*-
#* *
#* Copyright (c) 2017 Yorik van Havre <> *
#* *
#* This program is free software; you can redistribute it and/or modify *
#* it under the terms of the GNU Lesser General Public License (LGPL) *
#* as published by the Free Software Foundation; either version 2 of *
#* the License, or (at your option) any later version. *
#* for detail see the LICENCE text file. *
#* *
#* This program is distributed in the hope that it will be useful, *
#* but WITHOUT ANY WARRANTY; without even the implied warranty of *
#* GNU Library General Public License for more details. *
#* *
#* You should have received a copy of the GNU Library General Public *
#* License along with this program; if not, write to the Free Software *
#* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 *
#* USA *
#* *
from __future__ import print_function
import FreeCAD, Part, DraftGeomUtils, WorkingPlane, DraftVecUtils, math, Draft
from datetime import datetime
# This is roughly based on the no-fit polygon algorithm, used in
# SvgNest:
# Wikihouse plugin:
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."""
self.container = container
self.shapes = shapes
self.results = [] # storage for the different results
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."""
starttime =
# general conformity tests
print("Executing conformity tests ... ",end="")
if not self.container:
print("Empty container. Aborting")
if not self.shapes:
print("Empty shapes. Aborting")
if not isinstance(self.container,Part.Face):
print("Container is not a face. Aborting")
normal = self.container.normalAt(0,0)
for f in self.shapes:
if not isinstance(f,Part.Face):
print("One of the shapes is not a face. Aborting")
# check if all faces correctly oriented (same normal)
if f.normalAt(0,0).getAngle(normal) > TOLERANCE:
print("One of the face doesn't have the same orientation as the container. Aborting")
# allow to use a non-rectangular container
# manage margins/paddings
# allow to prevent or force specific rotations for a piece
# add genetic algo to swap pieces, and check if the result is better
# 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 = [[face.hashCode(),face] for face in self.shapes]
# build a clean copy so we don't touch the original
faces = list(self.indexedfaces)
# order by area
faces = sorted(faces,key=lambda face: face[1].Area)
# discretize non-linear edges and remove holes
nfaces = []
for face in faces:
nedges = []
allLines = True
for edge in face[1].OuterWire.OrderedEdges:
if isinstance(edge.Curve,(Part.LineSegment,Part.Line)):
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)
last = new
f = Part.Face(Part.Wire(nedges))
if not f.isValid():
if allLines:
print("Invalid face found in set. Aborting")
print("Face distretizing failed. Aborting")
faces = nfaces
# container for sheets with a first, empty sheet
sheets = [[]]
print("Everything OK (",,")")
# 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 = []
for rotation in ROTATIONS:
print(rotation,", ",end="")
hashcode = face[0]
rotface = face[1].copy()
if 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:
print("One face doesn't fit in the container. Aborting")
if bof.YLength > boc.YLength:
print("One face doesn't fit in the container. Aborting")
# 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]))
# 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
nofitpol = []
for placed in sheet:
pts = []
pi = 0
for placedvert in self.order(placed[1],right=True):
fpts = []
for i,rotvert in enumerate(rotverts):
facecopy = rotface.copy()
# 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
# also need to test for edge intersection, because even
# if all vertices are outside, the pieces could still
# overlap
# TODO this code is slow and could be otimized...
if outside:
for e1 in facecopy.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):
outside = False
if outside:
# 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
fpts = fpts[slicepoint:]+fpts[:slicepoint]
# create the polygon
if len(pts) < 3:
print("Error calculating a no-fit polygon. Aborting")
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):
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 = Part.Face(Part.Wire(pol.OuterWire.OrderedEdges[:i]+[ne]+pol.OuterWire.OrderedEdges[i+2:]))
if not pol.isValid():
# trying basic OCC fix
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
print("Unable to fix invalid no-fit polygon. Aborting")
if not pol.isValid():
# none of the fixes worked. Epic fail.
print("Invalid no-fit polygon. Aborting")
for p in sheet:[1])
#for i,p in enumerate(faceverts):
# Draft.makeText([str(i)],point=p)
# 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:
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] = [e]
edges = [e[0] for e in lut.values() if len(e) == 1]
pol = Part.Face(Part.Wire(edges))
# above method can fail sometimes. Try a slower method
w = DraftGeomUtils.findWires(edges)
if len(w) == 1:
if w[0].isClosed():
pol = Part.Face(w[0])
print("Error merging polygons. Aborting")
for e in edges:
# 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)
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:
trface = rotface.copy()
ok = True
for placed in sheet:
if ok:
for vert in trface.Vertexes:
if placed[1].isInside(vert.Point,TOLERANCE,False):
ok = False
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
if not ok:
if ok:
rotface = trface
print("Couldn't determine location on sheet. Aborting")
# check the X space occupied by this solution
bb = rotface.BoundBox
for placed in sheet:
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)
# 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)
facenumber += 1
print("Run time:",
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.plane()
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
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:
elif s == 0:
print("error computing winding direction")
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)
for sheet in result:
shapes = [self.container.OuterWire]
shapes.extend([face[1] for face in sheet])
comp = Part.makeCompound(shapes)
offset = offset.add(FreeCAD.Vector(1.1*self.container.BoundBox.XLength,0,0))
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 =
if result:

nortikin commented Jul 1, 2017

no need to import Draft, print_function

nortikin commented Jul 1, 2017

is it only for rectangles or for ngons also?

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