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fcgeo.py
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fcgeo.py
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#***************************************************************************
#* *
#* Copyright (c) 2009, 2010 *
#* Yorik van Havre <[email protected]>, Ken Cline <[email protected]> *
#* *
#* This program is free software; you can redistribute it and/or modify *
#* it under the terms of the GNU General Public License (GPL) *
#* 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 *
#* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
#* 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 *
#* *
#***************************************************************************
__title__="FreeCAD Draft Workbench - Geometry library"
__author__ = "Yorik van Havre, Jacques-Antoine Gaudin, Ken Cline"
__url__ = ["http://free-cad.sourceforge.net"]
"this file contains generic geometry functions for manipulating Part shapes"
import FreeCAD, Part, fcvec, math, cmath, FreeCADGui
from FreeCAD import Vector
NORM = Vector(0,0,1) # provisory normal direction for all geometry ops.
params = FreeCAD.ParamGet("User parameter:BaseApp/Preferences/Mod/Draft")
precision = params.GetInt("precision")
# Generic functions *********************************************************
def vec(edge):
"vec(edge) or vec(line) -- returns a vector from an edge or a Part.line"
# if edge is not straight, you'll get strange results!
if isinstance(edge,Part.Shape):
return edge.Vertexes[-1].Point.sub(edge.Vertexes[0].Point)
elif isinstance(edge,Part.Line):
return edge.EndPoint.sub(edge.StartPoint)
else:
return None
def edg(p1,p2):
"edg(Vector,Vector) -- returns an edge from 2 vectors"
if isinstance(p1,FreeCAD.Vector) and isinstance(p2,FreeCAD.Vector):
if fcvec.equals(p1,p2): return None
else: return Part.Line(p1,p2).toShape()
def getVerts(shape):
"getVerts(shape) -- returns a list containing vectors of each vertex of the shape"
p = []
for v in shape.Vertexes:
p.append(v.Point)
return p
def v1(edge):
"v1(edge) -- returns the first point of an edge"
return edge.Vertexes[0].Point
def isNull(something):
'''returns true if the given shape is null or the given placement is 0 or
if the given vector is (0,0,0)'''
if isinstance(something,Part.Shape):
return something.isNull()
elif isinstance(something,FreeCAD.Vector):
if something == Vector(0,0,0):
return True
else:
return False
elif isinstance(something,FreeCAD.Placement):
if (something.Base == Vector(0,0,0)) and (something.Rotation.Q == (0,0,0,1)):
return True
else:
return False
def isPtOnEdge(pt,edge) :
'''isPtOnEdge(Vector,edge) -- Tests if a point is on an edge'''
if isinstance(edge.Curve,Part.Line) :
orig = edge.Vertexes[0].Point
if fcvec.isNull(pt.sub(orig).cross(vec(edge))) :
return pt.sub(orig).Length <= vec(edge).Length and pt.sub(orig).dot(vec(edge)) >= 0
else :
return False
elif isinstance(edge.Curve,Part.Circle) :
center = edge.Curve.Center
axis = edge.Curve.Axis ; axis.normalize()
radius = edge.Curve.Radius
if round(pt.sub(center).dot(axis),precision) == 0 \
and round(pt.sub(center).Length - radius,precision) == 0 :
if len(edge.Vertexes) == 1 :
return True # edge is a complete circle
else :
begin = edge.Vertexes[0].Point
end = edge.Vertexes[-1].Point
if fcvec.isNull(pt.sub(begin)) or fcvec.isNull(pt.sub(end)) :
return True
else :
# newArc = Part.Arc(begin,pt,end)
# return fcvec.isNull(newArc.Center.sub(center)) \
# and fcvec.isNull(newArc.Axis-axis) \
# and round(newArc.Radius-radius,precision) == 0
angle1 = fcvec.angle(begin.sub(center))
angle2 = fcvec.angle(end.sub(center))
anglept = fcvec.angle(pt.sub(center))
if (angle1 < anglept) and (anglept < angle2):
return True
return False
def hasCurves(shape):
"checks if the given shape has curves"
for e in shape.Edges:
if not isInstance(e.Curve,Part.Line):
return True
return False
# edge functions *****************************************************************
def findEdge(anEdge,aList):
'''findEdge(anEdge,aList): returns True if anEdge is found in aList of edges'''
for e in range(len(aList)):
if str(anEdge.Curve) == str(aList[e].Curve):
if fcvec.equals(anEdge.Vertexes[0].Point,aList[e].Vertexes[0].Point):
if fcvec.equals(anEdge.Vertexes[-1].Point,aList[e].Vertexes[-1].Point):
return(e)
return None
def findIntersection(edge1,edge2,infinite1=False,infinite2=False,ex1=False,ex2=False) :
'''findIntersection(edge1,edge2,infinite1=False,infinite2=False):
returns a list containing the intersection point(s) of 2 edges.
You can also feed 4 points instead of edge1 and edge2'''
pt1 = None
if isinstance(edge1,FreeCAD.Vector) and isinstance(edge2,FreeCAD.Vector):
# we got points directly
pt1 = edge1
pt2 = edge2
pt3 = infinite1
pt4 = infinite2
infinite1 = ex1
infinite2 = ex2
elif isinstance(edge1.Curve,Part.Line) and isinstance(edge2.Curve,Part.Line) :
# we have 2 edges
pt1, pt2, pt3, pt4 = [edge1.Vertexes[0].Point,
edge1.Vertexes[1].Point,
edge2.Vertexes[0].Point,
edge2.Vertexes[1].Point]
if pt1:
# first check if we don't already have coincident endpoints
if (pt1 in [pt3,pt4]):
return [pt1]
elif (pt2 in [pt3,pt4]):
return [pt2]
#we have 2 straight lines
if fcvec.isNull(pt2.sub(pt1).cross(pt3.sub(pt1)).cross(pt2.sub(pt4).cross(pt3.sub(pt4)))):
vec1 = pt2.sub(pt1) ; vec2 = pt4.sub(pt3)
if fcvec.isNull(vec1) or fcvec.isNull(vec2):
return []
vec1.normalize() ; vec2.normalize()
cross = vec1.cross(vec2)
if not fcvec.isNull(cross) :
k = ((pt3.z-pt1.z)*(vec2.x-vec2.y)+(pt3.y-pt1.y)*(vec2.z-vec2.x)+ \
(pt3.x-pt1.x)*(vec2.y-vec2.z))/(cross.x+cross.y+cross.z)
vec1.scale(k,k,k)
int = pt1.add(vec1)
if infinite1 == False and not isPtOnEdge(int,edge1) :
return []
if infinite2 == False and not isPtOnEdge(int,edge2) :
return []
return [int]
else :
return [] # Lines have same direction
else :
return [] # Lines aren't on same plane
elif isinstance(edge1.Curve,Part.Circle) and isinstance(edge2.Curve,Part.Line) \
or isinstance(edge1.Curve,Part.Line) and isinstance(edge2.Curve,Part.Circle) :
# deals with an arc or circle and a line
edges = [edge1,edge2]
for edge in edges :
if isinstance(edge.Curve,Part.Line) :
line = edge
else :
arc = edge
dirVec = vec(line) ; dirVec.normalize()
pt1 = line.Vertexes[0].Point
pt2 = line.Vertexes[1].Point
pt3 = arc.Vertexes[0].Point
pt4 = arc.Vertexes[-1].Point
center = arc.Curve.Center
# first check for coincident endpoints
if (pt1 in [pt3,pt4]):
return [pt1]
elif (pt2 in [pt3,pt4]):
return [pt2]
if fcvec.isNull(pt1.sub(center).cross(pt2.sub(center)).cross(arc.Curve.Axis)) :
# Line and Arc are on same plane
dOnLine = center.sub(pt1).dot(dirVec)
onLine = Vector(dirVec) ; onLine.scale(dOnLine,dOnLine,dOnLine)
toLine = pt1.sub(center).add(onLine)
if toLine.Length < arc.Curve.Radius :
dOnLine = (arc.Curve.Radius**2 - toLine.Length**2)**(0.5)
onLine = Vector(dirVec) ; onLine.scale(dOnLine,dOnLine,dOnLine)
int = [center.add(toLine).add(onLine)]
onLine = Vector(dirVec) ; onLine.scale(-dOnLine,-dOnLine,-dOnLine)
int += [center.add(toLine).add(onLine)]
elif round(toLine.Length-arc.Curve.Radius,precision) == 0 :
int = [center.add(toLine)]
else :
return []
else : # Line isn't on Arc's plane
if dirVec.dot(arc.Curve.Axis) != 0 :
toPlane = Vector(arc.Curve.Axis) ; toPlane.normalize()
d = vec1.dot(toPlane)
dToPlane = center.sub(pt1).dot(toPlane)
toPlane = Vector(vec1)
toPlane.scale(dToPlane/d,dToPlane/d,dToPlane/d)
ptOnPlane = toPlane.add(pt1)
if round(ptOnPlane.sub(center).Length - arc.Curve.Radius,precision) == 0 :
int = [ptOnPlane]
else :
return []
else :
return []
if infinite1 == False :
for i in range(len(int)-1,-1,-1) :
if not isPtOnEdge(int[i],edge1) :
del int[i]
if infinite2 == False :
for i in range(len(int)-1,-1,-1) :
if not isPtOnEdge(int[i],edge2) :
del int[i]
return int
elif isinstance(edge1.Curve,Part.Circle) and isinstance(edge2.Curve,Part.Circle) :
# deals with 2 arcs or circles
cent1, cent2 = edge1.Curve.Center, edge2.Curve.Center
rad1 , rad2 = edge1.Curve.Radius, edge2.Curve.Radius
axis1, axis2 = edge1.Curve.Axis , edge2.Curve.Axis
c2c = cent2.sub(cent1)
if fcvec.isNull(axis1.cross(axis2)) :
if round(c2c.dot(axis1),precision) == 0 :
# circles are on same plane
dc2c = c2c.Length ;
if not fcvec.isNull(c2c): c2c.normalize()
if round(rad1+rad2-dc2c,precision) < 0 \
or round(rad1-dc2c-rad2,precision) > 0 or round(rad2-dc2c-rad1,precision) > 0 :
return []
else :
norm = c2c.cross(axis1)
if not fcvec.isNull(norm): norm.normalize()
if fcvec.isNull(norm): x = 0
else: x = (dc2c**2 + rad1**2 - rad2**2)/(2*dc2c)
y = abs(rad1**2 - x**2)**(0.5)
c2c.scale(x,x,x)
if round(y,precision) != 0 :
norm.scale(y,y,y)
int = [cent1.add(c2c).add(norm)]
int += [cent1.add(c2c).sub(norm)]
else :
int = [cent1.add(c2c)]
else :
return [] # circles are on parallel planes
else :
# circles aren't on same plane
axis1.normalize() ; axis2.normalize()
U = axis1.cross(axis2)
V = axis1.cross(U)
dToPlane = c2c.dot(axis2)
d = V.add(cent1).dot(axis2)
V.scale(dToPlane/d,dToPlane/d,dToPlane/d)
PtOn2Planes = V.add(cent1)
planeIntersectionVector = U.add(PtOn2Planes)
intTemp = findIntersection(planeIntersectionVector,edge1,True,True)
int = []
for pt in intTemp :
if round(pt.sub(cent2).Length-rad2,precision) == 0 :
int += [pt]
if infinite1 == False :
for i in range(len(int)-1,-1,-1) :
if not isPtOnEdge(int[i],edge1) :
del int[i]
if infinite2 == False :
for i in range(len(int)-1,-1,-1) :
if not isPtOnEdge(int[i],edge2) :
del int[i]
return int
else :
print "fcgeo: Unsupported curve type: (" + str(edge1.Curve) + ", " + str(edge2.Curve) + ")"
def mirror (point, edge):
"finds mirror point relative to an edge"
normPoint = point.add(findDistance(point, edge, False))
if normPoint:
normPoint_point = Vector.sub(point, normPoint)
normPoint_refl = fcvec.neg(normPoint_point)
refl = Vector.add(normPoint, normPoint_refl)
return refl
else:
return None
def findClosest(basepoint,pointslist):
'''
findClosest(vector,list)
in a list of 3d points, finds the closest point to the base point.
an index from the list is returned.
'''
if not pointslist: return None
smallest = 100000
for n in range(len(pointslist)):
new = basepoint.sub(pointslist[n]).Length
if new < smallest:
smallest = new
npoint = n
return npoint
def concatenate(shape):
"concatenate(shape) -- turns several faces into one"
edges = getBoundary(shape)
edges = sortEdges(edges)
try:
wire=Part.Wire(edges)
face=Part.Face(wire)
except:
print "fcgeo: Couldn't join faces into one"
return(shape)
else:
if not wire.isClosed(): return(wire)
else: return(face)
def getBoundary(shape):
"getBoundary(shape) -- this function returns the boundary edges of a group of faces"
# make a lookup-table where we get the number of occurrences
# to each edge in the fused face
if isinstance(shape,list):
shape = Part.makeCompound(shape)
lut={}
for f in shape.Faces:
for e in f.Edges:
hc= e.hashCode()
if lut.has_key(hc): lut[hc]=lut[hc]+1
else: lut[hc]=1
# filter out the edges shared by more than one sub-face
bound=[]
for e in shape.Edges:
if lut[e.hashCode()] == 1: bound.append(e)
return bound
def sortEdges(lEdges, aVertex=None):
"an alternative, more accurate version of Part.__sortEdges__"
#There is no reason to limit this to lines only because every non-closed edge always
#has exactly two vertices (wmayer)
#for e in lEdges:
# if not isinstance(e.Curve,Part.Line):
# print "Warning: sortedges cannot treat wired containing curves yet."
# return lEdges
def isSameVertex(V1, V2):
''' Test if vertexes have same coordinates with precision 10E(-precision)'''
if round(V1.X-V2.X,1)==0 and round(V1.Y-V2.Y,1)==0 and round(V1.Z-V2.Z,1)==0 :
return True
else :
return False
def lookfor(aVertex, inEdges):
''' Look for (aVertex, inEdges) returns count, the position of the instance
the position in the instance and the instance of the Edge'''
count = 0
linstances = [] #lists the instances of aVertex
for i in range(len(inEdges)) :
for j in range(2) :
if isSameVertex(aVertex,inEdges[i].Vertexes[j-1]):
instance = inEdges[i]
count += 1
linstances += [i,j-1,instance]
return [count]+linstances
if (len(lEdges) < 2):
if aVertex == None:
return lEdges
else:
result = lookfor(aVertex,lEdges)
if result[0] != 0:
if isSameVertex(aVertex,result[3].Vertexes[0]):
return lEdges
else:
if isinstance(result[3].Curve,Part.Line):
return [Part.Line(aVertex.Point,result[3].Vertexes[0].Point).toShape()]
elif isinstance(result[3].Curve,Part.Circle):
mp = findMidpoint(result[3])
return [Part.Arc(aVertex.Point,mp,result[3].Vertexes[0].Point).toShape()]
else:
return lEdges
olEdges = [] # ol stands for ordered list
if aVertex == None:
for i in range(len(lEdges)*2) :
if len(lEdges[i/2].Vertexes) > 1:
result = lookfor(lEdges[i/2].Vertexes[i%2],lEdges)
if result[0] == 1 : # Have we found an end ?
olEdges = sortEdges(lEdges, result[3].Vertexes[result[2]])
return olEdges
# if the wire is closed there is no end so choose 1st Vertex
return sortEdges(lEdges, lEdges[0].Vertexes[0])
else :
result = lookfor(aVertex,lEdges)
if result[0] != 0 :
del lEdges[result[1]]
next = sortEdges(lEdges, result[3].Vertexes[-((-result[2])^1)])
if isSameVertex(aVertex,result[3].Vertexes[0]):
olEdges += [result[3]] + next
else:
if isinstance(result[3].Curve,Part.Line):
newedge = Part.Line(aVertex.Point,result[3].Vertexes[0].Point).toShape()
olEdges += [newedge] + next
elif isinstance(result[3].Curve,Part.Circle):
mp = findMidpoint(result[3])
newedge = Part.Arc(aVertex.Point,mp,result[3].Vertexes[0].Point).toShape()
olEdges += [newedge] + next
else:
olEdges += [result[3]] + next
return olEdges
else :
return []
def superWire(edgeslist,closed=False):
'''superWire(edges,[closed]): forces a wire between edges that don't necessarily
have coincident endpoints. If closed=True, wire will always be closed'''
def median(v1,v2):
vd = v2.sub(v1)
vd.scale(.5,.5,.5)
return v1.add(vd)
edges = sortEdges(edgeslist)
print edges
newedges = []
for i in range(len(edges)):
curr = edges[i]
if i == 0:
if closed:
prev = edges[-1]
else:
prev = None
else:
prev = edges[i-1]
if i == (len(edges)-1):
if closed:
next = edges[0]
else:
next = None
else:
next = edges[i+1]
print i,prev,curr,next
if prev:
if curr.Vertexes[0].Point == prev.Vertexes[-1].Point:
p1 = curr.Vertexes[0].Point
else:
p1 = median(curr.Vertexes[0].Point,prev.Vertexes[-1].Point)
else:
p1 = curr.Vertexes[0].Point
if next:
if curr.Vertexes[-1].Point == next.Vertexes[0].Point:
p2 = next.Vertexes[0].Point
else:
p2 = median(curr.Vertexes[-1].Point,next.Vertexes[0].Point)
else:
p2 = curr.Vertexes[-1].Point
if isinstance(curr.Curve,Part.Line):
print "line",p1,p2
newedges.append(Part.Line(p1,p2).toShape())
elif isinstance(curr.Curve,Part.Circle):
p3 = findMidpoint(curr)
print "arc",p1,p3,p2
newedges.append(Part.Arc(p1,p3,p2).toShape())
else:
print "Cannot superWire edges that are not lines or arcs"
return None
print newedges
return Part.Wire(newedges)
def findMidpoint(edge):
"calculates the midpoint of an edge"
first = edge.Vertexes[0].Point
last = edge.Vertexes[-1].Point
if isinstance(edge.Curve,Part.Circle):
center = edge.Curve.Center
radius = edge.Curve.Radius
if len(edge.Vertexes) == 1:
# Circle
dv = first.sub(center)
dv = fcvec.neg(dv)
return center.add(dv)
axis = edge.Curve.Axis
chord = last.sub(first)
perp = chord.cross(axis)
perp.normalize()
ray = first.sub(center)
apothem = ray.dot(perp)
sagitta = radius - apothem
startpoint = Vector.add(first, fcvec.scale(chord,0.5))
endpoint = fcvec.scaleTo(perp,sagitta)
return Vector.add(startpoint,endpoint)
elif isinstance(edge.Curve,Part.Line):
halfedge = fcvec.scale(last.sub(first),.5)
return Vector.add(first,halfedge)
else:
return None
def complexity(obj):
'''
tests given object for shape complexity:
1: line
2: arc
3: circle
4: open wire with no arc
5: closed wire
6: wire with arcs
7: faces
8: faces with arcs
'''
shape = obj.Shape
if shape.Faces:
for e in shape.Edges:
if (isinstance(e.Curve,Part.Circle)): return 8
return 7
if shape.Wires:
for e in shape.Edges:
if (isinstance(e.Curve,Part.Circle)): return 6
for w in shape.Wires:
if w.isClosed(): return 5
return 4
if (isinstance(shape.Edges[0].Curve,Part.Circle)):
if len(shape.Vertexes) == 1:
return 3
return 2
return 1
def findPerpendicular(point,edgeslist,force=None):
'''
findPerpendicular(vector,wire,[force]):
finds the shortest perpendicular distance between a point and an edgeslist.
If force is specified, only the edge[force] will be considered, and it will be
considered infinite.
The function will return a list [vector_from_point_to_closest_edge,edge_index]
or None if no perpendicular vector could be found.
'''
if not isinstance(edgeslist,list):
try:
edgeslist = edgeslist.Edges
except:
return None
if (force == None):
valid = None
for edge in edgeslist:
dist = findDistance(point,edge,strict=True)
if dist:
if not valid: valid = [dist,edgeslist.index(edge)]
else:
if (dist.Length < valid[0].Length):
valid = [dist,edgeslist.index(edge)]
return valid
else:
edge = edgeslist[force]
dist = findDistance(point,edge)
if dist: return [dist,force]
else: return None
return None
def offset(edge,vector):
'''
offset(edge,vector)
returns a copy of the edge at a certain (vector) distance
if the edge is an arc, the vector will be added at its first point
and a complete circle will be returned
'''
if (not isinstance(edge,Part.Shape)) or (not isinstance(vector,FreeCAD.Vector)):
return None
if isinstance(edge.Curve,Part.Line):
v1 = Vector.add(edge.Vertexes[0].Point, vector)
v2 = Vector.add(edge.Vertexes[-1].Point, vector)
return Part.Line(v1,v2).toShape()
else:
rad = edge.Vertexes[0].Point.sub(edge.Curve.Center)
newrad = Vector.add(rad,vector).Length
return Part.Circle(edge.Curve.Center,NORM,newrad).toShape()
def isReallyClosed(wire):
"checks if a wire is really closed"
if len(wire.Edges) == len(wire.Vertexes): return True
v1 = wire.Vertexes[0].Point
v2 = wire.Vertexes[-1].Point
if fcvec.equals(v1,v2): return True
return False
def getNormal(shape):
"finds the normal of a shape, if possible"
n = Vector(0,0,1)
if shape.ShapeType == "Face":
n = shape.normalAt(0.5,0.5)
elif shape.ShapeType == "Edge":
if isinstance(shape.Curve,Part.Circle):
n = shape.Curve.Axis
else:
for e in shape.Edges:
if isinstance(e.Curve,Part.Circle):
n = e.Curve.Axis
break
e1 = vec(shape.Edges[0])
for i in range(1,len(shape.Edges)):
e2 = vec(shape.Edges[i])
if 0.1 < abs(e1.getAngle(e2)) < 1.56:
n = e1.cross(e2).normalize()
break
vdir = FreeCADGui.ActiveDocument.ActiveView.getViewDirection()
if n.getAngle(vdir) < 0.78: n = fcvec.neg(n)
return n
def offsetWire(wire,dvec,bind=False,occ=False):
'''
offsetWire(wire,vector,[bind]): offsets the given wire along the
given vector. The vector will be applied at the first vertex of
the wire. If bind is True (and the shape is open), the original
wire and the offsetted one are bound by 2 edges, forming a face.
'''
edges = sortEdges(wire.Edges)
norm = getNormal(wire)
closed = isReallyClosed(wire)
nedges = []
if occ:
l=abs(dvec.Length)
if not l: return None
if not wire.Wires:
wire = Part.Wire(edges)
try:
off = wire.makeOffset(l)
except:
return None
else:
return off
for i in range(len(edges)):
curredge = edges[i]
delta = dvec
if i != 0:
angle = fcvec.angle(vec(edges[0]),vec(curredge),norm)
delta = fcvec.rotate(delta,angle,norm)
nedge = offset(curredge,delta)
nedges.append(nedge)
nedges = connect(nedges,closed)
if bind and not closed:
e1 = Part.Line(edges[0].Vertexes[0].Point,nedges[0].Vertexes[0].Point).toShape()
e2 = Part.Line(edges[-1].Vertexes[-1].Point,nedges[-1].Vertexes[-1].Point).toShape()
alledges = edges.extend(nedges)
alledges = alledges.extend([e1,e2])
w = Part.Wire(alledges)
return w
else:
return nedges
def connect(edges,closed=False):
'''connects the edges in the given list by their intersections'''
nedges = []
for i in range(len(edges)):
curr = edges[i]
# print "fcgeo.connect edge ",i," : ",curr.Vertexes[0].Point,curr.Vertexes[-1].Point
if i > 0:
prev = edges[i-1]
else:
if closed:
prev = edges[-1]
else:
prev = None
if i < (len(edges)-1):
next = edges[i+1]
else:
if closed: next = edges[0]
else:
next = None
if prev:
# print "debug: fcgeo.connect prev : ",prev.Vertexes[0].Point,prev.Vertexes[-1].Point
v1 = findIntersection(curr,prev,True,True)[0]
else:
v1 = curr.Vertexes[0].Point
if next:
# print "debug: fcgeo.connect next : ",next.Vertexes[0].Point,next.Vertexes[-1].Point
v2 = findIntersection(curr,next,True,True)[0]
else:
v2 = curr.Vertexes[-1].Point
if isinstance(curr.Curve,Part.Line):
if v1 != v2:
nedges.append(Part.Line(v1,v2).toShape())
elif isinstance(curr.Curve,Part.Circle):
if v1 != v2:
nedges.append(Part.Arc(v1,findMidPoint(curr),v2))
return Part.Wire(nedges)
def findDistance(point,edge,strict=False):
'''
findDistance(vector,edge,[strict]) - Returns a vector from the point to its
closest point on the edge. If strict is True, the vector will be returned
only if its endpoint lies on the edge.
'''
if isinstance(point, FreeCAD.Vector):
if isinstance(edge.Curve, Part.Line):
segment = vec(edge)
chord = edge.Vertexes[0].Point.sub(point)
norm = segment.cross(chord)
perp = segment.cross(norm)
dist = fcvec.project(chord,perp)
if not dist: return None
newpoint = point.add(dist)
if (dist.Length == 0):
return None
if strict:
s1 = newpoint.sub(edge.Vertexes[0].Point)
s2 = newpoint.sub(edge.Vertexes[-1].Point)
if (s1.Length <= segment.Length) and (s2.Length <= segment.Length):
return dist
else:
return None
else: return dist
elif isinstance(edge.Curve, Part.Circle):
ve1 = edge.Vertexes[0].Point
if (len(edge.Vertexes) > 1):
ve2 = edge.Vertexes[-1].Point
else:
ve2 = None
center = edge.Curve.Center
segment = center.sub(point)
ratio = (segment.Length - edge.Curve.Radius) / segment.Length
dist = fcvec.scale(segment,ratio)
newpoint = Vector.add(point, dist)
if (dist.Length == 0):
return None
if strict and ve2:
ang1 = fcvec.angle(ve1.sub(center))
ang2 = fcvec.angle(ve2.sub(center))
angpt = fcvec.angle(newpoint.sub(center))
if ((angpt <= ang2 and angpt >= ang1) or (angpt <= ang1 and angpt >= ang2)):
return dist
else:
return None
else:
return dist
else:
print "fcgeo: Couldn't project point"
return None
else:
print "fcgeo: Couldn't project point"
return None
def angleBisection(edge1, edge2):
"angleBisection(edge,edge) - Returns an edge that bisects the angle between the 2 edges."
if isinstance(edge1.Curve, Part.Line) and isinstance(edge2.Curve, Part.Line):
p1 = edge1.Vertexes[0].Point
p2 = edge1.Vertexes[-1].Point
p3 = edge2.Vertexes[0].Point
p4 = edge2.Vertexes[-1].Point
int = findIntersection(edge1, edge2, True, True)
if int:
line1Dir = p2.sub(p1)
angleDiff = fcvec.angle(line1Dir, p4.sub(p3))
ang = angleDiff * 0.5
origin = int[0]
line1Dir.normalize()
dir = fcvec.rotate(line1Dir, ang)
return Part.Line(origin,origin.add(dir)).toShape()
else:
diff = p3.sub(p1)
origin = p1.add(fcvec.scale(diff, 0.5))
dir = p2.sub(p1); dir.normalize()
return Part.Line(origin,origin.add(dir)).toShape()
else:
return None
def findClosestCircle(point,circles):
"findClosestCircle(Vector, list of circles) -- returns the circle with closest center"
dist = 1000000
closest = None
for c in circles:
if c.Center.sub(point).Length < dist:
dist = c.Center.sub(point).Length
closest = c
return closest
def isCoplanar(faces):
"checks if all faces in the given list are coplanar"
if len(faces) < 2:
return True
base =faces[0].normalAt(.5,.5)
for i in range(1,len(faces)):
normal = faces[i].normalAt(.5,.5)
if (normal.getAngle(base) > .0001) and (normal.getAngle(base) < 3.1415):
return False
return True
def findWires(edges):
'''finds connected edges in the list, and returns a list of lists containing edges
that can be connected'''
def verts(shape):
return [shape.Vertexes[0].Point,shape.Vertexes[-1].Point]
def group(shapes):
shapesIn = shapes[:]
shapesOut = [shapesIn.pop()]
changed = False
for s in shapesIn:
if len(s.Vertexes) < 2:
continue
else:
clean = True
for v in verts(s):
for i in range(len(shapesOut)):
if clean and (v in verts(shapesOut[i])):
shapesOut[i] = Part.Wire(shapesOut[i].Edges+s.Edges)
changed = True
clean = False
if clean:
shapesOut.append(s)
return(changed,shapesOut)
working = True
edgeSet = edges
while working:
result = group(edgeSet)
working = result[0]
edgeSet = result[1]
return result[1]
def getTangent(edge,frompoint=None):
'''
returns the tangent to an edge. If from point is given, it is used to
calculate the tangent (only useful for an arc of course).
'''
if isinstance(edge.Curve,Part.Line):
return vec(edge)
elif isinstance(edge.Curve,Part.Circle):
if not frompoint:
v1 = edge.Vertexes[0].Point.sub(edge.Curve.Center)
else:
v1 = frompoint.sub(edge.Curve.Center)
return v1.cross(edge.Curve.Axis)
return None
def bind(w1,w2):
'''bind(wire1,wire2): binds 2 wires by their endpoints and
returns a face'''
w3 = Part.Line(w1.Vertexes[0].Point,w2.Vertexes[0].Point).toShape()
w4 = Part.Line(w1.Vertexes[-1].Point,w2.Vertexes[-1].Point).toShape()
return Part.Face(Part.Wire(w1.Edges+[w3]+w2.Edges+[w4]))
def cleanFaces(shape):
"removes inner edges from coplanar faces"
faceset = shape.Faces
def find(hc):
"finds a face with the given hashcode"
for f in faceset:
if f.hashCode() == hc:
return f
def findNeighbour(hface,hfacelist):
"finds the first neighbour of a face in a list, and returns its index"
eset = []
for e in find(hface).Edges:
eset.append(e.hashCode())
for i in range(len(hfacelist)):
for ee in find(hfacelist[i]).Edges:
if ee.hashCode() in eset:
return i
return None
# build lookup table
lut = {}
for face in faceset:
for edge in face.Edges:
if edge.hashCode() in lut:
lut[edge.hashCode()].append(face.hashCode())
else:
lut[edge.hashCode()] = [face.hashCode()]
# print "lut:",lut
# take edges shared by 2 faces
sharedhedges = []
for k,v in lut.iteritems():
if len(v) == 2:
sharedhedges.append(k)
# print len(sharedhedges)," shared edges:",sharedhedges
# find those with same normals
targethedges = []
for hedge in sharedhedges:
faces = lut[hedge]
n1 = find(faces[0]).normalAt(0.5,0.5)
n2 = find(faces[1]).normalAt(0.5,0.5)
if n1 == n2:
targethedges.append(hedge)
# print len(targethedges)," target edges:",targethedges
# get target faces
hfaces = []
for hedge in targethedges:
for f in lut[hedge]:
if not f in hfaces:
hfaces.append(f)
# print len(hfaces)," target faces:",hfaces
# sort islands
islands = [[hfaces.pop(0)]]
currentisle = 0
currentface = 0
found = True
while hfaces:
if not found:
if len(islands[currentisle]) > (currentface + 1):
currentface += 1
found = True
else:
islands.append([hfaces.pop(0)])
currentisle += 1
currentface = 0
found = True
else:
f = findNeighbour(islands[currentisle][currentface],hfaces)
if f != None:
islands[currentisle].append(hfaces.pop(f))
else:
found = False
# print len(islands)," islands:",islands
# make new faces from islands
newfaces = []
treated = []
for isle in islands:
treated.extend(isle)
fset = []
for i in isle: fset.append(find(i))
bounds = getBoundary(fset)
shp = Part.Wire(sortEdges(bounds))
shp = Part.Face(shp)
if shp.normalAt(0.5,0.5) != find(isle[0]).normalAt(0.5,0.5):
shp.reverse()
newfaces.append(shp)
# print "new faces:",newfaces
# add remaining faces
for f in faceset:
if not f.hashCode() in treated:
newfaces.append(f)
# print "final faces"
# finishing
fshape = Part.makeShell(newfaces)
if shape.isClosed():
fshape = Part.makeSolid(fshape)
return fshape
def isCubic(shape):
'''isCubic(shape): verifies if a shape is cubic, that is, has
8 vertices, 6 faces, and all angles are 90 degrees.'''
# first we try fast methods
if len(shape.Vertexes) != 8:
return False
if len(shape.Faces) != 6:
return False
if len(shape.Edges) != 12:
return False
for e in shape.Edges:
if not isinstance(e.Curve,Part.Line):
return False
# if ok until now, let's do more advanced testing
for f in shape.Faces:
if len(f.Edges) != 4: return False
for i in range(4):