def figuresMaxRadius(figures): maxRadius=0 for f in figuresIterator(figures): if f.dim==0: r=algebra.vectLen(f.position) if r>maxRadius: maxRadius=r return maxRadius
def figuresScale(figures, factor): for f in figuresIterator(figures): if f.dim==0: f.position=algebra.vectMult(factor, f.position)
def cutFigure(figure, hyperplane, reuseCache=False):
if not reuseCache:
for f in figure:
f.cuttingCache=None
if figure.cuttingCache: # Already computed
return figure.cuttingCache
def cache(left, section, right): # Caching before returning
if reuseCache:
figure.cuttingCache=left,section,right
else: # Remove cache
for f in figure:
del f.cuttingCache
return left, section, right
if figure.dim == 0: # Vertex
dist=hyperplane.orientedDistance(figure.position)
if abs(dist)<0.00001:
return cache([], [figure], [])
elif dist<0:
return cache([figure], [], [])
else:
return cache([], [], [figure])
else: # Edge, face, ...
left,middle,right = \
zip(*map(lambda f: cutFigure(f, hyperplane, True), figure.boundary))
left,middle,right = (reduce(lambda a,b: a+b, l) for l in (left,middle,right))
if not right and not left: # All in the hyperplane
return cache([], [figure], [])
elif not right: # Nothing right
return cache([figure], middle, [])
elif not left: # Nothing left
return cache([], middle, [figure])
elif figure.dim == 1: # Cutting edge
diff=algebra.vectDiff(right[0].position, left[0].position)
prod=algebra.dotProduct(diff, hyperplane.normal)
dist=hyperplane.orientedDistance(left[0].position)
vert=Vertex(algebra.vectSum(left[0].position, algebra.vectMult(-dist/prod, diff)))
leftEdge=Figure([left[0], vert])
rightEdge=Figure([right[0], vert])
return cache([leftEdge], [vert], [rightEdge])
else: # Cutting face (at least 2-dimensional)
middle.sort(key=attrgetter('dim'), reverse=True)
for f in figuresIterator(middle):
f.used=False
section=[]
middle2=set()
for f in middle:
if not f.used:
if f.dim == figure.dim-2:
middle2.add(f)
else:
section.append(f)
for f2 in f:
f2.used=True
for f in figuresIterator(middle):
del f.used
if True: # General case
def findComponents(figures, exclude):
for f in figures:
f.group=None
f.groupIndex=None
f.groupRank=0
for f2 in f.boundary:
f2.groupRank=0
f2.group=None
def find(f):
f2=f
while f.group:
f=f.group
while f2.group:
f3=f2.group
f2.group=f
f2=f3
return f
def union(parent, child):
parent=find(parent)
child=find(child)
if child == parent:
return
if parent.groupRank>child.groupRank:
child.group=parent
elif parent.groupRank == child.groupRank:
child.group=parent
parent.groupRank+=1
else:
parent.group=child
return
for f in figures:
for f2 in f.boundary:
if not f2 in exclude:
union(f, f2)
groups=[]
for f in figures:
g=find(f)
if g.groupIndex == None:
g.groupIndex=len(groups)
groups.append([])
groups[g.groupIndex].append(f)
for f in figures:
del f.group
del f.groupIndex
del f.groupRank
for f2 in f.boundary:
f2.group=None
del f2.group
f2.groupRank=None
del f2.groupRank
return groups
leftComp=findComponents(left, middle2)
rightComp=findComponents(right, middle2)
leftComp=[Figure(c) for c in leftComp]
rightComp=[Figure(c) for c in rightComp]
sectComp=[]
for f in leftComp:
comp=[set()]
for f2 in f.boundary:
comp[0] |= f2.boundary & middle2
sectComp.append(comp)
f.sect=comp
# sectComp=[ [set(vertices)] ]
for f in rightComp:
f.sect=[]
for c in sectComp:
m=c.pop()
for f in rightComp:
comp=[set()]
for f2 in f.boundary:
comp[0] |= f2.boundary & m
c.append(comp)
f.sect.append(comp)
# sectComp=[ [[set(vertices)]] ]
for l in sectComp:
for m in l:
m.append(Figure(m.pop()))
section.append(m[0])
for f in leftComp+rightComp:
for f2 in f.sect:
f.addToBoundary(f2[0])
del f.sect
else: # Convex only
newSect=Figure(middle2)
leftComp=[Figure(left + [newSect])]
rightComp=[Figure(right + [newSect])]
section.append(newSect)
return cache(leftComp, section, rightComp)