def dualPointFromHyperplane(hyperplane, centerPoint=None):
if not centerPoint:
centerPoint=(0,)*len(hyperplane.normal)
dist=hyperplane.orientedDistance(centerPoint)
if abs(dist) < 0.0001:
raise RuntimeError("Hyperplane passing through the center")
return algebra.vectSum(algebra.vectMult(-1/dist, hyperplane.normal), centerPoint)
def dualPointFromHyperplane(hyperplane, centerPoint=None):
if not centerPoint:
centerPoint=(0,)*len(hyperplane.normal)
dist=hyperplane.orientedDistance(centerPoint)
if abs(dist) < 0.0001:
raise RuntimeError("Hyperplane passing through the center")
return algebra.vectSum(algebra.vectMult(-1/dist, hyperplane.normal), centerPoint)
def cutFigure(wholeFigure, hyperplane): facesAscending=[] queue=[wholeFigure] mark=object() while queue: figure=queue.pop(0) if figure.mark==mark: continue figure.mark=mark facesAscending.insert(0,figure) queue.extend(figure.boundary) for figure in facesAscending: figure.usedInSection=False figure.sectionFacets=[] if figure.dim == 0: # Vertex dist=hyperplane.orientedDistance(figure.position) if abs(dist)<0.0001: figure.cuttingCache=([], [figure], []) elif dist>0: figure.cuttingCache=([], [], [figure]) else: figure.cuttingCache=([figure], [], []) continue; # Edge, face, ... left,middle,right = \ zip(*map(lambda f: f.cuttingCache, 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 figure.cuttingCache=([], [figure], []) continue if not right or not left: for f in middle: if f.dim==figure.dim-1: for f2 in f.boundary: f2.usedInSection=True figure.sectionFacets.append(f) middle2=[] for f in middle: if not f.usedInSection or f.dim == figure.dim-2: middle2.append(f) middle=middle2 if not right: # Nothing right figure.cuttingCache=([figure], middle, []) continue if not left: # Nothing left figure.cuttingCache=([], middle, [figure]) continue section=[] middle2=set() for f in middle: if f.dim == figure.dim-2: middle2.add(f) elif f.dim != figure.dim-1: section.append(f) middle=middle2 if 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))) vert.usedInSection=True leftEdge=Figure([left[0], vert]) rightEdge=Figure([right[0], vert]) leftEdge.sectionFacets=[vert] rightEdge.sectionFacets=[vert] figure.cuttingCache=([leftEdge], [vert], [rightEdge]) continue # Cutting face (at least 2-dimensional) leftComp=check.findComponents(left, middle) rightComp=check.findComponents(right, middle) leftComp=[Figure(c) for c in leftComp] rightComp=[Figure(c) for c in rightComp] for rightFigure in rightComp: rightFigure.sectionFacets=[] rightFigure.sectionRidges=set() for f in rightFigure.boundary: rightFigure.sectionRidges.update(f.sectionFacets) for leftFigure in leftComp: leftFigure.sectionFacets=[] leftRidges=set() for f in leftFigure.boundary: leftRidges.update(f.sectionFacets) for rightFigure in rightComp: rightRidges=rightFigure.sectionRidges commonRidges=leftRidges | rightRidges if commonRidges: f=Figure(commonRidges) f.usedInSection=True leftFigure.sectionFacets.append(f) rightFigure.sectionFacets.append(f) leftFigure.boundary.add(f) rightFigure.boundary.add(f) section.append(f) for f in middle: if not f.usedInSection: section.append(f) figure.cuttingCache=(leftComp, section, rightComp) ret=wholeFigure.cuttingCache; for figure in wholeFigure: del figure.cuttingCache del figure.usedInSection return ret;
def stellateFigure(figure):
objFigure.updateVerticesLists(figure)
objFigure.updateParentsLists(figure)
innerPoint=algebra.vectAvg(*[v.position for v in figure.vertices])
for f in figure.boundary:
f.hyperplane=spaceCuts.hyperplaneOfFacet(f, innerPoint);
f.hyperplane.origFacet=f
newFacets=[]
for f in figure.boundary:
facets=set()
for f2 in f.boundary:
facets.update(f2.parents)
facets.remove(f)
hyperplanes=[f2.hyperplane for f2 in facets]
hyperplane=f.hyperplane.inverse()
hyperplane.origFacet=f
apexPoint=algebra.vectAvg(*[v.position for v in f.vertices])
dist=float('inf')
for h in hyperplanes:
p=algebra.dotProduct(hyperplane.normal, h.normal)
if p<-0.0001:
d=-h.orientedDistance(apexPoint)/p
if d<0.0001:
raise RuntimeError("The figure is not convex")
elif d<dist:
dist=d
if dist == float('inf'):
raise RuntimeError("Infinite stellations are not supported")
hyperplanes.append(hyperplane)
apexInnerPoint=algebra.vectSum(apexPoint, algebra.vectMult(dist/2.0, hyperplane.normal))
apexFigure=spaceCuts.figureFromArea(hyperplanes, apexInnerPoint)
apexBaseFacet=[f3 for f3 in apexFigure.boundary if f3.origHypp.origFacet==f][0]
for f3 in apexFigure:
f3.origFace=None
apexFigure.rmFromBoundary(apexBaseFacet)
for apexFacet in apexFigure.boundary:
apexRidge=(apexFacet.boundary & apexBaseFacet.boundary).pop()
apexRidge.origFace=(apexFacet.origHypp.origFacet.boundary & f.boundary).pop()
objFigure.updateParentsLists(apexBaseFacet)
queue=[]
for apexRidge in apexBaseFacet.boundary:
queue.extend(apexRidge.boundary)
while queue:
apexFace=queue.pop(0)
if apexFace.origFace: continue
origP1=apexFace.parents[0].origFace
origP2=apexFace.parents[1].origFace
apexFace.origFace=(origP1.boundary & origP2.boundary).pop()
queue.extend(apexFace.boundary)
for f3 in apexBaseFacet:
del f3.parents
queue=[apexFigure]
apexFigure.mark=True
while queue:
apexFace=queue.pop(0)
if not apexFace.mark: continue
apexFace.mark=None
for apexFace2 in list(apexFace.boundary):
if apexFace2.origFace:
apexFace.boundary.remove(apexFace2)
apexFace.boundary.add(apexFace2.origFace)
else:
apexFace2.mark=True
queue.append(apexFace2)
newFacets.extend(apexFigure.boundary)
return objFigure.Figure(newFacets)
def stellateFigure(figure):
for f in figure.boundary:
for f2 in f:
f2.bounds=[]
for f in figure.boundary:
for f2 in f:
f2.bounds.append(f)
vertsPos=[v.position for v in figure if v.dim == 0]
innerPoint=algebra.vectMult(1.0/len(vertsPos), algebra.vectSum(*vertsPos))
figByBoundary=dict()
for f in sorted(figure, key=attrgetter("dim")):
if f.dim == 0:
pass
else:
figByBoundary[frozenset(f.boundary)]=f
newFacets=[]
for f in figure.boundary:
facets=set()
for f2 in f.boundary:
facets=facets.union(f2.bounds) # to be in-place
facets.remove(f)
hyperplanes=[spaceCuts.hyperplaneOfFacet(f2, innerPoint) for f2 in facets]
hyperplane=spaceCuts.hyperplaneOfFacet(f, innerPoint).inverse()
fv=[v.position for v in f if v.dim==0]
apexPoint=algebra.vectMult(1.0/len(fv), algebra.vectSum(*fv))
dist=float('inf')
for h in hyperplanes:
p=algebra.dotProduct(hyperplane.normal, h.normal)
if p<-0.0001:
d=-h.orientedDistance(apexPoint)/p
if d<0.0001:
raise RuntimeError("The figure is not convex")
elif d<dist:
dist=d
if dist == float('inf'):
raise RuntimeError("Infinite stellations are not supported")
hyperplanes.append(hyperplane)
apexInnerPoint=algebra.vectSum(apexPoint, algebra.vectMult(dist/2.0, hyperplane.normal))
apexFigure=spaceCuts.figureFromArea(hyperplanes, apexInnerPoint)
vertices=[v for v in f if v.dim == 0]
apexVertices=[v for v in apexFigure if v.dim == 0]
for f2 in sorted(apexFigure, key=attrgetter('dim')):
f2.copy=None
if f2.dim==0:
for v in vertices: # slow, can be improved
if algebra.pointsDist(v.position, f2.position) < 0.0001:
f2.copy = v
break
else:
boundary=set()
shared=True
for f3 in f2.boundary:
boundary.add(f3.copy or f3)
shared = shared and f3.copy
f2.boundary=boundary
if shared:
f2.copy=figByBoundary[frozenset(boundary)]
elif f2.dim==f.dim:
newFacets.append(f2)
return objFigure.Figure(newFacets)
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)