def isFigureConvex(figure): if not isFigureClosed(figure): return False innerPoint=algebra.vectAvg(*(v.position for v in figure if v.dim==0)) facetsInnerPoints=dict() edgesParents=dict() for facet in figure.boundary: facetsInnerPoints[facet]=algebra.vectAvg(*(v.position for v in facet if v.dim==0)) for edge in facet.boundary: if not edge in edgesParents: edgesParents[edge]=set() edgesParents[edge].add(facet) hyperplanes=spaceCuts.hyperplanesOfFigure(figure); for facet in figure.boundary: hyperplane=spaceCuts.hyperplaneOfFacet(facet, innerPoint) for edge in facet.boundary: facet2=[f for f in edgesParents[edge] if f!=facet][0] point=facetsInnerPoints[facet2] if hyperplane.orientedDistance(point)<0.0001: return False return True
def isFigureConvex(figure): if not isBoundaryComplete(figure): return False innerPoint=algebra.vectAvg(*(v.position for v in figure if v.dim==0)) facetsInnerPoints=dict() edgesParents=dict() for facet in figure.boundary: facetsInnerPoints[facet]=algebra.vectAvg(*(v.position for v in facet if v.dim==0)) for edge in facet.boundary: if not edge in edgesParents: edgesParents[edge]=set() edgesParents[edge].add(facet) hyperplanes=spaceCuts.hyperplanesOfFigure(figure); for facet in figure.boundary: hyperplane=spaceCuts.hyperplaneOfFacet(facet, innerPoint) for edge in facet.boundary: facet2=[f for f in edgesParents[edge] if f!=facet][0] point=facetsInnerPoints[facet2] if hyperplane.orientedDistance(point)<0.0001: return False return True
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)
