def createDual(figure, centerPoint=None):
if figure.dim<2:
raise RuntimeError("Figure has to have at least 2 dimensions")
dualFigure=Figure()
objFigure.updateVerticesLists(figure)
for f in figure:
f.dualCache=None
try:
for f in figure:
d=figure.dim-f.dim-1
if d<0: continue
if d==0: # create vertex of the dual figure using polar reciprocation
vertsPos=[v.position for v in f.vertices]
hyperplane=algebra.hyperplaneFromPoints(vertsPos)
f.dualCache=Vertex(dualPointFromHyperplane(hyperplane, centerPoint))
else:
f.dualCache=Figure()
f.dualCache.setDim(d,figure.spaceDim)
f.dualCache.origDualFace=f
for f in figure:
if f.dim<figure.dim:
for child in f.boundary:
child.dualCache.addToBoundary(f.dualCache)
if f.dim == 0:
dualFigure.addToBoundary(f.dualCache)
finally:
for f in figure:
del f.dualCache
return dualFigure
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)
