def hyperplanesOfFigure(figure):
hyperplanes = []
vertsPos = [v.position for v in figure if v.dim == 0]
innerPoint = algebra.vectAvg(*vertsPos)
for facet in figure.boundary:
hyperplanes.append(hyperplaneOfFacet(facet, innerPoint))
return hyperplanes
def hyperplanesOfFigure(figure): hyperplanes=[] vertsPos=[v.position for v in figure if v.dim == 0] innerPoint=algebra.vectAvg(*vertsPos) for facet in figure.boundary: hyperplanes.append(hyperplaneOfFacet(facet, innerPoint)) return hyperplanes
def cutOffFaces(figure, ratio, faces):
hyperplanes=[]
innerPoint=algebra.vectAvg(*[v.position for v in figure if v.dim==0])
for f in faces:
points=[v.position for v in f if v.dim==0]
basis=algebra.orthonormalBasisFromPoints(points)
normal=algebra.orthogonalizeVect(algebra.vectDiff(points[0], innerPoint), basis)
if algebra.vectLen(normal)<0.0001:
raise RuntimeError("Cannot cut faces")
hyperplanes.append(Hyperplane(normal, (1-ratio+algebra.dotProduct(normal, innerPoint)/algebra.vectLen(normal)**2)))
return cutOffConvex(figure, hyperplanes, innerPoint)
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)
