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
Exemple #3
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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)
Exemple #4
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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
Exemple #6
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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)