dodecahedron.py lsst::skymap::detail::dodecahedron::Dodecahedron lsst::skymap::detail::dodecahedron #!/usr/bin/envpython __all__=['Dodecahedron'] importmath importnumpy classDodecahedron: """Adodecahedronwithpositionsoffacesandassociatedvertices. Parameters ---------- withFacesOnPoles:`bool` IfTruecenterafaceoneachpole,elseputavertexoneachpole. """ def__init__(self,withFacesOnPoles=False): self._withFacesOnPoles_withFacesOnPoles=bool(withFacesOnPoles) #Basiscartesianvectorsdescribingthefacesofadodecahedron;thefullsetofvectorsisobtained #bychoosingbothsignsofeachnonzerocomponentofeachvector. #Theorientationoftheresultingdodecahedron,whileveryconvenient #forspecifyingfacevectors,isnotanorientationwewantsoitmustberotated. g=(1.0+math.sqrt(5.0))/2.0 faceBases=( (0,1,g), (1,g,0), (g,0,1), ) unrotFaceVecList=_computeFullVecList(faceBases) unrotVertexVecList=_computeDodecahedronVertices(unrotFaceVecList) ifself._withFacesOnPoles_withFacesOnPoles: #onefaceiscenteredoneachpole vec0,vec1=_findClosePair(unrotFaceVecList,0) rotMat=_computeCoordTransform(vec0,vec1) else: #onevertexisoneachpole vec0,vec1=_findClosePair(unrotVertexVecList,0) rotMat=_computeCoordTransform(vec0,vec1,vec1NegativeX=True) self.vertexVecListvertexVecList=[numpy.dot(rotMat,unrotVertexVec)forunrotVertexVecinunrotVertexVecList] unsortedFaceList=[numpy.dot(rotMat,unrotFaceVec)forunrotFaceVecinunrotFaceVecList] self.faceVecListfaceVecList=_sortedVectorList(unsortedFaceList) defgetFaceCtrList(self): """Returnalistoffacecenters. Returns ------- results:`list`of`numpy.ndarray` Alistoffacecenters(inindexorder);eachaunitvector. """ returnself.faceVecListfaceVecList[:] defgetFaceCtr(self,ind): """Returnthecenterofthespecifiedface. Parameters ---------- ind:`int` Indexofthefacetolookup. Returns ------- results:`np.ndarray` Facecenterasaunitvector. """ returnself.faceVecListfaceVecList[ind][:] defgetVertices(self,ind): """Returntheverticesforagivenface. Parameters ---------- ind:`int` Faceindex. Returns ------- sortedVertexList:`list`of`numpy.ndarray` Alistofvertices,eachaunitvector. """ faceVec=self.getFaceCtrgetFaceCtr(ind) vertexList,indList=_findCloseList(self.vertexVecListvertexVecList,faceVec) #sortvertexlistaboutfacevector(directionisrandom) sortedVertexList=[vertexList[0]] vertexList=list(vertexList[1:]) whilelen(vertexList)!=0: nearVertexList,nearInd=_findCloseList(vertexList,sortedVertexList[-1]) sortedVertexList.append(nearVertexList[0]) vertexList.pop(nearInd[0]) returnsortedVertexList defgetFaceInd(self,vec): """Returntheindexofthefacecontainingthecartesianvector. Parameters ---------- vec:`numpy.ndarray` Cartesianvector(lengthisignored). Returns ------- results:`numpy.ndarray` Indexoffacecontainingvec. """ returnnumpy.argmax(numpy.dot(self.faceVecListfaceVecList,vec)) defgetWithFacesOnPoles(self): returnself._withFacesOnPoles_withFacesOnPoles defcomputeRotationMatrix(angle,axis): """Returna3Drotationmatrixforrotationbyaspecifiedamountarounda specifiedaxis. Parameters ---------- angle:`float` Amountofrotation(rad). axis:`int` Axisofrotation;oneof0,1or2forx,yorz. """ cosAng=math.cos(angle) sinAng=math.sin(angle) rotMat=numpy.zeros((3,3),dtype=float) rotMat[axis,axis]=1 rotMat[(axis+1)%3,(axis+1)%3]=cosAng rotMat[(axis+2)%3,(axis+1)%3]=sinAng rotMat[(axis+1)%3,(axis+2)%3]=-sinAng rotMat[(axis+2)%3,(axis+2)%3]=cosAng returnrotMat def_computeCoordTransform(vec0,vec1,vec1NegativeX=False): """Computearotationmatrixthatputsvec0alongzandvec1along+xin thexzplane. Parameters ---------- vec0:`numpy.ndarray` vector0 vec1:`numpy.ndarray` vector1 vec1NegativeX:`bool` IfTruethenvec1isrotatedtofacenegativex. """ #rotatearoundxbyangleofvec0fromztoy xAng=math.atan2(vec0[1],vec0[2]) xRotMat=computeRotationMatrix(xAng,0) #rotatearoundyby-angleofrotatedvec0fromztox vec0RotX=numpy.dot(xRotMat,vec0) yAng=-math.atan2(vec0RotX[0],vec0RotX[2]) yRotMat=computeRotationMatrix(yAng,1) xyRotMat=numpy.dot(yRotMat,xRotMat) #rotatearoundzby-angleofrotatedvec1from+/-xtoy vec1RotXY=numpy.dot(xyRotMat,vec1) xVal=vec1RotXY[0] ifvec1NegativeX: xVal=-xVal zAng=-math.atan2(vec1RotXY[1],xVal) zRotMat=computeRotationMatrix(zAng,2) xyzRotMat=numpy.dot(zRotMat,xyRotMat) returnxyzRotMat def_computeDodecahedronVertices(faceVecList): """GivenavectoroffacepositionsofaDodecahedroncomputethevertices. """ closeIndSetList=[] vertexDict={} foriinrange(len(faceVecList)): closeIndSet=_findCloseIndexSet(faceVecList,i) iflen(closeIndSet)!=5: raiseRuntimeError("Found%sverticesinsteadof5near%s:%s"% (len(closeIndSet),faceVecList[i],closeIndSet)) closeIndSetList.append(closeIndSet) fori,iCloseIndSetinenumerate(closeIndSetList): forjiniCloseIndSet: jCloseIndSet=closeIndSetList[j] sharedCloseIndSet=iCloseIndSet.intersection(jCloseIndSet) iflen(sharedCloseIndSet)!=2: raiseRuntimeError("Found%sverticesinsteadof2near%sand%s:%s"% (len(sharedCloseIndSet),faceVecList[i],faceVecList[j], sharedCloseIndSet)) forkinsharedCloseIndSet: key=frozenset((i,j,k)) ifkeyinvertexDict: continue vertexVec=faceVecList[i]+faceVecList[j]+faceVecList[k] vertexVec/=numpy.sqrt(numpy.sum(vertexVec**2)) vertexDict[key]=vertexVec returnlist(vertexDict.values()) def_computeFullVecList(basisSet): """Givenacollectionofbasisvectors,computeallpermutationswithboth signsofallnonzerovalues. Forexample:: [(0,1,2)]->[(0,1,2),(0,-1,2),(0,1,-2),(0,-1,-2)] """ fullSet=[] forbasisVecinbasisSet: vecLen=math.sqrt(numpy.sum(numpy.array(basisVec)**2)) valueList=[] forbasisValueinbasisVec: ifbasisValue==0: valueList.append((0,)) else: valueList.append((basisValue,-basisValue)) fullSet+=list(numpy.array((x,y,z))/vecLen forzinvalueList[2] foryinvalueList[1] forxinvalueList[0] ) returnfullSet def_findCloseIndexSet(vecList,ind): """Givenalistofcartesianvectors,returnasetofindicesofthose closesttooneofthem. Thisisintendedforregulargridswheredistancesarequantized. Parameters ---------- vecList:`list` Listofcartesianvectors. ind:`int` Indexofvectortobenearest. """ dotProductList=numpy.round(numpy.dot(vecList,vecList[ind]),2) dotProductList[ind]=-9e99 minDist=numpy.max(dotProductList) indList=numpy.arange(len(dotProductList))[dotProductList==minDist] returnset(indList) def_findCloseList(vecList,vec): """Givenalistofcartesianvectors,returnallthoseclosesttoa specifiedposition Thisisintendedforregulargridswheredistancesarequantized Parameters ---------- vecList:`list` Listofcartesianvectors. vec:`iterable`of`float` Vectortobenear. Returns ------- retList:`list` Listofclosestvectors. indList:`list` Listifindicesofthosevectors. """ dotProductList=numpy.round(numpy.dot(vecList,vec),2) minDist=numpy.max(dotProductList) indList=numpy.arange(len(dotProductList))[dotProductList==minDist] retList=numpy.take(vecList,indList,0) returnretList,indList def_findClosePair(vecList,ind=0): """Givenalistofcartesianvectorsandanindex,returnthevectorand oneofitsclosestneighbors. Parameters ---------- vecList:`list`of`numpy.ndarray` Listofcartesianvectors. ind:`int` Indexoffirstvector. """ vec=vecList[ind] otherVecList=vecList[0:ind]+vecList[ind+1:] ind1=numpy.argmax(numpy.dot(otherVecList,vec)) returnvec,otherVecList[ind1] def_sortedVectorList(vecList): """Returnalistofcartesianvectorssortedbydecreasinglatitudeand increasinglongitude. """ defvecToSort(vec): ang=round(math.atan2(vec[1],vec[0]),2) ifang<0: ang+=2.0*math.pi return(-round(vec[2],1),ang,vec) decoratedList=[vecToSort(v)forvinvecList] decoratedList.sort() return[d[2]fordindecoratedList] if__name__=="__main__": numpy.set_printoptions(precision=2,suppress=True,linewidth=120) print("Dodecahedronwithverticesonpoles") vertexDodec=Dodecahedron(withFacesOnPoles=False) foriinrange(12): faceVec=vertexDodec.getFaceCtr(i) print("Face%2d:%s"%(i,faceVec))