Loading src/yapsut/__init__.py +1 −0 Original line number Diff line number Diff line Loading @@ -11,6 +11,7 @@ from .profiling import timer,timerDict from .struct import struct from .DummyCLI import DummyCLI from .nearly_even_split import nearly_even_split from .geometry import ElipsoidTriangulation #from import .grep #import .intervalls Loading src/yapsut/geometry.py 0 → 100644 +280 −0 Original line number Diff line number Diff line import numpy as np class ElipsoidTriangulation : """ creates an elipsoid triangulated """ @property def axis(self) : """ elipsoid axis""" return self._axis @property def shape(self) : """ grid shape""" return self._shape @property def nphi(self) : """ nphi shape""" return self._nphi @property def ntheta(self) : """ ntheta shape""" return self._ntheta @property def phi(self) : """ phi list""" return self._phi @property def theta(self) : """ theta list""" return self._theta @property def simplices(self) : """ list of triangles (simplices)""" return self._Triangles @property def simplices(self) : """ list of triangles (simplices)""" return self._Triangles @property def polarS(self) : """ list of polar coordinates (for each point in each simplice)""" return self._TrAng @property def polarS(self) : """ list of polar coordinates (simplices)""" return self._TrAng @property def vecS(self) : """ list of cartesian coordinates for each triangle""" return self._TrVec @property def verS(self) : """ list of cartesian coordinates for each triangle as versors""" return self._TrVec @property def normalS(self) : """ list of oriented normals for each triangle""" return self._TrNorm @property def polar_normalS(self) : """ list of intercepts for each triangle, polar coordinates""" return self._TrNormAng @property def interceptS(self) : """ list of intercepts for each triangle""" return self._TrItcp @property def areaS(self) : """ list of areas for each triangle""" return self._TrArea @property def areaS(self) : """ list of areas for each triangle""" return self._TrArea @property def vecCpsS(self) : """ list of coplanar coordinates for each triangle""" return self._TrVecCpl # def __len__(self) : return self._N # def __init__(self,a,b,c,nphi,ntheta) : self._axis=np.array([a,b,c]) self._nphi=nphi self._ntheta=ntheta self._shape=(ntheta,nphi) self._phi=np.linspace(0,1,self._nphi)*2*np.pi self._theta=np.linspace(0,1,self._ntheta)*np.pi phi=self._phi theta=self._theta # # map of triangles Triang=[] # north pole triangles itheta=0 iP=[0,0] for iiph in np.arange(nphi-1) : iph0=np.mod(iiph,nphi) iph1=np.mod(iiph+1,nphi) # T=[iP,[iph0,itheta+1],[iph1,itheta+1],'0,1'] Triang.append(T) # bands triangles Theta=[] for itheta in np.arange(1,ntheta-2) : itheta1=itheta+1 ss=str(itheta)+'-'+str(itheta+1) for iiph in np.arange(nphi-1) : iph0=np.mod(iiph,nphi) iph1=np.mod(iiph+1,nphi) # T=[[iph0,itheta],[iph0,itheta1],[iph1,itheta1],ss] Triang.append(T) # T=[[iph1,itheta1],[iph1,itheta],[iph0,itheta],ss] Triang.append(T) # south pole triangles itheta=ntheta-2 itheta1=ntheta-1 iP=[0,itheta1] ss='0-'+str(itheta1) for iiph in np.arange(nphi-1) : iph0=np.mod(iiph,nphi) iph1=np.mod(iiph+1,nphi) # T=[[iph0,itheta],iP,[iph1,itheta],ss] Triang.append(T) self._Triangles=Triang self._N=len(Triang) # convert map of triangles in angles TrAng=[] for BL in Triang : T=[] for iT in BL[:3] : T.append([phi[iT[0]],theta[iT[1]]]) TrAng.append(T) TrAng=np.array(TrAng) self._Angles=TrAng # convert map of triangles in vectors TrVec=[] for BL in Triang : T=[] for iT in BL[:3] : ph=phi[iT[0]] cph=np.cos(ph) ; sph=np.sin(ph) th=theta[iT[1]] cth=np.cos(th) ; sth=np.sin(th) T.append([cph*sth,sph*sth,c*cth]) TrVec.append(T) TrVec=np.array(TrVec) self._TrVec=TrVec # convert map of triangles in versors TrVers=[] for BL in TrVec : T=[] for iT in BL[:3] : T.append(iT/(iT.dot(iT))**0.5) TrVers.append(T) TrVers=np.array(TrVers) self._TrVers=TrVers # normals of triangles as vectors, angles and intercept of planes # TrDprod is for each triangle the n.dot(r_i) with r_i are the triangles vertex TrDprod=[] TrNorm=[] TrNormAng=[] TrItcp=[] for BL in TrVec : r1,r2,r3=BL d21=r2-r1 d31=r3-r1 cdprod=np.cross(d21,d31) n=cdprod/(cdprod.dot(cdprod))**0.5 # sgn=1 a1=n.dot(r1)/r1.dot(r1)**0.5 a2=n.dot(r2)/r2.dot(r2)**0.5 a3=n.dot(r3)/r3.dot(r3)**0.5 if a1<0 or a2<0 or a3<0 : n=-1*n sgn=-1 a1=n.dot(r1)/r1.dot(r1)**0.5 a2=n.dot(r2)/r2.dot(r2)**0.5 a3=n.dot(r3)/r3.dot(r3)**0.5 TrItcp.append([-n.dot(r1),sgn]) TrNorm.append(n) TrDprod.append([a1,a2,a3]) # TrNormAng.append([np.arctan2(n[1],n[0]),np.arccos(n[2])]) TrItcp=np.array(TrItcp) TrNorm=np.array(TrNorm) TrDprod=np.array(TrDprod) TrNormAng=np.array(TrNormAng) self._TrItcp=TrItcp self._TrNorm=TrNorm self._TrDprod=TrDprod self._TrNormAng=TrNormAng # computes the are of triangles and VecCpl, triangles vertex in coplanar representation TrVecCpl=[] TrArea = [] for ibl in np.arange(len(TrNorm)) : n=TrNorm[ibl] trv=TrVec[ibl] # nlo,nla=TrNormAng[ibl] cnlo=np.cos(nlo) cnla=np.cos(nla) snlo=np.sin(nlo) snla=np.sin(nla) # Mlo=np.array([[cnlo,-snlo,0],[snlo,cnlo,0],[0,0,1]]) Mla=np.array([[cnla,0,snla],[0,1,0],[-snla,0,cnla]]) #Mlo.dot(Mla.dot(np.array([0,0,1]))) Mlo.dot(Mla.dot(np.array([0,0,1]))) nrot=Mla.T.dot(Mlo.T.dot(n)) # # method of determinant and closed form # rotate triangle in coplanar coordinates (z = constant) ctr=np.array([Mla.T.dot(Mlo.T.dot(k)) for k in trv]) cr1,cr2,cr3=ctr TrVecCpl.append(ctr) # computes area closed form area1=0.5*abs(cr1[0]*(cr2[1]-cr3[1])+cr2[0]*(cr3[1]-cr1[1])+cr3[0]*(cr1[1]-cr2[1])) # computes area method of determinant ## z forced to be 1 #ctr[:,2]=1 #area2=0.5*scipy.linalg.det(ctr) #TrArea.append([area2,area1]) TrArea.append(area1) TrArea=np.array(TrArea).T TrVecCpl=np.array(TrVecCpl) self._TrArea=TrArea self._TrVecCpl=TrVecCpl # def dotNormals(self,v) : """ computes dot product between normals of simplices and a vector v """ return np.array([v.dot(k) for k in self.normalS]) # # da verificare #def rotateSimplices(self,lo,la) : #""" computes rotations of simplices #lo = longitude [rad] #la = latitude [rad] #""" #cnlo=np.cos(lo) #cnla=np.cos(la) #snlo=np.sin(lo) #snla=np.sin(la) ## #Mlo=np.array([[cnlo,-snlo,0],[snlo,cnlo,0],[0,0,1]]) #Mla=np.array([[cnla,0,snla],[0,1,0],[-snla,0,cnla]]) #out=[] #for T in self.vecS : #out.append(Mla.T.dot(Mlo.T.dot(k)) for k in T) #return np.array(out) # # da verificare #def rotateNormals(self,lo,la) : #""" computes rotations of normals #lo = longitude [rad] #la = latitude [rad] #""" #cnlo=np.cos(lo) #cnla=np.cos(la) #snlo=np.sin(lo) #snla=np.sin(la) ## #Mlo=np.array([[cnlo,-snlo,0],[snlo,cnlo,0],[0,0,1]]) #Mla=np.array([[cnla,0,snla],[0,1,0],[-snla,0,cnla]]) ## #return np.array([Mla.T.dot(Mlo.T.dot(k)) for k in self.normalS]) Loading
src/yapsut/__init__.py +1 −0 Original line number Diff line number Diff line Loading @@ -11,6 +11,7 @@ from .profiling import timer,timerDict from .struct import struct from .DummyCLI import DummyCLI from .nearly_even_split import nearly_even_split from .geometry import ElipsoidTriangulation #from import .grep #import .intervalls Loading
src/yapsut/geometry.py 0 → 100644 +280 −0 Original line number Diff line number Diff line import numpy as np class ElipsoidTriangulation : """ creates an elipsoid triangulated """ @property def axis(self) : """ elipsoid axis""" return self._axis @property def shape(self) : """ grid shape""" return self._shape @property def nphi(self) : """ nphi shape""" return self._nphi @property def ntheta(self) : """ ntheta shape""" return self._ntheta @property def phi(self) : """ phi list""" return self._phi @property def theta(self) : """ theta list""" return self._theta @property def simplices(self) : """ list of triangles (simplices)""" return self._Triangles @property def simplices(self) : """ list of triangles (simplices)""" return self._Triangles @property def polarS(self) : """ list of polar coordinates (for each point in each simplice)""" return self._TrAng @property def polarS(self) : """ list of polar coordinates (simplices)""" return self._TrAng @property def vecS(self) : """ list of cartesian coordinates for each triangle""" return self._TrVec @property def verS(self) : """ list of cartesian coordinates for each triangle as versors""" return self._TrVec @property def normalS(self) : """ list of oriented normals for each triangle""" return self._TrNorm @property def polar_normalS(self) : """ list of intercepts for each triangle, polar coordinates""" return self._TrNormAng @property def interceptS(self) : """ list of intercepts for each triangle""" return self._TrItcp @property def areaS(self) : """ list of areas for each triangle""" return self._TrArea @property def areaS(self) : """ list of areas for each triangle""" return self._TrArea @property def vecCpsS(self) : """ list of coplanar coordinates for each triangle""" return self._TrVecCpl # def __len__(self) : return self._N # def __init__(self,a,b,c,nphi,ntheta) : self._axis=np.array([a,b,c]) self._nphi=nphi self._ntheta=ntheta self._shape=(ntheta,nphi) self._phi=np.linspace(0,1,self._nphi)*2*np.pi self._theta=np.linspace(0,1,self._ntheta)*np.pi phi=self._phi theta=self._theta # # map of triangles Triang=[] # north pole triangles itheta=0 iP=[0,0] for iiph in np.arange(nphi-1) : iph0=np.mod(iiph,nphi) iph1=np.mod(iiph+1,nphi) # T=[iP,[iph0,itheta+1],[iph1,itheta+1],'0,1'] Triang.append(T) # bands triangles Theta=[] for itheta in np.arange(1,ntheta-2) : itheta1=itheta+1 ss=str(itheta)+'-'+str(itheta+1) for iiph in np.arange(nphi-1) : iph0=np.mod(iiph,nphi) iph1=np.mod(iiph+1,nphi) # T=[[iph0,itheta],[iph0,itheta1],[iph1,itheta1],ss] Triang.append(T) # T=[[iph1,itheta1],[iph1,itheta],[iph0,itheta],ss] Triang.append(T) # south pole triangles itheta=ntheta-2 itheta1=ntheta-1 iP=[0,itheta1] ss='0-'+str(itheta1) for iiph in np.arange(nphi-1) : iph0=np.mod(iiph,nphi) iph1=np.mod(iiph+1,nphi) # T=[[iph0,itheta],iP,[iph1,itheta],ss] Triang.append(T) self._Triangles=Triang self._N=len(Triang) # convert map of triangles in angles TrAng=[] for BL in Triang : T=[] for iT in BL[:3] : T.append([phi[iT[0]],theta[iT[1]]]) TrAng.append(T) TrAng=np.array(TrAng) self._Angles=TrAng # convert map of triangles in vectors TrVec=[] for BL in Triang : T=[] for iT in BL[:3] : ph=phi[iT[0]] cph=np.cos(ph) ; sph=np.sin(ph) th=theta[iT[1]] cth=np.cos(th) ; sth=np.sin(th) T.append([cph*sth,sph*sth,c*cth]) TrVec.append(T) TrVec=np.array(TrVec) self._TrVec=TrVec # convert map of triangles in versors TrVers=[] for BL in TrVec : T=[] for iT in BL[:3] : T.append(iT/(iT.dot(iT))**0.5) TrVers.append(T) TrVers=np.array(TrVers) self._TrVers=TrVers # normals of triangles as vectors, angles and intercept of planes # TrDprod is for each triangle the n.dot(r_i) with r_i are the triangles vertex TrDprod=[] TrNorm=[] TrNormAng=[] TrItcp=[] for BL in TrVec : r1,r2,r3=BL d21=r2-r1 d31=r3-r1 cdprod=np.cross(d21,d31) n=cdprod/(cdprod.dot(cdprod))**0.5 # sgn=1 a1=n.dot(r1)/r1.dot(r1)**0.5 a2=n.dot(r2)/r2.dot(r2)**0.5 a3=n.dot(r3)/r3.dot(r3)**0.5 if a1<0 or a2<0 or a3<0 : n=-1*n sgn=-1 a1=n.dot(r1)/r1.dot(r1)**0.5 a2=n.dot(r2)/r2.dot(r2)**0.5 a3=n.dot(r3)/r3.dot(r3)**0.5 TrItcp.append([-n.dot(r1),sgn]) TrNorm.append(n) TrDprod.append([a1,a2,a3]) # TrNormAng.append([np.arctan2(n[1],n[0]),np.arccos(n[2])]) TrItcp=np.array(TrItcp) TrNorm=np.array(TrNorm) TrDprod=np.array(TrDprod) TrNormAng=np.array(TrNormAng) self._TrItcp=TrItcp self._TrNorm=TrNorm self._TrDprod=TrDprod self._TrNormAng=TrNormAng # computes the are of triangles and VecCpl, triangles vertex in coplanar representation TrVecCpl=[] TrArea = [] for ibl in np.arange(len(TrNorm)) : n=TrNorm[ibl] trv=TrVec[ibl] # nlo,nla=TrNormAng[ibl] cnlo=np.cos(nlo) cnla=np.cos(nla) snlo=np.sin(nlo) snla=np.sin(nla) # Mlo=np.array([[cnlo,-snlo,0],[snlo,cnlo,0],[0,0,1]]) Mla=np.array([[cnla,0,snla],[0,1,0],[-snla,0,cnla]]) #Mlo.dot(Mla.dot(np.array([0,0,1]))) Mlo.dot(Mla.dot(np.array([0,0,1]))) nrot=Mla.T.dot(Mlo.T.dot(n)) # # method of determinant and closed form # rotate triangle in coplanar coordinates (z = constant) ctr=np.array([Mla.T.dot(Mlo.T.dot(k)) for k in trv]) cr1,cr2,cr3=ctr TrVecCpl.append(ctr) # computes area closed form area1=0.5*abs(cr1[0]*(cr2[1]-cr3[1])+cr2[0]*(cr3[1]-cr1[1])+cr3[0]*(cr1[1]-cr2[1])) # computes area method of determinant ## z forced to be 1 #ctr[:,2]=1 #area2=0.5*scipy.linalg.det(ctr) #TrArea.append([area2,area1]) TrArea.append(area1) TrArea=np.array(TrArea).T TrVecCpl=np.array(TrVecCpl) self._TrArea=TrArea self._TrVecCpl=TrVecCpl # def dotNormals(self,v) : """ computes dot product between normals of simplices and a vector v """ return np.array([v.dot(k) for k in self.normalS]) # # da verificare #def rotateSimplices(self,lo,la) : #""" computes rotations of simplices #lo = longitude [rad] #la = latitude [rad] #""" #cnlo=np.cos(lo) #cnla=np.cos(la) #snlo=np.sin(lo) #snla=np.sin(la) ## #Mlo=np.array([[cnlo,-snlo,0],[snlo,cnlo,0],[0,0,1]]) #Mla=np.array([[cnla,0,snla],[0,1,0],[-snla,0,cnla]]) #out=[] #for T in self.vecS : #out.append(Mla.T.dot(Mlo.T.dot(k)) for k in T) #return np.array(out) # # da verificare #def rotateNormals(self,lo,la) : #""" computes rotations of normals #lo = longitude [rad] #la = latitude [rad] #""" #cnlo=np.cos(lo) #cnla=np.cos(la) #snlo=np.sin(lo) #snla=np.sin(la) ## #Mlo=np.array([[cnlo,-snlo,0],[snlo,cnlo,0],[0,0,1]]) #Mla=np.array([[cnla,0,snla],[0,1,0],[-snla,0,cnla]]) ## #return np.array([Mla.T.dot(Mlo.T.dot(k)) for k in self.normalS])
