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HL(IL(HL0IL0HL8IL8HH9u|XH}HUHHJlH`E~;1HMfA.u z HH9u HuH}1HUD}~<1fA.Du z HH9EuHuH}HHM}~C1HMfA.uzHH9pu HuH}HUHM@yHHclv DHpHHH‰уH 1H}H}HDH I HLILHLILHLILHL IL HL(IL(HL0IL0HL8IL8HI9uDHpHHH‰уH #1H}HH)1H}LAALD L0AD AL0D@LPAD@ALPD`LpAD`ALpHHuHt(HHD ADA H HuL9DHEEAs 1HuHMHuHI9sIH9s1HpHHH‰уH s1H}lHH)1H}LAALD L0AD AL0D@LPAD@ALPD`LpAD`ALpHHuHt(HHD ADA H HuHuH9)HHHHtH}H4I4HHuH}HHUrWH I HLILHLILHLILHL IL HL(IL(HL0IL0HL8IL8HH9uL`HEHpH]ps 1HuHMHuHHUH9sHH9s1HpHHH‰уH s 1H]H}hHH)1H]H}LLD L0D L0D@LPD@LPD`LpD`LpHHuHt&HHD D H HuHuH9)HHHHtH]H}H4H4HHuH]H}HHUrWH H HLHLHLHLHLHLHL HL HL(HL(HL0HL0HL8HL8HH9u|XDhH}HUHwlHpH`E~;1HMfA.u z HH9u@HuH}1HUDE~?1HMfA.u z HH9EuHuH}HUD觿~A1HMHMf.u z HH9Eu蹽HuH}HUЉb蛽HHcl蘽 HH)1H}LAALD L0AD AL0D@LPAD@ALPD`LpAD`ALpHHuHt(HHD ADA H HuL9DHEEAs 1HuHMHuHH9sHH9s1HpHHH‰уH s1H}dHH)1H}LLD L0D L0D@LPD@LPD`LpD`LpHHuHt&HHD D H HuHuH9)HHHHtH}H4H4HHuH}HHUrWH H HLHLHLHLHLHLHL HL HL(HL(HL0HL0HL8HL8HH9uLpDHEELUAs 1HuHMHuHHUH9sHH9s1HpHHH‰уH s 1LUH}pHH)1LUH}AALLAD AL0D L0AD@ALPD@LPAD`ALpD`LpHHuHt(HHADA D H HuHuH9)HHHHtLUH}I4H4HHuLUH}HHUrWI H ILHLILHLILHLIL HL IL(HL(IL0HL0IL8HL8HH9u|XDhDMH}HULh`HpE~;1HMfA.u z HH9u2HuH}1HUDݺE~>1HMf.u z HH9EuHuH}HUD蚺E~B1HMHMf.u z HH9Eu諸HuH}HUDS茸HHc`艸HH H(H9DB@H[HVHnHiHGHBHZHUH3H.HFHAHH H(H9t Ht.HHH9t HtHHH9t HtHL f.UHAWAVAUATSHHuH@2HEFEHEH]E1H1莸ACD-HcH譸LEIcILEH߾UAC?HcHPuHP1EIcHMHHE؋E+E%H}LDH!H}Hu聸 H}HuDH}HuTH}Hu-DEArII9II91)HHHHtI4I4HHuHI I ILILILILILILIL IL IL(IL(IL0IL0IL8IL8HH9u.H}1HPHXH9t HtθHH H9t Ht豸HH[A\A]A^A_]ÉHpHHH‰уH s1pHH)1AALAALAD AL0AD AL0AD@ALPAD@ALPAD`ALpAD`ALpHHuHt*HHADA ADA H HuH9IH}DHEEHUAs 1HuHMHuHH9sHH9s1HpHHH‰уH s1HUdHH)1HULLD L0D L0D@LPD@LPD`LpD`LpHHuHt&H4HD2 2D3 3H HuHuH9)HHHHtHUH4H4HHuHUHHurWH H HLHLHLHLHLHLHL HL HL(HL(HL0HL0HL8HL8HH9uuMEL譵EHME~71AfA.u z HH9u輲HuH}1LDhE~>1HMf.u z HH9Eu}HuH}HUD%^HHc}^HHPHXH9 H%H HHPHXH9t Ht=HH H9t Ht Hx fDUHAWAVAUATSHHuHp.HEFEHEH]E1H1農AC?HcH ޲L EIcIDLEH߾腲ÍHcHX觲HLX1ۅHEHIHE؋E+E#H}LDyH}Hu貲 H}LHULH}HusDEArIDI9II91)HHHHtf.ItI4HHuHDILI ILILILILILILIL IL IL(IL(IL0IL0IL8IL8HH9u4H}(1HXH`H9t HtH H(H9t HtHHĸ[A\A]A^A_]ÉHpHHH‰уH s1sHH)1ADALAALAD AL0AD AL0AD@ALPAD@ALPfAD`ALpfAD`ALpHHuHt-HHfADALfADA H HuH91H}HEȉHMЅ}s 1HuHuIH9sHI9s1HpHHH‰уH s1jHH)1AALLAD AL0D L0AD@ALPD@LPfAD`ALpfD`LpHHuHt*HHfADA fD H HuHuH9)HHHHtI4H4HHuHHUr]fDI H ILHLILHLILHLIL HL IL(HL(IL0HL0IL8HL8HH9uuHMLL EHME~A1fADfA.u z HH9uHuH}1LD萮}~=1fAf.u z HH9Eu襬HuH}LHMM膬HuEH}覭iH|Hc}iHHXH`H9ns H%H HHXH`H9t HtHH H(H9t Ht+H胬 UHAWAVAUATSHHuH+HEFEHEL}E1L1άÍHcHLH]HcILEL蕬ÍHcH跬LE1H]HcILEH}XÍHcHP耬HHP1ۅHEHHMHHE؋E+E"H}LHUGH}LHU/H}HuHU(H}Hp:HEDž}rII9!IDI91)HHHHtI4ItHHuHDI ILILILILILILILIL IL IL(IL(IL0IL0IL8IL8HH9uMH}1HPHXH9t HtѬHH H9t Ht贬HHH9t Ht藬HH[A\A]A^A_]ÉHpHHH‰уH s1qHH)1AALADALAD AL0AD AL0AD@ALPAD@ALPAD`ALpAD`ALpHHuHt+HHADA ADALH HuH9#HEHM}s 1HuHuII9sII9s1HpHHH‰уH s1pHH)1AALAALAD AL0AD AL0AD@ALPAD@ALPAD`ALpAD`ALpHHuHt*HHADA ADA H HuHuH9)HHHHtDI4I4HHuHHUr]fDI I ILILILILILILIL IL IL(IL(IL0IL0IL8IL8HH9uHxHEHMȅHUS}s 1H}HMH}HH9sHH9s1HpHHH‰уHs1HUdHH)1HULLD L0D L0D@LPD@LPD`LpD`LpH HuHt&H4HD2 2D3 3H HuH}H9tcHHHHtHUf44HHuHUHHur)f LLLLL L HH9upLL0EHx}~=1@AfA.Du z HH9u$HuH}1LHMϦ}~=1AfA.u z HH9EuHuH}LHM茦}~G1f.@HMЋ ; u HH9Eu 蘤HuH}HUHMKxHHc}xHHPHXH9H/H*HBH=HHPHXH9t HtMHH H9t Ht0HHH9t HtHk fUHAWAVAUATSHHuHn%HEFEHEL}E1L1认ÍHcHФLH]HcILELuÍHcH藤LE1H]HcILEH}8ÍHcHP`HHP1ۅHEHHMHHE؋E+E"H}LHU'H}LHUH}HuHUH}HpHEDž}rII9!IDI91)HHHHtI4ItHHuHDI ILILILILILILILIL IL IL(IL(IL0IL0IL8IL8HH9uMH}آ1HPHXH9t Ht豤HH H9t Ht蔤HHH9t HtwHH[A\A]A^A_]ÉHpHHH‰уH s1qHH)1AALADALAD AL0AD AL0AD@ALPAD@ALPAD`ALpAD`ALpHHuHt+HHADA ADALH HuH9#HEHM}s 1HuHuII9sII9s1HpHHH‰уH s1pHH)1AALAALAD AL0AD AL0AD@ALPAD@ALPAD`ALpAD`ALpHHuHt*HHADA ADA H HuHuH9)HHHHtDI4I4HHuHHUr]fDI I ILILILILILILIL IL IL(IL(IL0IL0IL8IL8HH9uHxHEHMȅHUS}s 1H}HMH}HH9sHH9s1HpHHH‰уHs1HUdHH)1HULLD L0D L0D@LPD@LPD`LpD`LpH HuHt&H4HD2 2D3 3H HuH}H9tcHHHHtHUf44HHuHUHHur)f LLLLL L HH9upLLLEHx}~=1@AfA.Du z HH9uHuH}1LHM诞}~=1AfA.u z HH9EuĜHuH}LHMl}~G1f.@HMЋ ; u HH9Eu xHuH}HUHM+XHHc}XHHPHXH9H/H*HBH=HHPHXH9t Ht-HH H9t HtHHH9t HtHK fUHAWAVAUATSHh~HH HHDžDžHHpVHH͜;HHh貜 HH8藜ph8xH踚HHnH5H艜HњH:HhHHpHDžxEHhH߾xACD-HcH藛L1EIcIHEHMH߾9AC?HcHpYHp1EIcHHEHMHhALuH]C$HcHH1EIcHMHHEHh譚AC6HcH8ӚH81EIcHMHHEHUx+|^HhHΚYHhH賚>HhH蘚#HhH}HhHuD&HhHuD HhHuDHhHuDEELX^Ar#HEJHMH9sJH9Ee1D)HHLHLEH}I4H4HHuH5d1Hh1H8H@H9t HtHHH9t HtÚHpHxH9t Ht覚HHH9t Ht艚HHh[A\A]A^A_]HHLEH}H,I H ILHLILHLILHLIL HL IL(HL(IL0HL0IL8HL8HI9uDȃHpHHHAAH s 1H}HMhLH)1H}HMLLD L0D L0D@LPD@LPD`LpD`LpHHuMt&HID D H IuLXL9DHEEHMAs 1HuHEHuHH9sHH9Es1HpHHHAAH s 1H}HMhLH)1H}HMLLD L0D L0D@LPD@LPD`LpD`LpHHuMt&HID D H IuHuH9)HHHHtLEH}I4H4HHuLEH}HHUrWI H ILHLILHLILHLIL HL IL(HL(IL0HL0IL8HL8HH9uDHEEAs 1HuHEHuHH9sHH9Es1HpHHH‰уH s1H}dHH)1H}LLD L0D L0D@LPD@LPD`LpD`LpHHuHt&HHD D H HuHuH9)HHHHtH}H4H4HHuH}HHUrWH H HLHLHLHLHLHLHL HL HL(HL(HL0HL0HL8HL8HH9uDHEEHM`As 1HUHEHUHH9EsHEHH9Es1ЃHpHHHAAHs 1HMH}hLH)1HMH}LLD L0D L0D@LPD@LPD`LpD`LpH HuMt&HID D H IuHUH9t`IIIHtHMH}44HHuHMH}IHur'TTTTT T HH9uH}HuHU˓dHUHXE~@1HMf.u z HH9u"ԐHuHhHUDyE~E1HMHMf.u z HH9Eu"芐HuHhHUD/E~A1HMf.u z HH9Eu"DHuHhHUDE~?1HUHMЋ ; u HH9Eu"HuHhHUD豑ޏHHcdۏHH8H@H9H9H4HLHGH_HZHH8H@H9t Ht覒HHH9t Ht艒HpHxH9t HtlHHH9t HtOH觏 DUHAWAVAUATSHHHzHUH?HEHEEL}LҏAC$HcHHE1EIcHLEL藏AH]CD-HcH貏HE1EIcHMHLEH}RÍHcH8zH81҅HcHMHHEHUE+EH}HXH}H`gH}HhOH}HuDH}HuDH}HuЉގEE8ArHMJI9XKH9K1D)HHLHH}H4I4HHuH=H[A\A]A^A_]H5D1lH}1H8H@H9t HtЏHHH9t Ht賏HHH9t Ht薏HH[A\A]A^A_]H}H%H I HLILHLILHLILHL IL HL(IL(HL0IL0HL8IL8HI9uDHpHHH‰уH s1H}lHH)1H}LAALD L0AD AL0D@LPAD@ALPD`LpAD`ALpHHuHt(HHD ADA H HuL9DHEEAs 1HuHMHuHI9sIH9s1HpHHH‰уH s1H}lHH)1H}LAALD L0AD AL0D@LPAD@ALPD`LpAD`ALpHHuHt(HHD ADA H HuHuH9)HHHHtH}H4I4HHuH}HHUrWH I HLILHLILHLILHL IL HL(IL(HL0IL0HL8IL8HH9uLpHEHxHUcxs 1H}HMH]HHUH9sHH9s 1H؃HpHHHAAHs 1HUHMhLH)1HUHMLLD L0D L0D@LPD@LPD`LpD`LpH HuMt&H4ID2 2D1 1H IuH9Ht`HHHHtHUH]44HHuHUH]HHur' LLLLL L HH9uX`hH}Hu越EHxHpE~>1HMfA.u z HH9u蔇HuH}HUD<E~?1HMfA.u z HH9EuPHuH}HUD~;1HUHMЋ ; u HH9EuHuH}HUЉňH6Hc}HH8H@H9(-H/H*HBH=HH8H@H9t HtljHHH9t Ht誉HHH9t Ht草H UHAWAVAUATSH~kH0HH8HDž@DžHH0Hu苇5H0HxpExvH褅HHSH5HuH轅HHuH,HEHEEH]H߾pAC?HcH0萆L0E1EIcIDLEH߾4ÍHcHx\HLx1ۅHEHIHE؋E+E)H}Hhc$H}HpK H}LDH}LHUDEArIDI9II9 1)HHHHtItI4HHuHILI ILILILILILILIL IL IL(IL(IL0IL0IL8IL8HH9uIH5m1LH}ф1HxHEH9t Ht譆H0H8H9t Ht萆HHĨ[A\A]A^A_]H H߉HpHHH‰уH s1qHH)1ADALAALAD AL0AD AL0AD@ALPAD@ALPAD`ALpAD`ALpHHuHt+HHADALADA H HuH9,H}HEȉHMЅA}s 1HUHUIH9sHI9s1ЃHpHHH‰уHs1hHH)1AALLAD AL0D L0AD@ALPD@LPAD`ALpD`LpH HuHt(HHADA D H HuHUH9tSHHHHtA44HHuHHUr+A ALLALLAL L HH9uhpLLŃEHME~;1ADfA.u z HH9uǀHuH}LDp}~51A ; u HH9Eu荀HuH}LHMAnHHc}nHHxHEH9 H"HHHxHEH9t HtSH0H8H9t Ht6H莀 f.fUHH0HuHQ HEFEHEH}؃u)HuWtE諂Ht1H0]þ€1H0]HCHH0]fUHSH(HuHHE؋FEHEtH}111o%*EHt1 EHHH([]fDUHSH8HuHUHEȋFEHEH}usHuftuH}HuUtdH}HuDtSEMUdHz~Hu2Ht6H5HSH~H8[]þ1H8[]HHH8[]DUHAWAVAUATSHHxHwHEFEHELxE1L1ÍHcH*LH]HcILEL~ÍHcH ~L E1H]HcILEHx~ÍHcHX~HHX1ۅHEHHMHHE؋E+EumHxLHU~tlHxLHUh~tUHxHuHUb~t=HEHM }1HuvHx}1HXH`H9t HtH H(H9t HtHHH9t HtHH[A\A]A^A_]HuII9sIDI9s1HpHHH‰уH s1sHH)1AALADALAD AL0AD AL0AD@ALPAD@ALPfAD`ALpfAD`ALpHHuHt-HHfADA fADALH HuHuH9)HHHHtf.I4ItHHuHHUr]DI ILILILILILILILIL IL IL(IL(IL0IL0IL8IL8HH9uHEHM}s 1HuHuII9sII9s1HpHHH‰уH s1rHH)1AALAALAD AL0AD AL0AD@ALPAD@ALPfAD`ALpfAD`ALpHHuHt,HHfADA fADA H HuHuH9)HHHHtI4I4HHuHHUr]fDI I ILILILILILILIL IL IL(IL(IL0IL0IL8IL8HH9uHEHMȅHUZ}s 1H}HMH}HH9sHH9s1HpHHH‰уHs1HUfHH)1HULLD L0D L0D@LPD@LPfD`LpfD`LpH HuHt(H4HfD2 2fD3 3H HuH}H9tfHHHHt HUf.f44HHuHUHHur)f LLLLL L HH9uLLnzE}~@1AfA.Du z HH9EucwHuHx1LHM y}~L1f.AfA.u z HH9Eu"wHuHxLHMx}~G1f.HMЋ ; u HH9Eu#vHuHxHUHMxxvHHc}vHHXH`H9H/H*HBH=HHXH`H9t HtzyH H(H9t Ht]yHHH9t Ht@yHv UHAVSH=BH5HH vu~HvHL51uHt"HH5LH}uH uHvuHt"HH5LHLuH uHuH=uH[A^]DUH]wfDUHSPH"H50HdHtt H QtH[]H=AH[]jufDUHAVSH0HuHHEЋFEHEHEH}ȃu\Hu0vt^H]H=HxAtH=Hwt HpuLcNtHuLSttu1H0[A^]ÐUHAWAVSH(HuHHED~D}HG]ԉ]؅y8uHHLw(HEMA)AuQHuH}Iut|}L}tYH=LwAtOH=LvtffDUHSPHH= H5H7H XduHH=%dH5HHct H tH[]H=H[]=dfUHAVSH0HuHqpHEЋFEHEHEH}ȃuoHuetqH]H=t HfAt1H=HftH=Hft H-dLc cHuLc1d1H0[A^]f.@UHAWAVSH(HuHpHED~D}HG]ԉ]؅ycHHLw(HEMA)AuhHuH}c}L}tlH=c LeAtbH=LetOH=Let 1`HuH-HEDMUUEy\HHHG(HELe1L1S\AC?HcHs\LEIcIHEH]L\ACD-HcH6\H1EIcHHEH`H}[ALuH]C$HcH[HE1EIcHMHIDH}DHEE+ELuH}HuD[H]H}LD[H}HDx[H}Hu[H}Hp[H}HXo[H}HHT[IEELx" Ar#HEJHMH9 JH9E1D)HHLHH}H]H4H4HHuHuHHEDMUUEy_ZHH_HG(HELe1L1ZAC?HcH1ZLEIcIHEH]LYACD-HcHYH1EIcHHEH`H}YALuH]C$HcHYHE1EIcHMHIDH}HEE+E H]H}HuDhYLuH}HDMYH}LD6YH}HPZYH}HuEYqH}Hp-YYH}HXYAH}HX)H}HXH}HXDHhEpAr2HEHhHH9EHEHhHH9Ef1Hh)HHHH} H}H]H4H4HHuh H5VWE1H WHWE1HH}{WH} fWE1HH H9t Ht>YHHH9t Ht!YHHH9t HtYLHX[A\A]A^A_]11=1c1HpHHH‰уH su1H}H]HH H HLHLHLHLHLHLHL HL HL(HL(HL0HL0HL8HL8HI9uHH)1AALAALAD AL0AD AL0AD@ALPAD@ALPAD`ALpAD`ALpHHuHt*HHADA ADA H HuH9kH}EEyArHMJH9JH91D)HHLHtH}H4H4HHuH}HH H HLHLHLHLHLHLHL HL HL(HL(HL0HL0HL8HL8HI9uDHpHHH‰уH s1H}dHH)1H}LLD L0D L0D@LPD@LPD`LpD`LpHHuHt&HHD D H HuL9,PptAMH}HHHXH $LELMHuȺHM(ЉEHU*H}HHMLXHuHU(EHUE~>1HMfA.u z HH9u&RHuH1HUDSE~@1HMf.u z HI9u"QHuHHUDSQHuEHRQHuXHRQH'Hc}QIcDHpHHH‰уH s51H}H]II9IH9E1LuHH)1H}H]LLD L0D L0D@LPD@LPD`LpD`LpHHuHt&HHD D H HuLxL9Lu DEH`HhrArIH9HI91)HHHHtI4H4HHuH#I H ILHLILHLILHLIL HL IL(HL(IL0HL0IL8HL8HH9u؃HpHHH‰уH s1hHH)1AALLAD AL0D L0AD@ALPD@LPAD`ALpD`LpHHuHt(HHADA D H HuHhH9EEAr$HEJH9EHEJH9E1D)HHLHtH}H]H4H4HHuH}H]H#H H HLHLHLHLHLHLHL HL HL(HL(HL0HL0HL8HL8HI9uDHpHHH‰уH s 1H}H]hHH)1H}H]LLD L0D L0D@LPD@LPD`LpD`LpHHuHt&HHD D H HuL9}EXtPpH}HHL $LpLPHuHUHM(ЉEHUH`Hx?H}HLpLHuHUHM(EHUH`HxE~:1HMf.u z HH9uyLHuH}1HUD$NE~A1HMf.uzHH9hu6LHuH}HUDME~A1HMHMf.u z HI9uKHuH}HUDMKHupH}LKHuH}LKHfHc}KIHH H9Y^HpHHH‰уH 1LuH}H]HHhH H HLHLHLHLHLHLHL HL HL(HL(HL0HL0HL8HL8HH9u&HH)1LuAALAALAD AL0AD AL0AD@ALPAD@ALPAD`ALpAD`ALpHHuHt*HHADA ADA H HuHuH9)HHHHtI4I4HHuHHUrWI I ILILILILILILIL IL IL(IL(IL0IL0IL8IL8HH9uEEzArHEJH9JH9E1D)HHLHtH}H4H4HHuH}HH H HLHLHLHLHLHLHL HL HL(HL(HL0HL0HL8HL8HI9uDHpHHH‰уH s1H}dHH)1H}LLD L0D L0D@LPD@LPD`LpD`LpHHuHt&HHD D H HuL9,EpXt1HMfA.u z HH9uKGHuH1HUDHE~@1HMf.u z HI9u" GHuHHUDHFHuPHHFHuEHGFHuHGFH)Hc}FHhHpHHH‰уH s 1H}H]hHH)1H}H]LLD L0D L0D@LPD@LPD`LpD`LpHHuHt&HHD D H HuHhH9DHxEAr8HEHxHH9`H`HxHH9E1Hx)HHHHtH}H`H4H4HHu H}H`HHx4H H HLHLHLHLHLHLHL HL HL(HL(HL0HL0HL8HL8HH9uHxHpHHH‰уH s1H}H`kHH)1H}H`LLD L0D L0D@LPD@LPD`LpD`LpHHuHt&HHD D H HuHxH9EEAr$HEJH9EHEJH9E1D)HHLHtH}H]H4H4HHuH}H]H#H H HLHLHLHLHLHLHL HL 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KHHHHBH?HH9H6H7H58HEH2HHH)HHHxHeHRH?H,HHHHHHHHHHHH=*HHHHHHHHHHLHHkHHEHHHHHH HH HHHHHHH5HHHHHHHHHHHHHH~HkHXHEH2HH HHHkH=lHH|HiHVHCH0HHZHGHLLMHJHHDDHeHFH[HHH5H"H ;H8H9H2H/H0H)H&H'H5(H5H"HHHHH{HhHUHBH/HH HHHHHHHHqH:HH=HHHHHHHHHHLHHHHuHHHHHH HHiHHH@HHHH5HHHH7HHHHHHHHHHnH[HHH5H"HHHHJH[H=\HHlHYHFH3H H HJH7H<L=H:HH44HH6HKH8H%HH +H(HH"HHHHHH5H%HHHH H~HkHXHEH2HH HHHHHHHHtHaHHH= HHHHHHHHHHLHHHHHHHHHH HHHHHHHHH5HHHwHHHHHHHHHHqH^HKH8H%HHHHHHKH=LHoH\HIH6H#HHH:H'H,L-H*HH$$H%H&H;H(HHH HHHHHH HHH5HHHHHHnH[HHH5H"HHHHHHHHHwHdHQHHH=HHHHHHHuHHHLHHqHHHHHHHzH HH)HHHPHH~HH5HHzHgHHqHHHHHHHtHaHNH;H(HHHHHHZH;H=<rH_HLH9H&HHHH*HHLHHgHHHH+HHHH HHYHHH`HHHH5HHHHHH^HKH8H%HHHHHHHHHzHgHTHAHjHH=HHHHHHxHeHH]ÐUHAVSH=IHHtkHH mH腌HHEHmH%H=H%HHHmH5L[A^]H=H5%h%h%h%h%h%h%h%h%h%h%h%h%h%h%h%h%h%h%h%h%h%h%h%h%h%h%h%h%h%h%h%h%h%h%h%h%h%h%h%h%h%h%h%h%h%h%i%i%i%i%i% i% i%i%i%i%i%i%i%i%i%i% i%"i%$i%&i%(i%*i%,i%.i%0i%2i%4i%6i%8i%:i%i%@i%Bi%Di%Fi%Hi%Ji%Li%Ni%Pi%Ri%Ti%Vi%Xi%Zi%\i%^i%`i%bi%di%fi%hi%ji%li%ni%pi%ri%ti%vi%xi%zi%|i%~i%i%i%i%i%i%i%i%i%i%i%i%i%i%i%i%i%i%i%i%i%i%i%i%i%i%i%i%i%i%i%i%i%i%i%i%i%i%i%i%i%i%i%i%i%i%i%i%ihhh8hThghzhhhzhphfh\h#Rh8Hh[>hs4h*h hh hL iAS%$hhChnhhhhh9hahhhxhnh7dhiZhPhFhh4h*h hh hh3hVhuhhhhhhhOhzhhhvh9lhvbhXhNh Dh. :hV 0h &h h h h> he h h h h h+ hU h h h h h3 hk |h rh hhs^h Th1Jh,@hX6ho,h"hhhhhhhhh??@пп@cܥL@ư>п??.eBvtkAmoebaMinimizervtkCommonMathPython.vtkAmoebaMinimizervtkAmoebaMinimizer - nonlinear optimization with a simplex Superclass: vtkObject vtkAmoebaMinimizer will modify a set of parameters in order to find the minimum of a specified function. The method used is commonly known as the amoeba method, it constructs an n-dimensional simplex in parameter space (i.e. a tetrahedron if the number or parameters is 3) and moves the vertices around parameter space until a local minimum is found. The amoeba method is robust, reasonably efficient, but is not guaranteed to find the global minimum if several local minima exist. IsTypeOfV.IsTypeOf(string) -> int C++: static vtkTypeBool IsTypeOf(const char *type) Return 1 if this class type is the same type of (or a subclass of) the named class. Returns 0 otherwise. This method works in combination with vtkTypeMacro found in vtkSetGet.h. IsAV.IsA(string) -> int C++: vtkTypeBool IsA(const char *type) override; Return 1 if this class is the same type of (or a subclass of) the named class. Returns 0 otherwise. This method works in combination with vtkTypeMacro found in vtkSetGet.h. SafeDownCastV.SafeDownCast(vtkObjectBase) -> vtkAmoebaMinimizer C++: static vtkAmoebaMinimizer *SafeDownCast(vtkObjectBase *o) NewInstanceV.NewInstance() -> vtkAmoebaMinimizer C++: vtkAmoebaMinimizer *NewInstance() SetFunctionV.SetFunction(function) C++: void SetFunction(void (*f)(void *), void *arg) Specify the function to be minimized. When this function is called, it must get the parameter values by calling GetParameterValue() for each parameter, and then must call SetFunctionValue() to tell the minimizer what the result of the function evaluation was. The number of function evaluations used for the minimization can be retrieved using GetFunctionEvaluations(). SetParameterValueV.SetParameterValue(string, float) C++: void SetParameterValue(const char *name, double value) V.SetParameterValue(int, float) C++: void SetParameterValue(int i, double value) Set the initial value for the specified parameter. Calling this function for any parameter will reset the Iterations and the FunctionEvaluations counts to zero. You must also use SetParameterScale() to specify the step size by which the parameter will be modified during the minimization. It is preferable to specify parameters by name, rather than by number. SetParameterScaleV.SetParameterScale(string, float) C++: void SetParameterScale(const char *name, double scale) V.SetParameterScale(int, float) C++: void SetParameterScale(int i, double scale) Set the scale to use when modifying a parameter, i.e. the initial amount by which the parameter will be modified during the search for the minimum. It is preferable to identify scalars by name rather than by number. GetParameterScaleV.GetParameterScale(string) -> float C++: double GetParameterScale(const char *name) V.GetParameterScale(int) -> float C++: double GetParameterScale(int i) Set the scale to use when modifying a parameter, i.e. the initial amount by which the parameter will be modified during the search for the minimum. It is preferable to identify scalars by name rather than by number. GetParameterValueV.GetParameterValue(string) -> float C++: double GetParameterValue(const char *name) V.GetParameterValue(int) -> float C++: double GetParameterValue(int i) Get the value of a parameter at the current stage of the minimization. Call this method within the function that you are minimizing in order to get the current parameter values. It is preferable to specify parameters by name rather than by index. GetParameterNameV.GetParameterName(int) -> string C++: const char *GetParameterName(int i) For completeness, an unchecked method to get the name for particular parameter (the result will be nullptr if no name was set). GetNumberOfParametersV.GetNumberOfParameters() -> int C++: int GetNumberOfParameters() Get the number of parameters that have been set. InitializeV.Initialize() C++: void Initialize() Initialize the minimizer. This will reset the number of parameters to zero so that the minimizer can be reused. MinimizeV.Minimize() C++: virtual void Minimize() Iterate until the minimum is found to within the specified tolerance, or until the MaxIterations has been reached. IterateV.Iterate() -> int C++: virtual int Iterate() Perform one iteration of minimization. Returns zero if the tolerance stopping criterion has been met. SetFunctionValueV.SetFunctionValue(float) C++: virtual void SetFunctionValue(double _arg) Get the function value resulting from the minimization. GetFunctionValueV.GetFunctionValue() -> float C++: double GetFunctionValue() Get the function value resulting from the minimization. SetContractionRatioV.SetContractionRatio(float) C++: virtual void SetContractionRatio(double _arg) Set the amoeba contraction ratio. The default value of 0.5 gives fast convergence, but larger values such as 0.6 or 0.7 provide greater stability. GetContractionRatioMinValueV.GetContractionRatioMinValue() -> float C++: virtual double GetContractionRatioMinValue() Set the amoeba contraction ratio. The default value of 0.5 gives fast convergence, but larger values such as 0.6 or 0.7 provide greater stability. GetContractionRatioMaxValueV.GetContractionRatioMaxValue() -> float C++: virtual double GetContractionRatioMaxValue() Set the amoeba contraction ratio. The default value of 0.5 gives fast convergence, but larger values such as 0.6 or 0.7 provide greater stability. GetContractionRatioV.GetContractionRatio() -> float C++: virtual double GetContractionRatio() Set the amoeba contraction ratio. The default value of 0.5 gives fast convergence, but larger values such as 0.6 or 0.7 provide greater stability. SetExpansionRatioV.SetExpansionRatio(float) C++: virtual void SetExpansionRatio(double _arg) Set the amoeba expansion ratio. The default value is 2.0, which provides rapid expansion. Values between 1.1 and 2.0 are valid. GetExpansionRatioMinValueV.GetExpansionRatioMinValue() -> float C++: virtual double GetExpansionRatioMinValue() Set the amoeba expansion ratio. The default value is 2.0, which provides rapid expansion. Values between 1.1 and 2.0 are valid. GetExpansionRatioMaxValueV.GetExpansionRatioMaxValue() -> float C++: virtual double GetExpansionRatioMaxValue() Set the amoeba expansion ratio. The default value is 2.0, which provides rapid expansion. Values between 1.1 and 2.0 are valid. GetExpansionRatioV.GetExpansionRatio() -> float C++: virtual double GetExpansionRatio() Set the amoeba expansion ratio. The default value is 2.0, which provides rapid expansion. Values between 1.1 and 2.0 are valid. SetToleranceV.SetTolerance(float) C++: virtual void SetTolerance(double _arg) Specify the value tolerance to aim for during the minimization. GetToleranceV.GetTolerance() -> float C++: virtual double GetTolerance() Specify the value tolerance to aim for during the minimization. SetParameterToleranceV.SetParameterTolerance(float) C++: virtual void SetParameterTolerance(double _arg) Specify the parameter tolerance to aim for during the minimization. GetParameterToleranceV.GetParameterTolerance() -> float C++: virtual double GetParameterTolerance() Specify the parameter tolerance to aim for during the minimization. SetMaxIterationsV.SetMaxIterations(int) C++: virtual void SetMaxIterations(int _arg) Specify the maximum number of iterations to try before giving up. GetMaxIterationsV.GetMaxIterations() -> int C++: virtual int GetMaxIterations() Specify the maximum number of iterations to try before giving up. GetIterationsV.GetIterations() -> int C++: virtual int GetIterations() Return the number of interations that have been performed. This is not necessarily the same as the number of function evaluations. GetFunctionEvaluationsV.GetFunctionEvaluations() -> int C++: virtual int GetFunctionEvaluations() Return the number of times that the function has been evaluated. EvaluateFunctionV.EvaluateFunction() C++: void EvaluateFunction() Evaluate the function. This is usually called internally by the minimization code, but it is provided here as a public method. vtkObjectvtkObjectBase@zd@id@z@ivtkFunctionSetvtkCommonMathPython.vtkFunctionSetvtkFunctionSet - Abstract interface for sets of functions Superclass: vtkObject vtkFunctionSet specifies an abstract interface for set of functions of the form F_i = F_i(x_j) where F (with i=1..m) are the functions and x (with j=1..n) are the independent variables. The only supported operation is the function evaluation at x_j. @sa vtkImplicitDataSet vtkInterpolatedVelocityField vtkInitialValueProblemSolver V.SafeDownCast(vtkObjectBase) -> vtkFunctionSet C++: static vtkFunctionSet *SafeDownCast(vtkObjectBase *o) V.NewInstance() -> vtkFunctionSet C++: vtkFunctionSet *NewInstance() FunctionValuesV.FunctionValues([float, ...], [float, ...]) -> int C++: virtual int FunctionValues(double *x, double *f) Evaluate functions at x_j. x and f have to point to valid double arrays of appropriate sizes obtained with GetNumberOfFunctions() and GetNumberOfIndependentVariables. GetNumberOfFunctionsV.GetNumberOfFunctions() -> int C++: virtual int GetNumberOfFunctions() Return the number of functions. Note that this is constant for a given type of set of functions and can not be changed at run time. GetNumberOfIndependentVariablesV.GetNumberOfIndependentVariables() -> int C++: virtual int GetNumberOfIndependentVariables() Return the number of independent variables. Note that this is constant for a given type of set of functions and can not be changed at run time. (i)vtkInitialValueProblemSolverErrorCodesOUT_OF_DOMAINNOT_INITIALIZEDUNEXPECTED_VALUEvtkCommonMathPython.vtkInitialValueProblemSolver.ErrorCodesvtkCommonMathPython.vtkInitialValueProblemSolvervtkInitialValueProblemSolver - Integrate a set of ordinary differential equations (initial value problem) in time. Superclass: vtkObject Given a vtkFunctionSet which returns dF_i(x_j, t)/dt given x_j and t, vtkInitialValueProblemSolver computes the value of F_i at t+deltat. @warning vtkInitialValueProblemSolver and it's subclasses are not thread-safe. You should create a new integrator for each thread. @sa vtkRungeKutta2 vtkRungeKutta4 V.SafeDownCast(vtkObjectBase) -> vtkInitialValueProblemSolver C++: static vtkInitialValueProblemSolver *SafeDownCast( vtkObjectBase *o) V.NewInstance() -> vtkInitialValueProblemSolver C++: vtkInitialValueProblemSolver *NewInstance() ComputeNextStepV.ComputeNextStep([float, ...], [float, ...], float, float, float, float) -> int C++: virtual int ComputeNextStep(double *xprev, double *xnext, double t, double &delT, double maxError, double &error) V.ComputeNextStep([float, ...], [float, ...], [float, ...], float, float, float, float) -> int C++: virtual int ComputeNextStep(double *xprev, double *dxprev, double *xnext, double t, double &delT, double maxError, double &error) V.ComputeNextStep([float, ...], [float, ...], float, float, float, float, float, float, float) -> int C++: virtual int ComputeNextStep(double *xprev, double *xnext, double t, double &delT, double &delTActual, double minStep, double maxStep, double maxError, double &error) V.ComputeNextStep([float, ...], [float, ...], [float, ...], float, float, float, float, float, float, float) -> int C++: virtual int ComputeNextStep(double *xprev, double *dxprev, double *xnext, double t, double &delT, double &delTActual, double minStep, double maxStep, double maxError, double &error) Given initial values, xprev , initial time, t and a requested time interval, delT calculate values of x at t+delTActual (xnext). For certain concrete sub-classes delTActual != delT. This occurs when the solver supports adaptive stepsize control. If this is the case, the solver tries to change to stepsize such that the (estimated) error of the integration is less than maxError. The solver will not set the stepsize smaller than minStep or larger than maxStep. Also note that delT is an in/out argument. Adaptive solvers will modify delT to reflect the best (estimated) size for the next integration step. An estimated value for the error is returned (by reference) in error. Note that only some concrete sub-classes support this. Otherwise, the error is set to 0. This method returns an error code representing the nature of the failure: OutOfDomain = 1, NotInitialized = 2, UnexpectedValue = 3 SetFunctionSetV.SetFunctionSet(vtkFunctionSet) C++: virtual void SetFunctionSet(vtkFunctionSet *functionset) Set / get the dataset used for the implicit function evaluation. GetFunctionSetV.GetFunctionSet() -> vtkFunctionSet C++: virtual vtkFunctionSet *GetFunctionSet() Set / get the dataset used for the implicit function evaluation. IsAdaptiveV.IsAdaptive() -> int C++: virtual int IsAdaptive() Returns 1 if the solver uses adaptive stepsize control, 0 otherwise vtkMatrix3x3vtkCommonMathPython.vtkMatrix3x3vtkMatrix3x3 - represent and manipulate 3x3 transformation matrices Superclass: vtkObject vtkMatrix3x3 is a class to represent and manipulate 3x3 matrices. Specifically, it is designed to work on 3x3 transformation matrices found in 2D rendering using homogeneous coordinates [x y w]. @sa vtkTransform2D V.SafeDownCast(vtkObjectBase) -> vtkMatrix3x3 C++: static vtkMatrix3x3 *SafeDownCast(vtkObjectBase *o) V.NewInstance() -> vtkMatrix3x3 C++: vtkMatrix3x3 *NewInstance() DeepCopyV.DeepCopy(vtkMatrix3x3) C++: void DeepCopy(vtkMatrix3x3 *source) V.DeepCopy([float, float, float, float, float, float, float, float, float], vtkMatrix3x3) C++: static void DeepCopy(double elements[9], vtkMatrix3x3 *source) V.DeepCopy([float, float, float, float, float, float, float, float, float], (float, float, float, float, float, float, float, float, float)) C++: static void DeepCopy(double elements[9], const double newElements[9]) V.DeepCopy((float, float, float, float, float, float, float, float, float)) C++: void DeepCopy(const double elements[9]) Set the elements of the matrix to the same values as the elements of the source Matrix. ZeroV.Zero() C++: void Zero() V.Zero([float, float, float, float, float, float, float, float, float]) C++: static void Zero(double elements[9]) Set all of the elements to zero. IdentityV.Identity() C++: void Identity() V.Identity([float, float, float, float, float, float, float, float, float]) C++: static void Identity(double elements[9]) Set equal to Identity matrix InvertV.Invert(vtkMatrix3x3, vtkMatrix3x3) C++: static void Invert(vtkMatrix3x3 *in, vtkMatrix3x3 *out) V.Invert() C++: void Invert() V.Invert((float, float, float, float, float, float, float, float, float), [float, float, float, float, float, float, float, float, float]) C++: static void Invert(const double inElements[9], double outElements[9]) Matrix Inversion (adapted from Richard Carling in "Graphics Gems," Academic Press, 1990). TransposeV.Transpose(vtkMatrix3x3, vtkMatrix3x3) C++: static void Transpose(vtkMatrix3x3 *in, vtkMatrix3x3 *out) V.Transpose() C++: void Transpose() V.Transpose((float, float, float, float, float, float, float, float, float), [float, float, float, float, float, float, float, float, float]) C++: static void Transpose(const double inElements[9], double outElements[9]) Transpose the matrix and put it into out. MultiplyPointV.MultiplyPoint((float, float, float), [float, float, float]) C++: void MultiplyPoint(const double in[3], double out[3]) V.MultiplyPoint((float, float, float, float, float, float, float, float, float), (float, float, float), [float, float, float]) C++: static void MultiplyPoint(const double elements[9], const double in[3], double out[3]) Multiply3x3V.Multiply3x3(vtkMatrix3x3, vtkMatrix3x3, vtkMatrix3x3) C++: static void Multiply3x3(vtkMatrix3x3 *a, vtkMatrix3x3 *b, vtkMatrix3x3 *c) V.Multiply3x3((float, float, float, float, float, float, float, float, float), (float, float, float, float, float, float, float, float, float), [float, float, float, float, float, float, float, float, float]) C++: static void Multiply3x3(const double a[9], const double b[9], double c[9]) Multiplies matrices a and b and stores the result in c (c=a*b). AdjointV.Adjoint(vtkMatrix3x3, vtkMatrix3x3) C++: void Adjoint(vtkMatrix3x3 *in, vtkMatrix3x3 *out) V.Adjoint((float, float, float, float, float, float, float, float, float), [float, float, float, float, float, float, float, float, float]) C++: static void Adjoint(const double inElements[9], double outElements[9]) Compute adjoint of the matrix and put it into out. DeterminantV.Determinant() -> float C++: double Determinant() V.Determinant((float, float, float, float, float, float, float, float, float)) -> float C++: static double Determinant(const double elements[9]) Compute the determinant of the matrix and return it. SetElementV.SetElement(int, int, float) C++: void SetElement(int i, int j, double value) Sets the element i,j in the matrix. GetElementV.GetElement(int, int) -> float C++: double GetElement(int i, int j) Returns the element i,j from the matrix. IsIdentityV.IsIdentity() -> bool C++: bool IsIdentity() GetDataV.GetData() -> (float, ...) C++: double *GetData() Return a pointer to the first element of the matrix (double[9]). @V *vtkMatrix3x3PV *d *vtkMatrix3x3PP *d *d@P *dVV *vtkMatrix3x3 *vtkMatrix3x3VVV *vtkMatrix3x3 *vtkMatrix3x3 *vtkMatrix3x3PPP *d *d *d@VV *vtkMatrix3x3 *vtkMatrix3x3p_voidvtkMatrix4x4vtkCommonMathPython.vtkMatrix4x4vtkMatrix4x4 - represent and manipulate 4x4 transformation matrices Superclass: vtkObject vtkMatrix4x4 is a class to represent and manipulate 4x4 matrices. Specifically, it is designed to work on 4x4 transformation matrices found in 3D rendering using homogeneous coordinates [x y z w]. Many of the methods take an array of 16 doubles in row-major format. Note that OpenGL stores matrices in column-major format, so the matrix contents must be transposed when they are moved between OpenGL and VTK. @sa vtkTransform V.SafeDownCast(vtkObjectBase) -> vtkMatrix4x4 C++: static vtkMatrix4x4 *SafeDownCast(vtkObjectBase *o) V.NewInstance() -> vtkMatrix4x4 C++: vtkMatrix4x4 *NewInstance() V.DeepCopy(vtkMatrix4x4) C++: void DeepCopy(const vtkMatrix4x4 *source) V.DeepCopy([float, float, float, float, float, float, float, float, float, float, float, float, float, float, float, float], vtkMatrix4x4) C++: static void DeepCopy(double destination[16], const vtkMatrix4x4 *source) V.DeepCopy([float, float, float, float, float, float, float, float, float, float, float, float, float, float, float, float], (float, float, float, float, float, float, float, float, float, float, float, float, float, float, float, float) ) C++: static void DeepCopy(double destination[16], const double source[16]) V.DeepCopy((float, float, float, float, float, float, float, float, float, float, float, float, float, float, float, float) ) C++: void DeepCopy(const double elements[16]) Set the elements of the matrix to the same values as the elements of the given source matrix. V.Zero() C++: void Zero() V.Zero([float, float, float, float, float, float, float, float, float, float, float, float, float, float, float, float]) C++: static void Zero(double elements[16]) Set all of the elements to zero. V.Identity() C++: void Identity() V.Identity([float, float, float, float, float, float, float, float, float, float, float, float, float, float, float, float]) C++: static void Identity(double elements[16]) Set equal to Identity matrix V.Invert(vtkMatrix4x4, vtkMatrix4x4) C++: static void Invert(const vtkMatrix4x4 *in, vtkMatrix4x4 *out) V.Invert() C++: void Invert() V.Invert((float, float, float, float, float, float, float, float, float, float, float, float, float, float, float, float), [float, float, float, float, float, float, float, float, float, float, float, float, float, float, float, float]) C++: static void Invert(const double inElements[16], double outElements[16]) Matrix Inversion (adapted from Richard Carling in "Graphics Gems," Academic Press, 1990). V.Transpose(vtkMatrix4x4, vtkMatrix4x4) C++: static void Transpose(const vtkMatrix4x4 *in, vtkMatrix4x4 *out) V.Transpose() C++: void Transpose() V.Transpose((float, float, float, float, float, float, float, float, float, float, float, float, float, float, float, float) , [float, float, float, float, float, float, float, float, float, float, float, float, float, float, float, float]) C++: static void Transpose(const double inElements[16], double outElements[16]) Transpose the matrix and put it into out. V.MultiplyPoint((float, float, float, float), [float, float, float, float]) C++: void MultiplyPoint(const double in[4], double out[4]) V.MultiplyPoint((float, float, float, float, float, float, float, float, float, float, float, float, float, float, float, float) , (float, float, float, float), [float, float, float, float]) C++: static void MultiplyPoint(const double elements[16], const double in[4], double out[4]) V.MultiplyPoint((float, float, float, float)) -> (float, float, float, float) C++: float *MultiplyPoint(const float in[4]) MultiplyFloatPointV.MultiplyFloatPoint((float, float, float, float)) -> (float, float, float, float) C++: float *MultiplyFloatPoint(const float in[4]) MultiplyDoublePointV.MultiplyDoublePoint((float, float, float, float)) -> (float, float, float, float) C++: double *MultiplyDoublePoint(const double in[4]) Multiply4x4V.Multiply4x4(vtkMatrix4x4, vtkMatrix4x4, vtkMatrix4x4) C++: static void Multiply4x4(const vtkMatrix4x4 *a, const vtkMatrix4x4 *b, vtkMatrix4x4 *c) V.Multiply4x4((float, float, float, float, float, float, float, float, float, float, float, float, float, float, float, float) , (float, float, float, float, float, float, float, float, float, float, float, float, float, float, float, float), [float, float, float, float, float, float, float, float, float, float, float, float, float, float, float, float]) C++: static void Multiply4x4(const double a[16], const double b[16], double c[16]) Multiplies matrices a and b and stores the result in c. V.Adjoint(vtkMatrix4x4, vtkMatrix4x4) C++: void Adjoint(const vtkMatrix4x4 *in, vtkMatrix4x4 *out) V.Adjoint((float, float, float, float, float, float, float, float, float, float, float, float, float, float, float, float), [float, float, float, float, float, float, float, float, float, float, float, float, float, float, float, float]) C++: static void Adjoint(const double inElements[16], double outElements[16]) Compute adjoint of the matrix and put it into out. V.Determinant() -> float C++: double Determinant() V.Determinant((float, float, float, float, float, float, float, float, float, float, float, float, float, float, float, float) ) -> float C++: static double Determinant(const double elements[16]) Compute the determinant of the matrix and return it. V.GetData() -> (float, ...) C++: double *GetData() Returns the raw double array holding the matrix. @V *vtkMatrix4x4PV *d *vtkMatrix4x4VV *vtkMatrix4x4 *vtkMatrix4x4@PP *d *dVVV *vtkMatrix4x4 *vtkMatrix4x4 *vtkMatrix4x4@VV *vtkMatrix4x4 *vtkMatrix4x4vtkPolynomialSolversUnivariatevtkCommonMathPython.vtkPolynomialSolversUnivariatevtkPolynomialSolversUnivariate - polynomial solvers Superclass: vtkObject vtkPolynomialSolversUnivariate provides solvers for univariate polynomial equations with real coefficients. The Tartaglia-Cardan and Ferrari solvers work on polynomials of fixed degree 3 and 4, respectively. The Lin-Bairstow and Sturm solvers work on polynomials of arbitrary degree. The Sturm solver is the most robust solver but only reports roots within an interval and does not report multiplicities. The Lin-Bairstow solver reports multiplicities. For difficult polynomials, you may wish to use FilterRoots to eliminate some of the roots reported by the Sturm solver. FilterRoots evaluates the derivatives near each root to eliminate cases where a local minimum or maximum is close to zero. @par Thanks: Thanks to Philippe Pebay, Korben Rusek, David Thompson, and Maurice Rojas for implementing these solvers. V.SafeDownCast(vtkObjectBase) -> vtkPolynomialSolversUnivariate C++: static vtkPolynomialSolversUnivariate *SafeDownCast( vtkObjectBase *o) V.NewInstance() -> vtkPolynomialSolversUnivariate C++: vtkPolynomialSolversUnivariate *NewInstance() HabichtBisectionSolveV.HabichtBisectionSolve([float, ...], int, [float, ...], [float, ...], float) -> int C++: static int HabichtBisectionSolve(double *P, int d, double *a, double *upperBnds, double tol) V.HabichtBisectionSolve([float, ...], int, [float, ...], [float, ...], float, int) -> int C++: static int HabichtBisectionSolve(double *P, int d, double *a, double *upperBnds, double tol, int intervalType) V.HabichtBisectionSolve([float, ...], int, [float, ...], [float, ...], float, int, bool) -> int C++: static int HabichtBisectionSolve(double *P, int d, double *a, double *upperBnds, double tol, int intervalType, bool divideGCD) Finds all REAL roots (within tolerance tol) of the d -th degree polynomial\[ P[0] X^d + ... + P[d-1] X + P[d]\] in ] a[0] ; a[1]] using the Habicht sequence (polynomial coefficients are REAL) and returns the count nr. All roots are bracketed in the r first ] upperBnds[i] - tol ; upperBnds[i]] intervals. Returns -1 if anything went wrong (such as: polynomial does not have degree d, the interval provided by the other is absurd, etc.). * intervalType specifies the search interval as follows: * 0 = 00 = ]a,b[ * 1 = 10 = [a,b[ * 2 = 01 = ]a,b] * 3 = 11 = [a,b] * This defaults to 0. * The last non-zero item in the Habicht sequence is the gcd of P and P'. The * parameter divideGCD specifies whether the program should attempt to divide * by the gcd and run again. It works better with polynomials known to have * high multiplicities. When divideGCD != 0 then it attempts to divide by the * GCD, if applicable. This defaults to 0. * Compared to the Sturm solver the Habicht solver is slower, * although both are O(d^2). The Habicht solver has the added benefit * that it has a built in mechanism to keep the leading coefficients of the * result from polynomial division bounded above and below in absolute value. * This will tend to keep the coefficients of the polynomials in the sequence * from zeroi ... [Truncated] SturmBisectionSolveV.SturmBisectionSolve([float, ...], int, [float, ...], [float, ...], float) -> int C++: static int SturmBisectionSolve(double *P, int d, double *a, double *upperBnds, double tol) V.SturmBisectionSolve([float, ...], int, [float, ...], [float, ...], float, int) -> int C++: static int SturmBisectionSolve(double *P, int d, double *a, double *upperBnds, double tol, int intervalType) V.SturmBisectionSolve([float, ...], int, [float, ...], [float, ...], float, int, bool) -> int C++: static int SturmBisectionSolve(double *P, int d, double *a, double *upperBnds, double tol, int intervalType, bool divideGCD) Finds all REAL roots (within tolerance tol) of the d -th degree polynomial P[0] X^d + ... + P[d-1] X + P[d] in ] a[0] ; a[1]] using Sturm's theorem ( polynomial coefficients are REAL ) and returns the count nr. All roots are bracketed in the r first ] upperBnds[i] - tol ; upperBnds[i]] intervals. Returns -1 if anything went wrong (such as: polynomial does not have degree d, the interval provided by the other is absurd, etc.). * intervalType specifies the search interval as follows: * 0 = 00 = ]a,b[ * 1 = 10 = [a,b[ * 2 = 01 = ]a,b] * 3 = 11 = [a,b] * This defaults to 0. * The last non-zero item in the Sturm sequence is the gcd of P and P'. The * parameter divideGCD specifies whether the program should attempt to divide * by the gcd and run again. It works better with polynomials known to have * high multiplicities. When divideGCD != 0 then it attempts to divide by the * GCD, if applicable. This defaults to 0. * Constructing the Sturm sequence is O(d^2) in both time and space. * Warning: it is the user's responsibility to make sure the upperBnds * array is large enough to contain the maximal number of expected roots. * Note that nr is smaller or equal to the actual number of roots in * ] a[0] ; a[1]] since roots within \tol are lumped in the same bracket. * array is large enough to contain the ma ... [Truncated] FilterRootsV.FilterRoots([float, ...], int, [float, ...], int, float) -> int C++: static int FilterRoots(double *P, int d, double *upperBnds, int rootcount, double diameter) This uses the derivative sequence to filter possible roots of a polynomial. First it sorts the roots and removes any duplicates. If the number of sign changes of the derivative sequence at a root at upperBnds[i] == that at upperBnds[i] - diameter then the i^th value is removed from upperBnds. It returns the new number of roots. LinBairstowSolveV.LinBairstowSolve([float, ...], int, [float, ...], float) -> int C++: static int LinBairstowSolve(double *c, int d, double *r, double &tolerance) Seeks all REAL roots of the d -th degree polynomial c[0] X^d + ... + c[d-1] X + c[d] = 0 equation Lin-Bairstow's method ( polynomial coefficients are REAL ) and stores the nr roots found ( multiple roots are multiply stored ) in r.tolerance is the user-defined solver tolerance; this variable may be relaxed by the iterative solver if needed. Returns nr. Warning: it is the user's responsibility to make sure the r array is large enough to contain the maximal number of expected roots. FerrariSolveV.FerrariSolve([float, ...], [float, ...], [int, ...], float) -> int C++: static int FerrariSolve(double *c, double *r, int *m, double tol) Algebraically extracts REAL roots of the quartic polynomial with REAL coefficients X^4 + c[0] X^3 + c[1] X^2 + c[2] X + c[3] and stores them (when they exist) and their respective multiplicities in the r and m arrays, based on Ferrari's method. Some numerical noise can be filtered by the use of a tolerance tol instead of equality with 0 (one can use, e.g., VTK_DBL_EPSILON). Returns the number of roots. Warning: it is the user's responsibility to pass a non-negative tol. TartagliaCardanSolveV.TartagliaCardanSolve([float, ...], [float, ...], [int, ...], float) -> int C++: static int TartagliaCardanSolve(double *c, double *r, int *m, double tol) Algebraically extracts REAL roots of the cubic polynomial with REAL coefficients X^3 + c[0] X^2 + c[1] X + c[2] and stores them (when they exist) and their respective multiplicities in the r and m arrays. Some numerical noise can be filtered by the use of a tolerance tol instead of equality with 0 (one can use, e.g., VTK_DBL_EPSILON). The main differences with SolveCubic are that (1) the polynomial must have unit leading coefficient, (2) complex roots are discarded upfront, (3) non-simple roots are stored only once, along with their respective multiplicities, and (4) some numerical noise is filtered by the use of relative tolerance instead of equality with 0. Returns the number of roots. In memoriam Niccolo Tartaglia (1500 - 1559), unfairly forgotten. SolveCubicV.SolveCubic(float, float, float, float) -> (float, ...) C++: static double *SolveCubic(double c0, double c1, double c2, double c3) V.SolveCubic(float, float, float, float, [float, ...], [float, ...], [float, ...], [int, ...]) -> int C++: static int SolveCubic(double c0, double c1, double c2, double c3, double *r1, double *r2, double *r3, int *num_roots) Solves a cubic equation c0*t^3 + c1*t^2 + c2*t + c3 = 0 when c0, c1, c2, and c3 are REAL. Solution is motivated by Numerical Recipes In C 2nd Ed. Return array contains number of (real) roots (counting multiple roots as one) followed by roots themselves. The value in roots[4] is a integer giving further information about the roots (see return codes for int SolveCubic() ). SolveQuadraticV.SolveQuadratic(float, float, float) -> (float, ...) C++: static double *SolveQuadratic(double c0, double c1, double c2) V.SolveQuadratic(float, float, float, [float, ...], [float, ...], [int, ...]) -> int C++: static int SolveQuadratic(double c0, double c1, double c2, double *r1, double *r2, int *num_roots) V.SolveQuadratic([float, ...], [float, ...], [int, ...]) -> int C++: static int SolveQuadratic(double *c, double *r, int *m) Solves a quadratic equation c0*t^2 + c1*t + c2 = 0 when c0, c1, and c2 are REAL. Solution is motivated by Numerical Recipes In C 2nd Ed. Return array contains number of (real) roots (counting multiple roots as one) followed by roots themselves. Note that roots[3] contains a return code further describing solution - see documentation for SolveCubic() for meaning of return codes. SolveLinearV.SolveLinear(float, float) -> (float, ...) C++: static double *SolveLinear(double c0, double c1) V.SolveLinear(float, float, [float, ...], [int, ...]) -> int C++: static int SolveLinear(double c0, double c1, double *r1, int *num_roots) Solves a linear equation c0*t + c1 = 0 when c0 and c1 are REAL. Solution is motivated by Numerical Recipes In C 2nd Ed. Return array contains number of roots followed by roots themselves. SetDivisionToleranceV.SetDivisionTolerance(float) C++: static void SetDivisionTolerance(double tol) Set/get the tolerance used when performing polynomial Euclidean division to find polynomial roots. This tolerance is used to decide whether the coefficient(s) of a polynomial remainder are close enough to zero to be neglected. GetDivisionToleranceV.GetDivisionTolerance() -> float C++: static double GetDivisionTolerance() Set/get the tolerance used when performing polynomial Euclidean division to find polynomial roots. This tolerance is used to decide whether the coefficient(s) of a polynomial remainder are close enough to zero to be neglected. dddPPP *d *d *ivtkQuaternionInterpolatorINTERPOLATION_TYPE_LINEARINTERPOLATION_TYPE_SPLINEvtkCommonMathPython.vtkQuaternionInterpolatorvtkQuaternionInterpolator - interpolate a quaternion Superclass: vtkObject This class is used to interpolate a series of quaternions representing the rotations of a 3D object. The interpolation may be linear in form (using spherical linear interpolation SLERP), or via spline interpolation (using SQUAD). In either case the interpolation is specialized to quaternions since the interpolation occurs on the surface of the unit quaternion sphere. To use this class, specify at least two pairs of (t,q[4]) with the AddQuaternion() method. Next interpolate the tuples with the InterpolateQuaternion(t,q[4]) method, where "t" must be in the range of (t_min,t_max) parameter values specified by the AddQuaternion() method (t is clamped otherwise), and q[4] is filled in by the method. There are several important background references. Ken Shoemake described the practical application of quaternions for the interpolation of rotation (K. Shoemake, "Animating rotation with quaternion curves", Computer Graphics (Siggraph '85) 19(3):245--254, 1985). Another fine reference (available on-line) is E. B. Dam, M. Koch, and M. Lillholm, Technical Report DIKU-TR-98/5, Dept. of Computer Science, University of Copenhagen, Denmark. @warning Note that for two or less quaternions, Slerp (linear) interpolation is performed even if spline interpolation is requested. Also, the tangents to the first and last segments of spline interpolation are (arbitrarily) defined by repeating the first and last quaternions. @warning There are several methods particular to quaternions (norms, products, etc.) implemented interior to this class. These may be moved to a separate quaternion class at some point. @sa vtkQuaternion V.SafeDownCast(vtkObjectBase) -> vtkQuaternionInterpolator C++: static vtkQuaternionInterpolator *SafeDownCast( vtkObjectBase *o) V.NewInstance() -> vtkQuaternionInterpolator C++: vtkQuaternionInterpolator *NewInstance() GetNumberOfQuaternionsV.GetNumberOfQuaternions() -> int C++: int GetNumberOfQuaternions() Return the number of quaternions in the list of quaternions to be interpolated. GetMinimumTV.GetMinimumT() -> float C++: double GetMinimumT() Obtain some information about the interpolation range. The numbers returned (corresponding to parameter t, usually thought of as time) are undefined if the list of transforms is empty. This is a convenience method for interpolation. GetMaximumTV.GetMaximumT() -> float C++: double GetMaximumT() Obtain some information about the interpolation range. The numbers returned (corresponding to parameter t, usually thought of as time) are undefined if the list of transforms is empty. This is a convenience method for interpolation. V.Initialize() C++: void Initialize() Reset the class so that it contains no data; i.e., the array of (t,q[4]) information is discarded. AddQuaternionV.AddQuaternion(float, vtkQuaterniond) C++: void AddQuaternion(double t, const vtkQuaterniond &q) V.AddQuaternion(float, [float, float, float, float]) C++: void AddQuaternion(double t, double q[4]) Add another quaternion to the list of quaternions to be interpolated. Note that using the same time t value more than once replaces the previous quaternion at t. At least one quaternions must be added to define an interpolation functios. RemoveQuaternionV.RemoveQuaternion(float) C++: void RemoveQuaternion(double t) Delete the quaternion at a particular parameter t. If there is no quaternion tuple defined at t, then the method does nothing. InterpolateQuaternionV.InterpolateQuaternion(float, vtkQuaterniond) C++: void InterpolateQuaternion(double t, vtkQuaterniond &q) V.InterpolateQuaternion(float, [float, float, float, float]) C++: void InterpolateQuaternion(double t, double q[4]) Interpolate the list of quaternions and determine a new quaternion (i.e., fill in the quaternion provided). If t is outside the range of (min,max) values, then t is clamped to lie within the range. SetInterpolationTypeV.SetInterpolationType(int) C++: virtual void SetInterpolationType(int _arg) Specify which type of function to use for interpolation. By default (SetInterpolationFunctionToSpline()), cubic spline interpolation using a modified Kochanek basis is employed. Otherwise, if SetInterpolationFunctionToLinear() is invoked, linear spherical interpolation is used between each pair of quaternions. GetInterpolationTypeMinValueV.GetInterpolationTypeMinValue() -> int C++: virtual int GetInterpolationTypeMinValue() Specify which type of function to use for interpolation. By default (SetInterpolationFunctionToSpline()), cubic spline interpolation using a modified Kochanek basis is employed. Otherwise, if SetInterpolationFunctionToLinear() is invoked, linear spherical interpolation is used between each pair of quaternions. GetInterpolationTypeMaxValueV.GetInterpolationTypeMaxValue() -> int C++: virtual int GetInterpolationTypeMaxValue() Specify which type of function to use for interpolation. By default (SetInterpolationFunctionToSpline()), cubic spline interpolation using a modified Kochanek basis is employed. Otherwise, if SetInterpolationFunctionToLinear() is invoked, linear spherical interpolation is used between each pair of quaternions. GetInterpolationTypeV.GetInterpolationType() -> int C++: virtual int GetInterpolationType() Specify which type of function to use for interpolation. By default (SetInterpolationFunctionToSpline()), cubic spline interpolation using a modified Kochanek basis is employed. Otherwise, if SetInterpolationFunctionToLinear() is invoked, linear spherical interpolation is used between each pair of quaternions. SetInterpolationTypeToLinearV.SetInterpolationTypeToLinear() C++: void SetInterpolationTypeToLinear() Specify which type of function to use for interpolation. By default (SetInterpolationFunctionToSpline()), cubic spline interpolation using a modified Kochanek basis is employed. Otherwise, if SetInterpolationFunctionToLinear() is invoked, linear spherical interpolation is used between each pair of quaternions. SetInterpolationTypeToSplineV.SetInterpolationTypeToSpline() C++: void SetInterpolationTypeToSpline() Specify which type of function to use for interpolation. By default (SetInterpolationFunctionToSpline()), cubic spline interpolation using a modified Kochanek basis is employed. Otherwise, if SetInterpolationFunctionToLinear() is invoked, linear spherical interpolation is used between each pair of quaternions. @dW vtkQuaterniond@dP *dvtkQuaterniond@dW &vtkQuaterniondvtkRungeKutta2vtkCommonMathPython.vtkRungeKutta2vtkRungeKutta2 - Integrate an initial value problem using 2nd order Runge-Kutta method. Superclass: vtkInitialValueProblemSolver This is a concrete sub-class of vtkInitialValueProblemSolver. It uses a 2nd order Runge-Kutta method to obtain the values of a set of functions at the next time step. @sa vtkInitialValueProblemSolver vtkRungeKutta4 vtkRungeKutta45 vtkFunctionSet V.SafeDownCast(vtkObjectBase) -> vtkRungeKutta2 C++: static vtkRungeKutta2 *SafeDownCast(vtkObjectBase *o) V.NewInstance() -> vtkRungeKutta2 C++: vtkRungeKutta2 *NewInstance() V.ComputeNextStep([float, ...], [float, ...], float, float, float, float) -> int C++: int ComputeNextStep(double *xprev, double *xnext, double t, double &delT, double maxError, double &error) override; V.ComputeNextStep([float, ...], [float, ...], [float, ...], float, float, float, float) -> int C++: int ComputeNextStep(double *xprev, double *dxprev, double *xnext, double t, double &delT, double maxError, double &error) override; V.ComputeNextStep([float, ...], [float, ...], float, float, float, float, float, float, float) -> int C++: int ComputeNextStep(double *xprev, double *xnext, double t, double &delT, double &delTActual, double minStep, double maxStep, double maxError, double &error) override; V.ComputeNextStep([float, ...], [float, ...], [float, ...], float, float, float, float, float, float, float) -> int C++: int ComputeNextStep(double *xprev, double *dxprev, double *xnext, double t, double &delT, double &delTActual, double minStep, double maxStep, double maxError, double &error) override; Given initial values, xprev , initial time, t and a requested time interval, delT calculate values of x at t+delT (xnext). delTActual is always equal to delT. Since this class can not provide an estimate for the error error is set to 0. maxStep, minStep and maxError are unused. This method returns an error code representing the nature of the failure: OutOfDomain = 1, NotInitialized = 2, UnexpectedValue = 3 vtkRungeKutta4vtkCommonMathPython.vtkRungeKutta4vtkRungeKutta4 - Integrate an initial value problem using 4th order Runge-Kutta method. Superclass: vtkInitialValueProblemSolver This is a concrete sub-class of vtkInitialValueProblemSolver. It uses a 4th order Runge-Kutta method to obtain the values of a set of functions at the next time step. @sa vtkInitialValueProblemSolver vtkRungeKutta45 vtkRungeKutta2 vtkFunctionSet V.SafeDownCast(vtkObjectBase) -> vtkRungeKutta4 C++: static vtkRungeKutta4 *SafeDownCast(vtkObjectBase *o) V.NewInstance() -> vtkRungeKutta4 C++: vtkRungeKutta4 *NewInstance() vtkRungeKutta45vtkCommonMathPython.vtkRungeKutta45vtkRungeKutta45 - Integrate an initial value problem using 5th order Runge-Kutta method with adaptive stepsize control. Superclass: vtkInitialValueProblemSolver This is a concrete sub-class of vtkInitialValueProblemSolver. It uses a 5th order Runge-Kutta method with stepsize control to obtain the values of a set of functions at the next time step. The stepsize is adjusted by calculating an estimated error using an embedded 4th order Runge-Kutta formula: Press, W. H. et al., 1992, Numerical Recipes in Fortran, Second Edition, Cambridge University Press Cash, J.R. and Karp, A.H. 1990, ACM Transactions on Mathematical Software, vol 16, pp 201-222 @sa vtkInitialValueProblemSolver vtkRungeKutta4 vtkRungeKutta2 vtkFunctionSet V.SafeDownCast(vtkObjectBase) -> vtkRungeKutta45 C++: static vtkRungeKutta45 *SafeDownCast(vtkObjectBase *o) V.NewInstance() -> vtkRungeKutta45 C++: vtkRungeKutta45 *NewInstance() V.ComputeNextStep([float, ...], [float, ...], float, float, float, float) -> int C++: int ComputeNextStep(double *xprev, double *xnext, double t, double &delT, double maxError, double &error) override; V.ComputeNextStep([float, ...], [float, ...], [float, ...], float, float, float, float) -> int C++: int ComputeNextStep(double *xprev, double *dxprev, double *xnext, double t, double &delT, double maxError, double &error) override; V.ComputeNextStep([float, ...], [float, ...], float, float, float, float, float, float, float) -> int C++: int ComputeNextStep(double *xprev, double *xnext, double t, double &delT, double &delTActual, double minStep, double maxStep, double maxError, double &error) override; V.ComputeNextStep([float, ...], [float, ...], [float, ...], float, float, float, float, float, float, float) -> int C++: int ComputeNextStep(double *xprev, double *dxprev, double *xnext, double t, double &delT, double &delTActual, double minStep, double maxStep, double maxError, double &error) override; Given initial values, xprev , initial time, t and a requested time interval, delT calculate values of x at t+delTActual (xnext). Possibly delTActual != delT. This may occur because this solver supports adaptive stepsize control. It tries to change to stepsize such that the (estimated) error of the integration is less than maxError. The solver will not set the stepsize smaller than minStep or larger than maxStep (note that maxStep and minStep should both be positive, whereas delT can be negative). Also note that delT is an in/out argument. vtkRungeKutta45 will modify delT to reflect the best (estimated) size for the next integration step. An estimated value for the error is returned (by reference) in error. This is the norm of the error vector if there are more than one function to be integrated. This method returns an error code representing the nature of the failure: OutOfDomain = 1, NotInitialized = 2, Une ... [Truncated] vtkCommonMathPython.vtkQuaternionvaluesvtkQuaternionvtkQuaternionfvtkCommonMathPython.vtkQuaternion_IdEvtkQuaternion- templated base type for storage of quaternions. Superclass: vtkTuple[float64,4] This class is a templated data type for storing and manipulating quaternions. The quaternions have the form [w, x, y, z]. Given a rotation of angle theta and axis v, the corresponding quaternion is [w, x, y, z] = [cos(theta/2), v*sin(theta/2)] This class implements the Spherical Linear interpolation (SLERP) and the Spherical Spline Quaternion interpolation (SQUAD). It is advised to use the vtkQuaternionInterpolator when dealing with multiple quaternions and or interpolations. @sa vtkQuaternionInterpolator vtkQuaternion() explicit vtkQuaternion(const double &scalar) explicit vtkQuaternion(const double *init) vtkQuaternion(const double &w, const double &x, const double &y, const double &z) vtkQuaternion(const &vtkQuaternion) this function takes no keyword argumentsvtkQuaternion_IdESquaredNormV.SquaredNorm() -> float C++: double SquaredNorm() Get the squared norm of the quaternion. NormV.Norm() -> float C++: double Norm() Get the norm of the quaternion, i.e. its length. ToIdentityV.ToIdentity() C++: void ToIdentity() Set the quaternion to identity in place. V.Identity() -> vtkQuaternion_IdE C++: static vtkQuaternion Identity() Return the identity quaternion. Note that the default constructor also creates an identity quaternion. NormalizeV.Normalize() -> float C++: double Normalize() Normalize the quaternion in place. Return the norm of the quaternion. NormalizedV.Normalized() -> vtkQuaternion_IdE C++: vtkQuaternion Normalized() Return the normalized form of this quaternion. ConjugateV.Conjugate() C++: void Conjugate() Conjugate the quaternion in place. ConjugatedV.Conjugated() -> vtkQuaternion_IdE C++: vtkQuaternion Conjugated() Return the conjugate form of this quaternion. V.Invert() C++: void Invert() Invert the quaternion in place. This is equivalent to conjugate the quaternion and then divide it by its squared norm. InverseV.Inverse() -> vtkQuaternion_IdE C++: vtkQuaternion Inverse() Return the inverted form of this quaternion. ToUnitLogV.ToUnitLog() C++: void ToUnitLog() Convert this quaternion to a unit log quaternion. The unit log quaternion is defined by: [w, x, y, z] = [0.0, v*theta]. UnitLogV.UnitLog() -> vtkQuaternion_IdE C++: vtkQuaternion UnitLog() Return the unit log version of this quaternion. The unit log quaternion is defined by: [w, x, y, z] = [0.0, v*theta]. ToUnitExpV.ToUnitExp() C++: void ToUnitExp() Convert this quaternion to a unit exponential quaternion. The unit exponential quaternion is defined by: [w, x, y, z] = [cos(theta), v*sin(theta)]. UnitExpV.UnitExp() -> vtkQuaternion_IdE C++: vtkQuaternion UnitExp() Return the unit exponential version of this quaternion. The unit exponential quaternion is defined by: [w, x, y, z] = [cos(theta), v*sin(theta)]. NormalizeWithAngleInDegreesV.NormalizeWithAngleInDegrees() C++: void NormalizeWithAngleInDegrees() Normalize a quaternion in place and transform it to so its angle is in degrees and its axis normalized. NormalizedWithAngleInDegreesV.NormalizedWithAngleInDegrees() -> vtkQuaternion_IdE C++: vtkQuaternion NormalizedWithAngleInDegrees() Returns a quaternion normalized and transformed so its angle is in degrees and its axis normalized. SetV.Set(float, float, float, float) C++: void Set(const double &w, const double &x, const double &y, const double &z) V.Set([float, float, float, float]) C++: void Set(double quat[4]) Set/Get the w, x, y and z components of the quaternion. GetV.Get([float, float, float, float]) C++: void Get(double quat[4]) Set/Get the w, x, y and z components of the quaternion. SetWV.SetW(float) C++: void SetW(const double &w) Set/Get the w component of the quaternion, i.e. element 0. GetWV.GetW() -> float C++: const double &GetW() Set/Get the w component of the quaternion, i.e. element 0. SetXV.SetX(float) C++: void SetX(const double &x) Set/Get the x component of the quaternion, i.e. element 1. GetXV.GetX() -> float C++: const double &GetX() Set/Get the x component of the quaternion, i.e. element 1. SetYV.SetY(float) C++: void SetY(const double &y) Set/Get the y component of the quaternion, i.e. element 2. GetYV.GetY() -> float C++: const double &GetY() Set/Get the y component of the quaternion, i.e. element 2. SetZV.SetZ(float) C++: void SetZ(const double &z) Set/Get the y component of the quaternion, i.e. element 3. GetZV.GetZ() -> float C++: const double &GetZ() Set/Get the y component of the quaternion, i.e. element 3. GetRotationAngleAndAxisV.GetRotationAngleAndAxis([float, float, float]) -> float C++: double GetRotationAngleAndAxis(double axis[3]) Set/Get the angle (in radians) and the axis corresponding to the axis-angle rotation of this quaternion. SetRotationAngleAndAxisV.SetRotationAngleAndAxis(float, [float, float, float]) C++: void SetRotationAngleAndAxis(double angle, double axis[3]) V.SetRotationAngleAndAxis(float, float, float, float) C++: void SetRotationAngleAndAxis(const double &angle, const double &x, const double &y, const double &z) Set/Get the angle (in radians) and the axis corresponding to the axis-angle rotation of this quaternion. ToMatrix3x3V.ToMatrix3x3([[float, float, float], [float, float, float], [float, float, float]]) C++: void ToMatrix3x3(double A[3][3]) Convert a quaternion to a 3x3 rotation matrix. The quaternion does not have to be normalized beforehand. @sa FromMatrix3x3() FromMatrix3x3V.FromMatrix3x3(((float, float, float), (float, float, float), ( float, float, float))) C++: void FromMatrix3x3(const double A[3][3]) Convert a 3x3 matrix into a quaternion. This will provide the best possible answer even if the matrix is not a pure rotation matrix. The method used is that of B.K.P. Horn. @sa ToMatrix3x3() SlerpV.Slerp(float, vtkQuaternion_IdE) -> vtkQuaternion_IdE C++: vtkQuaternion Slerp(double t, const vtkQuaternion &q) Interpolate quaternions using spherical linear interpolation between this quaternion and q1 to produce the output. The parametric coordinate t belongs to [0,1] and lies between (this,q1). @sa vtkQuaternionInterpolator InnerPointV.InnerPoint(vtkQuaternion_IdE, vtkQuaternion_IdE) -> vtkQuaternion_IdE C++: vtkQuaternion InnerPoint( const vtkQuaternion &q1, const vtkQuaternion &q2) Interpolates between quaternions, using spherical quadrangle interpolation. @sa vtkQuaternionInterpolator -@d-@P *d@W vtkQuaternion_IdEvtkCommonMathPython.vtkQuaternion_IfEvtkQuaternion- templated base type for storage of quaternions. Superclass: vtkTuple[float32,4] This class is a templated data type for storing and manipulating quaternions. The quaternions have the form [w, x, y, z]. Given a rotation of angle theta and axis v, the corresponding quaternion is [w, x, y, z] = [cos(theta/2), v*sin(theta/2)] This class implements the Spherical Linear interpolation (SLERP) and the Spherical Spline Quaternion interpolation (SQUAD). It is advised to use the vtkQuaternionInterpolator when dealing with multiple quaternions and or interpolations. @sa vtkQuaternionInterpolator vtkQuaternion() explicit vtkQuaternion(const float &scalar) explicit vtkQuaternion(const float *init) vtkQuaternion(const float &w, const float &x, const float &y, const float &z) vtkQuaternion(const &vtkQuaternion) vtkQuaternion_IfEV.SquaredNorm() -> float C++: float SquaredNorm() Get the squared norm of the quaternion. V.Norm() -> float C++: float Norm() Get the norm of the quaternion, i.e. its length. V.Identity() -> vtkQuaternion_IfE C++: static vtkQuaternion Identity() Return the identity quaternion. Note that the default constructor also creates an identity quaternion. V.Normalize() -> float C++: float Normalize() Normalize the quaternion in place. Return the norm of the quaternion. V.Normalized() -> vtkQuaternion_IfE C++: vtkQuaternion Normalized() Return the normalized form of this quaternion. V.Conjugated() -> vtkQuaternion_IfE C++: vtkQuaternion Conjugated() Return the conjugate form of this quaternion. V.Inverse() -> vtkQuaternion_IfE C++: vtkQuaternion Inverse() Return the inverted form of this quaternion. V.UnitLog() -> vtkQuaternion_IfE C++: vtkQuaternion UnitLog() Return the unit log version of this quaternion. The unit log quaternion is defined by: [w, x, y, z] = [0.0, v*theta]. V.UnitExp() -> vtkQuaternion_IfE C++: vtkQuaternion UnitExp() Return the unit exponential version of this quaternion. The unit exponential quaternion is defined by: [w, x, y, z] = [cos(theta), v*sin(theta)]. V.NormalizedWithAngleInDegrees() -> vtkQuaternion_IfE C++: vtkQuaternion NormalizedWithAngleInDegrees() Returns a quaternion normalized and transformed so its angle is in degrees and its axis normalized. V.Set(float, float, float, float) C++: void Set(const float &w, const float &x, const float &y, const float &z) V.Set([float, float, float, float]) C++: void Set(float quat[4]) Set/Get the w, x, y and z components of the quaternion. V.Get([float, float, float, float]) C++: void Get(float quat[4]) Set/Get the w, x, y and z components of the quaternion. V.SetW(float) C++: void SetW(const float &w) Set/Get the w component of the quaternion, i.e. element 0. V.GetW() -> float C++: const float &GetW() Set/Get the w component of the quaternion, i.e. element 0. V.SetX(float) C++: void SetX(const float &x) Set/Get the x component of the quaternion, i.e. element 1. V.GetX() -> float C++: const float &GetX() Set/Get the x component of the quaternion, i.e. element 1. V.SetY(float) C++: void SetY(const float &y) Set/Get the y component of the quaternion, i.e. element 2. V.GetY() -> float C++: const float &GetY() Set/Get the y component of the quaternion, i.e. element 2. V.SetZ(float) C++: void SetZ(const float &z) Set/Get the y component of the quaternion, i.e. element 3. V.GetZ() -> float C++: const float &GetZ() Set/Get the y component of the quaternion, i.e. element 3. V.GetRotationAngleAndAxis([float, float, float]) -> float C++: float GetRotationAngleAndAxis(float axis[3]) Set/Get the angle (in radians) and the axis corresponding to the axis-angle rotation of this quaternion. V.SetRotationAngleAndAxis(float, [float, float, float]) C++: void SetRotationAngleAndAxis(float angle, float axis[3]) V.SetRotationAngleAndAxis(float, float, float, float) C++: void SetRotationAngleAndAxis(const float &angle, const float &x, const float &y, const float &z) Set/Get the angle (in radians) and the axis corresponding to the axis-angle rotation of this quaternion. V.ToMatrix3x3([[float, float, float], [float, float, float], [float, float, float]]) C++: void ToMatrix3x3(float A[3][3]) Convert a quaternion to a 3x3 rotation matrix. The quaternion does not have to be normalized beforehand. @sa FromMatrix3x3() V.FromMatrix3x3(((float, float, float), (float, float, float), ( float, float, float))) C++: void FromMatrix3x3(const float A[3][3]) Convert a 3x3 matrix into a quaternion. This will provide the best possible answer even if the matrix is not a pure rotation matrix. The method used is that of B.K.P. Horn. @sa ToMatrix3x3() V.Slerp(float, vtkQuaternion_IfE) -> vtkQuaternion_IfE C++: vtkQuaternion Slerp(float t, const vtkQuaternion &q) Interpolate quaternions using spherical linear interpolation between this quaternion and q1 to produce the output. The parametric coordinate t belongs to [0,1] and lies between (this,q1). @sa vtkQuaternionInterpolator V.InnerPoint(vtkQuaternion_IfE, vtkQuaternion_IfE) -> vtkQuaternion_IfE C++: vtkQuaternion InnerPoint( const vtkQuaternion &q1, const vtkQuaternion &q2) Interpolates between quaternions, using spherical quadrangle interpolation. @sa vtkQuaternionInterpolator -@f-@P *f@W vtkQuaternion_IfEvtkQuaterniond - Double quaternion type. Superclass: vtkTuple[T,4] This class is uses vtkQuaternion with double type data. For further description, seethe templated class vtkQuaternion. @sa vtkQuaternionf vtkQuaternion Provided Types: vtkQuaternion[float64] => vtkQuaternion vtkQuaternion[float32] => vtkQuaternion vtkCommonMathPython.vtkQuaternionfvtkQuaternionf - no description provided. Superclass: vtkQuaternion[float32] vtkQuaternionf() explicit vtkQuaternionf(float w, float x, float y, float z) explicit vtkQuaternionf(float scalar) explicit vtkQuaternionf(const float *init) vtkQuaternionf(const &vtkQuaternionf) V.Identity() -> vtkQuaternionf C++: vtkQuaternionf Identity() Return the identity quaternion. Note that the default constructor also creates an identity quaternion. V.Normalized() -> vtkQuaternionf C++: vtkQuaternionf Normalized() Return the normalized form of this quaternion. V.Conjugated() -> vtkQuaternionf C++: vtkQuaternionf Conjugated() Return the conjugate form of this quaternion. V.Inverse() -> vtkQuaternionf C++: vtkQuaternionf Inverse() Return the inverted form of this quaternion. V.UnitLog() -> vtkQuaternionf C++: vtkQuaternionf UnitLog() Return the unit log version of this quaternion. The unit log quaternion is defined by: [w, x, y, z] = [0.0, v*theta]. V.UnitExp() -> vtkQuaternionf C++: vtkQuaternionf UnitExp() Return the unit exponential version of this quaternion. The unit exponential quaternion is defined by: [w, x, y, z] = [cos(theta), v*sin(theta)]. V.NormalizedWithAngleInDegrees() -> vtkQuaternionf C++: vtkQuaternionf NormalizedWithAngleInDegrees() Returns a quaternion normalized and transformed so its angle is in degrees and its axis normalized. V.Slerp(float, vtkQuaternionf) -> vtkQuaternionf C++: vtkQuaternionf Slerp(float t, const vtkQuaternionf &q) V.InnerPoint(vtkQuaternionf, vtkQuaternionf) -> vtkQuaternionf C++: vtkQuaternionf InnerPoint(const vtkQuaternionf &q1, const vtkQuaternionf &q2) @W vtkQuaternionfvtkCommonMathPython.vtkQuaterniondvtkQuaterniond - no description provided. Superclass: vtkQuaternion[float64] vtkQuaterniond() explicit vtkQuaterniond(double w, double x, double y, double z) explicit vtkQuaterniond(double scalar) explicit vtkQuaterniond(const double *init) vtkQuaterniond(const &vtkQuaterniond) V.Identity() -> vtkQuaterniond C++: vtkQuaterniond Identity() Return the identity quaternion. Note that the default constructor also creates an identity quaternion. V.Normalized() -> vtkQuaterniond C++: vtkQuaterniond Normalized() Return the normalized form of this quaternion. V.Conjugated() -> vtkQuaterniond C++: vtkQuaterniond Conjugated() Return the conjugate form of this quaternion. V.Inverse() -> vtkQuaterniond C++: vtkQuaterniond Inverse() Return the inverted form of this quaternion. V.UnitLog() -> vtkQuaterniond C++: vtkQuaterniond UnitLog() Return the unit log version of this quaternion. The unit log quaternion is defined by: [w, x, y, z] = [0.0, v*theta]. V.UnitExp() -> vtkQuaterniond C++: vtkQuaterniond UnitExp() Return the unit exponential version of this quaternion. The unit exponential quaternion is defined by: [w, x, y, z] = [cos(theta), v*sin(theta)]. V.NormalizedWithAngleInDegrees() -> vtkQuaterniond C++: vtkQuaterniond NormalizedWithAngleInDegrees() Returns a quaternion normalized and transformed so its angle is in degrees and its axis normalized. V.Slerp(float, vtkQuaterniond) -> vtkQuaterniond C++: vtkQuaterniond Slerp(double t, const vtkQuaterniond &q) V.InnerPoint(vtkQuaterniond, vtkQuaterniond) -> vtkQuaterniond C++: vtkQuaterniond InnerPoint(const vtkQuaterniond &q1, const vtkQuaterniond &q2) @W vtkQuaterniondindex out of rangevtkCommonMathPython.vtkTuplevtkTuplevtkCommonMathPython.vtkTuple_IdLi4EEvtkTuple - templated base type for containers of constant size. This class is a templated data type for storing and manipulating tuples. vtkTuple() explicit vtkTuple(const double &scalar) explicit vtkTuple(const double *init) vtkTuple(const &vtkTuple) vtkTuple_IdLi4EEGetSizeV.GetSize() -> int C++: int GetSize() Get the size of the tuple. V.GetData() -> (float, ...) C++: double *GetData() Get a pointer to the underlying data of the tuple. CompareV.Compare(vtkTuple_IdLi4EE, float) -> bool C++: bool Compare(const vtkTuple &other, const double &tol) Equality operator with a tolerance to allow fuzzy comparisons. @W vtkTuple_IdLi4EEvtkCommonMathPython.vtkTuple_IfLi4EEvtkTuple - templated base type for containers of constant size. This class is a templated data type for storing and manipulating tuples. vtkTuple() explicit vtkTuple(const float &scalar) explicit vtkTuple(const float *init) vtkTuple(const &vtkTuple) vtkTuple_IfLi4EEV.GetData() -> (float, ...) C++: float *GetData() Get a pointer to the underlying data of the tuple. V.Compare(vtkTuple_IfLi4EE, float) -> bool C++: bool Compare(const vtkTuple &other, const float &tol) Equality operator with a tolerance to allow fuzzy comparisons. @W vtkTuple_IfLi4EEvtkCommonMathPython.vtkTuple_IhLi2EEvtkTuple - templated base type for containers of constant size. This class is a templated data type for storing and manipulating tuples. vtkTuple() explicit vtkTuple(const unsigned char &scalar) explicit vtkTuple(const unsigned char *init) vtkTuple(const &vtkTuple) vtkTuple_IhLi2EEV.GetData() -> (int, ...) C++: unsigned char *GetData() Get a pointer to the underlying data of the tuple. V.Compare(vtkTuple_IhLi2EE, int) -> bool C++: bool Compare(const vtkTuple &other, const unsigned char &tol) Equality operator with a tolerance to allow fuzzy comparisons. -@B-@P *B@W vtkTuple_IhLi2EEvtkCommonMathPython.vtkTuple_IhLi3EEvtkTuple - templated base type for containers of constant size. This class is a templated data type for storing and manipulating tuples. vtkTuple() explicit vtkTuple(const unsigned char &scalar) explicit vtkTuple(const unsigned char *init) vtkTuple(const &vtkTuple) vtkTuple_IhLi3EEV.Compare(vtkTuple_IhLi3EE, int) -> bool C++: bool Compare(const vtkTuple &other, const unsigned char &tol) Equality operator with a tolerance to allow fuzzy comparisons. @W vtkTuple_IhLi3EEvtkCommonMathPython.vtkTuple_IhLi4EEvtkTuple - templated base type for containers of constant size. This class is a templated data type for storing and manipulating tuples. vtkTuple() explicit vtkTuple(const unsigned char &scalar) explicit vtkTuple(const unsigned char *init) vtkTuple(const &vtkTuple) vtkTuple_IhLi4EEV.Compare(vtkTuple_IhLi4EE, int) -> bool C++: bool Compare(const vtkTuple &other, const unsigned char &tol) Equality operator with a tolerance to allow fuzzy comparisons. @W vtkTuple_IhLi4EEvtkCommonMathPython.vtkTuple_IiLi2EEvtkTuple - templated base type for containers of constant size. This class is a templated data type for storing and manipulating tuples. vtkTuple() explicit vtkTuple(const int &scalar) explicit vtkTuple(const int *init) vtkTuple(const &vtkTuple) vtkTuple_IiLi2EEV.GetData() -> (int, ...) C++: int *GetData() Get a pointer to the underlying data of the tuple. V.Compare(vtkTuple_IiLi2EE, int) -> bool C++: bool Compare(const vtkTuple &other, const int &tol) Equality operator with a tolerance to allow fuzzy comparisons. -@i-@P *i@W vtkTuple_IiLi2EEvtkCommonMathPython.vtkTuple_IiLi3EEvtkTuple - templated base type for containers of constant size. This class is a templated data type for storing and manipulating tuples. vtkTuple() explicit vtkTuple(const int &scalar) explicit vtkTuple(const int *init) vtkTuple(const &vtkTuple) vtkTuple_IiLi3EEV.Compare(vtkTuple_IiLi3EE, int) -> bool C++: bool Compare(const vtkTuple &other, const int &tol) Equality operator with a tolerance to allow fuzzy comparisons. @W vtkTuple_IiLi3EEvtkCommonMathPython.vtkTuple_IiLi4EEvtkTuple - templated base type for containers of constant size. This class is a templated data type for storing and manipulating tuples. vtkTuple() explicit vtkTuple(const int &scalar) explicit vtkTuple(const int *init) vtkTuple(const &vtkTuple) vtkTuple_IiLi4EEV.Compare(vtkTuple_IiLi4EE, int) -> bool C++: bool Compare(const vtkTuple &other, const int &tol) Equality operator with a tolerance to allow fuzzy comparisons. @W vtkTuple_IiLi4EEvtkCommonMathPython.vtkTuple_IfLi2EEvtkTuple - templated base type for containers of constant size. This class is a templated data type for storing and manipulating tuples. vtkTuple() explicit vtkTuple(const float &scalar) explicit vtkTuple(const float *init) vtkTuple(const &vtkTuple) vtkTuple_IfLi2EEV.Compare(vtkTuple_IfLi2EE, float) -> bool C++: bool Compare(const vtkTuple &other, const float &tol) Equality operator with a tolerance to allow fuzzy comparisons. @W vtkTuple_IfLi2EEvtkCommonMathPython.vtkTuple_IfLi3EEvtkTuple - templated base type for containers of constant size. This class is a templated data type for storing and manipulating tuples. vtkTuple() explicit vtkTuple(const float &scalar) explicit vtkTuple(const float *init) vtkTuple(const &vtkTuple) vtkTuple_IfLi3EEV.Compare(vtkTuple_IfLi3EE, float) -> bool C++: bool Compare(const vtkTuple &other, const float &tol) Equality operator with a tolerance to allow fuzzy comparisons. @W vtkTuple_IfLi3EEvtkCommonMathPython.vtkTuple_IdLi2EEvtkTuple - templated base type for containers of constant size. This class is a templated data type for storing and manipulating tuples. vtkTuple() explicit vtkTuple(const double &scalar) explicit vtkTuple(const double *init) vtkTuple(const &vtkTuple) vtkTuple_IdLi2EEV.Compare(vtkTuple_IdLi2EE, float) -> bool C++: bool Compare(const vtkTuple &other, const double &tol) Equality operator with a tolerance to allow fuzzy comparisons. @W vtkTuple_IdLi2EEvtkCommonMathPython.vtkTuple_IdLi3EEvtkTuple - templated base type for containers of constant size. This class is a templated data type for storing and manipulating tuples. vtkTuple() explicit vtkTuple(const double &scalar) explicit vtkTuple(const double *init) vtkTuple(const &vtkTuple) vtkTuple_IdLi3EEV.Compare(vtkTuple_IdLi3EE, float) -> bool C++: bool Compare(const vtkTuple &other, const double &tol) Equality operator with a tolerance to allow fuzzy comparisons. @W vtkTuple_IdLi3EEvtkTuple - templated base type for containers of constant size. This class is a templated data type for storing and manipulating tuples. Provided Types: vtkTuple[float64,4] => vtkTuple vtkTuple[float32,4] => vtkTuple vtkTuple[uint8,2] => vtkTuple vtkTuple[uint8,3] => vtkTuple vtkTuple[uint8,4] => vtkTuple vtkTuple[int32,2] => vtkTuple vtkTuple[int32,3] => vtkTuple vtkTuple[int32,4] => vtkTuple vtkTuple[float32,2] => vtkTuple vtkTuple[float32,3] => vtkTuple vtkTuple[float64,2] => vtkTuple vtkTuple[float64,3] => vtkTuple real_initvtkCommonMathPythoncan't get dictionary for module vtkCommonMathPythonvtkCommonMathPython$    o ? ?> ? ?? ? ? ? ? >  ? ?? ? >?>>>>%>/>;>> / // /q/ / // // / / / / / ~ / / //"/,/. / // /q/ / // // / / / / / ~ / / //"/,/."nn    r"nn    r/nn    /nn    I    =   /  W   l/tt     @ @? @ @? @ @ ? ? ?  ? ?? ???????%?0?;?? @ @? @ @? @ @ ? ? ?  ? ?? ???????%?0?;?? @ @? @ @? @ @ ? ? ?  ? ?? ???????%?0?;??8<!aXQ X`CTWpg@th0(p%+3;(pHx0QPYw$ 1``pp`  p  0 pp  !0"#)p+P--P.`/1QQPSS@TTVWW0\]`@abpde0gjklnpopqPrtuwpx y0z{ |`Ї0Е@НP00@ @  $0%% &''(p*P//@01@23PTT@UV@WXPyy@z{@|}P0Ф0P@``@0@@Pp`pp`pppP!"p##@$$$$%% 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