7(9JX=,dd +(I)   1Courier New1Symbol New1Courier New1Courier NewTimesr NewTimes New Roman1Courier New1Courier New1Courier New1Courier NewXxV XxV XxV XxV ?/ <```@@@?~~~~~ԱޱޱԱ޿޿ph (((Pdd{  d<  p {2  Y? Um8?ã|@~7>zDۧ@v?).0 T????v'ؗ@E}Cv @ ': @k!@@qP@?@dddddddddddddddddddddddddddddddddddddddd /2??Uy@$$$Uy@r3܀@e8 v??F?????:PLHxT :L 1$Z4B4L 䝸  sin(u)cos(t) sin(u)sin(t)cos(u)Riemann Sphere52??@$$$~hcbȋW̄???????????L (8 *N 38Djc8ĕ 0N 001Projection Origin52??@$$$5Jp,9xʺ???>Ӈ]^?Bя?R遛?îV_?iD#a?)M@I????îV_?ӈG?)M@I?hn8`y8pHU\?Az????g\X!?ԚЌ 8 M5 ~h ˷ 001xP(p)yP(p)zp(P)Projection Part 252??@$$$wCE?ׂ53l?? ʍ !U? K?VƆ@ K????? ʍ !U? K?8K 8@@qP@RQ????@g\X!? Xz!TlJ L Z } a5 f a5 *(d*(H*d-J*g)+g*sqrt(g*g+d*d)*t)/(g*g+d*d)+(-g*(H*d-J*g)+d*sqrt(g*g+d*d)*t)/(g*g+d*d)0 -3.5;3.53.5Source Line in C 02??h!@$$$h!@?ٝʴg1n|%I&?aox?(: *B?|(u8+????~L:pd`\xXj+ d Z p5 e i P} 0rs(0)*(bc(0)*ca(g,d)*(cos(t)+1)-sa(g,d)*sin(t))0rs(0)*(bc(0)*sa(g,d)*(cos(t)+1)+ca(g,d)*sin(t))bc(0)^2-rs(0)^2*cos(t)0.0;2piParamet Image Circl52??@$$$G8>sHh???|hI|?PCJ-PQEglO?<'Z:?WZWW?3'ڈ????wO$u?_yk_]?EglO?PLHzDl iZX?9*0?ׂӍI3?пc7r????g\X!? tplzhl@< c | C xC(g,d)yC(g,d) bc(0)*bc(0)xP(p)yP(p)zP(p)Center to Image Pt42???$$$??OT%TrNO*IU@|Zŀ?????g\X!?84qvgT  ̰ 000d*(H*d-J*g)/(g*g+d*d)-g*(H*d-J*g)/(g*g+d*d)0C Vector Eta0 C 02??@$$$@?8xQqc-3RQ Z>@@qP@RQ????@g\X!? L jtvhn p W < *(d*(H*d-J*g)-g*sqrt(g*g+d*d)*t)/(g*g+d*d)+(-g*(H*d-J*g)-d*sqrt(g*g+d*d)*t)/(g*g+d*d)0 -3.5;3.53.5Source Line in C xyz2Sxb@(\(?@JXT@3sΘ?GzGzGz@ ףp= ףyt͘@QQ?gffffff@?h!??@h!@?@@@h!@@@@@@@@@tV@@@@h!@@@@@@@@26d26d26d (H*d-J*g)*(H*d-J*g)+(g*g+d*d)*(x*x+1)@@@h!@h!@@@@@@@@h!@@@@@@@@@@DenE3̞ 2(g*sqrt(g*g+d*d)*x+d*(H*d-J*g))/Den(x)xP͞ 2(d*sqrt(g*g+d*d)*x-g*(H*d-J*g))/Den(x)      !"#yP ((H*d-J*g)*(H*d-J*g)+(g*g+d*d)*(x*x-1))/Den(x) fa-"oHNpA =D ,n!h`zPeG~ (H*y-J*x)*y/Den(0)n(0)xC~ -(H*y-J*x)*x/Den(0)n(0)yC8 y*sgn(H*y-J*x)/sqrt(x*x+y*y)?@@@h!@h!@@@@@@@@tV@@@@h!@@@@@@ca@L -x*sgn(H*y-J*x)/sqrt(x*x+y*y)@@@h!@h!@@@@@@@@tV@@@@h!@@@@@@sa@` sqrt((g*g+d*d)/Den(0))rst sqrt(1-rs(x)^2)73@$sޏV3@KL3@nI3@cօ3@1-԰3@eߧɲ3@ ~ڴ3@f3@-ބ=3@-X`.3@8` ۽3@43@e*%3@;3@ɬb3@[jH3@GED3@O^3@[!3@k 3@>3@#P3@b9J磜3@,bc3@ (H*y-J*x)*(H*y-J*x)/Den(0)" )" )" )" )" )" )" )" )" zCProjection C Line ---> Circle on Sphere: Cartesian InputMf_ qK/ht`?/8T`)b@Times New Roman(x,y,z) = (sin(u)cos(t),sin(u)sin(t),cos(u)))wT*aA7?Ek䰰?1Courier New  (x,y,z) = (0,0,1)ownloads\@@@wT r,H!xV?'x?1Courier New  (x,y,z) = (xP(p),yP(p),zp(P))a)*(cos(O)+1)-sin(a)*sin(O)),swTyk'+ubHmY]@E` ?1Courier New | segment (0,0,1)<--(xP(p),yP(p),zp(P)))*(cos(O)+1)-sin(a)*siwTpήHa?ZTA@jF.?1Courier New 4 (x,y,z) = ((d*(H*d-J*g)+g*sqrt(g*g+d*d)*p)/(g*g+d*d),(-g*(H*wTa9a<l11@{]3SxL?1Courier New  segment (0,0,0)-->(H,J,0),Qsin(O),0)),b*sin(a)/sqrt(1-b*b)wTwxYlF%A K@ŕZ$܈?1Courier New  segment ((d*(H*d-J*g)+g*sqrt(g*g+d*d)*p)/(g*g+d*d),(-g*(H*d-?wT & 1:x?&|Ʉ?1Courier New \ (x,y,z) = ((d*(H*d-J*g)+g*sqrt(g*g+d*d)*t)/(g*g+d*d),(-g*(H*wT W$ʁ U?&|Ʉ?1Courier New  (x,y,z) = (rs(0)*(bc(0)*ca(g,d)*(cos(t)+1)-sa(g,d)*sin(t)),r wT6:A?8ѴƑ?1Courier New  (x,y,z) = (xC(g,d),yC(g,d),zC(g,d))))1-b*b)*sin(A),b*b)wT8 ,4W?jpܓ?1Courier New  segment (0,0,0)-->(ca(g,d)*rs(0),sa(g,d)*rs(0),bc(0))en(0))wTx{"͈}b9?K@p?1Courier New < segment (xC(g,d),yC(g,d),bc(0)*bc(0))-->(xP(p),yP(p),zP(p))wTzBaC~x ۃ@ Ugs?1Courier New  segment (0,0,0)-->(d*(H*d-J*g)/(g*g+d*d),-g*(H*d-J*g)/(g*g+dwTcX 8lP?nO?1Courier New  (x,y,z) = ((d*(H*d-J*g)-g*sqrt(g*g+d*d)*t)/(g*g+d*d),(-g*(H*wT Eޒ 2Cڨ~Ǫ@?1Courier New @@@h!@