7(9XX=,dd +(I)   1Courier New1Symbol New1Courier New1Courier NewTimesr NewTimes New Roman1Courier New1Courier New1Courier New1Courier NewX x!VX x!VX x!VX x!V?/ <```@@@?~~~~~ԱޱޱԱ޿޿ph (((Pdd{  d<  p {2 @/*@R! {[X@Pw[f @ 5N(@???{ ?o @z\ @@iW @cfff0&Xafff0@cfff< ṇ'@61wm@?033333??@^ߛOw?̌???:Ic@V@@?@ @@@?@@@@@@e8 XC#A@n3!;@?@dddddddddddddddddddddddddddddddddddddddd /2??Uy@$$$Uy@r3܀@e8 v??F?????(מݢ](H sin(u)cos(t) sin(u)sin(t)cos(u)Riemann Sphere52??@$$$:5A?bRC@r??????????? xXŸd`\Xwh pjTv001Projection Origin52??@$$$Fv? 2f؋???Q?JAytK?NP ?dԹg?HU\?Az????<וYA?^`d[$;$@001NX(O)NY(O)"b*cos(F)-sqrt(1-b*b)*sin(F)cos(O)Projection Part 152??@$$$hp=͔?Fi??2x=(k?3* "̍?2x=(k?tƃ@????2x=(k?3* "̍?Dզ40lAȢ{wN NX(O)/DZ(O) NY(O)/DZ(O)0Image pt in C plane42???$$$??G Ni36xRQSч4K@^Ⱦ?RQ????<וYA?xTTע99f9@9ĪDRSPS000sin(F)cos(A)/(b-cos(F))sin(F)sin(A)/(b-cos(F))0Vector Z Centere42???$$$??A<ֲ?iiX?r;`WS{?޽?ծ????<וYA?8vDADBlCtC0cCPACFJLNX(O)NY(O)#b*cos(F)-sqrt(1-b*b)*sin(F)*cos(O) NX(O)/DZ(O) NY(O)/DZ(O)0Projection Part 202??h!@$$$h!@?qMW?U[j2?XC#A@n3!;@???? hWC A,APnA@@@T)M\DLtJLLLHEL NX(t)/DZ(t) NY(t)/DZ(t)00.0;2piParametric Image ?02??h!@$$$h!@?;j W[? 6Z>??6Xe?n_bV?Xqi?#tzj>G????  9$d@ĥ@̚@">l@<PPJTN|"Oh=&O+4.NX(t)NY(t)"b*cos(F)-sqrt(1-b*b)*sin(F)cos(t)0.0;2piParametric Source352??@$$$=Ԥь????Q% ?̏\?>tF?Cƨq?&`sOPOsin(F)cos(A)/(b-cos(F))sin(F)sin(A)/(b-cos(F))0Image Circ Center42???$$$??CuO?sC&ݔ?/3?B8?????<וYA?9Q!|9E! D!c9(PP`XPsin(F)cos(A)/(b-cos(F))sin(F)sin(A)/(b-cos(F))0 NX(O)/DZ(O) NY(O)/DZ(O)0Radius to Image Ptxyz{٠?(\?JXT@ fXQ?9a Ԝ@YYܸ@~ffffff?QQ@?@h!@?@@@h!@h!@@@@@@@@h!@@@@@@@@@@@@$U$U$Usqrt(1-b*b)*(cos(F)*cos(A)*cos(x)-sin(A)*sin(x))+b*sin(F)*cos(A)\6i@UGЁ@9x@es"@MCiì@c i{@[,,@ Y"@47@\J10@#7?@RZc@mؔw@YC(@XQ@g:@-̓@$=@90!2@k NX@aGLL1+sqrt(1-b*b)*sin(F)*cos(x)-b*cos(F) !"#     DZ`Msqrt(1-b*b)*(cos(F)*sin(A)*cos(x)+cos(A)*sin(x))+b*sin(F)*sin(A)@X&3lz@jMI@l`@_bA@\gH@4Q7#@\8K`@߳@QKFՃ@=I @9_3>@Yu3l@sAA@&|/@s@UXބ@@dxb.p@*#@x'-h]/@NY5@Riemann Standard Projection SphereCircle ---> C fsG EJp@Xj]y?ҧy;X@Times New Roman(x,y,z) = (sin(u)cos(t),sin(u)sin(t),cos(u)))-&*aA7?r1OG?1Courier New 8A(x,y,z) = (0,0,1)ownloads\@@@-& r,H!xV?kaK!dL?1Courier New P9A(x,y,z) = (NX(O),NY(O),b*cos(F)-sqrt(1-b*b)sin(F)cos(O))s+1-&yk'+ubHmY]@gR?1Courier New :Asegment (0,0,1)--(NX(O),NY(O),b*cos(F)-sqrt(1-b*b)*sin(F)cos-&pήHa?ZTA@f1W?1Courier New M(x,y,z) = (NX(O)/DZ(O),NY(O)/DZ(O),0)R*sin(O),0)))sin(O),0-&a9a<l11@^2\?1Courier New Msegment (0,0,0)-->(sin(F)cos(A)/(b-cos(F)),sin(F)sin(A)/(b-c-&wxYlF%A K@XQ͘dg?1Courier New Msegment (NX(O),NY(O),b*cos(F)-sqrt(1-b*b)*sin(F)*cos(O))-->(?-& & 1:x?kxN,(sin(F)cos(A),sin(F)sin(A),cos(F))n^؎@-&x{"͈}b9?uj*?1Courier New M segment (b*sin(F)*cos(A),b*sin(F)*sin(A),b*cos(F))-->(NX(O),-&zBaC~x ۃ@z-L?1Courier New M (x,y,z) = (sin(F)cos(A)/(b-cos(F)),sin(F)sin(A)/(b-cos(F)),0-&>|烱Imt?zVy7T?1Courier New M segment (sin(F)cos(A)/(b-cos(F)),sin(F)sin(A)/(b-cos(F)),0)-?-&>|烱;/bE?{Dj]?1Courier New @@@h!@