ࡱ> oqnq_ Fbjbj 1>\>\.RR<6!! ...>0QQQ$8'QlQQQ'RR.>0[DQR.~>0Q>0p#ؔ ^Z0ޢEޢޢ8QQQQQQQ''QQQQQQQޢQQQQQQQQQ> : GEOMETRY OF POINTS, RAYS, PLANES AND CYLINDERS Ray  {x} = general location along ray {r} = known location on ray { EMBED Equation.3 } = unit direction of ray s = directed distance along ray from {r} to {x} {x} = {r} + s { EMBED Equation.3 }  Plane {x} = general location on plane {p} = known location on plane { EMBED Equation.3 } = unit normal to plane r = directed distance along perpendicular from origin to plane { EMBED Equation.3 }T {x} = { EMBED Equation.3 }T {p} = r  Cylinder {x} = general location on cylinder {p} = location on axis of cylinder { EMBED Equation.3 } = unit direction along axis of cylinder r = radius of cylinder ({x}-{p})T [ EMBED Equation.3 ]2 ({x}-{p}) = r2 { EMBED Equation.3 }= EMBED Equation.3  { EMBED Equation.3 }T{ EMBED Equation.3 } = 1 [ EMBED Equation.3 ] = EMBED Equation.3  [ EMBED Equation.3 ]T = -[ EMBED Equation.3 ] [ EMBED Equation.3 ]2 = EMBED Equation.3 = { EMBED Equation.3 }{ EMBED Equation.3 }T-[ I3 ] symmetric idempotent [ EMBED Equation.3 ]2 [ EMBED Equation.3 ]2 = [ EMBED Equation.3 ]2 Perpendicular from Point to Ray given {q} = known location of point {r} = known location on ray { EMBED Equation.3 } = known unit direction along ray [ EMBED Equation.3 ] = skew-symmetric matrix for { EMBED Equation.3 } find s = directed distance along { EMBED Equation.3 } from {r} to root of perpendicular s = { EMBED Equation.3 }T ({q}-{r}) find {d} = vector from {q} to root of perpendicular {d} = { EMBED Equation.3 } x { EMBED Equation.3 } x ({q}-{r}) = [ EMBED Equation.3 ]2 ({q}-{r}) Perpendicular from Point to Plane given {q} = location of point {p} = known location on plane { EMBED Equation.3 } = known unit normal to plane find d = directed distance along { EMBED Equation.3 } from {q} to root of perpendicular d = { EMBED Equation.3 }T({p}-{q})  find {d} = vector from {q} to root of perpendicular {d} = { EMBED Equation.3 }d = { EMBED Equation.3 }{ EMBED Equation.3 }T ({p}-{q}) Intersection of Ray and Plane given {r} = known location on ray { EMBED Equation.3 } = known unit direction of ray {p} = known location on plane  { EMBED Equation.3 } = known unit normal to plane ray {x} = {r} + s { EMBED Equation.3 } plane { EMBED Equation.3 }T {x} = { EMBED Equation.3 }T {p} find s = directed distance along { EMBED Equation.3 } from {r} to plane substitute ray equation into plane equation { EMBED Equation.3 }T {r} + s { EMBED Equation.3 }T { EMBED Equation.3 } = { EMBED Equation.3 }T {p} s = { EMBED Equation.3 }T ({p}-{r}) / ({ EMBED Equation.3 }T { EMBED Equation.3 }) Intersection of Ray and Cylinder  given {r} = known location on ray { EMBED Equation.3 } = known unit direction of ray {p} = known location on axis of cylinder { EMBED Equation.3 } = known unit direction along axis of cylinder r = known radius of cylinder find s = directed distance along { EMBED Equation.3 } from {r} to cylinder (two solutions at {x1} and {x2}) {d} = vector from {x} to root of perpendicular with axis of cylinder {d} = [ EMBED Equation.3 ]2 ({x}-{p}) {d}T{d} = r2 = ({x}-{p})T [ EMBED Equation.3 ]2 ({x}-{p}) ray {x} = {r} + s{ EMBED Equation.3 } r2 = ( {r} + s{ EMBED Equation.3 }-{p} )T [ EMBED Equation.3 ]2 ( {r} + s{ EMBED Equation.3 }-{p} ) r2 = s2{ EMBED Equation.3 }T[ EMBED Equation.3 ]2{ EMBED Equation.3 } + 2s({r}-{p})T[ EMBED Equation.3 ]2{ EMBED Equation.3 } + ({r}-{p})T [ EMBED Equation.3 ]2 ({r}-{p}) a s2 + b s + c = 0 a = { EMBED Equation.3 }T [ EMBED Equation.3 ]2 { EMBED Equation.3 } b = 2 ({r}-{p})T [ EMBED Equation.3 ]2 { EMBED Equation.3 } c = ({r}-{p})T [ EMBED Equation.3 ]2 ({r}-{p}) - r2 s1 , s2 =  EMBED Equation.3  if a = 0, ray is parallel to axis of cylinder if b2 < 4ac, ray does not intersect cylinder if b2 = 4ac, ray is tangent to cylinder if s1 and s2 have opposite signs, point {r} is inside cylinder Common Perpendicular between Two Rays  given {r1} = known location on ray 1 { EMBED Equation.3 1} = known unit direction of ray 1 {r2} = known location on ray 2 { EMBED Equation.3 2} = known unit direction of ray 2 find s1 = directed distance along { EMBED Equation.3 1} from {r1} to respective root of common perpendicular s2 = directed distance along { EMBED Equation.3 2} from {r2} to respective root of common perpendicular y = angle between rays sin y = norm( { EMBED Equation.3 1} x { EMBED Equation.3 2} ) = norm( [ EMBED Equation.3 1] { EMBED Equation.3 2} ) { EMBED Equation.3 3} = unit direction along common perpendicular { EMBED Equation.3 3} = [ EMBED Equation.3 1] { EMBED Equation.3 2} / sin y d = directed distance (length of common perpendicular) along { EMBED Equation.3 3} from ray 1 to ray 2 {r1} + s1 { EMBED Equation.3 1} + d { EMBED Equation.3 3} = {r2} + s2 { EMBED Equation.3 2}  EMBED Equation.3   EMBED Equation.3  OR find {q} = midpoint of common perpendicular using confluence of multiple rays with m=2 {q} = ( [ EMBED Equation.3 1] 2 + [ EMBED Equation.3 2] 2 )-1 ( [ EMBED Equation.3 1] 2 {r1} + [ EMBED Equation.3 2] 2 {r2} ) Confluence Point of Multiple Rays (m ( 2) given {ri} = known location on ray i, i = 1 to m { EMBED Equation.3 i} = known unit direction of ray i find {q} = least-squares confluence of rays for m = 2, {q} = midpoint of common perpendicular (least-squares intersection) {di} = vector from confluence to root of perpendicular to each ray i {di} = [ EMBED Equation.3 i] 2 ({q}-{ri}) SSQ =  EMBED Equation.3 {di}T{di} =  EMBED Equation.3  ({q}-{ri}) T[ EMBED Equation.3 i] 2 ({q}-{ri}) SSQ = {q}T ( EMBED Equation.3 [ EMBED Equation.3 i] 2 ) {q} - 2{q}T  EMBED Equation.3  ( [ EMBED Equation.3 i] 2 {ri}) +  EMBED Equation.3  ({ri} T[ EMBED Equation.3 i] 2 {ri}) minimize SSQ with respect to {q} by setting ( SSQ / ({q}T = 0 ( SSQ / ({q}T = 2 ( EMBED Equation.3  [ EMBED Equation.3 i] 2 ) {q} - 2  EMBED Equation.3  ( [ EMBED Equation.3 i] 2 {ri}) = 0 {q} = ( EMBED Equation.3  [ EMBED Equation.3 i] 2 )-1  EMBED Equation.3  ( [ EMBED Equation.3 i] 2 {ri})  Intersection of Two Planes  given {p1} = known location on plane 1 { EMBED Equation.3 1} = known unit normal to plane 1 {p2} = known location on plane 2 { EMBED Equation.3 2} = known unit normal to plane 2 find {q} = location on line of intersection { EMBED Equation.3 } = unit direction for line of intersection d = dihedral angle between planes sin d = norm( { EMBED Equation.3 1} x { EMBED Equation.3 2} ) = norm( [ EMBED Equation.3 1] { EMBED Equation.3 2} ) { EMBED Equation.3 3} = unit vector mutually perpendicular to { EMBED Equation.3 1} and { EMBED Equation.3 2} { EMBED Equation.3 3} = [ EMBED Equation.3 1] { EMBED Equation.3 2} / sin d { EMBED Equation.3 } = unit vector perpendicular to { EMBED Equation.3 1} and { EMBED Equation.3 3} { EMBED Equation.3 } = { EMBED Equation.3 1} x { EMBED Equation.3 3} = { EMBED Equation.3 1} x { EMBED Equation.3 1} x { EMBED Equation.3 2} / sin d = [ EMBED Equation.3 1] [ EMBED Equation.3 1] { EMBED Equation.3 2} / sin d {q} will lie along { EMBED Equation.3 } from {p1} {q} = {p1} + s { EMBED Equation.3 } {q} must lie in plane 2 { EMBED Equation.3 2}T{q} = { EMBED Equation.3 2}T{p2} { EMBED Equation.3 2}T{p1} + s { EMBED Equation.3 2}T { EMBED Equation.3 } = { EMBED Equation.3 2}T{p2} { EMBED Equation.3 2}T ({p2}-{p1}) = s { EMBED Equation.3 2}T [ EMBED Equation.3 1] [ EMBED Equation.3 1] { EMBED Equation.3 2} / sin d= -s ({ EMBED Equation.3 2}T [ EMBED Equation.3 1]T) ([ EMBED Equation.3 1] { EMBED Equation.3 2})/ sin d { EMBED Equation.3 2}T ({p2}-{p1}) = -s (sin d { EMBED Equation.3 3}T) (sin d { EMBED Equation.3 3}) / sin d= -s sin d s = - ( { EMBED Equation.3 2}T ({p2}-{p1}) ) / sin d {q} = {p1} + s { EMBED Equation.3 } OR create a third mutually orthogonal plane 3 with { EMBED Equation.3 3} and {p3}={p1} then solve for the intersection of these three pl/456tu   H I \ ] ^ _  ~to~ hYH*jhYEHUjS< hYCJUVhYOJQJjhYEHUj?< hYCJUVjhYEHUj3< hYCJUVjhYEHUj< hYCJUVjhYU hYCJ jhYCJUmHnHuhY hY5(/046Ws   ) G x ~    " $ j $a$   " $ 4 8 v x | ~    2 鹯霒܉|rj hYEHUjbJD hYCJUVhYH*OJQJj" hYEHU$jf|= hYCJUVmHnHujG hYEHUj?< hYCJUV hYCJ jhYCJUmHnHuhYOJQJ hYH*hYjhYUjlhYEHU( 4 b d S1RSw !~MNO`2 4 6 8 N P v x z | ~ /01234:;NOPQTU϶ܩܒܩ~ܩtjhYEHUjhYEHUjhYEHUjyJD hYCJUVjhYEHUjnJD hYCJUVj%hYEHU hYH*j<hYEHUjbJD hYCJUVhYjhYUjhYEHUjOJD hYCJUV-Uhijklmop+,-}j *hYEHUj"(hYEHUj9&hYEHU hYH*jP$hYEHUjg"hYEHUjbJD hYCJUVj_hYEHUjJD hYCJUV hYH*jhYUjvhYEHUjJD hYCJUVhY1-./0RSCDWXYZۢۘێۄj<5hYEHUja3hYEHUj1hYEHUj/hYEHUj-hYEHUj< hYCJUVjhYUmHnHuj+hYEHUj< hYCJUV hYCJ hYH*hYjhYU1)*=>?@ABst !"#$NObcdefgz{麰麦麜麂xj:BhYEHUj_@hYEHUjhYCJUmHnHuj>hYEHUj<hYEHUj:hYEHUj?< hYCJUV hYCJ hYH*j8hYEHUj< hYCJUVhYjhYUj7hYEHU/OPstHIz|78Zcd   78\]pqrs$%89:;<=EFYZ[\]^ĺĘj\MhYEHUjKhYEHUjIhYEHUjGhYEHUjhYUmHnHujEhYEHUj< hYCJUV hYCJ hYH*jDhYEHUj?< hYCJUVhYjhYU12345:;NOPQRS^_rstuvw鶬ܢܘ܎jYZhYEHUj~XhYEHUjVhYEHUjThYEHUj< hYCJUVjRhYEHU hYH*jQhYEHUj?< hYCJUVhYjhYUj7OhYEHU4XYf^`FH:<>@hjtv:<bdfhjlƼ鯥Ɠwrrr hYH*jchYEHUja< hYCJUV hYH*jahYEHUhYOJQJj_hYEHUj?< hYCJUVj^hYEHUj< hYCJUV hYCJ jhYCJUmHnHuhYjhYUj4\hYEHU,,.TVXZ`bdj~ 0246HJLVXZ\^ùïڥÛhYH*OJQJjlhYEHUjkhYEHUj3ihYEHUjXghYEHUj< hYCJUVj|ehYEHUja< hYCJUVjhYU hYH*hYhYOJQJ5    !"#$%89:;HIKL_`abcdst׬טjyhYEHUjxhYEHUj3vhYEHUjWthYEHUj|rhYEHUj< hYCJUVjphYEHUja< hYCJUV hYH*hYjhYUjnhYEHU8Hop%&NP ^`  ? { gd.     !"#5689LMNOPQ   F˭ hYH*hYH*OJQJhYOJQJj3hYEHUjXhYEHUj|hYEHUj}hYEHUj< hYCJUV hYH*jhYUj{hYEHUja< hYCJUVhY1FHJLPjlxz   " # A B U V W X Y ~  !!!!!!!X!Y!u!v!!½נננjJhYEHUjohYEHUjhYEHUj< hYCJUVjhYCJUmHnHu hY5 hY5>* hYH* hYH*h.hYjhYUjhYEHU$j; hYCJUVmHnHu3 V!!!P#R#$$%%.&/&G&H&`&a&d&e&&&T'U'V''''''(Z^Z!!!!!!!""H"J"^"`""""""""""""""" # ######@#B#D#F#H#T#V#|#~######$$ $"$$$׮jHhYEHUjmhYEHUjhYEHUjhYEHUj< hYCJUVjېhYEHUjhYEHUhYOJQJhY hYH*jhYUj%hYEHUj< hYCJUV4$$.$0$V$X$Z$\$^$d$f$$$$$$$$&%(%N%P%R%T%V%%%%%%%%%%%%%%&&&&& & &&&&&(&)&*&+&,&/&0&C&˯˥˛ˑjkhYEHUjhYEHUjhYEHUjڝhYEHUhYOJQJjhYEHUj< hYCJUV hYH*j#hYEHUj< hYCJUVjhYUhY7C&D&E&F&H&I&\&]&^&_&`&a&d&e&&&&&&&&&&&&&&&&&&'''' ''!'"'#'$'%'''('+','1'2'E'F'ܮܚܮܚܚܮܚܟܮjhYEHUj3hYEHU hYH* hYH*jWhYEHUj< hYCJUV hY\ hY5jhYEHUjE= hYCJUVhYjhYUjFhYEHUjE= hYCJUV1F'G'H'I'K'L'O'P'V'}'~''''''''''''' (p(s(t(((((((((((((((( ) )))))䶬䟕xj~hYEHU$j= hYCJUVmHnHujhYEHUj< hYCJUVjdzhYEHUj< hYCJUV hYCJ hY5 jhY5>* hY5>* hYH*hY hYH*jhYUjhYEHU/( (p(q(((i)j)x*z**+,,,,,,,,,,,,,,,,%-Z^Z)))))))0)1)2)3);)<)?)@)A)B)U)V)W)X)Y)[)\)d)e)u)v)x)y))))))))))))))))))))))))ׅjhYEHUj<hYEHUjFhYEHU$j= hYCJUVmHnHujjhYEHUj< hYCJUVjthYEHU$j= hYCJUVmHnHujhYU hYH* hYH*hY4))))))))))))*** *(***.*0*2*4*Z*\*^*`*b*f*h*n*p*******+++++++*+,+R+T+V+X+\+^+++jhYEHUhYOJQJ jhYOJQJjhYEHUjhYEHU$j= hYCJUVmHnHu hYH* hYH*jhYUjhYEHUj< hYCJUVhY5++++++++++++++,,,,, , , ,,!,",5,6,7,8,:,;,N,O,P,Q,R,T,U,W,Y,\,],p,q,r,s,w,x,,䵫̡䵗zj2hYEHU$j8= hYCJUVmHnHujVhYEHUj`hYEHUjhYEHUj< hYCJUVjhYEHU$j= hYCJUVmHnHu hYH*hY hYH*jhYUjhYEHU0,,,,,,,,,,,,,,,,,,,-----(-)-I-J-]-^-_-`-a-------..^.`.t.´®סס׀vnnhYOJQJjhYEHUj< hYCJUVjhYEHUjhYEHUj?< hYCJUV hYCJ jhYUmHnHujhYCJUmHnHu hYH*hY hYH*jhYUj(hYEHUj< hYCJUV+%-G-----------f/h/,1.1224464 5 555a6b699:`t.v............... /"/$/&/(/./0/V/X/Z/\/^/j/l////////0000 0.000V0X0Z0\0^0v0x000jhYEHUjhYEHUjhYEHUj'hYEHUjKhYEHUja< hYCJUVjphYEHU hYH*jhYEHUj?< hYCJUVhYjhYU4000000000000011111(1*10121X1Z1\1^11111111112 2 22222B2D2F2H2R2T2䡗yjhYEHUjhYEHUjhYEHUj%hYEHUj< hYCJUVhYOJQJjJhYEHUj?< hYCJUVjnhYEHUja< hYCJUVhY hYH*jhYUjhYEHU/T2z2|2~2222222222222222233(3*3,3.303:3<3b3d3f3h3j3z3|3333333333333333344jhYEHUjhYEHUja< hYCJUVhYOJQJjhYEHUj"hYEHUjGhYEHUjlhYEHU hYH*jhYUjhYEHUj?< hYCJUVhY5444 40424^4`444444444445555H5J5p5r5t5v5x5z5|55555555555555555555666 6 6ϻ䮤䮕䮋j hYEHUj hYEHU hYH*j! hYEHUj?< hYCJUVjFhYEHUjkhYEHUj< hYCJUVhYOJQJhY hYH*jhYUjhYEHU6 666 6!6"6#6$6&6'6:6;6<6=6B6C6V6W6X6Y6Z6[6\6^6_6c6d6w6x6y6z6{6|6}666666666666666666666ƼjhYEHUja< hYCJUVjhYEHUjChYEHUjhhYEHUjhYEHUj< hYCJUV hYH* hYH*jhYUjhYEHUj?< hYCJUVhY5666666666666666888888:8<8>8@8B8D8H8J8p8r8t8v8x8z8|888888888888888889999.9˯ˌj$hYEHUjC"hYEHUjg hYEHU hYH*jhYEHUhYOJQJjhYEHUj?< hYCJUV hYH*jhYEHUja< hYCJUVjhYUhY7.90929496989:9B9D9L9N9h9l9n9p9999999999999999999::&:(:N:P:R:T:V:X:Z:b:d:l:n:::::::::::L;ןjf-hYEHUj< hYCJUVj+hYEHUj)hYEHUj'hYEHUhYOJQJ hYH*hY hYH*jhYUj%hYEHUj?< hYCJUV:::::::::;;"$T‰ĉtvxz|~ҊԊ`L;N;t;v;x;z;|;;;;;<$&LNPRT<>@BDƉȉ 24Ⱦ󷭷~y hYH*j7hYEHUj?5hYEHU hYCJ jhYCJUmHnHu hY5 jhY5>* hY5>*j1hYEHUj:f= hYCJUVU hYH*jA/hYEHUj?< hYCJUVhYjhYU/anes to find {q}  EMBED Equation.3  Confluence of Multiple Planes (m ( 3)  given {pi} = known location on plane i, i = 1 to m { EMBED Equation.3 i} = known unit normal to plane i find {q} = confluence point { EMBED Equation.3 i}T {q} = { EMBED Equation.3 i}T {pi} for all i = 1 to m for m = 3, {q} = true intersection point  EMBED Equation.3   EMBED Equation.3  for m > 3, {q} = least-squares confluence point  EMBED Equation.3  {q} = ( EMBED Equation.3 ({ EMBED Equation.3 i} { EMBED Equation.3 i}T ) )-1  EMBED Equation.3  ({ EMBED Equation.3 i} { EMBED Equation.3 i}T {pi}) Confluence of an Axode For a pencil of n rays respectively passing through points {pi} with unit directions {ui}, the confluence {q} should have the minimum sum of squares SSQr of perpendicular distances from all rays. Individual perpendicular vectors {ri} from the confluence may be determined using cross product notation or skew-symmetric direction matrices [ EMBED Equation.3 i] as shown in Equation D1. Consequently the sum of squares of perpendicular distances is given in Equation D2 noting that the square of a skew-symmetric direction matrix is idempotent. Setting the partial derivative of the sum of squares with respect to the confluence equal to zero will minimize the sum of squares as shown in Equation D3. {ri} = {ui} {ui} ({q} - {pi}) = [ EMBED Equation.3 i]2 ({q} - {pi}) (D1) SSQr = S {ri}T{ri} = S ({q} - {pi})T [ EMBED Equation.3 i]2 ({q} - {pi}) (S for i=1 to n) (D2) {q} = ( S[ EMBED Equation.3 i]2 )-1 ( S[ EMBED Equation.3 i]2 {pi}) (D3) The central direction {uo} should have minimum sum of squares SSQf of angles from all rays. The sine of each angle fi can be defined using cross product or skew symmetric matrix notation in Equation D4. For small angular dispersion (fi < 15 degrees) the sum of squares of angles may be approximated using Equation D5. Setting the partial derivative of the sum of squares with respect to the central direction equal to zero as shown in Equation D6 will minimize the sum of squares by the eigensolution shown in Equation D7. For very small angular dispersion (fi < 5 degrees) the simple approximation in Equation D8 may also be appropriate. sin fi = norm({ui} {uo}) = norm([ EMBED Equation.3 i]{uo}) (D4) SSQf = S ({uo}T [ EMBED Equation.3 i]2 {uo}) (D5) (S[ EMBED Equation.3 i]2) {uo} = 0 (D6) {uo} = eigenvector of S[ EMBED Equation.3 i]2 for smallest eigenvalue (D7) {uo} = (S{ui}/n) / norm(S{ui}/n) (D8) extensive notes, code and images for 2D and 3D geometry http://paulbourke.net/geometry/  HYPERLINK "http://paulbourke.net/geometry/pointlineplane/" http://paulbourke.net/geometry/pointlineplane/  HYPERLINK "http://paulbourke.net/geometry/circlesphere/" http://paulbourke.net/geometry/circlesphere/  HYPERLINK "http://paulbourke.net/geometry/transformationprojection/" http://paulbourke.net/geometry/transformationprojection/ http://paulbourke.net/geometry/ellipsecirc/ {r} { EMBED Equation.3 } {x} s X { EMBED Equation.3 } {x} {p} Y r EDGE VIEW OF PLANE { EMBED Equation.3 } {p} {x} r {r} { EMBED Equation.3 } {q} s {d} {q} { EMBED Equation.3 } {p} {d} EDGE VIEW OF PLANE {r} { EMBED Equation.3 } {p} s EDGE VIEW OF PLANE { EMBED Equation.3 } { EMBED Equation.3 } {p} { EMBED Equation.3 } {r} s {x1} {x2} r {r1} {r2} { EMBED Equation.3 1} { EMBED Equation.3 2} {q} s2 s1 d for m = 2 {r1} {r2} { EMBED Equation.3 1} { EMBED Equation.3 2} {q} { EMBED Equation.3 i} {ri} {q} for m > 2 { EMBED Equation.3 1} { EMBED Equation.3 2} {p2} {p1} { EMBED Equation.3 3} s { EMBED Equation.3 } {q} d { EMBED Equation.3 1} { EMBED Equation.3 2} {p2} {p1} { EMBED Equation.3 3} {p3} {q} for m = 3 468:<>DF~ЊԊ֊.024<ȋʋ̋΋ >ǽ䪠䍃pfj:EhYEHU$j= hYCJUVmHnHujAhYEHU$jb= hYCJUVmHnHuj2>hYEHU$jИ= hYCJUVmHnHuj:hYEHU$j = hYCJUVmHnHu hY5 hYH*hY hYH*jhYUj8hYEHU&Ԋ68:<Ћҋ>@Br|$,š222 $dgd=e>@BDFLNtvxz|~ƌȌ$&(*,.068BDbpr׵דxth=eh`h=e5>*h`h`5>* h`5>*h/jNhYEHUjLhYEHUjJhYEHU$j8= hYCJUVmHnHu hYH*j IhYEHUhY hYH*jhYUj0GhYEHUj?< hYCJUV-"$DFDFHJL  $8:JLrtvxz|~ēƓГғԓjBA h=eCJUVh=e5OJQJ h=eEH h=eH*jvRh=eEHUh=eOJQJjPh=eEHUjBA h=eCJUVjh=eUh=e h=eH*= "$&(*<>RT”ĔȔ̔Ԕ֔ؔڔ VX468:NPTX^ùï h=eEHh=eOJQJh=eH*OJQJj"Xh=eEHUj>Vh=eEHUjBA h=eCJUVh=e5OJQJ h=eEH h=eH*h=e h=eH*jh=eUjZTh=eEHU<^`bz|ȚʚҚԚܚޚ "468:`bdfhjltv›٣j]h=eEHUjBA h=eCJUVj[h=eEHU h=eEH h=eH*h=e5OJQJh=eH*OJQJ h=eH*jZh=eEHUjBA h=eCJUVjh=eUh=e h=eEH h=eEHH*468<>BDHJbdhj24L *ptvxDPRxûʰʘʻʍãjhYUj dh/Ujbh/UhYhHKh/0Jjah/Ujh/U h/h/h/h=e5OJQJh=eOJQJ h=eH*h=e h=eH*jh=eUj_h=eEHU3DLNΠРؠڠLNVxz|~ĠƠȠʠBDFHbftvΡСJLrtvxܸʮܸܗܗvj< hYCJUVjnhYEHUjlhYEHUj?< hYCJUVj khYEHUjFihYEHUhYOJQJjlghYEHUj< hYCJUV hY5hYjhYUjehYEHUj< hYCJUV-VX`bfhpr¡ʡ̡ *<>FH||~ "*,`bjlpr|~.0VXZ\vxңԣ֣أڣ $&,.8NTV`bjlŻ飙飏 hY5CJjxhYEHUjAvhYEHUj< hYUVhYOJQJ hYH*jfthYEHUj< hYCJUVjrhYEHUj< hYCJUVhYjhYUjphYEHU4ޣ "(*0268NPZ\fh֤ؤ$&ʤ̤ΤФҤ  0FJLrtvxzȥʥҥԥ8䳩䳟䒈j<hYEHUj?< hYCJUVjbhYEHUjhYEHUj< hYUV hY5CJj}hYEHUj{hYEHUj< hYUVhY hYH*jhYUjyhYEHU1&.0FH~¥ĥΥХ BDLNRT¦ĦΦЦڦ8:<>NRVX~ȦʦԦ֦ަ *@BDFɿɰܺܺɦܺܟܛ h/h/h8 hY5CJjhYEHUj̈hYEHU hYH*jhYEHUj< hYUVhYOJQJhYjhYUjhYEHUj< hYCJUV%ڦܦ (*@BDF /0&P/ =!"#8$8% Dd ,B  S A? 2E1:mg>N!4D `!1:mg>NT@xcdd``^ @c112BYL%bL0YnB@?6 jjbnĒʂT+~35;a&brc * !Xr\ f `!ޱ>c * !Xr\*`!x5O; PK VNAK+/zh(Dc0[ewͼ7K ф9E)T0,2Y)ӧ2\]忯7!STG1%i)U55Ljq؆ R>}4.)b7 l1p6Izr_>t|È?1R|h}P좬鉹3?$0ݓMRۚ, Dd P  S A? "2Eʲ2VAA!+ `!ʲ2VAAT@Hxcdd``^ @c112BYL%bL0YnB@?6 jJbnĒʂT+~35;a&br<SE*&UT T@0UBq`~G%V.C``Ĥ\Y\ \#6$6NF0( 2lDd D`P   S A? "2wnȨ@GȐ/G `!wnȨ@GȐ/GX jx}J1ƿ$Ǯ\zGOg=>-(ЂO=   !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdeghijklmpsutvxwy{z|~}Root Entry F Dؔ r6Data fWordDocument1ObjectPool:!ؔ  Dؔ _1022678807F:!ؔ :!ؔ Ole CompObjfObjInfo  #&+./038;<=>?@CHMPSVWXYZ]`abcdgjmpsvy|}~ FMicrosoft Equation 3.0 DS Equation Equation.39q'vl{ 2u  FMicrosoft Equation 3.0 DS Equation Equation.39qEquation Native -_1022678835E F:!ؔ :!ؔ Ole CompObj fObjInfo Equation Native  -_1022678847F:!ؔ :!ؔ Ole  'vl{ 2u  FMicrosoft Equation 3.0 DS Equation Equation.39q'm0 2n CompObj fObjInfo Equation Native -_1022678867 F:!ؔ :!ؔ Ole CompObjfObjInfoEquation Native - FMicrosoft Equation 3.0 DS Equation Equation.39q'm0 2n  FMicrosoft Equation 3.0 DS Equation Equation.39q_1035304038@JF:!ؔ :!ؔ Ole CompObjfObjInfoEquation Native 0_1145704290"'F:!ؔ :!ؔ Ole CompObj fkIvI 2n FMicrosoft Equation 3.0 DS Equation Equation.39qG 2n  FMicrosoft Equation 3.0 DS EqObjInfo!Equation Native -_1145704271c$F:!ؔ :!ؔ Ole CompObj#%fObjInfo&!Equation Native "y_11457043021)F:!ؔ :!ؔ uation Equation.39q]( n x n y n z {} FMicrosoft Equation 3.0 DS Equation Equation.39qOle $CompObj(*%fObjInfo+'Equation Native (-mo 2n FMicrosoft Equation 3.0 DS Equation Equation.39q  0"n z n y n z 0"n x "n y n x_1145704313.F:!ؔ :!ؔ Ole )CompObj-/*fObjInfo0,Equation Native -_1145704388,63F:!ؔ :!ؔ Ole 1CompObj242f 0[] FMicrosoft Equation 3.0 DS Equation Equation.39q 2n FMicrosoft Equation 3.0 DS EqObjInfo54Equation Native 5-_11457044288F:!ؔ :!ؔ Ole 6CompObj797fObjInfo:9Equation Native :_1022678996=F:!ؔ :!ؔ uation Equation.39qlt n x2 "1n x n y n x n z n x n y n y2 "1n y n z n x n z n y n z n z2 "1[] FMicrosoft Equation 3.0 DS Equation Equation.39q'| 2u FMicrosoft Equation 3.0 DS EqOle ACompObj<>BfObjInfo?DEquation Native E-_1022680417;BF:!ؔ :!ؔ Ole FCompObjACGfObjInfoDIuation Equation.39q'| 2n FMicrosoft Equation 3.0 DS Equation Equation.39qbc4 "b Equation Native J-_1004860910GF:!ؔ :!ؔ Ole KCompObjFHLfAX<)z|Zl][7oof j XD4s<8cbLAE@%Y|H%C$AXaq,^z6yt0Vk2ꏱվ8W :|XODd P  S A? " 2F "5i,lXJ" `! "5i,lXJT`!xcdd``^ @c112BYL%bL0Yn B@?6 u Ҁ7$# AL aA $37X/\!(?71aT /*Zٸ30p1Usi#F{ּJ_W 2P;=`021)W†( L03/Dd P  S A? "2F "5i,lXJ" `! "5i,lXJT`!xcdd``^ @c112BYL%bL0Yn B@?6 u Ҁ7$# AL aA $37X/\!(?71aT /*Zٸ30p1Usi#F{ּJ_W 2P;=`021)W†( L03/Dd P  S A ? "2E{\Cמ(LO ! `!{\Cמ(LO T`!xcdd``^ @c112BYL%bL0Yn B@?6 u Ҁ7$# AL aA $37X/\!(?71aT /*"ظXt9W=Hk^% ̯vx `_+KRsAabÆĆ?E2Dd P  S A ? "2dݐ@Fi5tJ@ `!8ݐ@Fi5tJ@@0= xڍ=hQgf߽mN=$/4bwAsE8Q.BZVCڤ8RZ+&X˲yۇ0#㠯zF(EHYog+EELͰY; ePWyܘ D):4o/M5%&9"ͽCW$& b-|yQ<8_g\9p~r$9 io}NY>y5Jˏ ,shN ~UKq[V0~@;L?WL?#1o΅~PG`l}BCYD'gN/!N!48, `!1:mg>NT@xcdd``^ @c112BYL%bL0YnB@?6 jjbnĒʂT+~35;a&brN!4/ `!1:mg>NT@xcdd``^ @c112BYL%bL0YnB@?6 jjbnĒʂT+~35;a&brN!41 `!1:mg>NT@xcdd``^ @c112BYL%bL0YnB@?6 jjbnĒʂT+~35;a&brN!43 `!1:mg>NT@xcdd``^ @c112BYL%bL0YnB@?6 jjbnĒʂT+~35;a&brN!45 `!1:mg>NT@xcdd``^ @c112BYL%bL0YnB@?6 jjbnĒʂT+~35;a&brN!4[7 `!1:mg>NT@xcdd``^ @c112BYL%bL0YnB@?6 jjbnĒʂT+~35;a&br `!"rRE;0C2]T@Hxcdd``^ @c112BYL%bL0YnB@?6 jJbnĒʂT+~35;a&brN!44F `!1:mg>NT@xcdd``^ @c112BYL%bL0YnB@?6 jjbnĒʂT+~35;a&brN!4I `!1:mg>NT@xcdd``^ @c112BYL%bL0YnB@?6 jjbnĒʂT+~35;a&brN!4{O `!1:mg>NT@xcdd``^ @c112BYL%bL0YnB@?6 jjbnĒʂT+~35;a&brN!4 U `!1:mg>NT@xcdd``^ @c112BYL%bL0YnB@?6 jjbnĒʂT+~35;a&brN!4x\ `!1:mg>NT@xcdd``^ @c112BYL%bL0YnB@?6 jjbnĒʂT+~35;a&brN!4S^ `!1:mg>NT@xcdd``^ @c112BYL%bL0YnB@?6 jjbnĒʂT+~35;a&brN!4 b `!1:mg>NT@xcdd``^ @c112BYL%bL0YnB@?6 jjbnĒʂT+~35;a&brN!4g `!1:mg>NT@xcdd``^ @c112BYL%bL0YnB@?6 jjbnĒʂT+~35;a&brN!4wi `!1:mg>NT@xcdd``^ @c112BYL%bL0YnB@?6 jjbnĒʂT+~35;a&brN!4.m `!1:mg>NT@xcdd``^ @c112BYL%bL0YnB@?6 jjbnĒʂT+~35;a&brN!4 o `!1:mg>NT@xcdd``^ @c112BYL%bL0YnB@?6 jjbnĒʂT+~35;a&brN!4r `!1:mg>NT@xcdd``^ @c112BYL%bL0YnB@?6 jjbnĒʂT+~35;a&br S A ? =2F|B] 8 ["t `!|B] 8 [T`!xcdd``^ @c112BYL%bL0Yn B@?6 u Ҁ7$# AL aA $37X/\!(?71a] wpd`b`F\ y+0 j+e`v 0y{~adbR ,.I Pd!v2@f~5$Dd ,B ? S A? >2E1:mg>N!4wv `!1:mg>NT@xcdd``^ @c112BYL%bL0YnB@?6 jjbnĒʂT+~35;a&brN!4.z `!1:mg>NT@xcdd``^ @c112BYL%bL0YnB@?6 jjbnĒʂT+~35;a&brN!4} `!1:mg>NT@xcdd``^ @c112BYL%bL0YnB@?6 jjbnĒʂT+~35;a&br?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklopstuvwxyz{|}~C2F|B] 8 [" `!|B] 8 [T`!xcdd``^ @c112BYL%bL0Yn B@?6 u Ҁ7$# AL aA $37X/\!(?71a] wpd`b`F\ y+0 j+e`v 0y{~adbR ,.I Pd!v2@f~5$Dd ,B E S A? D2E1:mg>N!4 `!1:mg>NT@xcdd``^ @c112BYL%bL0YnB@?6 jjbnĒʂT+~35;a&brH%2ΤsS"C/x(u2g^" ?x}5vVu)h(QxT܌6Ĕ[$łDwq4^n:DOHe7/PsDd ,B H S A? G2E1:mg>N!4؇ `!1:mg>NT@xcdd``^ @c112BYL%bL0YnB@?6 jjbnĒʂT+~35;a&brN!4 `!1:mg>NT@xcdd``^ @c112BYL%bL0YnB@?6 jjbnĒʂT+~35;a&brN!4 `!1:mg>NT@xcdd``^ @c112BYL%bL0YnB@?6 jjbnĒʂT+~35;a&brN!4i `!1:mg>NT@xcdd``^ @c112BYL%bL0YnB@?6 jjbnĒʂT+~35;a&brN!4D `!1:mg>NT@xcdd``^ @c112BYL%bL0YnB@?6 jjbnĒʂT+~35;a&brN!4 `!1:mg>NT@xcdd``^ @c112BYL%bL0YnB@?6 jjbnĒʂT+~35;a&brN!4֔ `!1:mg>NT@xcdd``^ @c112BYL%bL0YnB@?6 jjbnĒʂT+~35;a&brN!4 `!1:mg>NT@xcdd``^ @c112BYL%bL0YnB@?6 jjbnĒʂT+~35;a&brN!4 `!1:mg>NT@xcdd``^ @c112BYL%bL0YnB@?6 jjbnĒʂT+~35;a&brN!4C `!1:mg>NT@xcdd``^ @c112BYL%bL0YnB@?6 jjbnĒʂT+~35;a&brN!4 `!1:mg>NT@xcdd``^ @c112BYL%bL0YnB@?6 jjbnĒʂT+~35;a&brN!4 `!1:mg>NT@xcdd``^ @c112BYL%bL0YnB@?6 jjbnĒʂT+~35;a&brN!4ԡ `!1:mg>NT@xcdd``^ @c112BYL%bL0YnB@?6 jjbnĒʂT+~35;a&brN!4 `!1:mg>NT@xcdd``^ @c112BYL%bL0YnB@?6 jjbnĒʂT+~35;a&br ۲}cu7[80\<"ܳZIoU&{ƾk'^K]|W|=LKCq&i2u5_7A&:l|SIikI5S&% v`?,;yX(eks}ua41{ N|6 略7߽ b!9rs۪9͸$%ywJ"+Վ}'^Q>D?ﭯ~E N3>'}qKrܖII@|:'ʋsM/wi|9Un{?87 E(Bk8׭sDd `J Y C A? "X2x~կom(J `!x~կom(J`'X xڍMOAǟ-**Y 6zF$$=z`40֗ZfcL$D/z~~_^<#`,o.v6gA `>q0Bp(-N4hhG{YAMhJ\;@ՠsf8;Z1bL!F7N3 Wcu[|Ta襣ho~%?56w?11Dd B Z S A ? Y2F|#]:Dx-dIh" `!|#]:Dx-dIhT`!Hxcdd``^ @c112BYL%bL0Yn B@?6 u ڀ7$# L aA $37X/\!(?71a] ˗0q10p1Usi#F{J_W 2P;=`021)W†(D;3X?4Dd B [ S A ? Z2F|#]:Dx-dIh"w `!|#]:Dx-dIhT`!Hxcdd``^ @c112BYL%bL0Yn B@?6 u ڀ7$# L aA $37X/\!(?71a] ˗0q10p1Usi#F{J_W 2P;=`021)W†(D;3X?4Dd B \ S A ? [2F|#]:Dx-dIh"S `!|#]:Dx-dIhT`!Hxcdd``^ @c112BYL%bL0Yn B@?6 u ڀ7$# L aA $37X/\!(?71a] ˗0q10p1Usi#F{J_W 2P;=`021)W†(D;3X?4Dd B ] S A ? \2F|#]:Dx-dIh"/ `!|#]:Dx-dIhT`!Hxcdd``^ @c112BYL%bL0Yn B@?6 u ڀ7$# L aA $37X/\!(?71a] ˗0q10p1Usi#F{J_W 2P;=`021)W†(D;3X?4Dd ,B ^ S A? ]2E1:mg>N!4 `!1:mg>NT@xcdd``^ @c112BYL%bL0YnB@?6 jjbnĒʂT+~35;a&brN!4 `!1:mg>NT@xcdd``^ @c112BYL%bL0YnB@?6 jjbnĒʂT+~35;a&brN!4i `!1:mg>NT@xcdd``^ @c112BYL%bL0YnB@?6 jjbnĒʂT+~35;a&brN!4 `!1:mg>NT@xcdd``^ @c112BYL%bL0YnB@?6 jjbnĒʂT+~35;a&brN!4 `!1:mg>NT@xcdd``^ @c112BYL%bL0YnB@?6 jjbnĒʂT+~35;a&brN!4 `!1:mg>NT@xcdd``^ @c112BYL%bL0YnB@?6 jjbnĒʂT+~35;a&brN!4 `!1:mg>NT@xcdd``^ @c112BYL%bL0YnB@?6 jjbnĒʂT+~35;a&br& `!"rRE;0C2]T@Hxcdd``^ @c112BYL%bL0YnB@?6 jJbnĒʂT+~35;a&brN!4- `!1:mg>NT@xcdd``^ @c112BYL%bL0YnB@?6 jjbnĒʂT+~35;a&br"E7r=OE|=T9E&gP,Eg3_b~62|s[G?}eO p=fz'+B|OCb|  z+bGX̷|KX o2mL^;f{x$9݄'yReDd B  S A? 2E"rRE;0C2]!<5 `!"rRE;0C2]T@Hxcdd``^ @c112BYL%bL0YnB@?6 jJbnĒʂT+~35;a&br,9!dQɑ8.G&jc7v<(IB̃^|yI/њi.{m(3[wZݳ}h&k E\M.o2t>h_Ϭ?- 5Ĭۭ_vUxk ]CG%EsS<\vhҼz{3ϦO⏚+5G|^|S.;⡩WϿC)`)~'xN{2ӾP94JmIҤe7Kntï:R:^'G~MO|.!Ei~K:z[\8}*ߣ]vG]z9RJFIoDd , B  S A? 2Ir![y9ev> `!Ir![y9e  x {xMhAΦ۵M "*4EăzP$)iFZ 'a J/҃E޼^^5jś&|8R*2yp @! 5a>C`0=Ȥ왦DG韼vu~$HF܍ZN4(Gk8_YZhԫD(ߔ#y hN+׀ 7}; B {#rb": =l36%6f_bV!O[Nv_N'P>(0[.d/Tod/*s/୍7܇L]Js[wl7c|`}.x^&r:}He]aFA `!>:}He]aF  (xkAk7զՊPd ( ޤ(hsT0QLSMf)KxX7/E)W=6~'&L}Je3ᄈ=n!D0~8Ʋ^'{⽲g`N~GN33$Z4zQ~&Z+iPX\h̖:D"eXr&""FTH@rqw7pE[h{qXK"a~HcM#}5s#&.:mo;Y/zffQ3?`fl(rCn{ f1~w ~ּfCݾB.Yj~Aşb?8P%KO;u$/yE]\ 2!/39;o߄_۱dnC^f so7oD/\kMlRAW+y=e˕YEJP_d$H,IMQ$KEy o}Ry~fVQl2_H^МcPc~ݤݤ~ zZk|`8Χ =[\_/mZcHH}ù;OBd* 1!٩F^j$BdDd B  S A? 2`.%9-g%Pv< ~E `!4.%9-g%PvH@2xcdd`` @bD"L1JE `xX0 Yjl R A@~ nj UXRYp7Ӂ`0L`;A 27)? d.PHqec) S_#2M? PHfnj_jBP~nbC&ah 77} \Psl `ph221)WBBv=3X<@Dd B  S A? 2E"rRE;0C2]!<tG `!"rRE;0C2]T@Hxcdd``^ @c112BYL%bL0YnB@?6 jJbnĒʂT+~35;a&brN!4p `!1:mg>NT@xcdd``^ @c112BYL%bL0YnB@?6 jjbnĒʂT+~35;a&brN!4v `!1:mg>NT@xcdd``^ @c112BYL%bL0YnB@?6 jjbnĒʂT+~35;a&brN!4`x `!1:mg>NT@xcdd``^ @c112BYL%bL0YnB@?6 jjbnĒʂT+~35;a&brN!4;z `!1:mg>NT@xcdd``^ @c112BYL%bL0YnB@?6 jjbnĒʂT+~35;a&brN!4| `!1:mg>NT@xcdd``^ @c112BYL%bL0YnB@?6 jjbnĒʂT+~35;a&brN!4} `!1:mg>NT@xcdd``^ @c112BYL%bL0YnB@?6 jjbnĒʂT+~35;a&brN!4[ `!1:mg>NT@xcdd``^ @c112BYL%bL0YnB@?6 jjbnĒʂT+~35;a&br@>  Heading 1$@& 5>*\DA D Default Paragraph FontViV  Table Normal :V 44 la (k (No List 6U`6 / Hyperlink >*B*phFV F =eFollowedHyperlink >*B*phOrPK![Content_Types].xmlN0EH-J@%ǎǢ|ș$زULTB l,3;rØJB+$G]7O٭VvnB`2ǃ,!"E3p#9GQd; H xuv 0F[,F᚜K sO'3w #vfSVbsؠyX p5veuw 1z@ l,i!b I jZ2|9L$Z15xl.(zm${d:\@'23œln$^-@^i?D&|#td!6lġB"&63yy@t!HjpU*yeXry3~{s:FXI O5Y[Y!}S˪.7bd|n]671. tn/w/+[t6}PsںsL. J;̊iN $AI)t2 Lmx:(}\-i*xQCJuWl'QyI@ھ m2DBAR4 w¢naQ`ԲɁ W=0#xBdT/.3-F>bYL%׭˓KK 6HhfPQ=h)GBms]_Ԡ'CZѨys v@c])h7Jهic?FS.NP$ e&\Ӏ+I "'%QÕ@c![paAV.9Hd<ӮHVX*%A{Yr Aբ pxSL9":3U5U NC(p%u@;[d`4)]t#9M4W=P5*f̰lk<_X-C wT%Ժ}B% Y,] A̠&oʰŨ; \lc`|,bUvPK! ѐ'theme/theme/_rels/themeManager.xml.relsM 0wooӺ&݈Э5 6?$Q ,.aic21h:qm@RN;d`o7gK(M&$R(.1r'JЊT8V"AȻHu}|$b{P8g/]QAsم(#L[PK-![Content_Types].xmlPK-!֧6 0_rels/.relsPK-!kytheme/theme/themeManager.xmlPK-!R%theme/theme/theme1.xmlPK-! ѐ' theme/theme/_rels/themeManager.xml.relsPK]  %(+FKPSVj"%9Tot .JOkqv$@FLhnsB2    glvk  051234Z[\]a %(+FKPSVj"%9Tot .JOkqv$@FLhns  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIB2 2 U-F!$$C&F'))+,t.0T24 66.9L;4>^x8F "#$%'(*+,./12346789;<=>?@ACTVWXYZ\_ac OH (%-:ԊV|&ڦF!&)-05:BU[]^`bdtH\^Qeg359MOWkmq.0Wkmr  "I]_]qsy+?A2FHQegj~- A C y   X l n {    / 1 p  ) + U i k &:<@TVZnp 46;OQi}+-sK_a*,1EGOce8LNsm\prm135IK_suz:NPSgiy02Uik  .05IKSgi  &(6JLo24;OQ`tv{  BVXcwy   - A C I ] _ d x z  !!"!6!8!V!j!l!z!!!!!!! " "E"Y"["""")#=#?####### $$$"$6$8$o$$$$$$$$$$$$$$$%%%%1%3%&&&D(X(Z((((((( ))!)+++,&,(,;,O,Q,,,,8-v----..Z..B2::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::XXX,@Bk:NPUiku')/CEPdf %9;Mac:::::::::::::::::::::8@^[Z(  t {I& s S"?ZB  S D%I&ZB  S D [! Z  3    Z  3 s !k  Z  3 {"{%s  H   # }-7H6)C K% Z   3 ! +$  H2 B #   H2 B # #+ +$ n !x$ / h C"?Z g 3  ye+I]-  ` l C  l+-  B2 Z   ' 1+2 [ s [?"BENG]LHNwI^TQ aSSaSS^T`TaSS^T`T$x$X&ZB \ S 7D!'!Z,ZB ] S 7D~M#'`B ^ c $7D! /`B _B c $[?D)-N2 `B 3 L-]-fB e s *D) "*N2 tB 3 L %%` v C vf$& ` k C k)V + n :J&  C"?ZB  S Dl!`B  c $ZDoQD&`  C : Z  3  "J$B Z  3 #z& H2 B # vQH2 B # a!!H2 B # #v$@Z  3  ZB  S D\#ZB  S D "$Z  3 & Lt s *  S"?ZB  S Dp$ "`B  c $ZDo '`  C : Z  3 e#s 5&k  Z  3  h "`  H2 B # /H2 B # ! -" Z  3 O!# ZB  S D")ZB  S Dy# I& Z  3 " ) Z  3 ' * H  # H6)j%N n 5+R  C"?Z 0 3  "y $q  ` 5 C !5 ! !B2     p'J 2 ! s [?"BENG]LHNwI^TQ aSSaSS^T`TaSS^T`T+%+{ZB $ S 7D((ZB % S 7D#4# `B & c $7D%5%R`B 'B c $[?D{" |"N2 (B 3 L]  fB . s *D$ &; ` 1 C "1 !  "` 2 C #2 q  #` 3 C $3Zl!d $N2 )B 3 Lj Z N2 +B 3 L#@X$N2 ,B 3 LH&&`B -B c $LDL H / # xH6)!$`B IB c $LD' `  C %#&  %`  C &$' &` 4 C '4^$ &|  ' t W#'. k S"? ZB l S D4 $%&ZB m S D5%S%(ZB n S D&c$+ZB o S D(#.N2 pB 3 ?%k %N2 qB 3 4!'!(N2 rB 3 <(@(N2 sB 3 I*O*N2 tB 3 't6(ZB u S D%#%o'ZB vB S Da5%~'ZB wB S D&'ZB x S D'(TB y C DK$$TB z C DM$$TB { C D% %TB | C D %P%TB } C DP&;'TB ~ C D&V;'TB  C Dg*( (TB  C D ((Z  3 6/$X$'P& 6`  C 7T#&#% 7`  C 8W(9) 8Z  3 9,. 9. n i>)   C"?` Z C (Zl%:>)2 (` [ C )[  )Z \ 3 *! *Z ] 3 +%T )L  +ZB O S D !]'ZB P S DF& ZB QB S D*#|9#N2 RB 3 %=&aN2 SB 3   FN2 TB 3 ")h#.n S#p#  #" K#h#TB U C DS##TB V C D#p#.n !Q>"  #" C# #TB W C D!Q>"TB X C D>">"` a C ,a # ,H  # xH6)"%H  # xH6)  ##`  C - r"  -`  C .$"i$a .H  # pgH6)%$&%`  C /$O' /`b #.  #" ?Z  3 0 ,w. 0`  C 1E$=& 1`  C 2' ) 2Z  3 3$ & 3Z  3 4})"u+ 4ZB  S D #s&ZB  S Do'+ZB B S D@ %O )N2 B 3 $S$N2 B 3  ' o(N2 B 3  R'~ 'TB  C Da % &TB  C D % %TB  C DY 6) m)TB  C D m) )`  C 5 & ( 5n -3c,  C"?Z  3 u"$ Z   3 $3'+ Z   3 3" $ Z   3 %k'c `  C  -#!  `  C   S#  `B  c $DjJ  fB  s *ZDjJ #ZB  S D +$ZB  S Ds$S'k`B  c $Do!+#&H2 B # 3"s"H2 B # %%ZB  S D K%H  # D.H6)T#Z  3  I%c,   n qev*p&  C"? Z  3 C!  b#" CTB  C DKTB  C D&'_!TB  C D'TB  C D% &g!TB  C DmC&tTB  C D^"o h#TB  C D &eE&TB  C Djf#ZB B S D%x*&ZB  S D }"W T2 B C L  HZ  3 Dr#'(! D`  C E $g' EZ  3 F"|r" FT2 B C L""5ZB  S D ""ZB B S D"i[#ZB  S D"='XTB  C DP#Sv*2#TB  C D}[ TB  C D&r*GTB  C Dq W#)#T2 B C L&6\&|T2 B C L\JZB  S DlZ  3 GCY)E GZ  3 HcYD  HZ  3 I ` $L IZ  3 J#$p& JTB  C D!x$TB  C D !ZB  S DHKZB  S D]%&p b /+  #" ? Z  3 :%r M)j :fB  s *DjJ"$oTB  C D>9h TB  C D)?*TB  C D_B6*TB  C D"t)TB  C D6( TB  C D"RTB  C D'4(TB  C D ?ZB B S D& }( ZB  S DK"T2 B C L gZB  S Dq#; ( ZB  S D&%t P(C T2 B C LT(j ( T2 B C Lr# #p N  3 zH6)#K @( Z  3 ;e # ;Z  3 <F !> <Z  3 ='w+o  =`  C >5!$ >`  C ?$ \'  ?Z  3 @4$'  @Z  3 A7! $  A2 B CENG=H*-J RQ `Tj};`Tj}; R}; R9f!`  C BV&!} BTB  C D/ k\ z  +  c"$?ZB  S D  )[`B  c $ZD' )Z  3 !# Z  3 $( *  Z   3 u(* H   # }-7H6) 'Z   3 " u% H2  B # !b"H2  B # .'r 'H2 B # )C*,Z  3 (  + ZB  S D)")B S  ??0![4G* [ BCf"B2s tI-& th# tP#B t-" tI$ t:;& tl!t&.S tk4#D t`%X tIN%t/1 9;A%K%R%W%%%%%@&B&(($(&(+(-(q(u({(}(((I)K)+)+++++ ,,.,0,X,Z,f,h,,,,,,,.-1/1@2C278XY  *+  ./!%WX  bf*+  d g * 4 o q ] b N R ; < = ? z } UY.4\b cd (-sthm(,%&E G T!V!!!!!""n"r"""@#A#c#g#######=$@$$$A%W%@&B&((=(A(}((((++, ,9,;,X,Z,f,h,j,x,,,,,,,......./ / //G/H/L/M/T/U/t/u/x/y/|/}/////////////1020Q0R0U0V0Y0[0_0a0000000 1 1(1)1-1/1314171=11111021242:2@2C2333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333369PWnq1Wnrh4_v:QyK"" $ $"$9$o$$$$$$A%,-8---................../// / ///////)/+/,/C/D/F/I/K/N/P/Q/S/V/X/Y/p/q/s/v/x/y/{/~//////////////////////000-0.000305060M0N0P0S0U0V0X0\0^0b0d0e0g0k0m0q0s000000000000000000000 1 111*1,101215171A1C1]1_1y1{111111111111111111222 2 2'2)2-2/22242>2@2C269PWnq1Wnr4_v:Qy"" $ $"$9$o$$$$$$A%,8---...C2{8 Y/`=e. 6..@A%A%A%A%xxxx x x x !"B2@ @8@@@"$L@*X@.024l@8:UnknownG*Ax Times New Roman5Symbol3. *Cx ArialA$BCambria Math"qhL'!;'RK!' T' T!24..3QHP ?.2!xx .GEOMETRY OF POINTS, RAYS, PLANES AND CYLINDERSclaper H J Sommer