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=1:Bvisible*o3>+B#style.visibility<*%(D' =-6B'blinds(horizontal)*<3<*D' =%(D' =%(DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B'blinds(horizontal)*<3<*D' =%(DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B'blinds(horizontal)*<3<*DF' =%(D' =%(DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B'blinds(horizontal)*<3<*DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B'blinds(horizontal)*<3<*+8+0+  +"#*  E=@%(    TA??Picture 14"@ \W   p@70e0e`?Title 1P  0 5Computation of the metric average - the metric faces 06 4g 6n   `70e0e`?,Content Placeholder 20`k 0 :Let A, B be simple polygons and let F be a Voronoi face of VDB , we call a connected component of as a metric face originating from F. , r ccc c7  6  T7?Rectangle 5"@tD<4___PPT9@ X I  2  T7?Rectangle 8"@tD<4___PPT9@ T   4  V 7?Rectangle 10"@tD<4___PPT9@ T     c 8A# &??Object 9#" `?9  &   F@7?TextBox 10"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, 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``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!gdrs/downrev.xmlDQK0߅pdeCtc?6&IoAfP; FʸVBr,&t ;HH6 L2,C\,PN/8&q{rk|r -Wn;b-4TV[x_wb%vRNG`?~.a+Q%aǏ`c !eլ |PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!gdrs/downrev.xmlPK "3 ,$  ~The transform is a continuous and one-to-one function from F to . 4 p     x   c 8A( +??Object 8#"?PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!gWdrs/downrev.xmlDA0!<ˢ*R*t=x|6϶ؼ&qo1reqbuΩߺ7<2)xݚbT}*] 2XJddmI T n 94sXȰeFx7 v2yM?/wS?F+KrPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!gWdrs/downrev.xmlPKR, O8 +$@ v   s <A) ,??Object 9"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!Sdrs/downrev.xmlDOMk@ 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Let k be the combinatorial complexity (the sum of the number of vertices, the number of edges, and the number of faces) of the overlay of the arrangements representing the sets and . `       (             ` 0  0 T??Rectangle 2"@D<4___PPT9@ R   H  0 F@@?TextBox 16"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!h-)drs/downrev.xmlDJ1F!MTa۴VkAI)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!Tdrs/downrev.xmlDAK1F!& VY"Zjk븙7m7x&w@1G qVDD f V&yCmnEpP͹L%izš=rV"Qj,=:. {zTm׮Y>/vN^- 2 ?WbJD<}Fg62E %rPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!Tdrs/downrev.xmlPK   ,$ Then: k is .D       u 0 s >AD P??Object 12"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!MWdrs/downrev.xmlDOj0|p4Uh5ʰl֜$`a0ɇֲ<A\Yrv}AL vXh3X¡@M2T  siHᦓ,˥SC UߗQr\W)we "N7K:@PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!MWdrs/downrev.xmlPK@  8 P$@x 0 s <AE Q??Object 4"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!L2drs/downrev.xmlDAk@ޚM6&u FbՃ^I06dWM} 87,L+ԻƲ(A\Zp_=MA8L ~A>=0ƟtJ wɠlGoA=ܴrǯ`aƎ5(H6/T|%OOE*8o < ?|o PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!L2drs/downrev.xmlPK@ X 8 Q$@~ 0 s <AF R??Object 5#"`PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!+drs/downrev.xmlDAk@2BouӴR*--xcΆ6s(xyrp gϓqmͥi *Ddg2KsoK%!r4PZ"a[b.seJm;Ikt$vX4TҪzq[^ҏ, />7'c T!+B/zPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!+drs/downrev.xmlPK `  8 R$@u 0 FD?TextBox 19"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!qodrs/downrev.xmlDMk1ECxjRRF)UA(Z77GT]wr&vL1$< 0rWƵ`)SyG`6MRvtKJ9Tk>+]\blx)pܢqeAckc%lf>6c8`o{뱘_yCQQiVS4j)SP.EhPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!qodrs/downrev.xmlPK  3,$  z Then the run-time complexity of the computation of the metric average is . *9 B {  { u 0 s <AG S??Object 3#"`ýPK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!<drs/downrev.xmlDO͊0/;YzfflJIim=~|h[׎.ĥ5W | dcR0}T*B%bTJ_#C}%uC \&JZ96(7T6*ʍɄЌG8_iJ~ƿ-@c' nW PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!<drs/downrev.xmlPK@ H p0 8 S$@ 0 s >AG T??Object 13#"`PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!\e"3drs/downrev.xmlDO0 ~okZQDYݓE eM*KǮ!͵Cm!M]ZN+ %6-)y-.Sܫ֣aYԇwc4$NrPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!\e"3drs/downrev.xmlPK  8 T$@2 0 VD?Rectangle 15"@D<4___PPT9@ R   {  0 c :AH U??Object 14#"?PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!8ݩdrs/downrev.xmlDOMk0v\ d qyt6oJٺ_b5V\ȇƱ$A\9pt< BD:&W ZXh.X¡@&Ʈ2T,Řاp,K }·_oeϦw_*8o " .ZAg/io\PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!8ݩdrs/downrev.xmlPK  8 U$@  33___PPT10.D%0&+8tD' = @B D' = @BA?%,( < +O%,( < +DS' =%(D' =%(DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*0%(D' =-6B'blinds(horizontal)*<3<*0DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*0%(D' =-6B'blinds(horizontal)*<3<*0D ' =%(D ' =%(DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*0%(D' =-6B'blinds(horizontal)*<3<*0DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*0%(D' =-6B'blinds(horizontal)*<3<*0DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*0%(D' =-6B'blinds(horizontal)*<3<*0DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<* 0%(D' =-6B'blinds(horizontal)*<3<* 0D' =%(DJ' =%(DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*0%(D' =-6B'blinds(horizontal)*<3<*0DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<* 0%(D' =-6B'blinds(horizontal)*<3<* 0DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*0%(D' =-6B'blinds(horizontal)*<3<*0++0+ 0 ++0+0 ++0+0 +" 4(  4 4  p70e0e`?Title 1 `  0 TExamples g z 4 RA??Picture 3j&  4 D@D?TextBox 4  6The metric average of two simple convex polygons with &7 6   7 0 4 T D?Rectangle 5"@D<4___PPT9@ R    4 c 8AI V??Object 4#" `? ZXy V 33___PPT10i.I!n+D=' = @B +" 8~(  8, 8  p@0e0e`?Title 1 `}  0 h Examples (1). gc z 8 RA??Picture 2]  8 D@?TextBox 3pp@ .The metric average of two simple polygons with/ /  /  8 c 8AI W??Object 3#" `?ca^ W 33___PPT10i.L!y^{+D=' = @B +"  Am9m <!m(  <3 <  p@0e0e`?Title 1 `}  0 o#Connectedness of the metric average$$g $l < DA??p1  9 < DqI?TextBox 3`  iThe metric average of two intersecting simple polygons can be a union of several disjoin conic polygons.j j  j z < DA??p2#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK![uVdrs/downrev.xmlDAk1CxZ(bzryn7/&7B|ì6kĝP{0+ĥ75WΧDϤI6 s|{+ r`cls)Cia8yW9Iv4>52Sj.֜,Tފo1|Mt)j}NѰ.ADi4djx; PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-![uVdrs/downrev.xmlPK  ,$D  < D`sI?TextBox 5"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!drs/downrev.xmlDJ1E&VZDE$8I$ӿ7^Şc#\NMw;)GN̨kos' ħLC%ej ;J0/]\b줎t(p+ґCx۵~[ߘ*RKD1o70ѮRP܊i9PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!drs/downrev.xmlPK  ,$ 0The connectedness problem is model by a graph.1 1  1 w PS*s>xL;P  <C *Group 13#"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!0\drs/downrev.xmlDOk@ouDĊP#Lٷ!͟o-zf76M#z\mYA@V\*?pYccL ͞h;'g_a6tKn;>Ȯ!M#WQ* *li_Q8lqO5I|6 i+nPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!0\drs/downrev.xmlPK `  ,$@   < D@.G?TextBox 6PS*s>xL;P #Vertices: connected components of ,   -$  $  < s <AL Z??Object 6 bKH7H:P Zv H:P9EW  <C *Group 14#"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!|drs/downrev.xmlDA0oVQEd]<ȂUXhmy)M,Yo{SWZVO"ę% x ydeR `M}.] DJdMlMm \7FB,9,XӾ_vYٞ29ŤhV <~Z  7OPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!|drs/downrev.xmlPK P ,$@ < D -G?TextBox 8H:P9EW o- metric faces of      < s <AK Y??Object 8"`p%Q/U Y x hC84W8f>?^  <C *Group 15#"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!R&drs/downrev.xmlDOk@&B-=BUo3 f߆6}Pq0hSj ERtxZpYccL`=l1v/ꏾ.Am"+*2%v}])uCF.U9,TRVQq?~*~-KR1݀4_C+x+PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!R&drs/downrev.xmlPK 3,$@  < F,G?TextBox 11hC84W8f>?^ n- metric faces of      < s <AJ X??Object 9"`p%JX/\ XT  < luI?0Flowchart: Connector 32#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!5#drs/downrev.xmlDAO0 FHHX 1eL k68U_ֳާ7S{6p9*@:n .&RF&GJ0LKگrD©Dm}u[F' c36FI)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!)Edrs/downrev.xmlDMK1@!fAڴJc2Y o o歷řRWp@ W|1xRp k&s˽(kT`c-e֖E BreL4 "w\VՃt8rb'K~;v>#^ǖRۛyic#U5ϻg3SRPJjA 7?PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!)Edrs/downrev.xmlPK Cp$@<4___PPT9@ V A  R < lwIP?0Flowchart: Connector 32#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!%drs/downrev.xmlDOK1G!fAڴT\Jc2Y!oo [og7<vQ ||1xRp k&S˽(kT`c-e֖E BrL4 "w\V՝t8`1ғ%~;v.#^ǖRF~?jLiѽ?`WR PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!%drs/downrev.xmlPKm P p$@<4___PPT9@ V A  S < lyIP?0Flowchart: Connector 32#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!drs/downrev.xmlDMK0!MAEd"x*{iSm>Hms(J|H9`fJ ʥMPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!drs/downrev.xmlPKp p$@ <4___PPT9@ V A  S < l?P?0Flowchart: Connector 32#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!{drs/downrev.xmlDQK0Co.]dec":|Mn&)u}?Xْji?G~_+O Ryi}Wj\h_7LLQA˪YPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!{drs/downrev.xmlPKm s p$D <4___PPT9@ V A  U < l`Dp?0Flowchart: Connector 32#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!1ydrs/downrev.xmlDMK@Eax;bbHKk5f>:3ɿwp˽˙/G= [#q`X՛V[y(@HF` K8rq{3R٫[ &$ѕXSY&u'5}5y=ޤt|s]۾t.6Ysk'ݸzy ?_<qNG߫=^BKIpPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!1ydrs/downrev.xmlPK P ] p$@ <4___PPT9@ V A  V < l@{Ip?0Flowchart: Connector 32#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!drs/downrev.xmlDMK@Eax;b "mDpyMR3;˽˙-݋3Y#q`S[ՙFGzAHFQo K9b~{3Bًy &$nYSX&u5}%u,{FMI-9~kh q~񔯾|ND!^ǟ%*zNm)D\RM_PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!drs/downrev.xmlPK @=p$@ <4___PPT9@ V A  V < l Gp?0Flowchart: Connector 32#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!{;ddrs/downrev.xmlDMK@Eax;b "mDpyMR3;˽˙-݋3Y#q`S[ՙFGzAHFQo K9b~{3Bًy &$nYSX&u5}%u,{FMI-9~kh q~񔯾|ND!^ǟ%*zNm)D\RM_PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!{;ddrs/downrev.xmlPK P-p$@<4___PPT9@ V A  V < l!Gp?0Flowchart: Connector 32#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK![Xdrs/downrev.xmlDMK@Eax;bA "mDpyMR3;˽˙-݋3Y#q`S[ՙFGzAHFQo K9b~{3Bًy &$nYSX&u5}%u,{FMI-9~kh q~񔯾|ND!^ǟ%*zNm)D\RM_PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-![Xdrs/downrev.xmlPK Jpp$@<4___PPT9@ V A  V < l#Gp?0Flowchart: Connector 32#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!drs/downrev.xmlDMk@E/u!!u)+5R5Lb3L5h{93_WF$3cyAHFQo K9rq7Bٛ &$nYSX&u'5}-u,Τ\KU۾x7Ysk'ðzyEJt?}"{ I.&MPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!drs/downrev.xmlPK ] p$@<4___PPT9@ V A  V < l $Gp?0Flowchart: Connector 32#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!^ drs/downrev.xmlDMO@E&3q'Ц2c 4wΣ-v>N\ޜ3[ gF$3j0rfF.6"AL(HB+Cݲ0Mk)KY:ZrrNUf)_}e1.w C?K<.U* gR%$4PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!^ drs/downrev.xmlPK 0 p$@<4___PPT9@ V A  V < l@%Gp?0Flowchart: Connector 32#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!έdrs/downrev.xmlDMO@&͐xLSY1N@; ލ=Nb5^\ه ڪ4ުC"D2zkXV݂ eoclDP6FW eMafTn {gjLjhk% v9|d1D!?._T$v:P%$4?PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!έdrs/downrev.xmlPK p$@<4___PPT9@ V A  V < l`&Gp?0Flowchart: Connector 32#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK! drs/downrev.xmlDMO@E&3q'02c 4wΣ-v>N\ޜ3[ gF$3j0rfF.6"AL(HB+Cݲ0Mk)KY:ZrrNUf)_}e1.w C?K<.U* gR%$4PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-! drs/downrev.xmlPK   #p$@<4___PPT9@ V A  2 < V'G?Rectangle 11"@D<4___PPT9@ R   2 < V(G?Rectangle 31"@D<4___PPT9@ R   W < l)Gp?0Flowchart: Connector 32#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!1drs/downrev.xmlDMK@@a(!4xjm$&C=ox3oL/Nb笄Iltg .ZΒ",W3Uhw[:R#Xbc$)1-'ΓevpchPuf!˞ѨVyzm Ǫq~>| ^ۛe "ѐ?JZ*5<=a=C*& kPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!1drs/downrev.xmlPK ` p$D<4___PPT9@ V A   < TAx??Picture 12"@0@ 33Z4R4___PPT1024.r!p>+*D0' = @B Dy0' = @BA?%,( < +O%,( < +D' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<* <%(D' =-6B'blinds(horizontal)*<3<* <D' =%(DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =-6B'blinds(horizontal)*<3<*<DS' =%(D' =%(DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<* <%(D' =-6B'blinds(horizontal)*<3<* <DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<* <%(D' =-6B'blinds(horizontal)*<3<* <Dg ' =%(D ' =%(DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<* <%(D' =-6B'blinds(horizontal)*<3<* <DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =-6B'blinds(horizontal)*<3<*<DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =-6B'blinds(horizontal)*<3<*<DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =-6B'blinds(horizontal)*<3<*<DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =-6B'blinds(horizontal)*<3<*<D3' =%(D' =%(DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<* <%(D' =-6B'blinds(horizontal)*<3<* <DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =-6B'blinds(horizontal)*<3<*<DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =-6B'blinds(horizontal)*<3<*<DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =-6B'blinds(horizontal)*<3<*<DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =-6B'blinds(horizontal)*<3<*<DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =-6B'blinds(horizontal)*<3<*<DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =-6B'blinds(horizontal)*<3<*<DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =-6B'blinds(horizontal)*<3<*<DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =-6B'blinds(horizontal)*<3<*<DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =-6B'blinds(horizontal)*<3<*<+H+0+ < ++0+ < ++0+< ++0+< ++0+< ++0+< ++0+< ++0+< ++0+< ++0+< ++0+< ++0+< ++0+< ++0+< ++0+< +"  //@3(  @ @ F *G?Title 1"rlPK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!/sdrs/shapexml.xmlUKo0 tZ'YF-AZ5dHr#eIwƇ2)Gnn7f+鼲&g[(3ltrř` Ȍoϟn /_PIBVOm- J*xtvK `J'^"@>DWf5'$8@!g*hG-RA:U"c-g.$LM(ʘ6tlŖoÍu>LH1\~_l#L7$) z[99(Vr?;.u06n/քx)/9Ӹ^3ɜ4FFi-H𵘈Vno[Oݐ yl͛8461xjN 52l*UՒg\).[doMY2 Aة%ncQl)OpwV -`^x$5Ne B57טS7ȽժayĴx8;3Y?v4c1֐Nga[bJz(V`8UTJ#>!8/cwD%\RHhJ][0d<йS1|,).ʸFv\|= PK!drs/downrev.xmlDK0p\jlH0DV{k`sk{x8-דH! niÝ5IL֫ˋ%VڝyKc:!+TЧ+)cۓŸp8wG,C'usAEq/-=z{jU0qux4T7ID)//M+q|-DAAv˦PK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!/s*drs/shapexml.xmlPK-!`drs/downrev.xmlPKa `B:2___PPT9  'Connectedness of the metric average (1)((. ( z @ DA??p2"@4 > L @ l`0GP?0Flowchart: Connector 32"@< N D<4___PPT9@ V A  L  @ l1Gp?0Flowchart: Connector 32"@  D<4___PPT9@ V A  L  @ l{Ip?0Flowchart: Connector 32"@  D<4___PPT9@ V A  L  @ l`|Ip?0Flowchart: Connector 32"@oQD<4___PPT9@ V A  L  @ l`Ip?0Flowchart: Connector 32"@ qbD<4___PPT9@ V A  2  @ V`D?Rectangle 11"@D<4___PPT9@ R    @ F }I?TextBox 30` D<4___PPT9@ V    z @ s >AM [??Object 19`p [2 @ V3G?Rectangle 21"@D<4___PPT9@ R   w 5%p>)= @C *Group 64#"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!0\drs/downrev.xmlDOk@ouDĊP#Lٷ!͟o-zf76M#z\mYA@V\*?pYccL ͞h;'g_a6tKn;>Ȯ!M#WQ* *li_Q8lqO5I|6 i+nPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!0\drs/downrev.xmlPK ,$D\ /@ F0K?TextBox 225%p>)= h are called metric connected if and only if the set is connected.4i   A  i  @ s >AO ]??Object 22"` 1h+J7 ] @ c :AP ^??Object 20"?^& , ^P @ F@5G?TextBox 24"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!wOedrs/downrev.xmlDJ1E!MiBAZfvI$ۿ7`3˙/đbrk)`o5>^f RFo 4)rq}5ʄq[Q$>UWRc|aM&ȹJM%ebOϖkvƼo&uup=;j"Ӑ/ϼ<7SZc5ѬϟљLQC+\PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!wOedrs/downrev.xmlPK  ,$ dThere is an edge on the graph between each two vertices corresponding to metric connected elements.e e  e B @ tp0Ԕ?,Straight Connector 33#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!drs/downrev.xmlDOK0 0 {M]]>6fRo||ϙ/;[r` kyX.9fyG}(E aBI C5đsa[J=Z~%I*-V 66TW{Ih6IϏn"P{t|' PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!drs/downrev.xmlPKP 9Y ,$@L @ l 7Gp?0Flowchart: Connector 32"@] ` D<4___PPT9@ V A  + @ l@8Gp?0Flowchart: Connector 32#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!)Hdrs/downrev.xmlDMK@@!*RB춈4xjM$5ݵM{fl1>;5'26Ui$|T(a #XoofT({1[>b% Ihctb[&ֱI`FߠtIrSԙt%o-߻-TU8n8՗7q餼^_ I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!(drs/downrev.xmlDAK@FaUĴ"mD6Nhv7]߻xt>*Hl+[[+x+wje#X.kw;>c-Ć419b6&gyC1F)hi_F,qn^q'xQT(PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!(drs/downrev.xmlPK    D<4___PPT9@ V A  B @ np0Ԕ?,Straight Connector 46#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!ͅdrs/downrev.xmlDOk0 }nQR6.r$a{v).rQ"5p9}Jb <(vʆ4rĄS\CuyL0˭ c5F(Vcǒp~Kq-a:My}w2_}R,@pdPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!ͅdrs/downrev.xmlPKI  ,$@B @@ tZp0Ԕ?,Straight Connector 49#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!(GEdrs/downrev.xmlDOMk@ eoIQSRWZ㐝ffgcv1[z庳P+ ipRi?y1)j8Xbݕt9R9*0!40dO]COZ -^cC,Ŋc T_7s_2ƣn"Pw4w r PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!(GEdrs/downrev.xmlPKQ`,$@B @ tp0Ԕ?,Straight Connector 53#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!1vwFdrs/downrev.xmlDOk0~'m&Q"A2ޚ-6D@>\7qa2V Kg4|v !"l_ ^=?-17#݊X!G u].e(kƮ#Ny1A_IOᶕR3iPcG5j5 7Ŷ?d/a"{ot;PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!1vwFdrs/downrev.xmlPK ,$@B @ tZp0Ԕ?,Straight Connector 57#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK! drs/downrev.xmlDOKk1lvk"^u۰.n&KA6sB>45qtJáؼ`4\)jܸwtJ9jcr)CY0vq4n[esiPcGl5 59*ܨ^j6~ADSpoM? I7 PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-! drs/downrev.xmlPK O ,$@B @@ tZp0Ԕ?,Straight Connector 65#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!80 drs/downrev.xmlDOMk@ eoDSRWZ㐝ffgcv1[z庳P+ fqtť~dcRp#p\+r !sT`Bhr)}aȢ8r"lK[p[ˇ$YH =*?VI7s_2ƣn"Pw,w r PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!80 drs/downrev.xmlPKq  ,$@B @ np0Ԕ?,Straight Connector 67#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!mSdrs/downrev.xmlDOk0~?6S7'ҙz6g[\J_yh:q5g +iydeRC6aOt}%bɠٞ8rW;n:$KiPcO66 xn)r!Qq:n@x]qr1w 2PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!mSdrs/downrev.xmlPK  ` ,$@B @ tp0Ԕ?,Straight Connector 71#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!NMqEdrs/downrev.xmlDOk0~?|2:F@2V_lͥ$2> wqa6U Kg4 !"lجGO+̍ED ᐣ:.25Y S'ŘاpʹRpj]M [֓]4{oe;PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!NMqEdrs/downrev.xmlPK Y ,$@ B @ tZp0Ԕ?,Straight Connector 73#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!0drs/downrev.xmlDOk0~?|i榮3_v4$_y`[q'4A\:pT잗 BD6:& ?`=07ݏ)C\Pd1L]G/-}%>Vd\Zl85ѶxbJkF wZOHC?{_I7/PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!0drs/downrev.xmlPK < ,$@ B @ tp0Ԕ?,Straight Connector 75#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!S<drs/downrev.xmlDOk@~e X%UD,x됝f4Cޛ~X UWcd"m6p:~bB&wZ>?-{R$c\J]uyzI־ֶǛVgY=6, ;8._ocZ*˽ۖgc^_'DC7]糉;2^>PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!S<drs/downrev.xmlPK N M ,$@ B @@ tZp0Ԕ?,Straight Connector 77#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!1Cdrs/downrev.xmlDOn0WA8T%`-Eb9p8%@H[ghl).T±~/A9]p`[AtL na1<0lC.bTJ{"܏-\1ܖ5Ib`Elw^A{v#r "PPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!1Cdrs/downrev.xmlPK g ,$@ B  @@ tWp0Ԕ?,Straight Connector 79#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!Hdrs/downrev.xmlDAk@B2tb b :d$4;[9za޼vtZqm˵9] b (v0Ycft)bĄCLP50|O,FYZb:HT;lY飡uλ+?48@E;R?].@pdPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!Hdrs/downrev.xmlPK  M ,$@ B !@ np0Ԕ?,Straight Connector 81#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!!}drs/downrev.xmlDOM0/T]DQDE*x-6dMoxXuOj]eYh έPp9o?g GX[&/rZ>jD"KQA}J m#wAa[Hbᦖ$Jdžڔ?v<|˰>dn=o{xPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!!}drs/downrev.xmlPKv N w ,$@B "@@ tZp0Ԕ?,Straight Connector 83#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!drs/downrev.xmlDOKk@ eo1X-ފCCvMUnAm>,Vč_:V0' sK.g> kZ{ ̴nP>C&:,#!¦{ Ld&- ִ5VǷvo>.M+5/~_u?)o_PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!drs/downrev.xmlPK | ,$@B #@ tp0Ԕ?,Straight Connector 85#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 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61#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!F,drs/downrev.xmlDj0DBolč!k톐bmmSke$%v>*zf f7r ]& {n|55II)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!Bdrs/downrev.xmlDA0!I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!R&drs/downrev.xmlDOk@&B-=BUo3 f߆6}Pq0hSj ERtxZpYccL`=l1v/ꏾ.Am"+*2%v}])uCF.U9,TRVQq?~*~-KR1݀4_C+x+PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!R&drs/downrev.xmlPKx,$DD .@ FJ?TextBox 67Yx_` P is connected iff the metric connectivity graph is connected 4Q '    Q  @ s >AN \??Object 40HZT/` \o -@ DA??p1"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 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Ddrs/downrev.xmlDOj0|pMj ۍͱ)kNJˏm-:j}X,A\8]q{.AvL ݌Gk̵|JBRE?s qnlK[)=bũ`C_*n~0z]~&]KT߭@S >%yPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-! Ddrs/downrev.xmlPK4 P ,$D/@@@ @@ @ @@ @@)@@@@@ @@ @@ @ @ @ @!@"@#@)@(@ @*@ @+@ 33? ?___PPT10>."0=+uD>' = @B D=' = @BA?%,( < +O%,( < +D' =%(D' =%(DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*@%(D' =-6B'blinds(horizontal)*<3<*@D,' =%(D:,' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*@%(D' =-6B'blinds(horizontal)*<3<*@DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*+@%(D' =-6B'blinds(horizontal)*<3<*+@DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<**@%(D' =-6B'blinds(horizontal)*<3<**@DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*#@%(D' =-6B'blinds(horizontal)*<3<*#@DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*"@%(D' =-6B'blinds(horizontal)*<3<*"@DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*!@%(D' =-6B'blinds(horizontal)*<3<*!@DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<* @%(D' =-6B'blinds(horizontal)*<3<* @DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*@%(D' =-6B'blinds(horizontal)*<3<*@DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*@%(D' =-6B'blinds(horizontal)*<3<*@DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*@%(D' =-6B'blinds(horizontal)*<3<*@DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*@%(D' =-6B'blinds(horizontal)*<3<*@DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*@%(D' =-6B'blinds(horizontal)*<3<*@DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*@%(D' =-6B'blinds(horizontal)*<3<*@DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*@%(D' =-6B'blinds(horizontal)*<3<*@DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*@%(D' =-6B'blinds(horizontal)*<3<*@DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*@%(D' =-6B'blinds(horizontal)*<3<*@DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*@%(D' =-6B'blinds(horizontal)*<3<*@DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*@%(D' =-6B'blinds(horizontal)*<3<*@DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*(@%(D' =-6B'blinds(horizontal)*<3<*(@D' =%(D' =%(DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*,@%(D' =-6B'blinds(horizontal)*<3<*,@Dt' =%(D' =%(D^' =A@BBBB0B%()))D' =,54*3>Bfillcolor=@BPB<*@D' =1:B solid*a3>Bfill.type<*@D' =1:B true*]3>Bfill.on<*@D^' =A@BBBB0B%()))D' =,54*3>Bfillcolor=@BPB<*@D' =1:B solid*a3>Bfill.type<*@D' =1:B true*]3>Bfill.on<*@D' =%(D' =%(DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*-@%(D' =-6B'blinds(horizontal)*<3<*-@++0+@ ++0+@ ++0+@ +"nQ 88@D8(  D7  D  p1K0e0e`?Title 1 `  0 s'Connectedness of the metric average (2)((g (  D D?TextBox 2@ K CSeveral propositions considering metric connectedness, for example:D D D 0  D T 4K?Rectangle 2"@D<4___PPT9@ R   0  D T@5K?Rectangle 4"@D<4___PPT9@ R   0 D T`6K?Rectangle 6"@D<4___PPT9@ R   2 D V7K?Rectangle 10"@D<4___PPT9@ R   2 D V8K?Rectangle 12"@D<4___PPT9@ R   2 D V9K?Rectangle 14"@D<4___PPT9@ R   2 D V:K?Rectangle 16"@D<4___PPT9@ R   Z w H.,Ќ I DC *Group 21#"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!0\drs/downrev.xmlDOk@ouDĊP#Lٷ!͟o-zf76M#z\mYA@V\*?pYccL ͞h;'g_a6tKn;>Ȯ!M#WQ* *li_Q8lqO5I|6 i+nPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!0\drs/downrev.xmlPK `,$D D D@?TextBox 4H.,Ќ I #Proposition: Let be simple polygons and be metric faces , . are metric connected if and only if there are points and , satisfying: and . 8$    $  D c 8AQ _??Object 1#" `?(л-n2pb2 _ D c 8AR `??Object 3#" `? aл-"lf3 ` D c 8AS a??Object 5#" `?( 3/8 a D c 8AR b??Object 7#" `?81 3 v<8 b D c 8AT c??Object 9#" `?5%28S-4= c D c :AU d??Object 11#" `?p>28kN= d D c :AV e??Object 13"?X $Y>b@D e  D c :AW f??Object 15"?GLY>hD fT D F`I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK! drs/downrev.xmlDJ1E&(26-*Z𜼙D'/c۩_op˽˙Gߋk8(M0; ׇk)#%ώX56©F 6硖25   R  D TA??Picture 23#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!=Vdrs/downrev.xmlDOKk@n]EBKAoCv̆fgCvk-զSK ƣqtɅ).@rL ~fTt?B)*0!ԩ>7dя\Mk,Bn+9IXrl0XPu S>3?wTK/~t?x\PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!=Vdrs/downrev.xmlPK (,$@ D TA??Picture 24#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!J%drs/downrev.xmlDOMk1ao5QPV<qIPms6#j & qt͕W"1)Sf\RwH!rT`bls)Cib8qg-}%[ f٫Xsj0қr {z鈊,uchV "_~ie6w rPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!J%drs/downrev.xmlPK  B,$D D TA??Picture 25#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!drs/downrev.xmlDOk0~7L]7j! 2ЪoGse%4v |iĕZ_[V0$ k.w/> kl,_?>0Ӷ-]P>CU.#wa[JbM#_d$ *t/FMWԇteVǯROD>oi PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!drs/downrev.xmlPK ,$D  D F@K?TextBox 25"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!drs/downrev.xmlDQk0p{etFC5MX$j {z=P; FʸNs,&t {H"W%_݁.uXXPrMr`1:^3b-4V{~w:3DcW8m_ԛP,+u(HrY5k_PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!drs/downrev.xmlPK  0 ,$ i condition 1       D F AK?TextBox 26"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!C _drs/downrev.xmlDKk1p DFPv;3 cLRg .7βd0 `렌o%>^^ $)|v}5J-+*s*Sa|cUľ!C˃ƎFo`:gXJۛa ,Ӑǟ_yA) G`a%Z4~PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!C _drs/downrev.xmlPK  @0 ,$ i condition 2       D F@BK?TextBox 27"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK! drs/downrev.xmlDJ1E!MZPdRm iM&Yn>w8|p8sL6xH`_m}px}x2yM]p͔*.~CnETɹLaGiz%kBt[#] urԓtd}i0p}:|;]lѼwVZ! LFS\Q- g?PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-! drs/downrev.xmlPK  @ ,$ i condition 3       33VN___PPT10.."P+%D"' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*D%(D' =-6B'blinds(horizontal)*<3<*DD' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*D%(D' =-6B'blinds(horizontal)*<3<*DDS' =%(D' =%(DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*D%(D' =-6B'blinds(horizontal)*<3<*DDT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*D%(D' =-6B'blinds(horizontal)*<3<*DDS' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*D%(D' =-6B'blinds(horizontal)*<3<*DDG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*D%(D' =-6B'blinds(horizontal)*<3<*DDS' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*D%(D' =-6B'blinds(horizontal)*<3<*DDG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*D%(D' =-6B'blinds(horizontal)*<3<*D++0+D ++0+D ++0+D ++0+D +"] /K'K`00HH(  H? H  p`FK0e0e`?Title 1 `}  0 {/The metric average of two simple polygonal sets00g 0J H HGK?Rectangle 2% \A set consisting of pairwise disjoint polygons with holes is termed a simple polygonal set.4] G    ] G H DHK?TextBox 3"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!Ldrs/downrev.xmlDJ1!M]j7`~dlooB/| ^(AM^Da}@)6&vEҠ<4RR2Iu)s/M}//]z~nW߭>-nNZh}z2߁`rl4\薇 SPݪi9PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!Ldrs/downrev.xmlPKl` ,$ `The segment Voronoi diagram induced by the boundary of a simple polygonal set is well defined. a a  a  H DIK?TextBox 4"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK![drs/downrev.xmlDJ1E& ": Jk?uf:INB{93[GJŠv@PhqӰ|y>p +OaC-w@BPe*)sccāBژI)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!B3drs/downrev.xmlDAk@^nh*R(jk̾UwB|ĕWZV0G 3K+ˤN mo"@%NtYA]AdK-M%ߣh,  髠촿Gomr^mk]~_{II)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!+drs/downrev.xmlDAk@ayB/ m4 RF=$}F[(87lњJܨqea8\~A8L `1vfh{>.Au" 2膶&6}M.u7|OiP`M낲Kz5 R=yʥk̔z)OZA<{'\9PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!+drs/downrev.xmlPK 4 8 h$@0  H T MK?Rectangle 6"@D<4___PPT9@ R   } H c 8AZ i??Object 5#"?PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!ądrs/downrev.xmlDOk1~ jVFP*x|n˚D7B-:ӈ9_YV0' s+.>ߟ |@X&_a1|a7tۆBD !>/ɠۖ8z' (]!{Fd$ VJl鵤uR\zJD.+ ~+ ?PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!ądrs/downrev.xmlPK $ 8 i$@  H F@NK?TextBox 12"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!kudrs/downrev.xmlDAK1F!&Z6-"Z븙D7ɚv;=be!i)`Ij1bOYgjIx`R7ң `{KkxyY])R φ BC~۵cUO[ =9\(i8NerPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!kudrs/downrev.xmlPK P `@[,$ /The metric faces are conic polygons with holes.0 0  0 L  H l`OKp?0Flowchart: Connector 13"@.PD<4___PPT9@ V A  L H l Pp?0Flowchart: Connector 14"@ V D<4___PPT9@ V A  L H l!Pp?0Flowchart: Connector 15"@6D<4___PPT9@ V A  L H l#Pp?0Flowchart: Connector 16"@FD<4___PPT9@ V A  L H l $Pp?0Flowchart: Connector 17"@PD<4___PPT9@ V A  L H l@%Pp?0Flowchart: Connector 18"@n vD<4___PPT9@ V A  L H l`&Pp?0Flowchart: Connector 19"@ & D<4___PPT9@ V A  L H l'Pp?0Flowchart: Connector 20"@fUD<4___PPT9@ V A  L H l(Pp?0Flowchart: Connector 21"@:pD<4___PPT9@ V A  B H tZpԔ?,Straight Connector 24"@J  B H tZpԔ?,Straight Connector 27"@  B H tZpԔ?,Straight Connector 32"@:*B H@ tZpԔ?,Straight Connector 36"@F}FB H tXpԔ?,Straight Connector 38"@ B H tpԔ?,Straight Connector 50"@e{B H@ tZpԔ?,Straight Connector 52"@{-];B H npԔ?,Straight Connector 55"@E; B H@ npԔ?,Straight Connector 57"@)fYL H l`,Pp?0Flowchart: Connector 58"@D<4___PPT9@ V A  L  H l p?0Flowchart: Connector 59"@ f@D<4___PPT9@ V A  L !H l@p?0Flowchart: Connector 60"@Z  D<4___PPT9@ V A  L "H l`p?0Flowchart: Connector 61"@ZD<4___PPT9@ V A  L #H lp?0Flowchart: Connector 62"@  D<4___PPT9@ V A  B $H@ tVpԔ?,Straight Connector 64"@3B %H tpԔ?,Straight Connector 66"@ LB &H tpԔ?,Straight Connector 68"@  B 'H tZpԔ?,Straight Connector 76"@ZL (H lp?0Flowchart: Connector 77"@  D<4___PPT9@ V A  L )H l p?0Flowchart: Connector 78"@D<4___PPT9@ V A  L *H l p?0Flowchart: Connector 79"@j p D<4___PPT9@ V A  L +H l p?0Flowchart: Connector 82"@:   D<4___PPT9@ V A  B ,H@ tZpԔ?,Straight Connector 84"@}v B -H tpԔ?,Straight Connector 86"@F B .H@ npԔ?,Straight Connector 88"@  B /H@ tZpԔ?,Straight Connector 90"@F  B 0H vXpԔ?.Straight Connector 103"@ Z/@HHHHHHHHHHHHHHH HHH H HH $H %H &H "HH'H)H*H,H-H*H(H.H+H(H/H0H 33 ___PPT10.$hY+"D' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D' =-6B'blinds(horizontal)*<3<*HD ' =%(D ' =%(DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D' =-6B'blinds(horizontal)*<3<*HDG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D' =-6B'blinds(horizontal)*<3<*HDG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D' =-6B'blinds(horizontal)*<3<*HDT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D' =-6B'blinds(horizontal)*<3<*HD' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<* H%(D' =-6B'blinds(horizontal)*<3<* H++0+H ++0+H ++0+ H +"c pLLL(  LC  L  p౎0e0e`?Title 1 `  0 3The metric average of two simple polygonal sets (1)44g 4n  L H`?Rectangle 2x  LLet the metric face F be a conic polygon P with holes .hM         M 0  L T?Rectangle 2"@D<4___PPT9@ R    L c 8A[ j??Object 1"?  ju L D?TextBox 5"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK! 3drs/downrev.xmlDJ1EB!;XPdlZDZۂ u'/$ӿ7^ĉbr5N:ǭDB  +μ>@8UWRڒ4 =q=c+MsNN==[^klξ,NQ-O 2  /jc4LA4gtf)SP܊i9PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-! 3drs/downrev.xmlPKp,$ tThe operation is a continuous and one-to-one function from F to 4u e    u 0 L T`?Rectangle 4"@D<4___PPT9@ R   { L c 8A( k??Object 3#"?PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!drs/downrev.xmlDj1 }p Z("8ݜ.&'& x97l=uq} .nR{yF\b4\3߇J$!ɢ8y*;<'5reiPcK˚d6q.Q%_ k`8dp_PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!drs/downrev.xmlPKp 8 k$@0 L T෎?Rectangle 6"@D<4___PPT9@ R   y L c 8A\ l??Object 5#"?PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!ytgdrs/downrev.xmlDAk1 jV*[ EmﯛMjlR]|wDm *h˵u "&d.0)Pigij!KT`RjJ)cec쇆8{lk[I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!drs/downrev.xmlDJ1E&U) ~sfINB{93 G0)u0[ G)#3%M//&Xp-w©B 6羒2ՖI)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!9]Xdrs/downrev.xmlDAk@ hTG5 ; ٍ+Yӈ u`:@V\*86/3#kl,?rZi{=]r_a6tv}])u7(k QQFA8II6iI%p\PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!9]Xdrs/downrev.xmlPK 8 m$@2 L V?Rectangle 10"@D<4___PPT9@ R   { L c 8A^ n??Object 9#"?PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!Sdrs/downrev.xmlDj@ }zW7JtDJ$=wWo-z97̴L'n|kYA:J@WV\+8o |@Y&POS̵7v>GM}.2G':!JWKᦓ$ɤB=λQmvOö]~J^_D!k`%މW@?PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!Sdrs/downrev.xmlPK  8 n$@2 L V@?Rectangle 12"@D<4___PPT9@ R    L c :A_ o??Object 113"`?PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK! ))drs/downrev.xmlDAk@B nS%u VG5 ; դ+gmą:_; l?-FsL.Pa*6YGuC])M}F&JͤŚB-}TTVeɷK㐿4{^ t^z'^PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-! ))drs/downrev.xmlPK `` 8 o$@" L B,Pp?h1"@`D<4___PPT9@ V A  L L lp?0Flowchart: Connector 21"@.D<4___PPT9@ V A  L L lp?0Flowchart: Connector 22"@6D<4___PPT9@ V A  L L lOp?0Flowchart: Connector 24"@(~D<4___PPT9@ V A  " L B Op?h2"@PD<4___PPT9@ V A  L L l@Op?0Flowchart: Connector 26"@D<4___PPT9@ V A  " L B`Op?h3"@jD<4___PPT9@ V A  L L lOp?0Flowchart: Connector 28"@phD<4___PPT9@ V A  L L lO `?0Flowchart: Connector 42"@0D<4___PPT9@ V A  L L lOp?0Flowchart: Connector 47"@rD<4___PPT9@ V A  L L lOp?0Flowchart: Connector 48"@xD<4___PPT9@ V A  L  L lOp?0Flowchart: Connector 49"@BpD<4___PPT9@ V A  L !L l Op?0Flowchart: Connector 50"@ hD<4___PPT9@ V A  z L s >A` p??Object 15`X pz  L s >Aa q??Object 16bhB qB "L s @OB$ChDEF Q&RUVWpԔ?$h@H'''$hFreeform 45"@ D<4___PPT9@ R   B #L s `OBn CDEF QRUVWpԔ?n @G G n Freeform 46"@ D<4___PPT9@ R   B $L s OB CDEF QRUVWpԔ? @m m  Freeform 47"@<D<4___PPT9@ R   B %L s OBCDEF QRUVWpԔ?@  Freeform 48"@<WD<4___PPT9@ R   B &L s OB CDEF QRUVWpԔ? @  Freeform 49"@WD<4___PPT9@ R   B 'L s  OB6CÜDEF QRUVWpԔ?6Ü@B)B)6ÜFreeform 50"@D<4___PPT9@ R   B (L s @OBCDEF QRUVWpԔ?@o ڢڢFreeform 51"@9D<4___PPT9@ R   B )L s `OBBCU_DEF QRUVWpԔ?U_B@ya5a5BU_Freeform 52"@D<4___PPT9@ R   B *L s OB9C` DEF Q&RUVWpԔ?9` @U U U 9` Freeform 53"@9D<4___PPT9@ R   B +L s OB$C7DEF QRUVWpԔ?$7@H,,$7Freeform 54"@D<4___PPT9@ R   B ,L s  OB,C$DEF QRUVWpԔ?$,@S00,$Freeform 56"@hD<4___PPT9@ R   B -L s @OBBCDEF QRUVWpԔ?B@a599BFreeform 57"@_D<4___PPT9@ R   B .L s `OBCDEF QRUVWpԔ?@Freeform 58"@D<4___PPT9@ R   L /L lOp?0Flowchart: Connector 26"@&D<4___PPT9@ V A  V 0L lO?0Flowchart: Connector 26#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!+>drs/downrev.xmlDAO1&fLI1 a*röm7m]==N{/{Ӳ0eNj| Y0Pjtg[ҩ KrbrC`lv  nZ~eܠAaGCu4t|Zq|2VF'7 X>?|VB xHwa,1D\RMPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!+>drs/downrev.xmlPK V 1 p$@<4___PPT9@ V A  U 1L lO?0Flowchart: Connector 26#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!#drs/downrev.xmlDQO0M5M:ĈL 1F|K[`';޴L>hgG06>wOBD+u `c.ŖtbĆP+2F#c%M6=(UQ}NFӍN_ߎOʨlR q{ӿ<ER ~5켖%H^@KIPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!#drs/downrev.xmlPK p& p$@ <4___PPT9@ V A  U 2L lO?0Flowchart: Connector 26#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!"drs/downrev.xmlDAO1&fLI a*röm7m]==y/{Ӳ0eNj| Y0Pjtg[ҩ KrbrC`lv)K7-ϲGnP۴WE::>p8>l+VϓRۛe,R +_T!<$jz-K tIIPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!"drs/downrev.xmlPK  PV p$@<4___PPT9@ V A  V 3L lO?0Flowchart: Connector 26#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!+Bdrs/downrev.xmlDN0DHuQ'TҺBfلGmlvۄ,G3:3_cA;+ d6Nj xy"Z$` 鎶C[ 6(@F0q=7S- n:~eܠAaO/zoiiFW X!JZgT)vq뵬0D\RM'PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!+Bdrs/downrev.xmlPK  j p$@<4___PPT9@ V A  V 4L l`pT?0Flowchart: Connector 26#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!drs/downrev.xmlDn0DE8 TUȒn/%vۑm b.G3:Xe'A;+`2΀Զv,D[gI@VҝmI*6,AlQ9"a:;8o0.=ܴ|eܠAaG/h5dZ?J!nFX>wz- a,1D\RMPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!drs/downrev.xmlPK @0p$@ <4___PPT9@ V A  V 5L lqT?0Flowchart: Connector 26#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!탯drs/downrev.xmlDN0DHuQDҺBfلGmlvۄ,G3:3_cA;+`:ɀmԶv,D;gIHˋ9mE:,Al(P/8"az9o0[.=t6AmӃž^5?ӌͯtZ=W X!JZgT)vq뵬0D\RM'PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!탯drs/downrev.xmlPK    p$@<4___PPT9@ V A  V 6L 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Y0Pbt1\-Tņ% 9 P1v9Vd0]G6u{ }åsd=7mzPы::>lp~;>*Vi)e,Rǟ?/nWkYb$4/~PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!Ddrs/downrev.xmlPK pfp$@ <4___PPT9@ V A  U 7L lsT?0Flowchart: Connector 26#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!ӧ&drs/downrev.xmlDQO0M% :$ 1F|K[`';V޴L>hgL'06^BD+u `Za.ŖtbĆP+2&#c%Mol jvNFw;3>M_QۇY)ͨ\_*q;%H^@KIPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!ӧ&drs/downrev.xmlPK  p$@ <4___PPT9@ V A  U 8L ltT?0Flowchart: Connector 26#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!˂`bdrs/downrev.xmlDQO0M5 :$N 1F|K[`';޴L>hgL'06>BD+u `]-0bK:Wa bCT]y בMy1EpY6M ;zQTU'#@NߎϦ}eqV qs??ERa=콖%H^@KIPK-![Content_Types].xmlPK-!Z,[ 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=-6B'blinds(horizontal)*<3<*LDG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*L%(D' =-6B'blinds(horizontal)*<3<*LDG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*L%(D' =-6B'blinds(horizontal)*<3<*LD#' =%(D#' =%(DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*L%(D' =-6B'blinds(horizontal)*<3<*LDT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*L%(D' =-6B'blinds(horizontal)*<3<*LDG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*L%(D' =-6B'blinds(horizontal)*<3<*LDT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*0L%(D' =-6B'blinds(horizontal)*<3<*0LDT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*1L%(D' =-6B'blinds(horizontal)*<3<*1LDT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*4L%(D' =-6B'blinds(horizontal)*<3<*4LDT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*6L%(D' =-6B'blinds(horizontal)*<3<*6LDT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*7L%(D' =-6B'blinds(horizontal)*<3<*7LDT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*8L%(D' =-6B'blinds(horizontal)*<3<*8LDT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*9L%(D' =-6B'blinds(horizontal)*<3<*9LDT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*:L%(D' =-6B'blinds(horizontal)*<3<*:LDT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*;L%(D' =-6B'blinds(horizontal)*<3<*;LDT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*+B#style.visibility<*=L%(D' =-6B'blinds(horizontal)*<3<*=LDT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*>L%(D' =-6B'blinds(horizontal)*<3<*>LD(' =%(DR(' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*KL%(D' =-6B'blinds(horizontal)*<3<*KLDG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*L%(D' =-6B'blinds(horizontal)*<3<*LDT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*HL%(D' =-6B'blinds(horizontal)*<3<*HLDT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*3L%(D' =-6B'blinds(horizontal)*<3<*3LDT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*5L%(D' =-6B'blinds(horizontal)*<3<*5LDT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*2L%(D' =-6B'blinds(horizontal)*<3<*2LDT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*?L%(D' =-6B'blinds(horizontal)*<3<*?LDT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*DL%(D' =-6B'blinds(horizontal)*<3<*DLDT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*EL%(D' =-6B'blinds(horizontal)*<3<*ELDT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*FL%(D' =-6B'blinds(horizontal)*<3<*FLDT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*GL%(D' =-6B'blinds(horizontal)*<3<*GLDT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*IL%(D' =-6B'blinds(horizontal)*<3<*ILDT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*CL%(D' =-6B'blinds(horizontal)*<3<*CLDT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*BL%(D' =-6B'blinds(horizontal)*<3<*BLDT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*AL%(D' =-6B'blinds(horizontal)*<3<*ALDT' =A@BBB B0B%(D' 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F>P&(  P P  pDK0e0e`?Title 1 `}  0 TExamples g 0 P T?Rectangle 4"@ D<4___PPT9@ R   z P RA??Picture 7  N P F?TextBox 160 `$ ^ , where A is a polygon and B consists of two polygons contained in A. 8_ ]  * _ 2 P V?Rectangle 18"@ D<4___PPT9@ R    P c :Ab s??Object 17"?` LP  s 33___PPT10i.3%?+D=' = @B +" T(  T T  p@0e0e`?Title 1 `@  0 X Examples (1) g 0 T T?Rectangle 4"@ D<4___PPT9@ R    T c 8Ac t??Object 3#" `?-  t T D?TextBox 5 P+ &,where A, B are simple polygonal sets.(' %   '  T RA??Picture 7"@`  33___PPT10i.4%V+D=' = @B +"& -%p (  p p  p@@0e0e`?Title 1 `}  0 W Future work g n p D?TextBox 2"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!F|drs/downrev.xmlDJ1E&*Nj𜼙N^$mop˽˙-Fߋk(M0; ϗ)#%XfXp56©B 6硒25MAd?v7D:}Eg֘2E ŭKPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!F|drs/downrev.xmlPK <P@0,$  An algorithm for the computation of the metric average of two-dimensional compact sets with boundaries consisting of spline curves    J p HW?Rectangle 3"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!kao$drs/downrev.xmlDMk1E ݔq%QD(StLI2$E˹,ȇYAtXhvΒ M&X)w+:c2Ć  5 דy1GpeQI)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!Tܗdrs/downrev.xmlDKK1!\MZdlZDZkKn;`c7tasx;ˎ ^@#_e|+ᰟ?<KBI)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK![:drs/downrev.xmlDMK1E!'o&I2&{ ]^\d6N9&+B#style.visibility<*p%(D' =-6B'blinds(horizontal)*<3<*pD' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =-6B'blinds(horizontal)*<3<*pD' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =-6B'blinds(horizontal)*<3<*pD' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =-6B'blinds(horizontal)*<3<*p++0+p ++0+p ++0+p ++0+p +"  t(  t t  p 0e0e`?Title 1 `}  0 V References g * t  0e0e`?,Content Placeholder 2` `P 0 DZ. Artstein,  Piecewise linear approximation of set valued maps , Journal of Approximation Theory, vol. 56, pp. 41-47, 1989. F. Aurenhammer, R Klein, "Voronoi Diagrams" in Handbook of Computational Geometry, J. R. Sack, J. Urrutia, Eds., Amsterdam: Elsevier, 2000, pp. 201-290. N. Dyn, E. Farkhi, A. Mokhov,  Approximation of univariate set-valued functions - an overview , Serdica, vol. 33, pp. 495-514, 2007. D. Halperin, "Arrangements", in Handbook of Discrete and Computational Geometry, J. E. Goodman, J. O Rourke, Eds., Chapman & Hall/CRC, 2nd edition, 2004, pp 529 562. 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X c 8Ae x??Object 9"?8%LT9gW_ x X F?TextBox 32v\RЌ0Z ^(**)     33___PPT10.\wN+z{Du' = @B D0' = @BA?%,( < +O%,( < +D' =%(D' =%(D+' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* X%(D' =-g6B fade*<3<* XD' =%(D' =%(D+' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* X%(D' =-g6B fade*<3<* XD' =%(D' =%(D+' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*X%(D' =-g6B fade*<3<*XD' =%(D' =%(D+' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*X%(D' =-g6B fade*<3<*XD' =%(D' =%(D+' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* X%(D' =-g6B fade*<3<* X+"U HK@K\(K(  \  \  p`V0e0e`?Title 1 `  0 Appendix A: Computation of the metric average with Voronoi diagrams  the mathematics (1),ZYg Zd   \ s BVRectangle 2"PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!7wrdrs/shapexml.xmlXQo0~`uJW5IlP>WN c[Cg;PZm:CH|wUђjäHp礍̙%~:h12p)h뫏.Ul*skUE&ӒBXY45TXbPɣn9*  TDkewˑF,O)F`rL3p`)⨖q-@ѮuxUv&o#, JphiyCb(ax {3'?~roS` z$&ˡƄG$bIxm{abMevbg;k kO#M*D*BH! DF(Ŕ'6̡d(n/7~JJ ex 5DFڞ4.&*s2vfWoe!E⦰oe7*AM/\OW崚BG}Xxyʛ=zI>P%nL&)N{뜶D-Ibբ=lzҰla^ug/ l<SKC1 WB26Ń'țV©WAV!VeJtjf;/HI)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!0\drs/downrev.xmlDOk@ouDĊP#Lٷ!͟o-zf76M#z\mYA@V\*?pYccL ͞h;'g_a6tKn;>Ȯ!M#WQ* *li_Q8lqO5I|6 i+nPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!0\drs/downrev.xmlPK  ,$D \ s B VRectangle 6"d^PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!-drs/shapexml.xmlUQo0~`ubJF PUsuIpqlv(l0b9ǟ.wwׂ옱\Ɍw)aP%>f1%ց,A(2z`M~թKnibjߕf*ejp4Dft0P-~;LjNЕ-xx eFGH1Z02I`Km7)^?d*jEHz8@G(1Hb&u?8+e 3{.:D&t___PPT9  can be regarded as a function, .   \ s B XRectangle 8"60PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!LGdrs/shapexml.xmlTo0~¯6jIlB@〇c[C6)O9۟.}wF=NhU>%\1] )zֻyPHxA/&werSЭ&2Ƕ]ֶKɌ+52],l~a zOC.96;0mp4K.P"K7OA :Ŭ)9t8 '!瓛Q0D'0曥DXr}uR$8*Eb>a?w>p)IDuu oU8z=q!_#V NbWr yAG}(!ECe| U8  7k(W(x.[pgkSRu[/*k*AhR 9̓=A?As ??Object 13̰s@p3" |x HL* %H \C *Group 36#"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!R&drs/downrev.xmlDOk@&B-=BUo3 f߆6}Pq0hSj ERtxZpYccL`=l1v/ꏾ.Am"+*2%v}])uCF.U9,TRVQq?~*~-KR1݀4_C+x+PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!R&drs/downrev.xmlPK ,$D=  \ s D VRectangle 10"~PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK! l drs/shapexml.xmlW]o0}`uJ75T$T!ϕIpl6wle+Bu||=7psYqc+%3ںhReJ287Xd<nmZM`,m3:wNIb9PKaif6rCZ$fkRJ\XА@.-J$ssd04jy K@H$$YRUdnBU'Rv$~ 94ooݰT~purR;ʨ2l5.څD tx)@8V$P[:կqcBX7v 8;Kp PNWQF!Jhό6vLAI _PV,qц7`_*ɔYt=GK#H3Mȱ}zVܑ[aH0P㞗Ǻ ^>^5Jws t]:<]_bG/@4K(eiŲj8@iD<\᧌`T Qtb1[-GҏQa1PPjh*\TƁ;}=+UMLC5^ @n[z?[9qK#IUsK3IJtyՕ@-|ΌCe3,ƿ@2lG oWǃ2 ;ҏ7tڧwfmhCN~f홵G d%o8a[aØR%x.ǖ<}OH_(hu7PK!drs/downrev.xmlDAK1F!fi) VhofYL$7x ͗H>L';5I,Ws;MDpPq !aF[OYnYţs^08ҋ fޏE}l?LfWIgRٶntn8/5H^A˩\PK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-! l *drs/shapexml.xmlPK-!pdrs/downrev.xmlPKsHL* j8B:2___PPT9  aThe boundary of a metric face is a simple closed curve, so is its mapping under G, and thereforeFb(Q... b \ s @ VTextBox 12"ÐPK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!+drs/shapexml.xmlUn1W?XV , YeJiQBrfw-K _{!(H=?y\]oZyit!gBWzQ移 g>A- _O? m!|0ROZ8uu  `V F빝91Yc-gih1؄[aوzrgaV54O|Ӹ/+"NM08F!"-xt>ʲTX'p]fCr<\a !O|.E1:NT>T͝TX SN/#(|_!L)U$v=T"` hLRtOJ9w0BG&D*ȝc!C˂Ǝ^5ݏJmV}73B,Ba2>Tiy,/hS(ĕԂ~PK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!+*drs/shapexml.xmlPK-!edrs/downrev.xmlPKg AZL%HB:2___PPT9  !stands for the region bounded by ," !** "  \ s <Ao ??Object 6"`8-Bd5 HG  \ s <Ap ??Object 8"`PLk3BQ{G   \ c :Aq ??Object 16"?H+:3bO@ 2 \ VV?Rectangle 22"@D<4___PPT9@ R   2 \ VV?Rectangle 24"@mmD<4___PPT9@ R   1w H ~e \C *Group 38#"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!=ك(drs/downrev.xmlDAk@&-)% VzB g̾ 5+zffM ^D K?_>@8L [ϞVj;7 _a.ҕ5t b{>Ⱦ1M+_]l8,Ѧz-TĤ|ʗ Al ??Object 18.,]I9O  \ FV?TextBox 26H O 5The metric average can be computed as 6 6  6  \ c :Am ??Object 21"?PNvV  \ F V?TextBox 32HTM[ cwhere *   \ c :An ??Object 23"?n$ Zh~e  33  ___PPT10 .0+++RD ' = @B Dj ' = @BA?%,( < +O%,( < +D' =%(D' =%(D+' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*\%(D' =-g6B fade*<3<*\D' =%(D' =%(D+' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*\%(D' =-g6B fade*<3<*\D' =%(D' =%(D+' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*\%(D' =-g6B fade*<3<*\+" YQ0|9(  | | c 0e0ex?4Slide Image Placeholder 1   0r | # 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Dyn, E. Farkhi, A. Mokhov)OutlinePreliminary definitionsThe metric averageConic polygons with holesPlanar arrangementsSegment Voronoi diagrams2Computation of the metric average - the algorithm6Computation of the metric average - the metric faces 9Computation of the metric average - the metric faces(1) 6Computation of the metric average - the algorithm (1)6Computation of the metric average - the algorithm (2)6Computation of the metric average - the algorithm (3)Complexity bounds Examples Examples (1)$Connectedness of the metric average Slide 19(Connectedness of the metric average (2)0The metric average of two simple polygonal sets4The metric average of two simple polygonal sets (1) Examples Examples (1) Future work ReferencesVAppendix A: Computation of the metric average with Voronoi diagrams the mathematicsZAppendix A: Computation of the metric average with Voronoi diagrams the mathematics (1)  Fonts UsedThemeEmbedded OLE Servers Slide Titles  8@ _PID_HLINKSA http://www.cgal.org/http://www.cgal.org/_)>shayshay  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~                           ! 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