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Mathematical algorithms such problems solve using unification, i.e. standardisation of task applied for similar problems. Such approach can be fitted with: 4. Selection of the most appropriate algorithm; 5. 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"0ka ew*5BpJ;zhP I_I*J`E~DMH D* y+U`uv6 nȇ8aE6[[\;SEp3_HNI!P(-v<Eq$1u Eh̥wݾTtRgy7~ZcsL96+1;#m#gԂQ0,tIi≟& 8\P* J($r6srEc8VYYXD 8k\M4㹦:mZiAc9]hIYsE(mh/I%}ܤ\@b^RY:-tvtZ2hhN= k=gva/ Igx\I<(N6%-vqC|$Oŏ4Ch)!s䢩LFM:IJ[cqȤ(U.IVK. pC讔A sؽ݅ FL=+5X$I97 N8JXAkr&Ҽ`ps}]ZoI޿_o}RmbQs۬U.q,jn[v˵;QȣfYbkz`CvGnb@]QYb|FKE= S.ЂpOgܗ-2B:rX= ec/LJ(h4xZPZޒ;mweQZJ֎m;=D-dVaRQeQgxxIs:LLzzܪWB@^s:CZ~P}gxr)\HǙl.{[/e5Z̒gg2|.lz[tغo˯*tP-EFL!, C10aD_~L$ODzeKcEPnBO/|y%^f.zR[=wi(ې" (C9E"1HTEJKl2!p-,tsd3K)7 7 K]ZUyU-n-l/t/p a][ -V0))6 j~ͽc_nڱ@(XΪ031_TDUr0P u)GBZy Q^O"!Qڮ!HR=%0m׊*B}urovu/5O nǛ)kvtsLg^bO!rUP 0[?[ѯ*o؝jtE!" R?8kwR:A>Q)~J?J[jY6dRW-#~D} aYV{1fU //wPK!,drs/downrev.xmlDAK1F!fPڴ*mN7Mt,ɸ{=oxo\+z`<*@QP?LA$F )b~y1RPFdO%*0])e 9LБCglxrۢH=Nr/׻UHsWjX>`yUQ_Ջ-=`b r_PK-!2<>[Content_Types].xmlPK-!]  ,_rels/.relsPK-!Re6(drs/shapexml.xmlPK-!,= drs/downrev.xmlPKA   The new values are estimated using relatively simple mathematical equation; The influence of each hard data is inversely proportional to its distance of estimated point (location). Number of hard data (z1...zn) is limited to radius of circle/ellipsoid centred in unknown point. The result is strongly depend on distance exponent (p). 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This is not strictly interpolation, but zonal estimation. Although not such precise, this rough approach can be only proper when small number of data exist as input. Any outcome based on 5 or less hard data is not map, but estimation, where only approximation of data scaling can be given. That is represents by zones (zonal estimation). 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Bj% ,U<R9Bx?P  c(e$'C_JAe:a/{;ql]߮Fzힻ(~s1a۠H']ij dWJI 묈 4v$nҥ1<" aʮ%:+ GyzB_5;l8a';~wzТe5`+ fJ"M8e8bԌPֿD_s~5Zı;Aknu޳tή`萬&|ލML 1pZ'Q*W' D4k\hsPBǀ&m&מ OɤZ@>IZcۘl\ xT2E.;\@Sz9tKeo,K3 (7Dc_aBuDue18BY"0># 2蕠chʅy7g r *S޻'z l6g 3Ր/dEGlJf`cH$vf@d<ìl`֊ߟBO>xϏS, F[-x&qS~!RU3. fd G䎅miCc ҅7-F/KL*tl>|$9J9vK(Nw{DXQ Tv&s/<Ӵ{STN;S%roXQ7Zhfo6hquZ:PK!! Fdrs/downrev.xmlDN0DHuQGVQ*v}Vc;M= XftFglNB#xe\'s{S ;0SbKKSJcb\\Z,CU1mϗBbъױ:Iy}5=?K42/]IXX6Q5DAB˶PK-!2<>[Content_Types].xmlPK-!]  ,_rels/.relsPK-! h=!(drs/shapexml.xmlPK-!! Fdrs/downrev.xmlPK]  aExample 2: Nearest neighborhood estimation. Coloured zones shows zonal values, and and data are points in the centre of polygon.  "IJIIII  x A2??FNearest2DInterpolExamplePicture 11Image:Nearest2DInterpolExample.png a ݢ|  x nxx|??Rectangle 12"I C PK!2<>[Content_Types].xmlAN0EH%,BM #{X$ccB{{&m TҞy?٫vՌ}Z_VH68O}6ōV;dnV]DVBz9v I&]Hd9DУkce\%C7;Dp{KU!["jK8 p&î8By/ O4;Tϐ#La\bDR7q[,į W pov+ fCPK!]  _rels/.relsj1 @h_B֐BWaLΖ5yB/dˠA 0xM e`J FG2p%}iRdITD10Z)4(I9`mtB{ƁmtπnTg 險,ܗr>j1W*@ŀӚZ7O#KOiPK!PWAdrs/shapexml.xmlVn6;+dْUcpNcAKT"Idh%o+tH?I{A7MIъ,B%<-el}w1C SHl]zW^]!ս*r)^U'9)q}+`-^e&Lb 9NUY[ͫP|5Hcs0%;# j 7LxrU7hA As8Fi-k B3]|XS[Dy,*2۶ulvB{d#Qv]D XND`(ʴ@Ѱ(EWZGˁvc2@)e8^P[i\ԥ(bSDpuG朗};vYl8eZ xz\?kӽ^/0Kr<(u2U}㢩@k9мS!.$ZIlsbR)_r_#ѽЩJMlz8yh)s=0 /->X;n˧PK!`bdrs/downrev.xmlDj0EBwPF r&2$#Mc+h{9N' N"AsǫDdt{HL5ڏӞ[ .06d1.@.u9JpLpeJK* U@s5fy=QˋiwiqŻ'+Q/Z2W :]ad _M 7?PK-!2<>[Content_Types].xmlPK-!]  ,_rels/.relsPK-!PWA(drs/shapexml.xmlPK-!`b2drs/downrev.xmlPK8  = HExample 3: Using of regular point grid for zonal estimation (ideal case)I I",I? v x NA??Picture 15 q  x n|??Rectangle 16". 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O^)Zz ],ʉ%c "r~v曙8",Ä eƽidh }%+vmS7IQZ-&,$eINZ8-Uiȍң 󣌄~Ϩ[M vY~rIFM ;Hq _0 ,WTчPgX] d0fYr1a ܚoF*J%959h:-AeR &A@[nvM\Yn78Eypc;e&=un4ˋX6U' )=? J|Oa+dם$Hq! &utRY3~X}wuL71[Ck {NBg*t۹aqeI/kBՔE@(q:$IX9D9,sÖ0HXFisrۦ8MӶ\Ӳ;Nr:pCi `\a2qp܄]s_4qEHjIVi&tt2p`V/=]B%3d ܍&G옂?n5S Zd%F!^$K_b2%P.i](PN*O5_dBXszJR+U( N!|p%!ÿB& ZؓBt|0TONW|ްH \瑍z jFLYp @.*eØ]$eBg2?||?wǿoIj"ɢ^r+!q,*n%vm^rGŮSa׭C_vGnd^wA]Q۪ SFx?;CA?4g)y@y {,\ D߭nD+YKY@-k'B XڭȺltZkd)eض!א5 X]*JEϊ:kͩ0c!q"H*XpB#^gQ_V{ x ?">J= L^frijBx ɥH чpo~r%69!m$y6dM0N~gJv Ki=#gy2G9c-zN(~$Q$8 b&BF~sWeԛ?!WbBߗ[ЮWHreV-~u(.%92N6piW[Content_Types].xmlPK-!]  ,_rels/.relsPK-!Z[X(drs/shapexml.xmlPK-!-C drs/downrev.xmlPK ( The simple linear equation describe idea of Kriging. In practice it is extended in matrix equations. 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PK!2<>[Content_Types].xmlAN0EH%,BM #{X$ccB{{&m TҞy?٫vՌ}Z_VH68O}6ōV;dnV]DVBz9v I&]Hd9DУkce\%C7;Dp{KU!["jK8 p&î8By/ O4;Tϐ#La\bDR7q[,į W pov+ fCPK!]  _rels/.relsj1 @h_B֐BWaLΖ5yB/dˠA 0xM e`J FG2p%}iRdITD10Z)4(I9`mtB{ƁmtπnTg 險,ܗr>j1W*@ŀӚZ7O#KOiPK!$֏)drs/shapexml.xmlZn6w tZe2c S철%*BENݴ3lo+쐔,;KgI2%Q9wHuF9EYh 8edj-THbL9#uA ޷߼EaV ZHZ"Z xNKȰSq)XDmoe8e gPH4o g01@SJ[y <:+Ji&x*/`2 fki*Hh.b >~1ZxNDP8?(BM4h%){0@FP4xIJrKρLg{mb{Nسw}ł i 4|ƕFUz8T iHڻɘ t)yCڕD[ܶځ==K(/ZT$_+ n5E=F5IN|ZHa<2EG42nj_Эȣ0ѡmWޝ/!5æ956'@vs/4MAT" }\ϖY H4-\_a778㲲B US8#y&$ h|5wrM򀕘-U(I#$H  [=|?ЗϿ_~_>]~ X`Qm7zzaA3=~U!~{ܐ劭&7ĵGX`E@wƙܙjVtk[Content_Types].xmlPK-!]  ,_rels/.relsPK-!$֏)(drs/shapexml.xmlPK-!bdrs/downrev.xmlPK    ,Where are: MSEmetode - Mean Square Error of selected algorithm; izmj.vrij. - measured value (hard data) of varibale at location  i ; procj.vrij. - estimated value of variable at location  i .~ ""*, " "E""<" I  (I 3II II I (II II I  33___PPT10u.ЏQ+D=' = @B +     (  g  d|??Text Box 2") # PK!2<>[Content_Types].xmlAN0EH%,BM #{X$ccB{{&m TҞy?٫vՌ}Z_VH68O}6ōV;dnV]DVBz9v I&]Hd9DУkce\%C7;Dp{KU!["jK8 p&î8By/ O4;Tϐ#La\bDR7q[,į W pov+ fCPK!]  _rels/.relsj1 @h_B֐BWaLΖ5yB/dˠA 0xM e`J FG2p%}iRdITD10Z)4(I9`mtB{ƁmtπnTg 險,ܗr>j1W*@ŀӚZ7O#KOiPK!AzQdrs/shapexml.xmlXnF;,xg?9d)XKbe$S@ :K&C/|3;7;_l\3Q3 GEˑ RIc[V/y9J?հ+)aWE+YQ2ߒBT£앂UK*a<954,ůQtz}&H xA8a dRlci "7U(tRDWUm?Vł^LW_͊Ѹ`ߞ1ek~F-o~*b0e $"*X$ n`[vd8` v!(a ̰]2ZJ", )>$:<Ͳ}]@f|eZWK|ϰ xZ,9YqlSmOo8ft{/4EU$YT=8\izuF@VZEƸM3Ai< u<{h:pFϚ89%^ }+0-; CT')gMDxrddi>2H&.fo}xȾfۢmEu.bz o.b[1+"o{xv߃K=qA˱%A†l#/nUFԣHjUP48Qu55:uPn|Y% \:h}$$ùb}v| qF벫.CMfpTp㡤S"ut5=B U2K62(#UlQ6WvnI3hgPGs5\/6ڷ\/9Zhp 5ͬSC净jy+\ȐZrX+!Xbo)a ؉ r 52S9QH-αSwzDZ;E1\$4*ӌQXTW=~΁j顾w/0)'Ox56!Ǯ/ӯ,tU{[F#'a t#+a[Content_Types].xmlPK-!]  ,_rels/.relsPK-!AzQ(drs/shapexml.xmlPK-!drs/downrev.xmlPK @` PART VIII CONCLUSION& h22&0I I  33___PPT10u.[Content_Types].xmlAN0EH%,BM #{X$ccB{{&m TҞy?٫vՌ}Z_VH68O}6ōV;dnV]DVBz9v I&]Hd9DУkce\%C7;Dp{KU!["jK8 p&î8By/ O4;Tϐ#La\bDR7q[,į W pov+ fCPK!]  _rels/.relsj1 @h_B֐BWaLΖ5yB/dˠA 0xM e`J FG2p%}iRdITD10Z)4(I9`mtB{ƁmtπnTg 險,ܗr>j1W*@ŀӚZ7O#KOiPK!m drs/shapexml.xmlVn6?k,ٲl 4pNeAK" |O-M&_%):dY-lRx=>ݮbhC*OpLjTd%_'7Hi3 H>jT'кu:*-hEQSk0N-\ *~ԩH7z.(%*aaIf4kFQw}8f"U-_dl3lбb[P) XXX{G У{Vh^.KQsD]àw%8gir4 YOaC}߂w8Z*-/ƄA lfJJ&9%XMK^YI!,z9bL20C[/_z^W8Y&CtCҍi4xax=?'qqV2( O*S)TT26o {e/&8C8ԂU*5Uy\P♥Kq8s&Ӿ?{Co0G}o2^z WUpĕUP@ d*f"nYd[b\(kQN4)ql&2݁RjR˂PX|G9u%! cCXxuG'̶lɅ!bᕩPDdwCs˯9IcӲ-&`^;/4bi߶^șQ v6PE!@_1A(d'~ 6VDQL~\6- Z׼5`:uT(F;0?8GkWW 䛝u,)xq\աMđ Hk"#6UYG O*u3V9#I0"[.v-^ hn*:ssCa=}oqu]K!r; V]i8/r:)<d:F9hIif%1-@9IMYQ-DEx~ßO=}0Pk/U'}X@+6Q͉$+~Y@8 u+UJնxPK!>drs/downrev.xmlDN0DHH\uRBݪPlmb#$iC9fFom+z8Vp7@WN|} BD:&G _^̰n XP&Ʈ2T Y nŘ8$m}Ң`G UMhnh5OO]=||ǥRWD1w~=?Z+Eؿw H^AKPK-!2<>[Content_Types].xmlPK-!]  ,_rels/.relsPK-!m (drs/shapexml.xmlPK-!>drs/downrev.xmlPK  Conclusion6 P &&  I   d |??Text Box 3" Å PK!2<>[Content_Types].xmlAN0EH%,BM #{X$ccB{{&m TҞy?٫vՌ}Z_VH68O}6ōV;dnV]DVBz9v I&]Hd9DУkce\%C7;Dp{KU!["jK8 p&î8By/ O4;Tϐ#La\bDR7q[,į W pov+ fCPK!]  _rels/.relsj1 @h_B֐BWaLΖ5yB/dˠA 0xM e`J FG2p%}iRdITD10Z)4(I9`mtB{ƁmtπnTg 險,ܗr>j1W*@ŀӚZ7O#KOiPK! Edrs/shapexml.xml[nF;,xgDJH KaX.z4VbM. $S@ :)GN#Plcu3̘zfGeya ¸!?L yAy@qr߽N{yJ`3{iߘEk4rbJRand1-]4ҌQiYFLCnQjdN2}:A8glQA -R,`S(t~ UAFO3/~%3FmJR9P*+s$jrSt^$4 LSܶ@/7@붚-=Vv<+Zt,KO{H .Mx˒"xPȘ_NQ^PGx2 h[AЈ MP*(A(u}㷮==tCӱ 3A`8<G-Noug~ɴx'q.W賆0P* L+Ca+5}0li ++[wWvӱͮ9xLu-ϴ۱s0Z(Tù"`(f[z/W,ְF{qXDa7< ?]@\l$ԯmN3]2́7Cq;txPIiIx\I4N)N L DoyVo4]?`_dɒ◰g4GhI!#8Tfrє.#JgT$v/dBXKz*RkUҨ u;!+0 29op xRɃq"ʋqq-g6)a8*^b $`S ʀMOaa"AW<椸Iٔarr̮iS2Y3Z[>M>}?w7$BmdQq۬2E[ڈ/]QЗ.mW6(<*v;5vz*d>4ž ͙A0d}_<lZ'~!A mWf"̀usv(`%k5 zԲF{ $;mwֲB(`%n%kdžvԲB(`v(_ukSa*C'ƭ*{ `3:CZF}Y!| 0DZ:8:,2y)KՊ-%HxR泅H 'esط`"q X]i7 (+l[Content_Types].xmlPK-!]  ,_rels/.relsPK-! E(drs/shapexml.xmlPK-!wt drs/downrev.xmlPKz ] ___PPT9 yDeterministical interpolation methods are still dominant mathematical algorithms for mapping (comparing with stochastic, probablisitc, Monte Carlo estimation or hand-made mapping). The main advantage of such approach is one solution accepted as true representation of volume or plane. The most applied in the group of easy and fast interpolations are Inverse Distance Weighting and Moving Average. The most applied for mostly the best linear estimation in mapping is Kriging. For small datasets and irregular distributed hard data hand-made maps still could be the best approach, especially if are interpolated by experienced expert.z!@2>""" " """" "  $"$7("( ,",]0"0XyIIIkI  33___PPT10e+D=' = @B +"|  @P(  P P # g|pApA??Rectangle 7"i c PK!2<>[Content_Types].xmlAN0EH%,BM #{X$ccB{{&m TҞy?٫vՌ}Z_VH68O}6ōV;dnV]DVBz9v I&]Hd9DУkce\%C7;Dp{KU!["jK8 p&î8By/ O4;Tϐ#La\bDR7q[,į W pov+ fCPK!]  _rels/.relsj1 @h_B֐BWaLΖ5yB/dˠA 0xM e`J FG2p%}iRdITD10Z)4(I9`mtB{ƁmtπnTg 險,ܗr>j1W*@ŀӚZ7O#KOiPK!,QOdrs/shapexml.xmlXn6wt;QA-Q(:vR}a6`7}<@_ar,Y%ðeɅCyMUT4gyfe) v60;Zi4сyI_IJ8DmZ|lm,ʕ8!B/FV)y$ i)QRU!%ؚd;YzI&E~ĭQ2E֍<f[6vy)D{F]"G#]2(`dŕi"F \IGN;ΰU5`U Kaׁ\k"gl^t󊈺uvqu}*4 HHȹH@J^a&)Y̯7x ߪ_B63eMsm#6NxE$p;C:?_~߽߯~iiWFt`El`F]D~vLJGa<6uK!BՀJn vv-wL[Y0(8WW#8v!Vq9ÖdY\ѯ#&%4 ڹcyM%%%.Jf@\Ot[X+RW3֒O;'.ONUŬip)Oyj1{lB`>H3e1%@IBln[RwWѥz_PK! #drs/downrev.xmlDN0 @HCd$n,H(&AWڲ&l8z֛/GӉ3:q [9Zg0"ZBۛ9f 6ւ%6dϤ UCd7yNI2[iPuܞ>Qzn\D1?O T4}e[]bk\PK-!2<>[Content_Types].xmlPK-!]  ,_rels/.relsPK-!,QO(drs/shapexml.xmlPK-! #Sdrs/downrev.xmlPKX  -  t*  R P  Z<?Rectangle 2"tnPK!2<>[Content_Types].xmlAN0EH%,BM #{X$ccB{{&m TҞy?٫vՌ}Z_VH68O}6ōV;dnV]DVBz9v I&]Hd9DУkce\%C7;Dp{KU!["jK8 p&î8By/ O4;Tϐ#La\bDR7q[,į W pov+ fCPK!]  _rels/.relsj1 @h_B֐BWaLΖ5yB/dˠA 0xM e`J FG2p%}iRdITD10Z)4(I9`mtB{ƁmtπnTg 險,ܗr>j1W*@ŀӚZ7O#KOiPK!-D;drs/shapexml.xmlMO0 H(w !@HMcڊƉhcݐ9yZ\T" ߻׻8Y=az]ެBA2qJݦ cn/|@GI1!"#%HzgٽqБ):|M󰉪’KnGk3M+ c#C2dOsJ.>qE<_^l7N e.^$ZwhU:1޾f;?+6ELIPK!vDdrs/downrev.xmlDOj0 qYJ#CH(!J3t :^K7d$q ގ܉|hU2d3O !59K `y}Ycih8ZJTؗRcl3}-G NY6M ѐ{vN|`yQj:w+/sM_Y0D ҥt0 7PK-!2<>[Content_Types].xmlPK-!]  ,_rels/.relsPK-!-D;(drs/shapexml.xmlPK-!vDgdrs/downrev.xmlPKct2     P  |pApA[Content_Types].xmlAN0EH%,BM #{X$ccB{{&m TҞy?٫vՌ}Z_VH68O}6ōV;dnV]DVBz9v I&]Hd9DУkce\%C7;Dp{KU!["jK8 p&î8By/ O4;Tϐ#La\bDR7q[,į W pov+ fCPK!]  _rels/.relsj1 @h_B֐BWaLΖ5yB/dˠA 0xM e`J FG2p%}iRdITD10Z)4(I9`mtB{ƁmtπnTg 險,ܗr>j1W*@ŀӚZ7O#KOiPK!Tdrs/shapexml.xmlUn6?%[l#vn#0l{$RM*I9N^S-K&_萔m,r8y3oxP2RqpcDy"҂o`4)a1~ j*Uck]:$BT^&dI4r۩$Ukᢒu\ZJ#%wDE t.Fp&ĖQÝ!B$;C%T{_q .~JwYщ>$UfrRH?Te, ΝST6U2Pa__YO6_QxQt`>&ߏnm;@NpiJm' ~eHD/QvD 4BXG:LTTŬ+5.}谴Pz{84n#¶ЇI?:_`뛨GI' v2aUNR[5TZvޠ,6 (S|2oz7`yaL`t^(74*F R9gd۔l}%I 6 u1V:4kjShGiK #L Z.#FUԯ5# ^ꩭFAމ;.gJt#<cLV*1&J*9|"BFCP;aĵ0TmZ`0;!kzN>% 6++=8 64ېxah#drg3R*&T /?o)spYĺd=e1m{|-&%Tۯdj4q ,q~}yϟ_=֡J%2=9eG?PK!kdrs/downrev.xmlDOK@Ga4Ң_hZO$$vIw [Fӊ|U0$ N׶T}YRp3SRD *LPTd0L\G69妕i̥ƅ ;h6`>:?oo@0 ^tlI10y/F rPK-!2<>[Content_Types].xmlPK-!]  ,_rels/.relsPK-!T(drs/shapexml.xmlPK-!kqdrs/downrev.xmlPKw K   6  ̙3380___PPT10.@xS|  `X(  X X # |pApA??Rectangle 7"i c PK!2<>[Content_Types].xmlAN0EH%,BM #{X$ccB{{&m TҞy?٫vՌ}Z_VH68O}6ōV;dnV]DVBz9v I&]Hd9DУkce\%C7;Dp{KU!["jK8 p&î8By/ O4;Tϐ#La\bDR7q[,į W pov+ fCPK!]  _rels/.relsj1 @h_B֐BWaLΖ5yB/dˠA 0xM e`J FG2p%}iRdITD10Z)4(I9`mtB{ƁmtπnTg 險,ܗr>j1W*@ŀӚZ7O#KOiPK!4Odrs/shapexml.xmlXn6wt;lu ۉYz9k('Eo6`vӷv>J6+d,p("s?.r:+t٦E\&8Ϭ4jDRykΗ_8;F@~?48$F`u֓r؆A2>[]J$;|)tsX|YRkHӢnyERxo*Tij |M#3 <{`$2bZ`]'%X lHJ%/,ALH~t(gY? 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