(*^ ::[ Information = "This is a Mathematica Notebook file. It contains ASCII text, and can be transferred by email, ftp, or other text-file transfer utility. It should be read or edited using a copy of Mathematica or MathReader. If you received this as email, use your mail application or copy/paste to save everything from the line containing (*^ down to the line containing ^*) into a plain text file. On some systems you may have to give the file a name ending with ".ma" to allow Mathematica to recognize it as a Notebook. The line below identifies what version of Mathematica created this file, but it can be opened using any other version as well."; FrontEndVersion = "Macintosh Mathematica Notebook Front End Version 2.2"; MacintoshStandardFontEncoding; fontset = title, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, bold, e8, 24, "Times"; fontset = subtitle, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, bold, e6, 18, "Times"; fontset = subsubtitle, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, italic, e6, 14, "Times"; fontset = section, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, grayBox, M22, bold, a20, 18, "Times"; fontset = subsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, blackBox, M19, bold, a15, 14, "Times"; fontset = subsubsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, whiteBox, M18, bold, a12, 12, "Times"; fontset = text, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times"; fontset = smalltext, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 10, "Times"; fontset = input, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeInput, M42, N23, bold, L-5, 12, "Courier"; fontset = output, output, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L-5, 12, "Courier"; fontset = message, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, R65535, L-5, 12, "Courier"; fontset = print, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L-5, 12, "Courier"; fontset = info, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, B65535, L-5, 12, "Courier"; fontset = postscript, PostScript, formatAsPostScript, output, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeGraphics, M7, l34, w282, h287, 12, "Courier"; fontset = name, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, italic, 10, "Geneva"; fontset = header, inactive, noKeepOnOnePage, preserveAspect, M7, 12, "Times"; fontset = leftheader, inactive, L2, 12, "Times"; fontset = footer, inactive, noKeepOnOnePage, preserveAspect, center, M7, 12, "Times"; fontset = leftfooter, inactive, L2, 12, "Times"; fontset = help, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 10, "Times"; fontset = clipboard, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times"; fontset = completions, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times"; fontset = special1, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times"; fontset = special2, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times"; fontset = special3, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times"; fontset = special4, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times"; fontset = special5, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times"; paletteColors = 256; automaticGrouping; currentKernel; ] :[font = title; inactive; preserveAspect; startGroup] Ulysses an hyperflexible tool for the analysis of spatial patterns ;[s] 2:0,2;7,1;67,-1; 3:0,25,18,Times,1,24,0,0,0;1,25,18,Times,1,24,65535,0,0;1,41,30,Times,3,40,65535,0,0; :[font = subsubtitle; inactive; preserveAspect] Copyright: Francesco Romani, Sara Colombini and Paolo Cavallini1996. :[font = text; inactive; preserveAspect] Programs may be freely copied and distributed, provided that they are not altered in any way. Modified versions may be circulated only with written permission from authors. Comments & collaborations are welcome! Contact: cavallini@unisi.it Snail-mail: Paolo Cavallini Dipartimento di Biologia Animale e Genetica ÒLeo PardiÓ Universitˆ degli Studi di Firenze via Romana 17/19 I-50125 Firenze Italy ;[s] 3:0,0;222,1;240,0;398,-1; 2:2,13,9,Times,0,12,0,0,0;1,13,10,Courier,0,12,0,0,0; :[font = section; inactive; preserveAspect; startGroup] First steps to run the program :[font = text; inactive; preserveAspect; fontLeading = 0; endGroup] The program can be used easily if your are accustomed to Mathematica. For non-Mathematica users, here are a few hints. Please write if you would find further details useful. They will be included in next versions. 1. Initialize it (Menu Action, then Evaluate Initialization), or select the "Initialization" cell and press enter 2. Go to Input data and enter your filename 3. Run Input data by pressing enter (not return) 4. Run the analyses you want ;[s] 15:0,0;57,1;68,0;78,1;89,0;237,3;243,0;250,3;273,0;291,2;305,0;337,2;347,0;379,2;389,0;450,-1; 4:8,12,9,Times,0,12,0,0,0;2,12,9,Times,2,12,0,0,0;3,18,14,Times,1,18,0,0,0;2,15,12,Monaco,1,12,0,0,0; :[font = section; inactive; preserveAspect; startGroup] How do I.....? :[font = subsubsection; inactive; Cclosed; preserveAspect; startGroup] Save graphs for editing :[font = text; inactive; preserveAspect; endGroup] Select graph; Menu Edit; Copy, then Edit; Convert Clipboard (best formats are EPS and Adobe Illustrator for the Mac; EPS for DOS and Win) ;[s] 5:0,0;19,1;29,0;36,1;59,0;138,-1; 2:3,13,9,Times,0,12,0,0,0;2,16,12,Chicago,0,12,0,0,0; :[font = subsubsection; inactive; Cclosed; preserveAspect; startGroup] Input parameters in formulas :[font = text; inactive; preserveAspect; endGroup] Be careful: Mathematica keeps track of the approximation; therefore, to have greater precision, write, e.g. 2.0 instead of 2 etc ;[s] 3:0,0;12,1;23,0;129,-1; 2:2,13,9,Times,0,12,0,0,0;1,13,9,Times,2,12,0,0,0; :[font = subsubsection; inactive; Cclosed; preserveAspect; startGroup] Combine different figures :[font = text; inactive; preserveAspect; endGroup] e.g. overlay a minimum convex polygon to a kernel analysis: you may define a new name for each of the plots you want to combine: mcp=MinimumConvexPolygon[data,Green]; this command stores the minimum convex polygon plot in "mcp"; you can similarly store other plots, then show them one on top of the other with the following command (the option PlotRange->All allows the visualization of areas outside the location, to include kernel isolines Show[mcp,plotKernel[95],PlotRange->All]; ;[s] 6:0,0;129,1;167,0;344,1;358,0;442,1;483,-1; 2:3,13,9,Times,0,12,0,0,0;3,13,10,Courier,1,12,0,0,0; :[font = subsubsection; inactive; Cclosed; preserveAspect; startGroup] Change the plot area :[font = text; inactive; preserveAspect] to include in the plot large areas unused by the animal; this may be useful to overlay plots of different animals, or to show the external isolines of kernel in case they exceed the plot area. You can change directly the x1, x2, y1, y2 limits of the plot in the relevant formula, e.g. from: :[font = input; preserveAspect] cp=ContourPlot[funz[x,y],{x,x1,x2},{y,y1,y2} :[font = text; inactive; preserveAspect] to: :[font = input; preserveAspect; endGroup; endGroup] cp=ContourPlot[funz[x,y],{x,3000,4000},{y,3000,4000} :[font = section; inactive; initialization; Cclosed; preserveAspect; startGroup] Initialization :[font = subsubsection; inactive; initialization; Cclosed; preserveAspect; startGroup] General :[font = input; initialization; preserveAspect; endGroup] *) Off[General::spell1]; Off[General::spell]; Needs["Graphics`Colors`"]; Needs["DiscreteMath`ComputationalGeometry`"]; Needs["Statistics`DescriptiveStatistics`"]; (* :[font = subsubsection; inactive; initialization; Cclosed; preserveAspect; startGroup] Data input (from text file) :[font = text; inactive; initialization; preserveAspect] Notes: ¥ Take[#,{1,2}] tells the program which columns in your file are x and y coordinates (in this case, 1 and 2). If your file is organized differently, just change the values. ¥ WordSeparators tells the program which characters are taken as separators between successive columns (in this case: space, comma, and tab. You can modify this line according to the structure of your file (e.g. including also ";", etc.) ¥ StringTake[#[[1]],1]=!="*" drops rows of data marked with "*" (this is to eliminate problematic fixes or to select only specific fixes) ;[s] 6:0,2;5,0;9,1;22,0;420,1;446,0;556,-1; 3:3,13,9,Times,0,12,0,0,0;2,13,10,Courier,1,12,0,0,0;1,13,9,Times,1,12,0,0,0; :[font = input; initialization; preserveAspect; endGroup] *) Clear[ReadData]; ReadData[file_String,crit_:(True&)] := Module[{is,righeint,c1,c2},is=OpenRead[file]; If[is[[0]]==InputStream,data=ReadList[is,Word, WordSeparators -> {" ",",","\t"},RecordLists->True]; Close[is]; (* drop of comment rows *) data=Select[data,(StringTake[#[[1]],1]=!="*")&]; data=Select[data,crit]; data=ToExpression[Map[Take[#,{1,2}]&,data]]; n=Length[data],data={};0 data={};0]]; (* :[font = subsubsection; inactive; initialization; Cclosed; preserveAspect; startGroup] Common Data Structure :[font = text; inactive; initialization; preserveAspect] It contains global variables useful for further calculations of the program: data = fixes (x,y locations) n = number of fixes distinctdata = distinct (i.e., not identical) locations ndist = number of distinct fixes fr = frequancy of occurrence for each distinct fix xmin,ymin,xmax,ymax = extreme coordinates of locations x1, y1, x2, y2 = range of graphic display (it can be modified by the user) :[font = input; initialization; preserveAspect; endGroup] *) Clear[CommDataStruct]; CommDataStruct := Module[ {deltax,deltay}, {fr,distinctdata}=Transpose[Frequencies[data]]; ndist=Length[distinctdata]; (* determination of the range of data *) {xmin,ymin}=MapThread[Min,data]; {xmax,ymax}=MapThread[Max,data]; (* delta = displacement for graphic display *) deltax=Which[(xmax-xmin)<=8,2,(xmax-xmin)<=60, Ceiling[(xmax-xmin)*0.5],True,Ceiling[(xmax-xmin)*0.35]]; deltay=Which[(ymax-ymin)<=8,2,(ymax-ymin)<=100, Ceiling[(ymax-ymin)*0.5],True,Ceiling[(ymax-ymin)*0.35]]; {x1=xmin-deltax,x2=xmax+deltax}; {y1=ymin-deltay,y2=ymax+deltay};]; (* :[font = subsubsection; inactive; initialization; Cclosed; preserveAspect; startGroup] Auxiliary calculus functions :[font = text; inactive; initialization; preserveAspect] It calculates basic functions for further calculation :[font = input; initialization; preserveAspect] *) locationplot[location_] := ListPlot[location,PlotStyle->{PointSize[0.02]}, PlotRange->All,AspectRatio->Automatic, DisplayFunction->Identity]; (* :[font = input; initialization; preserveAspect] *) Frequencies[list_] := Map[{Count[list,#],#}&,Union[list]]; (* :[font = text; inactive; initialization; preserveAspect] This function converts the results of home range calculation in square m, hectares or square km :[font = input; initialization; preserveAspect; endGroup] *) ConvertMeasureUnit[ris_] := Which[ris<10000,{N[Floor[ris 10]/10],"m2"}, ris<1000000,{N[Floor[ris/1000]/10],"ha"}, True,{N[Floor[ris/100000]/10],"km2"}]; (* :[font = subsubsection; inactive; initialization; Cclosed; preserveAspect; startGroup] Basic distance statistics :[font = text; inactive; initialization; preserveAspect] The function "DistStat" gives: average and minimum distance among all locations, and average distance between consecutive locations. It can be a help helps for choosing a grid size or the step of integration in Kernel analyses. ;[s] 3:0,0;15,1;23,0;229,-1; 2:2,13,9,Times,0,12,0,0,0;1,13,9,Times,1,12,0,0,0; :[font = input; initialization; preserveAspect; endGroup] *) Clear[DistStat]; DistStat := Module[{diff,m},diff=Sqrt[Map[(#.#)&, Flatten[Table[(distinctdata[[i]]-distinctdata[[j]]), {i,2,ndist},{j,1,i-1}],1]]]; {N[Floor[200 (Plus@@diff)/(n (n-1))]/100],N[Min[diff]], N[Floor[100(Plus@@(Map[Sqrt[#.#]&, Drop[data,-1]-Drop[data,1]])/(n-1))]/100]}]; (* :[font = subsubsection; inactive; initialization; Cclosed; preserveAspect; startGroup] Grid Cell Count :[font = input; initialization; preserveAspect; endGroup] *) Clear[GridCellCount]; GridCellCount[side_] := Module[{copydata,nquad, extremes,delta,minfrequ,maxfrequ,g2,frequ,out,UM, MinGridX,MinGridY,MaxGridX,MaxGridY,fc}, copydata=Floor[data*10]/10; copydata=Map[(#-Mod[#,side])&, copydata]; {frequ,copydata}=Transpose[Frequencies[copydata]]; nquad=Length[copydata]; {out,UM}=ConvertMeasureUnit[N[nquad*side*side]]; Print["Home range area: ",out," ",UM]; {MinGridX,MinGridY}=MapThread[Min,copydata]; {MaxGridX,MaxGridY}=MapThread[Max,copydata]+side; {minfrequ,maxfrequ}={Min[frequ],Max[frequ]}; delta=(maxfrequ-minfrequ); If[TrueQ[delta>0], Show[Graphics[Table[fvgcc=0.7-(frequ[[i]]-minfrequ) /delta/2; {RGBColor[1,fvgcc,fvgcc], Rectangle[copydata[[i]],copydata[[i]]+side]}, {i,1,nquad}]], GridLines-> {Table[i,{i,MinGridX-side,MaxGridX+side,side}], Table[i,{i,MinGridY-side,MaxGridY+side,side}]}, Frame->True, AspectRatio->Automatic, PlotLabel->"Grid Cell Count", PlotRange->{ {Min[xmin,MinGridX]-0.6,Max[xmax,MaxGridX]+0.6}, {Min[ymin,MinGridY]-0.6,Max[ymax,MaxGridY]+0.6}}, DisplayFunction->$DisplayFunction]]]; (* :[font = subsubsection; inactive; initialization; Cclosed; preserveAspect; startGroup] Minimum convex polygon :[font = text; inactive; initialization; preserveAspect] This group of functions calculates the area of the minimum convex polygon enclosing all locations. It finds aritmetic, geometric, and harmonic centre, and allows the exclusion (function Elimin) of some % of locations furthest from one of the centres at user's choice. NOTE: geometric centre and harmonic centre are scale-dependent; their use cannot therefore be recommended! ;[s] 5:0,0;188,1;194,0;272,2;277,0;379,-1; 3:3,13,9,Times,0,12,0,0,0;1,13,10,Courier,1,12,0,0,0;1,13,9,Times,1,12,0,0,0; :[font = input; initialization; preserveAspect] *) Clear[AritmeticCentre]; AritmeticCentre := N[Floor[((Plus@@data)/n) 10]/10]; (* :[font = input; initialization; preserveAspect] *) Clear[GeometricCentre]; GeometricCentre := N[Floor[(Power[Times@@data,1/n]) 10]/10]; (* :[font = text; inactive; initialization; preserveAspect] HarmonicCentre Given the extremes of the grid (bottom left and top right),and the side of the grid, the function generates a grid and calculates the harmonic mean function. The side of the grid may be chosen as 1/4 of average distance between locations. It incorporates Spencer and Barrett (1984) modification. :[font = input; initialization; preserveAspect] *) Clear[HarmonicCentre]; HarmonicCentre[side_] := Module[ {xsin,xdes,ysin,ydes,grid,HM,HarmonicList,Carm}, (* to avoid the coincidence between a grid node and a location: *) {xsin=x1+0.0001,xdes=x2+0.0001}; {ysin=y1+0.0001,ydes=y2+0.0001}; grid=Flatten[Table[{x,y},{x,xsin,xdes,side}, {y,ysin,ydes,side}],1]; HM=Compile [{x,y},Evaluate[Plus@@Map[ (1/Sqrt[(#[[1]]-x)^2 + (#[[2]]-y)^2])&,data]/n]]; HarmonicList=MapThread[HM,Transpose[grid]]; Carm=grid[[ Position[HarmonicList,Max[HarmonicList]][[1,1]]]]]; (* :[font = text; inactive; initialization; preserveAspect] Elimin :[font = input; initialization; preserveAspect] *) Clear[Elimin]; Elimin[perc_,data_,centre_] := Module[ {eliminatelocation,distances,dataplus,shortdataplus,dist, truncateddata}, (* The following function calculates the number of locations corresponding to the percentage given by the user*) eliminatelocation=Ceiling[perc*Length[data]/100]; (* The following function calculates the vector of distances from each location to centre *) distances=Map[(#.#)&, Map[(centre-#)&, data]]; dataplus=Transpose[ {distances,data} ]; shortdataplus=Drop[Sort[dataplus],-eliminatelocation]; {dist,truncateddata} = Transpose[shortdataplus]; truncateddata]; (* ;[s] 5:0,0;135,1;256,0;308,1;407,0;622,-1; 2:3,12,10,Courier,1,12,0,0,0;2,12,9,Times,0,12,0,0,0; :[font = text; inactive; initialization; preserveAspect] AritmeticGeometricHarmonic given the side of the grid (necessary to calculate the harmonic centre), this function visualizes a plot of data and the three centres :[font = input; initialization; preserveAspect] *) Clear[AritmeticGeometricHarmonic]; AritmeticGeometricHarmonic[sideo_] := Module[ {PP,carit,cgeo,carmo},PP[location_] := ListPlot[location,PlotStyle->{PointSize[0.02]}, PlotRange->{{x1,x2},{y1,y2}}, AspectRatio->Automatic, DisplayFunction->Identity]; Print["Aritmetic centre (in blue) : x, y ", carit=AritmeticCentre]; Print["Geometric centre (in yellow): x, y ", cgeo=GeometricCentre]; Print["Harmonic centre (in red) : x, y ", carmo=HarmonicCentre[sideo]]; Show[{PP[data], Graphics[{PointSize[0.04],RGBColor[1,1,0],Point[cgeo], PointSize[0.018],RGBColor[0,0,1],Point[carit], PointSize[0.04],RGBColor[1,0,0],Point[carmo]}]}, Frame->True,Axes->False, AspectRatio->Automatic, PlotRange->{{xmin-0.2,xmax+0.2}, {ymin-0.2,ymax+0.2}}, DisplayFunction->$DisplayFunction]]; (* :[font = text; inactive; initialization; preserveAspect] StudyHarmonic This function shows how the location of harmonic centre varies according to the grid cell size chosen :[font = input; initialization; preserveAspect] *) Clear[StudyHarmonic]; StudyHarmonic[sidemin_,sidemax_,step_] := Module[{list,list2}, list={}; For[i=sidemin,i<=sidemax,i+=step, list=Union[list,{{i,HarmonicCentre[i]}}]]; Print["Side-Harmonic Centre = ",list]; list2=Map[(#[[2]])&,list]; ListPlot[list2, PlotStyle->{PointSize[0.035]}, PlotRange->{{x1,x2},{y1,y2}}, AspectRatio->Automatic, Axes->False, Frame->True]]; (* :[font = text; inactive; initialization; preserveAspect] area (it calculates the area of the tile, as in the MCP method) :[font = input; initialization; preserveAspect] *) area[list_] := Module[{i,centre,distances,l1,l2,l3,n,tmp,p}, n=Length[list]; centre=(Plus@@list)/n; distances=Map[Sqrt[#.#]&,Map[(#-centre)&,list]]; tmp=0; For[i=1,i<=n,i++, l1=distances[[i]]; l2=distances[[Mod[i,n]+1]]; l3=Abs[Complex@@(list[[i]]-list[[Mod[i,n]+1]])]; (* p= 1/2 perimeter *) p=(l1+l2+l3)/2; tmp+=Sqrt[p Times@@(p-{l1,l2,l3}) ]];tmp] (* ;[s] 3:0,0;283,1;305,0;368,-1; 2:2,12,10,Courier,1,12,0,0,0;1,12,10,Courier,0,12,0,0,0; :[font = text; inactive; initialization; preserveAspect] MinimumConvexPolygon :[font = input; initialization; preserveAspect; endGroup] *) Clear[MinimumConvexPolygon]; MinimumConvexPolygon[data_,color_:Black] := Module[ {cu,pl,location2,lp,out,UM}, (* It returns a list of vertices of minimum convex polygon *) cu=ConvexHull[data]; pl=Table[data[[cu[[i]]]],{i,1,Length[cu]}]; {out,UM}=ConvertMeasureUnit[N[area[pl]]]; Print["Area= ",out," ",UM]; Show[Graphics[{{color, (* here you can change the size of locations to be plotted *) PointSize[0.04],Point/@data}, Line[Append[pl,First[pl]]]}], AspectRatio->Automatic, Axes->False,Frame->True, PlotRange->{{xmin-0.2,xmax+0.2},{ymin-0.2,ymax+0.2}}, DisplayFunction->$DisplayFunction]]; (* ;[s] 5:0,0;122,1;192,0;386,1;448,0;676,-1; 2:3,12,10,Courier,1,12,0,0,0;2,12,10,Courier,0,12,0,0,0; :[font = subsubsection; inactive; initialization; Cclosed; preserveAspect; startGroup] Auxiliary functions for Voronoi tesselations :[font = text; inactive; initialization; preserveAspect] locationplotbis :[font = input; initialization; preserveAspect] *) locationplotbis[location_] := ListPlot[location,PlotStyle->{PointSize[0.03]}, PlotRange->All,AspectRatio->Automatic, DisplayFunction->Identity]; (* :[font = text; inactive; initialization; preserveAspect] showVoronoi (it shows both data and tiles (see Wray et al. 1992) :[font = input; initialization; preserveAspect] *) Clear[showVoronoi]; showVoronoi[diagvert_,diagval_,s_] := Module[{lp,d}, lp=locationplot[distinctdata]; d=DiagramPlot[distinctdata,diagvert,diagval, LabelPoints->False, DisplayFunction->Identity]; Show[{lp,d},DisplayFunction->$DisplayFunction, Axes->True, PlotLabel->s, PlotRange->{{vxmin,vxmax},{vymin,vymax}}]]; (* :[font = text; inactive; initialization; preserveAspect] eliminopen (it eliminates open tiles) :[font = input; initialization; preserveAspect] *) eliminopen[{lv_,la_}] := Module[ {i,n,j,lvv,laa,limit}, lvv=lv; laa=la; n=Length[lvv]; For[i=n,(Head[lvv[[i]]]==Ray) && (i>0),i--, lvv=Drop[lvv,-1]]; j=1;limit=Length[laa]; While[j<=limit, If[ Select[laa[[j,2]],(#>i)&] != {}, laa=Drop[laa,{j}];limit-- ,j++]];{lvv,laa}]; (* :[font = text; inactive; initialization; preserveAspect] indexTOvertex (takes the list of indices to vertices in diagvert, appends the first element to close the tile and returns the list of vertices) :[font = input; initialization; preserveAspect] *) indexTOvertex[indices_,list_] := Map[ list[[#]]&,Append[indices,indices[[1]]]]; (* :[font = text; inactive; initialization; preserveAspect] areatile (given the list: {n. of tile, indices of vertices}, it returns the list: {area of the tile,{n. of tile, indices of vertices}}) :[font = input; initialization; preserveAspect] *) areatile[list_,diagvert_] := Map[ {area[indexTOvertex[#[[2]],diagvert]],#}&,list]; (* :[font = text; inactive; initialization; preserveAspect] areasfreq (given the list: {area of the tile,{n. of tile, indices of vertices}}, it returns the list: {area of the tile/frequency,{n. of tile, indices of vertices}, area of the tile, frequency}) (note: frequency and tiles are in the same order because both are ordered in correspondence with locations) :[font = input; initialization; preserveAspect] *) areasfreq[list_] := Map[ {#[[1]]/fr[[#[[2,1]]]],#[[2]],#[[1]],fr[[#[[2,1]]]]}&, list]; (* :[font = text; inactive; initialization; preserveAspect] polygon :[font = input; initialization; preserveAspect] *) Clear[polygon]; polygon[newpp_,newvert_,col_] := Map[Graphics[{GrayLevel[col[[#[[3]]]]], Polygon[indexTOvertex[#[[2]],newvert]]}]&, Table[{newpp[[i,1]],newpp[[i,2]],i},{i,Length[newpp]}]]; (* :[font = text; inactive; initialization; preserveAspect] polygoncolors (given the tiles to show, it returns colored tiles) :[font = input; initialization; preserveAspect; endGroup] *) Clear[polygoncolors]; polygoncolors[newpp_,newvert_,col_] := Map[Graphics[{Hue[0.5+((1-col[[#[[3]]]])/2.8)],Polygon[ indexTOvertex[#[[2]],newvert]]}]&,Table[{newpp[[i,1]], newpp[[i,2]],i},{i,Length[newpp]}]]; (* :[font = subsubsection; inactive; initialization; Cclosed; preserveAspect; startGroup] Voronoi function :[font = input; preserveAspect; endGroup; endGroup] Clear[Voronoi]; Voronoi[perc_] := Module[ {s,p,diagvert,diagval,aaf,pp,aareal,aareal1,frequency, frequency1,frequency2,locatperc,areas,out,UM, nperc,index,partialarea,newpp,usedvert,newvert,g, pmin,pmax,delta,h,polygon}, (* diagvert= vertices+radii for tesselation diagval= index to sample in distinctdata with list (sorted counterclockwise) of indices to vertices of the tile *) {diagvert,diagval}=VoronoiDiagram[distinctdata]; {diagvert,diagval}=eliminopen[{diagvert,diagval}]; {vxmin,vymin}=MapThread[Min,diagvert]; {vxmax,vymax}=MapThread[Max,diagvert]; {vxmin,vymin}={vxmin,vymin}-0.5; {vxmax,vymax}={vxmax,vymax}+0.5; (* p = sorted list of the areas of the tiles on frequency *) p=Sort[areasfreq[areatile[diagval,diagvert]]]; (* aaf=area on frequency aareal= real area of the tile pp={n. of tile,list of indices of vertices} aaf is needed only to sort the list delta=range of tile importance note: area is calculated for closed tiles only *) {aaf,pp,aareal,frequency}=Transpose[p]; {pmin,pmax}={First[aaf],Last[aaf]}; delta=pmax-pmin; locatperc=N[Floor[n*perc/100]]; nperc=Length[perc]; (* nperc= how many percentages are calculated (* g=h={0,0,0,0,0,0};*) frequency1 = foldsum of all frequencies aareal1 = foldsum of all real areas of tiles *) frequency1=Rest[FoldList[Plus,0,frequency]]; aareal1=Rest[FoldList[Plus,0,aareal]]; col=(aaf-pmin)/delta; (* This is to select all tiles that are necessary to reach the requested % of total HR *) Do[frequency2=Select[frequency1,(#<=locatperc[[i]])&]; Print["Real %: ",Ceiling[100 Last[frequency2]/n]]; index=Length[frequency2]; (* n of selected tiles *) partialarea=If[ index>0, N[aareal1[[index]]], 0]; {out,UM}=ConvertMeasureUnit[partialarea]; newpp=Take[pp,index]; s=ToString[perc[[i]]]<>"%:"<>ToString[out]<>" "<>UM; If[newpp!={}, usedvert=Union[Flatten[Transpose[newpp][[2]]]]; newvert=diagvert[[usedvert]]; newpp= Map[ {#[[1]], Table[Position[usedvert,#[[2,k]]][[1,1]], {k,Length[#[[2]]]}]} &,newpp]; lpbis=locationplotbis[distinctdata]; d=DiagramPlot[distinctdata,newvert,newpp, LabelPoints->False,DisplayFunction->Identity]; c=polygoncolors[newpp,newvert,col]; r=(#[[2]]/#[[1]])&[{-1,1}.#&/@ PlotRange[shw=Show[{d,c,lpbis}, DisplayFunction->Identity, Axes->False, Frame->True, PlotRange->All]]]; shw=Show[shw,DisplayFunction->$DisplayFunction, Axes->False, Frame->True, PlotRange->All, AspectRatio->r], Print[s]],{i,nperc}]; shw]; ;[s] 11:0,0;244,1;404,0;648,1;709,0;756,1;972,0;1117,1;1285,0;1391,1;1481,0;2537,-1; 2:6,12,10,Courier,1,12,0,0,0;5,12,9,Times,0,12,0,0,0; :[font = section; inactive; Cclosed; preserveAspect; startGroup] Input data :[font = text; inactive; preserveAspect] This section is for uploading data (x, y locations). In this configuartion, the program takes only the first and second columns (but this can be changed; see Initialization; Data input (from text file)). Any row preceded by an asterisk (*) will be dropped. Note: 1. Coordinates must be given in meters 2. A subset of points may be excluded from the analysis. For instance, the command: ReadData["HD:Radiotrack:Data:Jay",(#[[3]]=="1990/04/24")&];data drops all location with "1990/04/24" in the third column. The command returns the number of locations and a list of them. To specify the name of the file to be analyzed: Select the path name currently choosen, then: Menu Action; Prepare Input; Paste File Pathname...; then select your file from dialog window. ;[s] 10:0,0;158,1;174,2;201,0;386,4;449,0;573,2;620,0;672,3;717,0;761,-1; 5:5,13,9,Times,0,12,0,0,0;1,19,14,Times,1,18,0,0,0;2,13,9,Times,1,12,0,0,0;1,16,12,Chicago,0,12,0,0,0;1,13,10,Courier,1,12,0,0,0; :[font = input; preserveAspect; startGroup] ReadData["Ulisse:Documents:Home range:Data:Examples:jay.txt"] data CommDataStruct; :[font = output; output; inactive; preserveAspect] 17 ;[o] 17 :[font = output; output; inactive; preserveAspect; endGroup; endGroup] {{3550, 4100}, {3550, 4200}, {3650, 4200}, {3600, 4150}, {3550, 4200}, {3550, 4200}, {3500, 4200}, {3750, 4250}, {3550, 4200}, {3550, 4250}, {3700, 4250}, {3550, 4250}, {3600, 4200}, {3550, 4250}, {3450, 4250}, {3550, 4250}, {3550, 4200}} ;[o] {{3550, 4100}, {3550, 4200}, {3650, 4200}, {3600, 4150}, {3550, 4200}, {3550, 4200}, {3500, 4200}, {3750, 4250}, {3550, 4200}, {3550, 4250}, {3700, 4250}, {3550, 4250}, {3600, 4200}, {3550, 4250}, {3450, 4250}, {3550, 4250}, {3550, 4200}} :[font = section; inactive; Cclosed; preserveAspect; startGroup] Basic statistics :[font = text; inactive; preserveAspect] This section calculates average and minimum distance among all locations, and average distance between consecutive locations. These results can be useful for selecting several parameters (grid size in Grid Cell Count, integration step in Kernel analyses). :[font = input; preserveAspect; startGroup] DistStat :[font = output; output; inactive; preserveAspect; endGroup; endGroup] {43.55, 50., 99.62} ;[o] {43.55, 50., 99.62} :[font = section; inactive; Cclosed; preserveAspect; startGroup] Data compression :[font = text; inactive; preserveAspect] This secion can be used to shorten computation time with large amount of data. The program builds a grid, and data are moved to the closest grid intersection. Total sample size remains unaltered. The parameter is the grid size (the larger, the more approximation and the less computation time). :[font = subsubsection; inactive; preserveAspect; startGroup] Definition :[font = input; preserveAspect; endGroup] Clear[Compress]; Compress[side_] := (data=Map[(#-Mod[#,side])&,data+side/2]); :[font = subsubsection; inactive; preserveAspect; startGroup] Call :[font = input; preserveAspect; endGroup; endGroup] Compress[10]; :[font = section; inactive; Cclosed; preserveAspect; startGroup] Grid Cell Count :[font = text; inactive; preserveAspect] The parameter is the grid size (in meters) :[font = input; preserveAspect; startGroup] GridCellCount[50]; :[font = print; inactive; preserveAspect] Home range area: 2.5 ha :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 36; pictureTop = 1; pictureWidth = 282; pictureHeight = 161; endGroup; endGroup] %! %%Creator: Mathematica %%AspectRatio: .57289 MathPictureStart %% Graphics /Courier findfont 10 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You can choose a colour to plot data. 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[(4180)] -0.0125 .26698 1 0 Mshowa p .002 w 0 .33356 m .00625 .33356 L s P [(4200)] -0.0125 .33356 1 0 Mshowa p .002 w 0 .40013 m .00625 .40013 L s P [(4220)] -0.0125 .40013 1 0 Mshowa p .002 w 0 .46671 m .00625 .46671 L s P [(4240)] -0.0125 .46671 1 0 Mshowa p .001 w 0 .01398 m .00375 .01398 L s P p .001 w 0 .0273 m .00375 .0273 L s P p .001 w 0 .04061 m .00375 .04061 L s P p .001 w 0 .05393 m .00375 .05393 L s P p .001 w 0 .08056 m .00375 .08056 L s P p .001 w 0 .09387 m .00375 .09387 L s P p .001 w 0 .10719 m .00375 .10719 L s P p .001 w 0 .12051 m .00375 .12051 L s P p .001 w 0 .14714 m .00375 .14714 L s P p .001 w 0 .16045 m .00375 .16045 L s P p .001 w 0 .17377 m .00375 .17377 L s P p .001 w 0 .18708 m .00375 .18708 L s P p .001 w 0 .21372 m .00375 .21372 L s P p .001 w 0 .22703 m .00375 .22703 L s P p .001 w 0 .24035 m .00375 .24035 L s P p .001 w 0 .25366 m .00375 .25366 L s P p .001 w 0 .28029 m .00375 .28029 L s P p .001 w 0 .29361 m .00375 .29361 L s P p .001 w 0 .30692 m 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.2004 .50067 L s P p .001 w .23369 .49692 m .23369 .50067 L s P p .001 w .26698 .49692 m .26698 .50067 L s P p .001 w .30027 .49692 m .30027 .50067 L s P p .001 w .36684 .49692 m .36684 .50067 L s P p .001 w .40013 .49692 m .40013 .50067 L s P p .001 w .43342 .49692 m .43342 .50067 L s P p .001 w .46671 .49692 m .46671 .50067 L s P p .001 w .53329 .49692 m .53329 .50067 L s P p .001 w .56658 .49692 m .56658 .50067 L s P p .001 w .59987 .49692 m .59987 .50067 L s P p .001 w .63316 .49692 m .63316 .50067 L s P p .001 w .69973 .49692 m .69973 .50067 L s P p .001 w .73302 .49692 m .73302 .50067 L s P p .001 w .76631 .49692 m .76631 .50067 L s P p .001 w .7996 .49692 m .7996 .50067 L s P p .001 w .86618 .49692 m .86618 .50067 L s P p .001 w .89947 .49692 m .89947 .50067 L s P p .001 w .93276 .49692 m .93276 .50067 L s P p .001 w .96605 .49692 m .96605 .50067 L s P p .002 w 0 .50067 m 1 .50067 L s P p .002 w .99375 .00067 m 1 .00067 L s P p .002 w .99375 .06724 m 1 .06724 L s P p .002 w .99375 .13382 m 1 .13382 L s P p .002 w .99375 .2004 m 1 .2004 L s P p .002 w .99375 .26698 m 1 .26698 L s P p .002 w .99375 .33356 m 1 .33356 L s P p .002 w .99375 .40013 m 1 .40013 L s P p .002 w .99375 .46671 m 1 .46671 L s P p .001 w .99625 .01398 m 1 .01398 L s P p .001 w .99625 .0273 m 1 .0273 L s P p .001 w .99625 .04061 m 1 .04061 L s P p .001 w .99625 .05393 m 1 .05393 L s P p .001 w .99625 .08056 m 1 .08056 L s P p .001 w .99625 .09387 m 1 .09387 L s P p .001 w .99625 .10719 m 1 .10719 L s P p .001 w .99625 .12051 m 1 .12051 L s P p .001 w .99625 .14714 m 1 .14714 L s P p .001 w .99625 .16045 m 1 .16045 L s P p .001 w .99625 .17377 m 1 .17377 L s P p .001 w .99625 .18708 m 1 .18708 L s P p .001 w .99625 .21372 m 1 .21372 L s P p .001 w .99625 .22703 m 1 .22703 L s P p .001 w .99625 .24035 m 1 .24035 L s P p .001 w .99625 .25366 m 1 .25366 L s P p .001 w .99625 .28029 m 1 .28029 L s P p .001 w .99625 .29361 m 1 .29361 L s P p .001 w .99625 .30692 m 1 .30692 L s P p .001 w .99625 .32024 m 1 .32024 L s P p .001 w .99625 .34687 m 1 .34687 L s P p .001 w .99625 .36019 m 1 .36019 L s P p .001 w .99625 .3735 m 1 .3735 L s P p .001 w .99625 .38682 m 1 .38682 L s P p .001 w .99625 .41345 m 1 .41345 L s P p .001 w .99625 .42676 m 1 .42676 L s P p .001 w .99625 .44008 m 1 .44008 L s P p .001 w .99625 .4534 m 1 .4534 L s P p .001 w .99625 .48003 m 1 .48003 L s P p .001 w .99625 .49334 m 1 .49334 L s P p .002 w 1 0 m 1 .50067 L s P P p P 0 0 m 1 0 L 1 .50067 L 0 .50067 L closepath clip newpath p p 0 1 0 r p .04 w .33356 .00067 Mdot .33356 .33356 Mdot .66644 .33356 Mdot .5 .16711 Mdot .33356 .33356 Mdot .33356 .33356 Mdot .16711 .33356 Mdot .99933 .5 Mdot .33356 .33356 Mdot .33356 .5 Mdot .83289 .5 Mdot .33356 .5 Mdot .5 .33356 Mdot .33356 .5 Mdot .00067 .5 Mdot .33356 .5 Mdot .33356 .33356 Mdot P P .004 w .99933 .5 m .83289 .5 L .33356 .5 L .00067 .5 L .33356 .00067 L .99933 .5 L s P % End of Graphics MathPictureEnd :[font = text; inactive; preserveAspect; animationSpeed = 62] Plot of locations with three estimators of activity centre (aritmetic, geometric, harmonic). The coordinates of the centres are also given. The parameter is the grid size for the calculation of harmonic centre. Caution! The geometric and harmonic centres depend on the scale used; they are not stable, and cannot therefore be compared across animals or areas! ;[s] 3:0,0;211,1;279,0;360,-1; 2:2,13,9,Times,0,12,0,0,0;1,13,9,Times,1,12,0,0,0; :[font = input; Cclosed; preserveAspect; startGroup; animationSpeed = 62] AritmeticGeometricHarmonic[100]; :[font = print; inactive; preserveAspect] Aritmetic centre (in blue) : x, y {3573.5, 4211.7} Geometric centre (in yellow): x, y {3572.8, 4211.5} Harmonic centre (in red) : x, y {3545., 4247.} :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 282; pictureHeight = 141; endGroup] %! %%Creator: Mathematica %%AspectRatio: .50067 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations -11.484 0.00332889 -13.6478 0.00332889 [ [(3450)] .00067 0 0 2 Msboxa [(3500)] .16711 0 0 2 Msboxa [(3550)] .33356 0 0 2 Msboxa [(3600)] .5 0 0 2 Msboxa [(3650)] .66644 0 0 2 Msboxa [(3700)] .83289 0 0 2 Msboxa [(3750)] .99933 0 0 2 Msboxa [(4100)] -0.0125 .00067 1 0 Msboxa [(4120)] -0.0125 .06724 1 0 Msboxa [(4140)] -0.0125 .13382 1 0 Msboxa [(4160)] -0.0125 .2004 1 0 Msboxa [(4180)] -0.0125 .26698 1 0 Msboxa [(4200)] -0.0125 .33356 1 0 Msboxa [(4220)] -0.0125 .40013 1 0 Msboxa [(4240)] -0.0125 .46671 1 0 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 .50167 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p p .002 w .00067 0 m .00067 .00625 L s P [(3450)] .00067 0 0 2 Mshowa p .002 w .16711 0 m .16711 .00625 L s P [(3500)] .16711 0 0 2 Mshowa p .002 w .33356 0 m .33356 .00625 L s P [(3550)] .33356 0 0 2 Mshowa p .002 w .5 0 m .5 .00625 L s P [(3600)] .5 0 0 2 Mshowa p .002 w .66644 0 m .66644 .00625 L s P [(3650)] .66644 0 0 2 Mshowa p .002 w .83289 0 m .83289 .00625 L s P [(3700)] .83289 0 0 2 Mshowa p .002 w .99933 0 m .99933 .00625 L s P [(3750)] .99933 0 0 2 Mshowa p .001 w .03395 0 m .03395 .00375 L s P p .001 w .06724 0 m .06724 .00375 L s P p .001 w .10053 0 m .10053 .00375 L s P p .001 w .13382 0 m .13382 .00375 L s P p .001 w .2004 0 m .2004 .00375 L s P p .001 w .23369 0 m .23369 .00375 L s P p .001 w .26698 0 m .26698 .00375 L s P p .001 w .30027 0 m .30027 .00375 L s P p .001 w .36684 0 m .36684 .00375 L s P p .001 w .40013 0 m .40013 .00375 L s P p .001 w .43342 0 m .43342 .00375 L s P p .001 w .46671 0 m .46671 .00375 L s P p .001 w .53329 0 m .53329 .00375 L s P p .001 w .56658 0 m .56658 .00375 L s P p .001 w .59987 0 m .59987 .00375 L s P p .001 w .63316 0 m .63316 .00375 L s P p .001 w .69973 0 m .69973 .00375 L s P p .001 w .73302 0 m .73302 .00375 L s P p .001 w .76631 0 m .76631 .00375 L s P p .001 w .7996 0 m .7996 .00375 L s P p .001 w .86618 0 m .86618 .00375 L s P p .001 w .89947 0 m .89947 .00375 L s P p .001 w .93276 0 m .93276 .00375 L s P p .001 w .96605 0 m .96605 .00375 L s P p .002 w 0 0 m 1 0 L s P p .002 w 0 .00067 m .00625 .00067 L s P [(4100)] -0.0125 .00067 1 0 Mshowa p .002 w 0 .06724 m .00625 .06724 L s P [(4120)] -0.0125 .06724 1 0 Mshowa p .002 w 0 .13382 m .00625 .13382 L s P [(4140)] -0.0125 .13382 1 0 Mshowa p .002 w 0 .2004 m .00625 .2004 L s P [(4160)] -0.0125 .2004 1 0 Mshowa p .002 w 0 .26698 m .00625 .26698 L s P [(4180)] -0.0125 .26698 1 0 Mshowa p .002 w 0 .33356 m .00625 .33356 L s P [(4200)] -0.0125 .33356 1 0 Mshowa p .002 w 0 .40013 m .00625 .40013 L s P [(4220)] -0.0125 .40013 1 0 Mshowa p .002 w 0 .46671 m .00625 .46671 L s P [(4240)] -0.0125 .46671 1 0 Mshowa p .001 w 0 .01398 m .00375 .01398 L s P p .001 w 0 .0273 m .00375 .0273 L s P p .001 w 0 .04061 m .00375 .04061 L s P p .001 w 0 .05393 m .00375 .05393 L s P p .001 w 0 .08056 m .00375 .08056 L s P p .001 w 0 .09387 m .00375 .09387 L s P p .001 w 0 .10719 m .00375 .10719 L s P p .001 w 0 .12051 m .00375 .12051 L s P p .001 w 0 .14714 m .00375 .14714 L s P p .001 w 0 .16045 m .00375 .16045 L s P p .001 w 0 .17377 m .00375 .17377 L s P p .001 w 0 .18708 m .00375 .18708 L s P p .001 w 0 .21372 m .00375 .21372 L s P p .001 w 0 .22703 m .00375 .22703 L s P p .001 w 0 .24035 m .00375 .24035 L s P p .001 w 0 .25366 m .00375 .25366 L s P p .001 w 0 .28029 m .00375 .28029 L s P p .001 w 0 .29361 m .00375 .29361 L s P p .001 w 0 .30692 m .00375 .30692 L s P p .001 w 0 .32024 m .00375 .32024 L s P p .001 w 0 .34687 m .00375 .34687 L s P p .001 w 0 .36019 m .00375 .36019 L s P p .001 w 0 .3735 m .00375 .3735 L s P p .001 w 0 .38682 m .00375 .38682 L s P p .001 w 0 .41345 m .00375 .41345 L s P p .001 w 0 .42676 m .00375 .42676 L s P p .001 w 0 .44008 m .00375 .44008 L s P p .001 w 0 .4534 m .00375 .4534 L s P p .001 w 0 .48003 m .00375 .48003 L s P p .001 w 0 .49334 m .00375 .49334 L s P p .002 w 0 0 m 0 .50067 L s P P p p .002 w .00067 .49442 m .00067 .50067 L s P p .002 w .16711 .49442 m .16711 .50067 L s P p .002 w .33356 .49442 m .33356 .50067 L s P p .002 w .5 .49442 m .5 .50067 L s P p .002 w .66644 .49442 m .66644 .50067 L s P p .002 w .83289 .49442 m .83289 .50067 L s P p .002 w .99933 .49442 m .99933 .50067 L s P p .001 w .03395 .49692 m .03395 .50067 L s P p .001 w .06724 .49692 m .06724 .50067 L s P p .001 w .10053 .49692 m .10053 .50067 L s P p .001 w .13382 .49692 m .13382 .50067 L s P p .001 w .2004 .49692 m .2004 .50067 L s P p .001 w .23369 .49692 m .23369 .50067 L s P p .001 w .26698 .49692 m .26698 .50067 L s P p .001 w .30027 .49692 m .30027 .50067 L s P p .001 w .36684 .49692 m .36684 .50067 L s P p .001 w .40013 .49692 m .40013 .50067 L s P p .001 w .43342 .49692 m .43342 .50067 L s P p .001 w .46671 .49692 m .46671 .50067 L s P p .001 w .53329 .49692 m .53329 .50067 L s P p .001 w .56658 .49692 m .56658 .50067 L s P p .001 w .59987 .49692 m .59987 .50067 L s P p .001 w .63316 .49692 m .63316 .50067 L s P p .001 w .69973 .49692 m .69973 .50067 L s P p .001 w .73302 .49692 m .73302 .50067 L s P p .001 w .76631 .49692 m .76631 .50067 L s P p .001 w .7996 .49692 m .7996 .50067 L s P p .001 w .86618 .49692 m .86618 .50067 L s P p .001 w .89947 .49692 m .89947 .50067 L s P p .001 w .93276 .49692 m .93276 .50067 L s P p .001 w .96605 .49692 m .96605 .50067 L s P p .002 w 0 .50067 m 1 .50067 L s P p .002 w .99375 .00067 m 1 .00067 L s P p .002 w .99375 .06724 m 1 .06724 L s P p .002 w .99375 .13382 m 1 .13382 L s P p .002 w .99375 .2004 m 1 .2004 L s P p .002 w .99375 .26698 m 1 .26698 L s P p .002 w .99375 .33356 m 1 .33356 L s P p .002 w .99375 .40013 m 1 .40013 L s P p .002 w .99375 .46671 m 1 .46671 L s P p .001 w .99625 .01398 m 1 .01398 L s P p .001 w .99625 .0273 m 1 .0273 L s P p .001 w .99625 .04061 m 1 .04061 L s P p .001 w .99625 .05393 m 1 .05393 L s P p .001 w .99625 .08056 m 1 .08056 L s P p .001 w .99625 .09387 m 1 .09387 L s P p .001 w .99625 .10719 m 1 .10719 L s P p .001 w .99625 .12051 m 1 .12051 L s P p .001 w .99625 .14714 m 1 .14714 L s P p .001 w .99625 .16045 m 1 .16045 L s P p .001 w .99625 .17377 m 1 .17377 L s P p .001 w .99625 .18708 m 1 .18708 L s P p .001 w .99625 .21372 m 1 .21372 L s P p .001 w .99625 .22703 m 1 .22703 L s P p .001 w .99625 .24035 m 1 .24035 L s P p .001 w .99625 .25366 m 1 .25366 L s P p .001 w .99625 .28029 m 1 .28029 L s P p .001 w .99625 .29361 m 1 .29361 L s P p .001 w .99625 .30692 m 1 .30692 L s P p .001 w .99625 .32024 m 1 .32024 L s P p .001 w .99625 .34687 m 1 .34687 L s P p .001 w .99625 .36019 m 1 .36019 L s P p .001 w .99625 .3735 m 1 .3735 L s P p .001 w .99625 .38682 m 1 .38682 L s P p .001 w .99625 .41345 m 1 .41345 L s P p .001 w .99625 .42676 m 1 .42676 L s P p .001 w .99625 .44008 m 1 .44008 L s P p .001 w .99625 .4534 m 1 .4534 L s P p .001 w .99625 .48003 m 1 .48003 L s P p .001 w .99625 .49334 m 1 .49334 L s P p .002 w 1 0 m 1 .50067 L s P P p P 0 0 m 1 0 L 1 .50067 L 0 .50067 L closepath clip newpath p p p .02 w .33356 .00067 Mdot .33356 .33356 Mdot .66644 .33356 Mdot .5 .16711 Mdot .33356 .33356 Mdot .33356 .33356 Mdot .16711 .33356 Mdot .99933 .5 Mdot .33356 .33356 Mdot .33356 .5 Mdot .83289 .5 Mdot .33356 .5 Mdot .5 .33356 Mdot .33356 .5 Mdot .00067 .5 Mdot .33356 .5 Mdot .33356 .33356 Mdot P P p 1 1 0 r .04 w .40945 .37184 Mdot 0 0 1 r .018 w .41178 .3725 Mdot 1 0 0 r .04 w .31691 .49001 Mdot P P % End of Graphics MathPictureEnd :[font = text; inactive; preserveAspect; animationSpeed = 62] Minimum convex polygon excluding some percentage of locations furthest from one of the centres of activity (aritmetic, geometric, harmonic, or user-defined). The first parameter in Elimin indicates the percentage of locations to exclude, the second the data set to utilize, the third the centre chosen (AritmeticCentre, GeometricCentre, HarmonicCentre). The x, y coordinates of a point of user's interest may be used instead (putting them within curly brackets). ;[s] 5:0,0;181,1;187,0;303,1;351,0;463,-1; 2:3,13,9,Times,0,12,0,0,0;2,13,10,Courier,1,12,0,0,0; :[font = input; Cclosed; preserveAspect; startGroup] MinimumConvexPolygon[Elimin[50,data,AritmeticCentre],Yellow]; :[font = print; inactive; preserveAspect] Area= 1249.9 m2 :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 282; pictureHeight = 141; endGroup] %! %%Creator: Mathematica %%AspectRatio: .50067 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations -11.484 0.00332889 -13.6478 0.00332889 [ [(3450)] .00067 0 0 2 Msboxa [(3500)] .16711 0 0 2 Msboxa [(3550)] .33356 0 0 2 Msboxa [(3600)] .5 0 0 2 Msboxa [(3650)] .66644 0 0 2 Msboxa [(3700)] .83289 0 0 2 Msboxa [(3750)] .99933 0 0 2 Msboxa [(4100)] -0.0125 .00067 1 0 Msboxa [(4120)] -0.0125 .06724 1 0 Msboxa [(4140)] -0.0125 .13382 1 0 Msboxa [(4160)] -0.0125 .2004 1 0 Msboxa [(4180)] -0.0125 .26698 1 0 Msboxa [(4200)] -0.0125 .33356 1 0 Msboxa [(4220)] -0.0125 .40013 1 0 Msboxa [(4240)] -0.0125 .46671 1 0 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 .50167 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p p .002 w .00067 0 m .00067 .00625 L s P [(3450)] .00067 0 0 2 Mshowa p .002 w .16711 0 m .16711 .00625 L s P [(3500)] .16711 0 0 2 Mshowa p .002 w .33356 0 m .33356 .00625 L s P [(3550)] .33356 0 0 2 Mshowa p .002 w .5 0 m .5 .00625 L s P [(3600)] .5 0 0 2 Mshowa p .002 w .66644 0 m .66644 .00625 L s P [(3650)] .66644 0 0 2 Mshowa p .002 w .83289 0 m .83289 .00625 L s P [(3700)] .83289 0 0 2 Mshowa p .002 w .99933 0 m .99933 .00625 L s P [(3750)] .99933 0 0 2 Mshowa p .001 w .03395 0 m .03395 .00375 L s P p .001 w .06724 0 m .06724 .00375 L s P p .001 w .10053 0 m .10053 .00375 L s P p .001 w .13382 0 m .13382 .00375 L s P p .001 w .2004 0 m .2004 .00375 L s P p .001 w .23369 0 m .23369 .00375 L s P p .001 w .26698 0 m .26698 .00375 L s P p .001 w .30027 0 m .30027 .00375 L s P p .001 w .36684 0 m .36684 .00375 L s P p .001 w .40013 0 m .40013 .00375 L s P p .001 w .43342 0 m .43342 .00375 L s P p .001 w .46671 0 m .46671 .00375 L s P p .001 w .53329 0 m .53329 .00375 L s P p .001 w .56658 0 m .56658 .00375 L s P p .001 w .59987 0 m .59987 .00375 L s P p .001 w .63316 0 m .63316 .00375 L s P p .001 w .69973 0 m .69973 .00375 L s P p .001 w .73302 0 m .73302 .00375 L s P p .001 w .76631 0 m .76631 .00375 L s P p .001 w .7996 0 m .7996 .00375 L s P p .001 w .86618 0 m .86618 .00375 L s P p .001 w .89947 0 m .89947 .00375 L s P p .001 w .93276 0 m .93276 .00375 L s P p .001 w .96605 0 m .96605 .00375 L s P p .002 w 0 0 m 1 0 L s P p .002 w 0 .00067 m .00625 .00067 L s P [(4100)] -0.0125 .00067 1 0 Mshowa p .002 w 0 .06724 m .00625 .06724 L s P [(4120)] -0.0125 .06724 1 0 Mshowa p .002 w 0 .13382 m .00625 .13382 L s P [(4140)] -0.0125 .13382 1 0 Mshowa p .002 w 0 .2004 m .00625 .2004 L s P [(4160)] -0.0125 .2004 1 0 Mshowa p .002 w 0 .26698 m .00625 .26698 L s P [(4180)] -0.0125 .26698 1 0 Mshowa p .002 w 0 .33356 m .00625 .33356 L s P [(4200)] -0.0125 .33356 1 0 Mshowa p .002 w 0 .40013 m .00625 .40013 L s P [(4220)] -0.0125 .40013 1 0 Mshowa p .002 w 0 .46671 m .00625 .46671 L s P [(4240)] -0.0125 .46671 1 0 Mshowa p .001 w 0 .01398 m .00375 .01398 L s P p .001 w 0 .0273 m .00375 .0273 L s P p .001 w 0 .04061 m .00375 .04061 L s P p .001 w 0 .05393 m .00375 .05393 L s P p .001 w 0 .08056 m .00375 .08056 L s P p .001 w 0 .09387 m .00375 .09387 L s P p .001 w 0 .10719 m .00375 .10719 L s P p .001 w 0 .12051 m .00375 .12051 L s P p .001 w 0 .14714 m .00375 .14714 L s P p .001 w 0 .16045 m .00375 .16045 L s P p .001 w 0 .17377 m .00375 .17377 L s P p .001 w 0 .18708 m .00375 .18708 L s P p .001 w 0 .21372 m .00375 .21372 L s P p .001 w 0 .22703 m .00375 .22703 L s P p .001 w 0 .24035 m .00375 .24035 L s P p .001 w 0 .25366 m .00375 .25366 L s P p .001 w 0 .28029 m .00375 .28029 L s P p .001 w 0 .29361 m .00375 .29361 L s P p .001 w 0 .30692 m .00375 .30692 L s P p .001 w 0 .32024 m .00375 .32024 L s P p .001 w 0 .34687 m .00375 .34687 L s P p .001 w 0 .36019 m .00375 .36019 L s P p .001 w 0 .3735 m .00375 .3735 L s P p .001 w 0 .38682 m .00375 .38682 L s P p .001 w 0 .41345 m .00375 .41345 L s P p .001 w 0 .42676 m .00375 .42676 L s P p .001 w 0 .44008 m .00375 .44008 L s P p .001 w 0 .4534 m .00375 .4534 L s P p .001 w 0 .48003 m .00375 .48003 L s P p .001 w 0 .49334 m .00375 .49334 L s P p .002 w 0 0 m 0 .50067 L s P P p p .002 w .00067 .49442 m .00067 .50067 L s P p .002 w .16711 .49442 m .16711 .50067 L s P p .002 w .33356 .49442 m .33356 .50067 L s P p .002 w .5 .49442 m .5 .50067 L s P p .002 w .66644 .49442 m .66644 .50067 L s P p .002 w .83289 .49442 m .83289 .50067 L s P p .002 w .99933 .49442 m .99933 .50067 L s P p .001 w .03395 .49692 m .03395 .50067 L s P p .001 w .06724 .49692 m .06724 .50067 L s P p .001 w .10053 .49692 m .10053 .50067 L s P p .001 w .13382 .49692 m .13382 .50067 L s P p .001 w .2004 .49692 m .2004 .50067 L s P p .001 w .23369 .49692 m .23369 .50067 L s P p .001 w .26698 .49692 m .26698 .50067 L s P p .001 w .30027 .49692 m .30027 .50067 L s P p .001 w .36684 .49692 m .36684 .50067 L s P p .001 w .40013 .49692 m .40013 .50067 L s P p .001 w .43342 .49692 m .43342 .50067 L s P p .001 w .46671 .49692 m .46671 .50067 L s P p .001 w .53329 .49692 m .53329 .50067 L s P p .001 w .56658 .49692 m .56658 .50067 L s P p .001 w .59987 .49692 m .59987 .50067 L s P p .001 w .63316 .49692 m .63316 .50067 L s P p .001 w .69973 .49692 m .69973 .50067 L s P p .001 w .73302 .49692 m .73302 .50067 L s P p .001 w .76631 .49692 m .76631 .50067 L s P p .001 w .7996 .49692 m .7996 .50067 L s P p .001 w .86618 .49692 m .86618 .50067 L s P p .001 w .89947 .49692 m .89947 .50067 L s P p .001 w .93276 .49692 m .93276 .50067 L s P p .001 w .96605 .49692 m .96605 .50067 L s P p .002 w 0 .50067 m 1 .50067 L s P p .002 w .99375 .00067 m 1 .00067 L s P p .002 w .99375 .06724 m 1 .06724 L s P p .002 w .99375 .13382 m 1 .13382 L s P p .002 w .99375 .2004 m 1 .2004 L s P p .002 w .99375 .26698 m 1 .26698 L s P p .002 w .99375 .33356 m 1 .33356 L s P p .002 w .99375 .40013 m 1 .40013 L s P p .002 w .99375 .46671 m 1 .46671 L s P p .001 w .99625 .01398 m 1 .01398 L s P p .001 w .99625 .0273 m 1 .0273 L s P p .001 w .99625 .04061 m 1 .04061 L s P p .001 w .99625 .05393 m 1 .05393 L s P p .001 w .99625 .08056 m 1 .08056 L s P p .001 w .99625 .09387 m 1 .09387 L s P p .001 w .99625 .10719 m 1 .10719 L s P p .001 w .99625 .12051 m 1 .12051 L s P p .001 w .99625 .14714 m 1 .14714 L s P p .001 w .99625 .16045 m 1 .16045 L s P p .001 w .99625 .17377 m 1 .17377 L s P p .001 w .99625 .18708 m 1 .18708 L s P p .001 w .99625 .21372 m 1 .21372 L s P p .001 w .99625 .22703 m 1 .22703 L s P p .001 w .99625 .24035 m 1 .24035 L s P p .001 w .99625 .25366 m 1 .25366 L s P p .001 w .99625 .28029 m 1 .28029 L s P p .001 w .99625 .29361 m 1 .29361 L s P p .001 w .99625 .30692 m 1 .30692 L s P p .001 w .99625 .32024 m 1 .32024 L s P p .001 w .99625 .34687 m 1 .34687 L s P p .001 w .99625 .36019 m 1 .36019 L s P p .001 w .99625 .3735 m 1 .3735 L s P p .001 w .99625 .38682 m 1 .38682 L s P p .001 w .99625 .41345 m 1 .41345 L s P p .001 w .99625 .42676 m 1 .42676 L s P p .001 w .99625 .44008 m 1 .44008 L s P p .001 w .99625 .4534 m 1 .4534 L s P p .001 w .99625 .48003 m 1 .48003 L s P p .001 w .99625 .49334 m 1 .49334 L s P p .002 w 1 0 m 1 .50067 L s P P p P 0 0 m 1 0 L 1 .50067 L 0 .50067 L closepath clip newpath p p 1 1 0 r p .04 w .33356 .33356 Mdot .33356 .33356 Mdot .33356 .33356 Mdot .33356 .33356 Mdot .33356 .33356 Mdot .5 .33356 Mdot .33356 .5 Mdot .33356 .5 Mdot P P .004 w .5 .33356 m .33356 .5 L .33356 .33356 L .5 .33356 L s P % End of Graphics MathPictureEnd :[font = text; inactive; preserveAspect] This plots the harmonic centre with different grid sizes, and reports their coordinates. Parameters are: minimum grid size, maximum grid size, step. :[font = input; Cclosed; preserveAspect; startGroup] StudyHarmonic[50,200,50]; :[font = print; inactive; preserveAspect] Side-Harmonic Centre = {{50, {3545., 4197.}}, {100, {3545., 4247.}}, {150, {3495., 4197.}}, {200, {3545., 4247.}}} :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 282; pictureHeight = 141; endGroup; endGroup] %! %%Creator: Mathematica %%AspectRatio: .50196 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations -6.55882 0.00196078 -7.93529 0.00196078 [ [(3400)] .10784 0 0 2 Msboxa [(3500)] .30392 0 0 2 Msboxa [(3600)] .5 0 0 2 Msboxa [(3700)] .69608 0 0 2 Msboxa [(3800)] .89216 0 0 2 Msboxa [(4050)] -0.0125 .00588 1 0 Msboxa [(4100)] -0.0125 .10392 1 0 Msboxa [(4150)] -0.0125 .20196 1 0 Msboxa [(4200)] -0.0125 .3 1 0 Msboxa [(4250)] -0.0125 .39804 1 0 Msboxa [(4300)] -0.0125 .49608 1 0 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 .50296 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p p .002 w .10784 0 m .10784 .00625 L s P [(3400)] .10784 0 0 2 Mshowa p .002 w .30392 0 m .30392 .00625 L s P [(3500)] .30392 0 0 2 Mshowa p .002 w .5 0 m .5 .00625 L s P [(3600)] .5 0 0 2 Mshowa p .002 w .69608 0 m .69608 .00625 L s P [(3700)] .69608 0 0 2 Mshowa p .002 w .89216 0 m .89216 .00625 L s P [(3800)] .89216 0 0 2 Mshowa p .001 w .14706 0 m .14706 .00375 L s P p .001 w .18627 0 m .18627 .00375 L s P p .001 w .22549 0 m .22549 .00375 L s P p .001 w .26471 0 m .26471 .00375 L s P p .001 w .34314 0 m .34314 .00375 L s P p .001 w .38235 0 m .38235 .00375 L s P p .001 w .42157 0 m .42157 .00375 L s P p .001 w .46078 0 m .46078 .00375 L s P p .001 w .53922 0 m .53922 .00375 L s P p .001 w .57843 0 m .57843 .00375 L s P p .001 w .61765 0 m .61765 .00375 L s P p .001 w .65686 0 m .65686 .00375 L s P p .001 w .73529 0 m .73529 .00375 L s P p .001 w .77451 0 m .77451 .00375 L s P p .001 w .81373 0 m .81373 .00375 L s P p .001 w .85294 0 m .85294 .00375 L s P p .001 w .06863 0 m .06863 .00375 L s P p .001 w .02941 0 m .02941 .00375 L s P p .001 w .93137 0 m .93137 .00375 L s P p .001 w .97059 0 m .97059 .00375 L s P p .002 w 0 0 m 1 0 L s P p .002 w 0 .00588 m .00625 .00588 L s P [(4050)] -0.0125 .00588 1 0 Mshowa p .002 w 0 .10392 m .00625 .10392 L s P [(4100)] -0.0125 .10392 1 0 Mshowa p .002 w 0 .20196 m .00625 .20196 L s P [(4150)] -0.0125 .20196 1 0 Mshowa p .002 w 0 .3 m .00625 .3 L s P [(4200)] -0.0125 .3 1 0 Mshowa p .002 w 0 .39804 m .00625 .39804 L s P [(4250)] -0.0125 .39804 1 0 Mshowa p .002 w 0 .49608 m .00625 .49608 L s P [(4300)] -0.0125 .49608 1 0 Mshowa p .001 w 0 .02549 m .00375 .02549 L s P p .001 w 0 .0451 m .00375 .0451 L s P p .001 w 0 .06471 m .00375 .06471 L s P p .001 w 0 .08431 m .00375 .08431 L s P p .001 w 0 .12353 m .00375 .12353 L s P p .001 w 0 .14314 m .00375 .14314 L s P p .001 w 0 .16275 m .00375 .16275 L s P p .001 w 0 .18235 m .00375 .18235 L s P p .001 w 0 .22157 m .00375 .22157 L s P p .001 w 0 .24118 m .00375 .24118 L s P p .001 w 0 .26078 m .00375 .26078 L s P p .001 w 0 .28039 m .00375 .28039 L s P p .001 w 0 .31961 m .00375 .31961 L s P p .001 w 0 .33922 m .00375 .33922 L s P p .001 w 0 .35882 m .00375 .35882 L s P p .001 w 0 .37843 m .00375 .37843 L s P p .001 w 0 .41765 m .00375 .41765 L s P p .001 w 0 .43725 m .00375 .43725 L s P p .001 w 0 .45686 m .00375 .45686 L s P p .001 w 0 .47647 m .00375 .47647 L s P p .002 w 0 0 m 0 .50196 L s P P p p .002 w .10784 .49571 m .10784 .50196 L s P p .002 w .30392 .49571 m .30392 .50196 L s P p .002 w .5 .49571 m .5 .50196 L s P p .002 w .69608 .49571 m .69608 .50196 L s P p .002 w .89216 .49571 m .89216 .50196 L s P p .001 w .14706 .49821 m .14706 .50196 L s P p .001 w .18627 .49821 m .18627 .50196 L s P p .001 w .22549 .49821 m .22549 .50196 L s P p .001 w .26471 .49821 m .26471 .50196 L s P p .001 w .34314 .49821 m .34314 .50196 L s P p .001 w .38235 .49821 m .38235 .50196 L s P p .001 w .42157 .49821 m .42157 .50196 L s P p .001 w .46078 .49821 m .46078 .50196 L s P p .001 w .53922 .49821 m .53922 .50196 L s P p .001 w .57843 .49821 m .57843 .50196 L s P p .001 w .61765 .49821 m .61765 .50196 L s P p .001 w .65686 .49821 m .65686 .50196 L s P p .001 w .73529 .49821 m .73529 .50196 L s P p .001 w .77451 .49821 m .77451 .50196 L s P p .001 w .81373 .49821 m .81373 .50196 L s P p .001 w .85294 .49821 m .85294 .50196 L s P p .001 w .06863 .49821 m .06863 .50196 L s P p .001 w .02941 .49821 m .02941 .50196 L s P p .001 w .93137 .49821 m .93137 .50196 L s P p .001 w .97059 .49821 m .97059 .50196 L s P p .002 w 0 .50196 m 1 .50196 L s P p .002 w .99375 .00588 m 1 .00588 L s P p .002 w .99375 .10392 m 1 .10392 L s P p .002 w .99375 .20196 m 1 .20196 L s P p .002 w .99375 .3 m 1 .3 L s P p .002 w .99375 .39804 m 1 .39804 L s P p .002 w .99375 .49608 m 1 .49608 L s P p .001 w .99625 .02549 m 1 .02549 L s P p .001 w .99625 .0451 m 1 .0451 L s P p .001 w .99625 .06471 m 1 .06471 L s P p .001 w .99625 .08431 m 1 .08431 L s P p .001 w .99625 .12353 m 1 .12353 L s P p .001 w .99625 .14314 m 1 .14314 L s P p .001 w .99625 .16275 m 1 .16275 L s P p .001 w .99625 .18235 m 1 .18235 L s P p .001 w .99625 .22157 m 1 .22157 L s P p .001 w .99625 .24118 m 1 .24118 L s P p .001 w .99625 .26078 m 1 .26078 L s P p .001 w .99625 .28039 m 1 .28039 L s P p .001 w .99625 .31961 m 1 .31961 L s P p .001 w .99625 .33922 m 1 .33922 L s P p .001 w .99625 .35882 m 1 .35882 L s P p .001 w .99625 .37843 m 1 .37843 L s P p .001 w .99625 .41765 m 1 .41765 L s P p .001 w .99625 .43725 m 1 .43725 L s P p .001 w .99625 .45686 m 1 .45686 L s P p .001 w .99625 .47647 m 1 .47647 L s P p .002 w 1 0 m 1 .50196 L s P P p P 0 0 m 1 0 L 1 .50196 L 0 .50196 L closepath clip newpath p p .035 w .39216 .29412 Mdot .39216 .39216 Mdot .29412 .29412 Mdot .39216 .39216 Mdot P P % End of Graphics MathPictureEnd :[font = section; inactive; Cclosed; preserveAspect; startGroup] Voronoi :[font = text; inactive; preserveAspect] The only parameter is the choosen percentage of inclusion. This can be different to the real %, due to the geometry of tiles (especially with few locations. :[font = input; Cclosed; preserveAspect; startGroup] Voronoi[{95}]; :[font = print; inactive; preserveAspect] Real %: 53 :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 282; pictureHeight = 225; endGroup; endGroup] %! %%Creator: Mathematica %%AspectRatio: .8 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations -4.13492 0.00126984 -4.64762 0.00126984 [ [(3300)] .05556 0 0 2 Msboxa [(3400)] .18254 0 0 2 Msboxa [(3500)] .30952 0 0 2 Msboxa [(3600)] .43651 0 0 2 Msboxa [(3700)] .56349 0 0 2 Msboxa [(3800)] .69048 0 0 2 Msboxa [(3900)] .81746 0 0 2 Msboxa [(4000)] .94444 0 0 2 Msboxa [(3700)] -0.0125 .05079 1 0 Msboxa [(3800)] -0.0125 .17778 1 0 Msboxa [(3900)] -0.0125 .30476 1 0 Msboxa [(4000)] -0.0125 .43175 1 0 Msboxa [(4100)] -0.0125 .55873 1 0 Msboxa [(4200)] -0.0125 .68571 1 0 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 .801 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p p .002 w .05556 0 m .05556 .00625 L s P [(3300)] .05556 0 0 2 Mshowa p .002 w .18254 0 m .18254 .00625 L s P [(3400)] .18254 0 0 2 Mshowa p .002 w .30952 0 m .30952 .00625 L s P [(3500)] .30952 0 0 2 Mshowa p .002 w .43651 0 m .43651 .00625 L s P [(3600)] .43651 0 0 2 Mshowa p .002 w .56349 0 m .56349 .00625 L s P [(3700)] .56349 0 0 2 Mshowa p .002 w .69048 0 m .69048 .00625 L s P [(3800)] .69048 0 0 2 Mshowa p .002 w .81746 0 m .81746 .00625 L s P [(3900)] .81746 0 0 2 Mshowa p .002 w .94444 0 m .94444 .00625 L s P [(4000)] .94444 0 0 2 Mshowa p .001 w .08095 0 m .08095 .00375 L s P p .001 w .10635 0 m .10635 .00375 L s P p .001 w .13175 0 m .13175 .00375 L s P p .001 w .15714 0 m .15714 .00375 L s P p .001 w .20794 0 m .20794 .00375 L s P p .001 w .23333 0 m .23333 .00375 L s P p .001 w .25873 0 m .25873 .00375 L s P p .001 w .28413 0 m .28413 .00375 L s P p .001 w .33492 0 m .33492 .00375 L s P p .001 w .36032 0 m .36032 .00375 L s P p .001 w .38571 0 m .38571 .00375 L s P p .001 w .41111 0 m .41111 .00375 L s P p .001 w .4619 0 m .4619 .00375 L s P p .001 w .4873 0 m .4873 .00375 L s P p .001 w .5127 0 m .5127 .00375 L s P p .001 w .5381 0 m .5381 .00375 L s P p .001 w .58889 0 m .58889 .00375 L s P p .001 w .61429 0 m .61429 .00375 L s P p .001 w .63968 0 m .63968 .00375 L s P p .001 w .66508 0 m .66508 .00375 L s P p .001 w .71587 0 m .71587 .00375 L s P p .001 w .74127 0 m .74127 .00375 L s P p .001 w .76667 0 m .76667 .00375 L s P p .001 w .79206 0 m .79206 .00375 L s P p .001 w .84286 0 m .84286 .00375 L s P p .001 w .86825 0 m .86825 .00375 L s P p .001 w .89365 0 m .89365 .00375 L s P p .001 w .91905 0 m .91905 .00375 L s P p .001 w .03016 0 m .03016 .00375 L s P p .001 w .00476 0 m .00476 .00375 L s P p .001 w .96984 0 m .96984 .00375 L s P p .001 w .99524 0 m .99524 .00375 L s P p .002 w 0 0 m 1 0 L s P p .002 w 0 .05079 m .00625 .05079 L s P [(3700)] -0.0125 .05079 1 0 Mshowa p .002 w 0 .17778 m .00625 .17778 L s P [(3800)] -0.0125 .17778 1 0 Mshowa p .002 w 0 .30476 m .00625 .30476 L s P [(3900)] -0.0125 .30476 1 0 Mshowa p .002 w 0 .43175 m .00625 .43175 L s P [(4000)] -0.0125 .43175 1 0 Mshowa p .002 w 0 .55873 m .00625 .55873 L s P [(4100)] -0.0125 .55873 1 0 Mshowa p .002 w 0 .68571 m .00625 .68571 L s P [(4200)] -0.0125 .68571 1 0 Mshowa p .001 w 0 .07619 m .00375 .07619 L s P p .001 w 0 .10159 m .00375 .10159 L s P p .001 w 0 .12698 m .00375 .12698 L s P p .001 w 0 .15238 m .00375 .15238 L s P p .001 w 0 .20317 m .00375 .20317 L s P p .001 w 0 .22857 m .00375 .22857 L s P p .001 w 0 .25397 m .00375 .25397 L s P p .001 w 0 .27937 m .00375 .27937 L s P p .001 w 0 .33016 m .00375 .33016 L s P p .001 w 0 .35556 m .00375 .35556 L s P p .001 w 0 .38095 m .00375 .38095 L s P p .001 w 0 .40635 m .00375 .40635 L s P p .001 w 0 .45714 m .00375 .45714 L s P p .001 w 0 .48254 m .00375 .48254 L s P p .001 w 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.23333 .79625 m .23333 .8 L s P p .001 w .25873 .79625 m .25873 .8 L s P p .001 w .28413 .79625 m .28413 .8 L s P p .001 w .33492 .79625 m .33492 .8 L s P p .001 w .36032 .79625 m .36032 .8 L s P p .001 w .38571 .79625 m .38571 .8 L s P p .001 w .41111 .79625 m .41111 .8 L s P p .001 w .4619 .79625 m .4619 .8 L s P p .001 w .4873 .79625 m .4873 .8 L s P p .001 w .5127 .79625 m .5127 .8 L s P p .001 w .5381 .79625 m .5381 .8 L s P p .001 w .58889 .79625 m .58889 .8 L s P p .001 w .61429 .79625 m .61429 .8 L s P p .001 w .63968 .79625 m .63968 .8 L s P p .001 w .66508 .79625 m .66508 .8 L s P p .001 w .71587 .79625 m .71587 .8 L s P p .001 w .74127 .79625 m .74127 .8 L s P p .001 w .76667 .79625 m .76667 .8 L s P p .001 w .79206 .79625 m .79206 .8 L s P p .001 w .84286 .79625 m .84286 .8 L s P p .001 w .86825 .79625 m .86825 .8 L s P p .001 w .89365 .79625 m .89365 .8 L s P p .001 w .91905 .79625 m .91905 .8 L s P p .001 w .03016 .79625 m .03016 .8 L s P p .001 w .00476 .79625 m .00476 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Cclosed; preserveAspect; startGroup] Kernel :[font = subsection; inactive; Cclosed; preserveAspect; startGroup] Initialization (to run before Kernel analyses) ;[s] 3:0,0;14,1;46,0;47,-1; 2:2,16,12,Times,1,14,0,0,0;1,16,12,Times,0,14,0,0,0; :[font = subsubsection; inactive; Cclosed; preserveAspect; startGroup] Practical choice of smoothing factor h with Reference Method :[font = input; preserveAspect; endGroup] Clear[ReferenceMethod]; ReferenceMethod := Module[ {sigmaqx,sigmaqy,sigma,href}, {sigmaqx,sigmaqy}=Map[Variance,Transpose[data]]; sigma=Sqrt[(sigmaqx + sigmaqy)/2]; href=sigma*(n^(-1/6))]; :[font = subsubsection; inactive; Cclosed; preserveAspect; startGroup] Practical choice of smoothing factor h with Least Square Cross-Validation Method :[font = input; preserveAspect; endGroup] Clear[CrossValidationMethod]; CrossValidationMethod := Module[ {href,hcv,CV,diff}, diff=Map[(#.#)&,Flatten[Table[(data[[i]]-data[[j]]), {i,2,n},{j,1,i-1}], 1]]; CV=Compile[{loc},Evaluate[(2 Apply[Plus, Exp[-diff/(4loc^2)] -4Exp[-diff/(2loc^2)] ] -3n)/ (4Pi loc^2 n^2) + 1/(Pi n loc^2)]]; (*Plot[CV[x],{x,0.001,10}];*) href=ReferenceMethod; Sort[Table[{CV[ii href],ii href},{ii,0.2,1.4,0.2}]][[1,2]] //N]; ;[s] 3:0,0;308,1;337,0;432,-1; 2:2,7,10,Courier,1,12,0,0,0;1,7,10,Courier,0,12,0,0,0; :[font = subsubsection; inactive; Cclosed; preserveAspect; startGroup] Definition of kernel function (Standard Normal Bivariate) :[font = input; preserveAspect; endGroup] K[{x0_,y0_}]:=Exp[-{x0,y0}.{x0,y0}/2]/(2Pi); :[font = subsubsection; inactive; Cclosed; preserveAspect; startGroup] Fixed Kernel :[font = input; preserveAspect; endGroup] Clear[FixedKernel]; FixedKernel[Ker_,acca_] := Compile[{x,y},Evaluate[ 1/(n acca^2)*(Map[Ker[({x,y}-#)/acca]&, distinctdata].fr)]]; :[font = subsubsection; inactive; Cclosed; preserveAspect; startGroup] Adaptive Kernel (It requires the execution of the Fixed Kernel) ;[s] 4:0,0;16,1;50,0;62,1;64,-1; 2:2,13,9,Times,1,12,0,0,0;2,13,9,Times,0,12,0,0,0; :[font = input; preserveAspect; endGroup] Clear[AdaptiveKernel]; AdaptiveKernel[Ker1_,acca1_] := Module[ {g,ffix,lambda,H}, ffix=FixedKernel[Ker1,acca1]; g=Exp[1/n Plus@@(Log[MapThread[ffix,Transpose[data]]])]; lambda=(MapThread[ffix,Transpose[distinctdata]]/g)^(-1/2); (* H = list containing a smoothing parameter for each distinct sample *) H=acca1 lambda; Compile[{x,y},Evaluate[ 1/n*Plus@@(Map[Ker1,Map[({x,y}-#)&,distinctdata]/H]* fr/(H^2))]]]; :[font = subsubsection; inactive; Cclosed; preserveAspect; startGroup] Definitions for plots & calculations :[font = input; preserveAspect; endGroup; endGroup] Clear[KernelMethod]; KernelMethod[funz_,Delta_,perc_] := Module[ {areabase,fv,fv1,fv2,fv3,xv,yv, psi,cp,lp,areahr,s,g,diff,out,UM}, areabase=Delta^2; (* fv = list volumes for integration *) fv=Flatten[Table[funz[x,y] areabase, {x,x1,x2,Delta},{y,y1,y2,Delta}],1]; (* sort of volumes from larger to smaller *) fv1=Reverse[Sort[fv]]; Plot3D[funz[x,y],{x,x1,x2},{y,y1,y2}, PlotPoints->40, BoxRatios->{1,1,0.6}, PlotLabel->"Density function", PlotRange->{{x1,x2},{y1,y2},{0,fv1[[1]]/areabase}}]; (* partial sum of all volumes *) fv2=Rest[FoldList[Plus,0,fv1]]; Print[ "Estimated integral of f= ", Last[fv2] ]; cp=s=g={0,0,0,0}; (* selection of all points necessaries to reach the required percentage *) Do [fv3=Select[fv2,( #<(perc[[i]]/100) )&]; If[fv3=={},Print[perc[[i]],"% area = 0"];Continue[]]; (* volumes are sorted from larger and sums are executed in series; therefore, the last element used in fv3 is the height psi for cuttting the function f to obtain the required percentage. The value of f in this point is taken from the correspondent fv1 *) psi=fv1[[Length[fv3]]]/areabase; cp=ContourPlot[funz[x,y],{x,x1,x2},{y,y1,y2}, Contours->{psi}, ContourShading->False, PlotPoints->25, DisplayFunction->Identity]; lp=Graphics[{Red,PointSize[0.01],Point/@data}]; {out,UM}=ConvertMeasureUnit[N[Length[fv3] areabase]]; s=ToString[perc[[i]]]<>"%:"<>ToString[out]<>" "<>UM; plotKernel[perc[[i]]]=Show[lp,cp,DisplayFunction-> $DisplayFunction,PlotLabel->s,PlotRange->All, Frame->True],{i,1,Length[perc]}];]; ;[s] 11:0,0;156,1;195,0;293,1;337,0;551,1;583,0;685,1;761,0;869,1;1143,0;1676,-1; 2:6,12,10,Courier,1,12,0,0,0;5,12,10,Courier,0,12,0,0,0; :[font = subsection; inactive; Cclosed; preserveAspect; startGroup] Description :[font = text; inactive; preserveAspect; endGroup] Unlike other programs, it is possible to choose kernel functions (or define new ones) and smoothing factors (optimal calculated h or user-defined); ¥ first parameter: method (fixed or adaptive kernel) ¥ second: choice of the smoothing factor (reference, least-square crossvalidation, or chosed by the user) ¥ third: integration grid (in meters; we suggest to set it to 1/10 of minimum distance between distinct locations; see Basic statistics); if the estimated integral of f is outside the range 0.95-1.05, we suggest to re-run the analysis with a finer integration grid (and therefore with higher computation times) ¥ fourth: chosen percentages of locations to be included in the range (0-100). After the analysis, each plot can be recalled with the command Show[plotKernel[95],PlotRange->All]; (asking the desired percentage of inclusion as a parameter; in this case, 95) ;[s] 5:0,0;426,1;442,0;761,2;798,0;876,-1; 3:3,13,9,Times,0,12,0,0,0;1,16,12,Times,1,14,0,0,0;1,13,10,Courier,1,12,0,0,0; :[font = subsection; inactive; Cclosed; preserveAspect; startGroup] Examples :[font = input; Cclosed; preserveAspect; startGroup] KernelMethod[FixedKernel[K,ReferenceMethod],5,{95}] :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 282; pictureHeight = 257] %! %%Creator: Mathematica %%AspectRatio: .91155 MathPictureStart %% SurfaceGraphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.0249562 0.998249 0.00368239 0.998249 [ [(Density function)] .5 .91155 0 -1.5 Msboxa [(3400)] .12604 .23259 .99508 1 Msboxa [(3600)] .34958 .14242 .83867 1 Msboxa [(3800)] .5953 .0434 .68225 1 Msboxa [(4100)] .74855 .11903 -1 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.45871 .87464 .45138 .86917 .44444 Metetra .734 .797 .902 r .86917 .44444 .87464 .45138 .88879 .44484 .88332 .43726 Metetra .709 .772 .901 r .88332 .43726 .88879 .44484 .9031 .43906 .89764 .43107 Metetra .689 .754 .901 r .89764 .43107 .9031 .43906 .91755 .43387 .91212 .42563 Metetra .678 .744 .901 r .91212 .42563 .91755 .43387 .93212 .42902 .92674 .42065 Metetra .653 .734 .909 r .39968 .57575 .40693 .58268 .41902 .57929 .41181 .57243 Metetra .634 .731 .918 r .41181 .57243 .41902 .57929 .43117 .57633 .42398 .56964 Metetra .6 .727 .934 r .42398 .56964 .43117 .57633 .44335 .57406 .43619 .56771 Metetra .545 .72 .954 r .43619 .56771 .44335 .57406 .45559 .57266 .44845 .56687 Metetra .474 .712 .973 r .44845 .56687 .45559 .57266 .4679 .57203 .46078 .567 Metetra .414 .714 .985 r .46078 .567 .4679 .57203 .48029 .57169 .47319 .56752 Metetra .408 .743 .993 r .47319 .56752 .48029 .57169 .49277 .57092 .4857 .56753 Metetra .454 .793 .999 r .4857 .56753 .49277 .57092 .50534 .56922 .49832 .56642 Metetra .477 .824 .998 r .49832 .56642 .50534 .56922 .51799 .56688 .51103 .56457 Metetra .354 .782 .972 r .51103 .56457 .51799 .56688 .53072 .56524 .52381 .56368 Metetra 0 .483 .73 r .52381 .56368 .53072 .56524 .54355 .5662 .5367 .5661 Metetra .586 .018 0 r .5367 .5661 .54355 .5662 .55652 .57106 .54975 .57348 Metetra .729 .25 .108 r .54975 .57348 .55652 .57106 .56968 .57928 .56301 .58513 Metetra .725 .295 .227 r .56301 .58513 .56968 .57928 .58302 .58795 .57648 .59736 Metetra .639 .23 .252 r .57648 .59736 .58302 .58795 .59644 .59272 .59006 .6046 Metetra .427 .034 .189 r .59006 .6046 .59644 .59272 .6098 .58992 .60355 .60214 Metetra .60355 .60214 .6098 .58992 .62298 .57873 .61681 .58892 Metetra .61681 .58892 .62298 .57873 .63594 .5616 .6298 .56814 Metetra .866 .947 .588 r .6298 .56814 .63594 .5616 .6488 .54273 .64264 .54518 Metetra .933 .969 .728 r .64264 .54518 .6488 .54273 .66168 .52589 .65549 .52483 Metetra .898 .943 .829 r .65549 .52483 .66168 .52589 .67472 .5131 .66852 .50964 Metetra .807 .896 .906 r .66852 .50964 .67472 .5131 .68798 .50465 .68179 .49994 Metetra .683 .839 .958 r .68179 .49994 .68798 .50465 .70149 .49985 .69535 .49483 Metetra .548 .783 .986 r .69535 .49483 .70149 .49985 .71523 .49764 .70916 .49296 Metetra .424 .74 .992 r .70916 .49296 .71523 .49764 .72915 .49694 .7232 .49298 Metetra .34 .723 .984 r .7232 .49298 .72915 .49694 .74322 .49669 .73738 .49357 Metetra .324 .744 .976 r .73738 .49357 .74322 .49669 .75735 .49594 .75165 .49356 Metetra .378 .799 .973 r .75165 .49356 .75735 .49594 .7715 .49401 .76591 .49211 Metetra .482 .868 .974 r .76591 .49211 .7715 .49401 .78561 .49053 .78011 .48875 Metetra .604 .923 .97 r .78011 .48875 .78561 .49053 .79965 .48536 .79422 .48331 Metetra .709 .948 .955 r .79422 .48331 .79965 .48536 .81361 .47855 .8082 .47585 Metetra .777 .942 .933 r .8082 .47585 .81361 .47855 .82748 .47041 .82207 .46674 Metetra .806 .915 .913 r .82207 .46674 .82748 .47041 .84132 .46152 .83587 .45671 Metetra .804 .878 .901 r .83587 .45671 .84132 .46152 .85519 .45264 .8497 .4467 Metetra .781 .84 .897 r .8497 .4467 .85519 .45264 .86917 .44444 .86366 .43754 Metetra .749 .805 .897 r .86366 .43754 .86917 .44444 .88332 .43726 .87779 .42966 Metetra .718 .777 .899 r .87779 .42966 .88332 .43726 .89764 .43107 .89213 .42303 Metetra .695 .757 .9 r .89213 .42303 .89764 .43107 .91212 .42563 .90665 .41733 Metetra .68 .745 .901 r .90665 .41733 .91212 .42563 .92674 .42065 .92131 .4122 Metetra .65 .733 .91 r .39237 .56877 .39968 .57575 .41181 .57243 .40452 .56551 Metetra .627 .729 .921 r .40452 .56551 .41181 .57243 .42398 .56964 .41672 .56289 Metetra .584 .722 .938 r .41672 .56289 .42398 .56964 .43619 .56771 .42896 .56132 Metetra .512 .708 .96 r .42896 .56132 .43619 .56771 .44845 .56687 .44124 .56107 Metetra .415 .688 .975 r .44124 .56107 .44845 .56687 .46078 .567 .45358 .562 Metetra .332 .677 .978 r .45358 .562 .46078 .567 .47319 .56752 .46601 .56343 Metetra .322 .706 .981 r .46601 .56343 .47319 .56752 .4857 .56753 .47855 .56429 Metetra .381 .766 .99 r .47855 .56429 .4857 .56753 .49832 .56642 .49122 .56386 Metetra .404 .8 .986 r .49122 .56386 .49832 .56642 .51103 .56457 .50397 .56264 Metetra .217 .712 .918 r .50397 .56264 .51103 .56457 .52381 .56368 .51681 .56266 Metetra .331 0 0 r .51681 .56266 .52381 .56368 .5367 .5661 .52976 .56682 Metetra .696 .177 0 r .52976 .56682 .5367 .5661 .54975 .57348 .54288 .5771 Metetra .775 .337 .21 r .54288 .5771 .54975 .57348 .56301 .58513 .55624 .59265 Metetra .758 .358 .294 r .55624 .59265 .56301 .58513 .57648 .59736 .56984 .60893 Metetra .672 .288 .31 r .56984 .60893 .57648 .59736 .59006 .6046 .58357 .61898 Metetra .462 .092 .25 r .58357 .61898 .59006 .6046 .60355 .60214 .59721 .61692 Metetra 0 0 .04 r .59721 .61692 .60355 .60214 .61681 .58892 .61057 .60144 Metetra .61057 .60144 .61681 .58892 .6298 .56814 .62361 .57656 Metetra .876 .921 .527 r .62361 .57656 .6298 .56814 .64264 .54518 .63644 .54903 Metetra .949 .955 .671 r .63644 .54903 .64264 .54518 .65549 .52483 .64926 .52479 Metetra .925 .95 .789 r .64926 .52479 .65549 .52483 .66852 .50964 .66227 .50692 Metetra .835 .919 .891 r .66227 .50692 .66852 .50964 .68179 .49994 .67556 .4958 Metetra .691 .862 .964 r .67556 .4958 .68179 .49994 .69535 .49483 .68916 .49027 Metetra .515 .788 .995 r .68916 .49027 .69535 .49483 .70916 .49296 .70306 .48869 Metetra .35 .718 .986 r .70306 .48869 .70916 .49296 .7232 .49298 .7172 .48938 Metetra .245 .68 .96 r .7172 .48938 .7232 .49298 .73738 .49357 .7315 .49076 Metetra .233 .7 .945 r .7315 .49076 .73738 .49357 .75165 .49356 .74588 .49146 Metetra .313 .771 .95 r .74588 .49146 .75165 .49356 .76591 .49211 .76026 .49046 Metetra .453 .86 .962 r .76026 .49046 .76591 .49211 .78011 .48875 .77455 .4872 Metetra .605 .93 .963 r .77455 .4872 .78011 .48875 .79422 .48331 .78872 .48146 Metetra .727 .958 .945 r .78872 .48146 .79422 .48331 .8082 .47585 .80274 .47331 Metetra .801 .949 .918 r .80274 .47331 .8082 .47585 .82207 .46674 .8166 .46318 Metetra .83 .92 .896 r .8166 .46318 .82207 .46674 .83587 .45671 .83038 .45195 Metetra .825 .884 .886 r .83038 .45195 .83587 .45671 .8497 .4467 .84417 .44077 Metetra .799 .846 .886 r .84417 .44077 .8497 .4467 .86366 .43754 .85809 .43062 Metetra .763 .81 .89 r .85809 .43062 .86366 .43754 .87779 .42966 .87222 .42201 Metetra .728 .781 .895 r .87222 .42201 .87779 .42966 .89213 .42303 .88657 .41492 Metetra .7 .759 .898 r .88657 .41492 .89213 .42303 .90665 .41733 .90112 .40895 Metetra .682 .747 .9 r .90112 .40895 .90665 .41733 .92131 .4122 .91583 .40367 Metetra .647 .732 .911 r .38499 .56172 .39237 .56877 .40452 .56551 .39718 .55852 Metetra .62 .727 .923 r .39718 .55852 .40452 .56551 .41672 .56289 .4094 .55608 Metetra .567 .716 .942 r .4094 .55608 .41672 .56289 .42896 .56132 .42166 .55485 Metetra .478 .693 .962 r .42166 .55485 .42896 .56132 .44124 .56107 .43395 .55517 Metetra .354 .657 .97 r .43395 .55517 .44124 .56107 .45358 .562 .4463 .55691 Metetra .249 .63 .96 r .4463 .55691 .45358 .562 .46601 .56343 .45875 .55925 Metetra .238 .657 .96 r .45875 .55925 .46601 .56343 .47855 .56429 .47132 .56099 Metetra .309 .727 .975 r .47132 .56099 .47855 .56429 .49122 .56386 .48402 .56132 Metetra .326 .761 .969 r .48402 .56132 .49122 .56386 .50397 .56264 .49683 .56084 Metetra .068 .613 .841 r .49683 .56084 .50397 .56264 .51681 .56266 .50972 .56199 Metetra .501 0 0 r .50972 .56199 .51681 .56266 .52976 .56682 .52272 .56815 Metetra .759 .28 .103 r .52272 .56815 .52976 .56682 .54288 .5771 .5359 .58167 Metetra .805 .394 .271 r .5359 .58167 .54288 .5771 .55624 .59265 .54934 .60154 Metetra .782 .401 .335 r .54934 .60154 .55624 .59265 .56984 .60893 .56307 .62225 Metetra .697 .329 .346 r .56307 .62225 .56984 .60893 .58357 .61898 .57695 .63538 Metetra .484 .128 .286 r .57695 .63538 .58357 .61898 .59721 .61692 .59075 .63379 Metetra 0 0 .065 r .59075 .63379 .59721 .61692 .61057 .60144 .60423 .61587 Metetra .60423 .61587 .61057 .60144 .62361 .57656 .61733 .58657 Metetra .896 .902 .492 r .61733 .58657 .62361 .57656 .63644 .54903 .63017 .55413 Metetra .96 .937 .626 r .63017 .55413 .63644 .54903 .64926 .52479 .64298 .5257 Metetra .945 .948 .748 r .64298 .5257 .64926 .52479 .66227 .50692 .65598 .50495 Metetra .861 .937 .871 r .65598 .50495 .66227 .50692 .67556 .4958 .66929 .49227 Metetra .701 .887 .966 r .66929 .49227 .67556 .4958 .68916 .49027 .68293 .4862 Metetra .483 .794 .999 r .68293 .4862 .68916 .49027 .70306 .48869 .6969 .48476 Metetra .279 .691 .971 r .6969 .48476 .70306 .48869 .7172 .48938 .71113 .48599 Metetra .164 .637 .93 r .71113 .48599 .7172 .48938 .7315 .49076 .72555 .48804 Metetra .17 .662 .919 r .72555 .48804 .7315 .49076 .74588 .49146 .74004 .48932 Metetra .282 .752 .942 r .74004 .48932 .74588 .49146 .76026 .49046 .75452 .48869 Metetra .455 .859 .966 r .75452 .48869 .76026 .49046 .77455 .4872 .76891 .48547 Metetra .628 .934 .965 r .76891 .48547 .77455 .4872 .78872 .48146 .78314 .47941 Metetra .755 .958 .937 r .78314 .47941 .78872 .48146 .80274 .47331 .79719 .47056 Metetra .825 .945 .902 r .79719 .47056 .80274 .47331 .8166 .46318 .81105 .45943 Metetra .849 .915 .877 r .81105 .45943 .8166 .46318 .83038 .45195 .8248 .44703 Metetra .842 .881 .869 r .8248 .44703 .83038 .45195 .84417 .44077 .83856 .43469 Metetra .815 .846 .873 r .83856 .43469 .84417 .44077 .85809 .43062 .85246 .42357 Metetra .776 .812 .882 r .85246 .42357 .85809 .43062 .87222 .42201 .86658 .41426 Metetra .736 .783 .89 r .86658 .41426 .87222 .42201 .88657 .41492 .88095 .40671 Metetra .705 .761 .896 r .88095 .40671 .88657 .41492 .90112 .40895 .89553 .40048 Metetra .685 .747 .899 r .89553 .40048 .90112 .40895 .91583 .40367 .91029 .39506 Metetra .644 .731 .912 r .37754 .5546 .38499 .56172 .39718 .55852 .38976 .55145 Metetra .613 .725 .925 r .38976 .55145 .39718 .55852 .4094 .55608 .40201 .54916 Metetra .552 .709 .944 r .40201 .54916 .4094 .55608 .42166 .55485 .41429 .54825 Metetra .446 .677 .962 r .41429 .54825 .42166 .55485 .43395 .55517 .4266 .54909 Metetra .299 .624 .96 r .4266 .54909 .43395 .55517 .4463 .55691 .43896 .55155 Metetra .178 .582 .939 r .43896 .55155 .4463 .55691 .45875 .55925 .45142 .55475 Metetra .168 .606 .938 r .45142 .55475 .45875 .55925 .47132 .56099 .46401 .55736 Metetra .248 .684 .96 r .46401 .55736 .47132 .56099 .48402 .56132 .47674 .55851 Metetra .252 .712 .951 r .47674 .55851 .48402 .56132 .49683 .56084 .48959 .55892 Metetra 0 .5 .758 r .48959 .55892 .49683 .56084 .50972 .56199 .50253 .5614 Metetra .616 .053 0 r .50253 .5614 .50972 .56199 .52272 .56815 .51557 .56983 Metetra .799 .349 .175 r .51557 .56983 .52272 .56815 .5359 .58167 .52879 .58688 Metetra .826 .435 .309 r .52879 .58688 .5359 .58167 .54934 .60154 .54231 .61133 Metetra .801 .434 .361 r .54231 .61133 .54934 .60154 .56307 .62225 .55615 .63674 Metetra .719 .36 .367 r .55615 .63674 .56307 .62225 .57695 .63538 .57019 .65316 Metetra .498 .148 .304 r .57019 .65316 .57695 .63538 .59075 .63379 .58415 .65207 Metetra 0 0 .058 r .58415 .65207 .59075 .63379 .60423 .61587 .59776 .63163 Metetra .7 .777 .292 r .59776 .63163 .60423 .61587 .61733 .58657 .61094 .59775 Metetra .92 .891 .478 r .61094 .59775 .61733 .58657 .63017 .55413 .62381 .56023 Metetra .971 .92 .594 r .62381 .56023 .63017 .55413 .64298 .5257 .63663 .52748 Metetra .959 .94 .711 r .63663 .52748 .64298 .5257 .65598 .50495 .64964 .50375 Metetra .885 .95 .846 r .64964 .50375 .65598 .50495 .66929 .49227 .66296 .48937 Metetra .715 .913 .963 r .66296 .48937 .66929 .49227 .68293 .4862 .67665 .48261 Metetra .459 .802 .999 r .67665 .48261 .68293 .4862 .6969 .48476 .69069 .48112 Metetra .227 .671 .954 r .69069 .48112 .6969 .48476 .71113 .48599 .705 .48264 Metetra .119 .608 .91 r .705 .48264 .71113 .48599 .72555 .48804 .7195 .48511 Metetra .151 .644 .916 r .7195 .48511 .72555 .48804 .74004 .48932 .73409 .48678 Metetra .296 .75 .956 r .73409 .48678 .74004 .48932 .75452 .48869 .74866 .48636 Metetra .492 .863 .984 r .74866 .48636 .75452 .48869 .76891 .48547 .76313 .4831 Metetra .667 .93 .971 r .76313 .4831 .76891 .48547 .78314 .47941 .77742 .47669 Metetra .783 .943 .929 r .77742 .47669 .78314 .47941 .79719 .47056 .79151 .46719 Metetra .843 .926 .886 r .79151 .46719 .79719 .47056 .81105 .45943 .80538 .45514 Metetra .862 .898 .859 r .80538 .45514 .81105 .45943 .8248 .44703 .81912 .44168 Metetra .853 .869 .852 r .81912 .44168 .8248 .44703 .83856 .43469 .83286 .42829 Metetra .825 .84 .859 r .83286 .42829 .83856 .43469 .85246 .42357 .84675 .4163 Metetra .785 .81 .873 r .84675 .4163 .85246 .42357 .86658 .41426 .86087 .40635 Metetra .743 .783 .885 r .86087 .40635 .86658 .41426 .88095 .40671 .87526 .39838 Metetra .709 .762 .893 r .87526 .39838 .88095 .40671 .89553 .40048 .88989 .39191 Metetra .687 .748 .898 r .88989 .39191 .89553 .40048 .91029 .39506 .90469 .38635 Metetra .642 .73 .913 r .37002 .5474 .37754 .5546 .38976 .55145 .38228 .54429 Metetra .608 .722 .926 r .38228 .54429 .38976 .55145 .40201 .54916 .39456 .54211 Metetra .54 .703 .945 r .39456 .54211 .40201 .54916 .41429 .54825 .40686 .54145 Metetra .421 .661 .96 r .40686 .54145 .41429 .54825 .4266 .54909 .41918 .54271 Metetra .259 .594 .949 r .41918 .54271 .4266 .54909 .43896 .55155 .43155 .54578 Metetra .131 .54 .92 r .43155 .54578 .43896 .55155 .45142 .55475 .44402 .54972 Metetra .125 .562 .921 r .44402 .54972 .45142 .55475 .46401 .55736 .45662 .55314 Metetra .205 .64 .95 r .45662 .55314 .46401 .55736 .47674 .55851 .46938 .55514 Metetra .187 .657 .936 r .46938 .55514 .47674 .55851 .48959 .55892 .48226 .5566 Metetra 0 .384 .681 r .48226 .5566 .48959 .55892 .50253 .5614 .49523 .56063 Metetra .694 .159 0 r .49523 .56063 .50253 .5614 .51557 .56983 .50831 .57155 Metetra .828 .399 .22 r .50831 .57155 .51557 .56983 .52879 .58688 .52156 .59232 Metetra .844 .466 .333 r .52156 .59232 .52879 .58688 .54231 .61133 .53513 .6215 Metetra .819 .459 .375 r .53513 .6215 .54231 .61133 .55615 .63674 .54907 .65172 Metetra .74 .384 .378 r .54907 .65172 .55615 .63674 .57019 .65316 .56325 .67149 Metetra .508 .158 .309 r .56325 .67149 .57019 .65316 .58415 .65207 .57737 .67097 Metetra 0 0 .021 r .57737 .67097 .58415 .65207 .59776 .63163 .59114 .64802 Metetra .779 .811 .33 r .59114 .64802 .59776 .63163 .61094 .59775 .60442 .60958 Metetra .946 .884 .479 r .60442 .60958 .61094 .59775 .62381 .56023 .61735 .56702 Metetra .98 .904 .574 r .61735 .56702 .62381 .56023 .63663 .52748 .6302 .53 Metetra .969 .93 .68 r .6302 .53 .63663 .52748 .64964 .50375 .64323 .50326 Metetra .905 .957 .818 r .64323 .50326 .64964 .50375 .66296 .48937 .65659 .4871 Metetra .733 .937 .954 r .65659 .4871 .66296 .48937 .67665 .48261 .67032 .47947 Metetra .452 .815 .995 r .67032 .47947 .67665 .48261 .69069 .48112 .6844 .47766 Metetra .209 .667 .945 r .6844 .47766 .69069 .48112 .705 .48264 .69878 .47915 Metetra .121 .607 .912 r .69878 .47915 .705 .48264 .7195 .48511 .71335 .4817 Metetra .185 .653 .936 r .71335 .4817 .7195 .48511 .73409 .48678 .72801 .48344 Metetra .354 .761 .983 r .72801 .48344 .73409 .48678 .74866 .48636 .74266 .48301 Metetra .55 .858 .997 r .74266 .48301 .74866 .48636 .76313 .4831 .75719 .4796 Metetra .705 .906 .967 r .75719 .4796 .76313 .4831 .77742 .47669 .77154 .47285 Metetra .802 .911 .915 r .77154 .47285 .77742 .47669 .79151 .46719 .78567 .46278 Metetra .85 .895 .869 r .78567 .46278 .79151 .46719 .80538 .45514 .79956 .44996 Metetra .865 .873 .842 r .79956 .44996 .80538 .45514 .81912 .44168 .81331 .43563 Metetra .857 .851 .836 r .81331 .43563 .81912 .44168 .83286 .42829 .82706 .4214 Metetra .83 .829 .846 r .82706 .4214 .83286 .42829 .84675 .4163 .84095 .40868 Metetra .791 .805 .863 r .84095 .40868 .84675 .4163 .86087 .40635 .85509 .3982 Metetra .748 .781 .88 r .85509 .3982 .86087 .40635 .87526 .39838 .86951 .3899 Metetra .712 .761 .891 r .86951 .3899 .87526 .39838 .88989 .39191 .88418 .38322 Metetra .689 .748 .897 r .88418 .38322 .88989 .39191 .90469 .38635 .89904 .37754 Metetra .64 .73 .913 r .36244 .54013 .37002 .5474 .38228 .54429 .37473 .53702 Metetra .604 .72 .926 r .37473 .53702 .38228 .54429 .39456 .54211 .38704 .53491 Metetra .532 .697 .945 r .38704 .53491 .39456 .54211 .40686 .54145 .39936 .53441 Metetra .406 .649 .957 r .39936 .53441 .40686 .54145 .41918 .54271 .41169 .53596 Metetra .239 .572 .94 r .41169 .53596 .41918 .54271 .43155 .54578 .42407 .53945 Metetra .113 .512 .909 r .42407 .53945 .43155 .54578 .44402 .54972 .43655 .54397 Metetra .109 .529 .913 r .43655 .54397 .44402 .54972 .45662 .55314 .44917 .54809 Metetra .181 .598 .942 r .44917 .54809 .45662 .55314 .46938 .55514 .46195 .55096 Metetra .132 .597 .922 r .46195 .55096 .46938 .55514 .48226 .5566 .47485 .55359 Metetra .314 0 0 r .47485 .55359 .48226 .5566 .49523 .56063 .48785 .55938 Metetra .751 .239 0 r .48785 .55938 .49523 .56063 .50831 .57155 .50093 .57299 Metetra .85 .437 .249 r .50093 .57299 .50831 .57155 .52156 .59232 .5142 .59757 Metetra .86 .49 .346 r .5142 .59757 .52156 .59232 .53513 .6215 .5278 .63147 Metetra .836 .481 .383 r .5278 .63147 .53513 .6215 .54907 .65172 .54181 .66642 Metetra .76 .405 .382 r .54181 .66642 .54907 .65172 .56325 .67149 .55611 .68951 Metetra .514 .159 .302 r .55611 .68951 .56325 .67149 .57737 .67097 .57041 .68958 Metetra .57041 .68958 .57737 .67097 .59114 .64802 .58434 .66427 Metetra .856 .844 .38 r .58434 .66427 .59114 .64802 .60442 .60958 .59776 .6215 Metetra .968 .877 .489 r .59776 .6215 .60442 .60958 .61735 .56702 .61078 .57416 Metetra .987 .89 .563 r .61078 .57416 .61735 .56702 .6302 .53 .62369 .53306 Metetra .977 .919 .657 r .62369 .53306 .6302 .53 .64323 .50326 .63676 .50341 Metetra .921 .959 .791 r .63676 .50341 .64323 .50326 .65659 .4871 .65015 .48544 Metetra .756 .956 .938 r .65015 .48544 .65659 .4871 .67032 .47947 .66392 .47674 Metetra .469 .838 .991 r .66392 .47674 .67032 .47947 .6844 .47766 .67805 .47429 Metetra .236 .689 .953 r .67805 .47429 .6844 .47766 .69878 .47915 .69246 .47533 Metetra .176 .635 .937 r .69246 .47533 .69878 .47915 .71335 .4817 .70707 .47753 Metetra .267 .682 .968 r .70707 .47753 .71335 .4817 .72801 .48344 .72178 .47897 Metetra .437 .766 .997 r .72178 .47897 .72801 .48344 .74266 .48301 .73647 .47826 Metetra .605 .832 .986 r .73647 .47826 .74266 .48301 .75719 .4796 .75106 .47457 Metetra .728 .861 .944 r .75106 .47457 .75719 .4796 .77154 .47285 .76546 .46748 Metetra .805 .864 .892 r .76546 .46748 .77154 .47285 .78567 .46278 .77964 .45697 Metetra .846 .855 .849 r .77964 .45697 .78567 .46278 .79956 .44996 .79357 .4436 Metetra .861 .842 .825 r .79357 .4436 .79956 .44996 .81331 .43563 .80736 .42866 Metetra .854 .829 .822 r .80736 .42866 .81331 .43563 .82706 .4214 .82113 .41384 Metetra .83 .814 .834 r .82113 .41384 .82706 .4214 .84095 .40868 .83505 .40063 Metetra .793 .796 .855 r .83505 .40063 .84095 .40868 .85509 .3982 .84923 .38979 Metetra .75 .777 .874 r .84923 .38979 .85509 .3982 .86951 .3899 .86369 .38123 Metetra .714 .759 .888 r .86369 .38123 .86951 .3899 .88418 .38322 .87841 .3744 Metetra .69 .747 .895 r .87841 .3744 .88418 .38322 .89904 .37754 .89332 .36862 Metetra .64 .729 .913 r .35479 .53277 .36244 .54013 .37473 .53702 .36711 .52965 Metetra .603 .718 .926 r .36711 .52965 .37473 .53702 .38704 .53491 .37945 .52755 Metetra .53 .693 .943 r .37945 .52755 .38704 .53491 .39936 .53441 .3918 .52709 Metetra .404 .641 .953 r .3918 .52709 .39936 .53441 .41169 .53596 .40415 .52876 Metetra .242 .561 .935 r .40415 .52876 .41169 .53596 .42407 .53945 .41655 .53248 Metetra .124 .498 .906 r .41655 .53248 .42407 .53945 .43655 .54397 .42903 .53735 Metetra .119 .508 .909 r .42903 .53735 .43655 .54397 .44917 .54809 .44166 .54203 Metetra .172 .56 .932 r .44166 .54203 .44917 .54809 .46195 .55096 .45445 .54574 Metetra .085 .534 .905 r .45445 .54574 .46195 .55096 .47485 .55359 .46737 .54966 Metetra .405 0 0 r .46737 .54966 .47485 .55359 .48785 .55938 .48037 .55739 Metetra .793 .301 .022 r .48037 .55739 .48785 .55938 .50093 .57299 .49345 .5738 Metetra .869 .466 .266 r .49345 .5738 .50093 .57299 .5142 .59757 .50672 .60217 Metetra .875 .51 .353 r .50672 .60217 .5142 .59757 .5278 .63147 .52032 .64061 Metetra .852 .499 .384 r .52032 .64061 .5278 .63147 .54181 .66642 .53437 .68004 Metetra .781 .423 .379 r .53437 .68004 .54181 .66642 .55611 .68951 .54878 .70627 Metetra .518 .151 .283 r .54878 .70627 .55611 .68951 .57041 .68958 .56323 .70697 Metetra .56323 .70697 .57041 .68958 .58434 .66427 .57734 .67956 Metetra .92 .867 .433 r .57734 .67956 .58434 .66427 .59776 .6215 .59092 .63289 Metetra .984 .869 .504 r .59092 .63289 .59776 .6215 .61078 .57416 .60406 .58124 Metetra .993 .877 .56 r .60406 .58124 .61078 .57416 .62369 .53306 .61706 .53644 Metetra .982 .908 .64 r .61706 .53644 .62369 .53306 .63676 .50341 .6302 .50408 Metetra .934 .956 .766 r .6302 .50408 .63676 .50341 .65015 .48544 .64364 .48428 Metetra .785 .971 .917 r .64364 .48428 .65015 .48544 .66392 .47674 .65745 .47432 Metetra .516 .869 .988 r .65745 .47432 .66392 .47674 .67805 .47429 .67161 .47087 Metetra .311 .734 .973 r .67161 .47087 .67805 .47429 .69246 .47533 .68604 .47102 Metetra .279 .685 .971 r .68604 .47102 .69246 .47533 .70707 .47753 .70067 .47238 Metetra .376 .711 .987 r .70067 .47238 .70707 .47753 .72178 .47897 .71539 .47309 Metetra .517 .757 .983 r .71539 .47309 .72178 .47897 .73647 .47826 .7301 .47181 Metetra .642 .79 .953 r .7301 .47181 .73647 .47826 .75106 .47457 .74472 .46769 Metetra .735 .807 .909 r .74472 .46769 .75106 .47457 .76546 .46748 .75918 .46027 Metetra .797 .813 .865 r .75918 .46027 .76546 .46748 .77964 .45697 .7734 .44948 Metetra .834 .813 .83 r .7734 .44948 .77964 .45697 .79357 .4436 .7874 .43583 Metetra .849 .809 .811 r .7874 .43583 .79357 .4436 .80736 .42866 .80124 .4206 Metetra .845 .804 .81 r .80124 .4206 .80736 .42866 .82113 .41384 .81507 .40551 Metetra .825 .797 .825 r .81507 .40551 .82113 .41384 .83505 .40063 .82905 .39207 Metetra .791 .785 .848 r .82905 .39207 .83505 .40063 .84923 .38979 .84328 .38105 Metetra .75 .771 .87 r .84328 .38105 .84923 .38979 .86369 .38123 .8578 .37237 Metetra .714 .757 .886 r .8578 .37237 .86369 .38123 .87841 .3744 .87258 .36545 Metetra .69 .746 .894 r .87258 .36545 .87841 .3744 .89332 .36862 .88755 .3596 Metetra .64 .729 .913 r .34706 .52533 .35479 .53277 .36711 .52965 .35942 .52216 Metetra .604 .717 .925 r .35942 .52216 .36711 .52965 .37945 .52755 .3718 .52 Metetra .533 .691 .94 r .3718 .52 .37945 .52755 .3918 .52709 .38417 .51948 Metetra .414 .639 .949 r .38417 .51948 .3918 .52709 .40415 .52876 .39656 .52109 Metetra .264 .56 .933 r .39656 .52109 .40415 .52876 .41655 .53248 .40897 .5248 Metetra .156 .498 .907 r .40897 .5248 .41655 .53248 .42903 .53735 .42147 .5298 Metetra .146 .496 .906 r .42147 .5298 .42903 .53735 .44166 .54203 .4341 .53486 Metetra .172 .525 .92 r .4341 .53486 .44166 .54203 .45445 .54574 .4469 .53937 Metetra .042 .469 .882 r .4469 .53937 .45445 .54574 .46737 .54966 .45981 .54465 Metetra .477 0 0 r .45981 .54465 .46737 .54966 .48037 .55739 .47281 .55443 Metetra .824 .349 .049 r .47281 .55443 .48037 .55739 .49345 .5738 .48587 .57369 Metetra .885 .49 .274 r .48587 .57369 .49345 .5738 .50672 .60217 .4991 .60569 Metetra .888 .527 .354 r .4991 .60569 .50672 .60217 .52032 .64061 .51269 .64831 Metetra .868 .515 .38 r .51269 .64831 .52032 .64061 .53437 .68004 .52676 .69179 Metetra .803 .44 .369 r .52676 .69179 .53437 .68004 .54878 .70627 .54125 .72085 Metetra .518 .131 .246 r .54125 .72085 .54878 .70627 .56323 .70697 .55584 .7222 Metetra .55584 .7222 .56323 .70697 .57734 .67956 .57014 .69307 Metetra .965 .876 .483 r .57014 .69307 .57734 .67956 .59092 .63289 .5839 .64313 Metetra .994 .859 .521 r .5839 .64313 .59092 .63289 .60406 .58124 .59721 .58783 Metetra .996 .865 .562 r .59721 .58783 .60406 .58124 .61706 .53644 .61032 .53984 Metetra .986 .897 .63 r .61032 .53984 .61706 .53644 .6302 .50408 .62355 .50506 Metetra .945 .949 .745 r .62355 .50506 .6302 .50408 .64364 .48428 .63706 .48347 Metetra .817 .977 .893 r .63706 .48347 .64364 .48428 .65745 .47432 .65091 .47207 Metetra .589 .903 .983 r .65091 .47207 .65745 .47432 .67161 .47087 .66508 .46727 Metetra .422 .79 .995 r .66508 .46727 .67161 .47087 .68604 .47102 .67951 .46605 Metetra .407 .736 .992 r .67951 .46605 .68604 .47102 .70067 .47238 .69412 .46609 Metetra .484 .729 .979 r .69412 .46609 .70067 .47238 .71539 .47309 .70883 .46566 Metetra .581 .737 .95 r .70883 .46566 .71539 .47309 .7301 .47181 .72354 .46351 Metetra .664 .747 .912 r .72354 .46351 .7301 .47181 .74472 .46769 .73818 .45883 Metetra .731 .757 .873 r .73818 .45883 .74472 .46769 .75918 .46027 .75267 .45112 Metetra .782 .766 .839 r .75267 .45112 .75918 .46027 .7734 .44948 .76696 .44021 Metetra .816 .773 .813 r .76696 .44021 .7734 .44948 .7874 .43583 .78103 .42656 Metetra .833 .777 .799 r .78103 .42656 .7874 .43583 .80124 .4206 .79496 .41139 Metetra .833 .78 .801 r .79496 .41139 .80124 .4206 .81507 .40551 .80887 .39637 Metetra .816 .779 .818 r .80887 .39637 .81507 .40551 .82905 .39207 .82293 .38299 Metetra .785 .774 .843 r .82293 .38299 .82905 .39207 .84328 .38105 .83725 .37199 Metetra .748 .764 .866 r .83725 .37199 .84328 .38105 .8578 .37237 .85184 .3633 Metetra .713 .753 .884 r .85184 .3633 .8578 .37237 .87258 .36545 .86668 .35636 Metetra .689 .745 .894 r .86668 .35636 .87258 .36545 .88755 .3596 .88172 .35047 Metetra .641 .729 .912 r .33927 .5178 .34706 .52533 .35942 .52216 .35167 .51455 Metetra .607 .717 .923 r .35167 .51455 .35942 .52216 .3718 .52 .36408 .51228 Metetra .542 .692 .937 r .36408 .51228 .3718 .52 .38417 .51948 .37649 .51159 Metetra .434 .641 .944 r .37649 .51159 .38417 .51948 .39656 .52109 .38891 .51297 Metetra .3 .568 .932 r .38891 .51297 .39656 .52109 .40897 .5248 .40134 .51644 Metetra .203 .506 .909 r .40134 .51644 .40897 .5248 .42147 .5298 .41386 .52133 Metetra .183 .491 .903 r .41386 .52133 .42147 .5298 .4341 .53486 .4265 .52658 Metetra .176 .494 .905 r .4265 .52658 .4341 .53486 .4469 .53937 .43929 .53181 Metetra .004 .406 .854 r .43929 .53181 .4469 .53937 .45981 .54465 .4522 .53846 Metetra .531 0 0 r .4522 .53846 .45981 .54465 .47281 .55443 .46517 .55033 Metetra .847 .386 .064 r .46517 .55033 .47281 .55443 .48587 .57369 .47819 .57235 Metetra .899 .509 .275 r .47819 .57235 .48587 .57369 .4991 .60569 .49138 .60767 Metetra .901 .541 .349 r .49138 .60767 .4991 .60569 .51269 .64831 .50492 .65394 Metetra .884 .53 .371 r .50492 .65394 .51269 .64831 .52676 .69179 .51897 .70086 Metetra .827 .456 .352 r .51897 .70086 .52676 .69179 .54125 .72085 .53352 .73234 Metetra .513 .092 .178 r .53352 .73234 .54125 .72085 .55584 .7222 .54825 .73433 Metetra .813 .889 .466 r .54825 .73433 .55584 .7222 .57014 .69307 .56273 .70398 Metetra .99 .871 .527 r .56273 .70398 .57014 .69307 .5839 .64313 .5767 .65156 Metetra .999 .846 .539 r .5767 .65156 .5839 .64313 .59721 .58783 .59019 .59343 Metetra .997 .852 .568 r .59019 .59343 .59721 .58783 .61032 .53984 .60346 .5429 Metetra .988 .885 .627 r .60346 .5429 .61032 .53984 .62355 .50506 .61679 .50606 Metetra .954 .939 .73 r .61679 .50606 .62355 .50506 .63706 .48347 .63037 .48278 Metetra .849 .976 .87 r .63037 .48278 .63706 .48347 .65091 .47207 .64427 .46979 Metetra .672 .929 .971 r .64427 .46979 .65091 .47207 .66508 .46727 .65845 .46332 Metetra .547 .837 .998 r .65845 .46332 .66508 .46727 .67951 .46605 .67286 .46032 Metetra .531 .771 .985 r .67286 .46032 .67951 .46605 .69412 .46609 .68743 .45861 Metetra .572 .733 .951 r .68743 .45861 .69412 .46609 .70883 .46566 .70211 .45666 Metetra .626 .715 .91 r .70211 .45666 .70883 .46566 .72354 .46351 .7168 .45339 Metetra .677 .711 .873 r .7168 .45339 .72354 .46351 .73818 .45883 .73145 .44804 Metetra .724 .716 .842 r .73145 .44804 .73818 .45883 .75267 .45112 .74598 .44006 Metetra .765 .726 .817 r .74598 .44006 .75267 .45112 .76696 .44021 .76033 .42921 Metetra .796 .738 .798 r .76033 .42921 .76696 .44021 .78103 .42656 .77449 .41585 Metetra .814 .748 .79 r .77449 .41585 .78103 .42656 .79496 .41139 .78852 .40106 Metetra .817 .757 .796 r .78852 .40106 .79496 .41139 .80887 .39637 .80255 .38644 Metetra .805 .762 .814 r .80255 .38644 .80887 .39637 .82293 .38299 .81672 .37338 Metetra .778 .763 .84 r .81672 .37338 .82293 .38299 .83725 .37199 .83113 .3626 Metetra .743 .758 .864 r .83113 .3626 .83725 .37199 .85184 .3633 .8458 .35403 Metetra .711 .75 .882 r .8458 .35403 .85184 .3633 .86668 .35636 .86072 .34712 Metetra .688 .743 .893 r .86072 .34712 .86668 .35636 .88172 .35047 .87582 .34123 Metetra .643 .729 .911 r .33141 .51018 .33927 .5178 .35167 .51455 .34384 .50684 Metetra .612 .718 .92 r .34384 .50684 .35167 .51455 .36408 .51228 .35629 .5044 Metetra .554 .694 .933 r .35629 .5044 .36408 .51228 .37649 .51159 .36875 .50343 Metetra .459 .648 .94 r .36875 .50343 .37649 .51159 .38891 .51297 .3812 .50443 Metetra .344 .581 .931 r .3812 .50443 .38891 .51297 .40134 .51644 .39367 .50747 Metetra .256 .521 .911 r .39367 .50747 .40134 .51644 .41386 .52133 .40621 .51202 Metetra .222 .492 .898 r .40621 .51202 .41386 .52133 .4265 .52658 .41887 .51728 Metetra .182 .47 .89 r .41887 .51728 .4265 .52658 .43929 .53181 .43165 .52311 Metetra 0 .35 .824 r .43165 .52311 .43929 .53181 .4522 .53846 .44453 .53108 Metetra .57 .063 0 r .44453 .53108 .4522 .53846 .46517 .55033 .45746 .54494 Metetra .863 .414 .069 r .45746 .54494 .46517 .55033 .47819 .57235 .47043 .56948 Metetra .911 .524 .269 r .47043 .56948 .47819 .57235 .49138 .60767 .48355 .60766 Metetra .913 .553 .339 r .48355 .60766 .49138 .60767 .50492 .65394 .49703 .65687 Metetra .9 .543 .356 r .49703 .65687 .50492 .65394 .51897 .70086 .51105 .70647 Metetra .852 .47 .322 r .51105 .70647 .51897 .70086 .53352 .73234 .52562 .73983 Metetra .493 .014 .046 r .52562 .73983 .53352 .73234 .54825 .73433 .54046 .74247 Metetra .936 .942 .602 r .54046 .74247 .54825 .73433 .56273 .70398 .55512 .71146 Metetra .997 .855 .563 r .55512 .71146 .56273 .70398 .5767 .65156 .56931 .65749 Metetra .997 .831 .557 r .56931 .65749 .5767 .65156 .59019 .59343 .58301 .59749 Metetra .994 .839 .578 r .58301 .59749 .59019 .59343 .60346 .5429 .59645 .54517 Metetra .988 .872 .628 r .59645 .54517 .60346 .5429 .61679 .50606 .60991 .50672 Metetra .96 .924 .721 r .60991 .50672 .61679 .50606 .63037 .48278 .62358 .48188 Metetra .879 .964 .848 r .62358 .48188 .63037 .48278 .64427 .46979 .63752 .46721 Metetra .749 .936 .947 r .63752 .46721 .64427 .46979 .65845 .46332 .65171 .45883 Metetra .656 .859 .977 r .65171 .45883 .65845 .46332 .67286 .46032 .66609 .45373 Metetra .63 .784 .956 r .66609 .45373 .67286 .46032 .68743 .45861 .68062 .44994 Metetra .638 .729 .914 r .68062 .44994 .68743 .45861 .70211 .45666 .69524 .4462 Metetra .659 .697 .874 r .69524 .4462 .70211 .45666 .7168 .45339 .7099 .44163 Metetra .685 .684 .843 r .7099 .44163 .7168 .45339 .73145 .44804 .72454 .43553 Metetra .716 .685 .819 r .72454 .43553 .73145 .44804 .74598 .44006 .73911 .42734 Metetra .749 .696 .801 r .73911 .42734 .74598 .44006 .76033 .42921 .75353 .4167 Metetra .777 .71 .789 r .75353 .4167 .76033 .42921 .77449 .41585 .76779 .40386 Metetra .796 .724 .785 r .76779 .40386 .77449 .41585 .78852 .40106 .78195 .38975 Metetra .801 .737 .793 r .78195 .38975 .78852 .40106 .80255 .38644 .79611 .37581 Metetra .791 .747 .813 r .79611 .37581 .80255 .38644 .81672 .37338 .8104 .36331 Metetra .768 .752 .839 r .8104 .36331 .81672 .37338 .83113 .3626 .82492 .35292 Metetra .737 .751 .864 r .82492 .35292 .83113 .3626 .8458 .35403 .83969 .34457 Metetra .707 .746 .882 r .83969 .34457 .8458 .35403 .86072 .34712 .85468 .33776 Metetra .687 .741 .893 r .85468 .33776 .86072 .34712 .87582 .34123 .86986 .33187 Metetra .646 .729 .909 r .32347 .50249 .33141 .51018 .34384 .50684 .33595 .49903 Metetra .619 .719 .918 r .33595 .49903 .34384 .50684 .35629 .5044 .34844 .49638 Metetra .568 .697 .928 r .34844 .49638 .35629 .5044 .36875 .50343 .36094 .49506 Metetra .488 .656 .935 r .36094 .49506 .36875 .50343 .3812 .50443 .37344 .49556 Metetra .39 .597 .928 r .37344 .49556 .3812 .50443 .39367 .50747 .38596 .49799 Metetra .309 .538 .911 r .38596 .49799 .39367 .50747 .40621 .51202 .39853 .50202 Metetra .26 .498 .894 r .39853 .50202 .40621 .51202 .41887 .51728 .41119 .50712 Metetra .189 .452 .877 r .41119 .50712 .41887 .51728 .43165 .52311 .42397 .51339 Metetra 0 .303 .796 r .42397 .51339 .43165 .52311 .44453 .53108 .43682 .52252 Metetra .594 .109 0 r .43682 .52252 .44453 .53108 .45746 .54494 .4497 .53816 Metetra .872 .432 .063 r .4497 .53816 .45746 .54494 .47043 .56948 .46261 .56483 Metetra .92 .535 .255 r .46261 .56483 .47043 .56948 .48355 .60766 .47565 .60522 Metetra .924 .563 .322 r .47565 .60522 .48355 .60766 .49703 .65687 .48904 .6565 Metetra .916 .554 .332 r .48904 .6565 .49703 .65687 .51105 .70647 .503 .70785 Metetra .878 .481 .275 r .503 .70785 .51105 .70647 .52562 .73983 .51757 .74248 Metetra .412 0 0 r .51757 .74248 .52562 .73983 .54046 .74247 .5325 .74575 Metetra .973 .918 .682 r .5325 .74575 .54046 .74247 .55512 .71146 .54733 .71472 Metetra .989 .829 .591 r .54733 .71472 .55512 .71146 .56931 .65749 .56174 .66024 Metetra .989 .812 .575 r .56174 .66024 .56931 .65749 .58301 .59749 .57566 .59944 Metetra .988 .823 .589 r .57566 .59944 .58301 .59749 .59645 .54517 .58929 .54616 Metetra .984 .856 .634 r .58929 .54616 .59645 .54517 .60991 .50672 .60291 .50659 Metetra .962 .905 .717 r .60291 .50659 .60991 .50672 .62358 .48188 .61667 .48039 Metetra .9 .942 .828 r .61667 .48039 .62358 .48188 .63752 .46721 .63066 .46402 Metetra .807 .922 .914 r .63066 .46402 .63752 .46721 .65171 .45883 .64486 .4536 Metetra .735 .856 .938 r .64486 .4536 .65171 .45883 .66609 .45373 .65921 .44622 Metetra .699 .782 .915 r .65921 .44622 .66609 .45373 .68062 .44994 .67369 .44017 Metetra .685 .722 .878 r .67369 .44017 .68062 .44994 .69524 .4462 .68825 .43449 Metetra .683 .685 .845 r .68825 .43449 .69524 .4462 .7099 .44163 .70287 .42853 Metetra .692 .667 .821 r .70287 .42853 .7099 .44163 .72454 .