[Vennerable-commits] r62 - in pkg/Vennerable: R inst/doc

[noreply at r-forge.r-project.org]

Author: js229
Date: 2009-09-27 17:52:50 +0200 (Sun, 27 Sep 2009)
New Revision: 62

Modified:
   pkg/Vennerable/R/02TissueDrawing.R
   pkg/Vennerable/inst/doc/Venn.Rnw
   pkg/Vennerable/inst/doc/Venn.pdf
Log:
make midline centroids default for two-sectors

Modified: pkg/Vennerable/R/02TissueDrawing.R
===================================================================
--- pkg/Vennerable/R/02TissueDrawing.R	2009-09-26 20:15:07 UTC (rev 61)
+++ pkg/Vennerable/R/02TissueDrawing.R	2009-09-27 15:52:50 UTC (rev 62)
@@ -1005,7 +1005,9 @@
 
 .face.centroid <- function(drawing,faceName) {
 	all.xy <- .face.toxy(drawing,faceName)
-	.polygon.centroid(all.xy)
+	res <- .polygon.centroid(all.xy)
+	names(res) <- "centroid"
+	res
 }
 
 .PlotFace.TissueDrawing <- function(drawing,faceName,dx=0.05,gp=gpar(),doDarkMatter=FALSE) {
@@ -1088,44 +1090,31 @@
 		drawing <- renameFaces(drawing,"DarkMatter",faceName)
 		# has the effect of treating as an ordinary face
 	}
-	faceCentroid <- .face.centroid(drawing,faceName=faceName);
-	rownames(faceCentroid)<-"centroid"
-	if (.is.point.within.face(drawing,faceName,faceCentroid)) {
-		return(faceCentroid)
+	edgeClasses <- .faceEdgeClasses(drawing,faceName)
+	if (all(edgeClasses=="VDedgeSector") & length(edgeClasses)==2) {
+		aPoint <- 	.face.midplace(drawing,faceName)
+		if (.is.point.within.face(drawing,faceName,aPoint )) {
+			return(aPoint )
+		} else {
+			aPoint <- .face.centroid(drawing,faceName=faceName)
+			if (.is.point.within.face(drawing,faceName,aPoint )) {
+				return(aPoint )
+			}
+		} 
+	} else { #otherwise test in other order
+		aPoint <- 	.face.centroid(drawing,faceName=faceName)
+		if (.is.point.within.face(drawing,faceName,aPoint )) {
+			return(aPoint )
+		} else {
+			aPoint <- .face.midplace(drawing,faceName=faceName);
+			if (.is.point.within.face(drawing,faceName,aPoint )) {
+				return(aPoint )
+			}
+		} 
 	}
-#browser()
-	# hmm. try the midpoint of each edge and form the centroid of those
-	# will be exactly what we want for two intersceting circle sectors
-	aPoint <- 	.face.midplace(drawing,faceName)
-	if (.is.point.within.face(drawing,faceName,aPoint )) {
-		return(aPoint )
-	}
 
+	# ok, just try and find some corner guaranteed to be inside
 
-	if (FALSE) { # old method 
-	# find a point on the edge which is ideally not a node
-	amidpoint <- .find.point.on.face(drawing,faceName)
-
-	# create a line from the centroid to past that point, and call it a chord
-	chord.from.xy <- faceCentroid 
-	grad <- faceCentroid-amidpoint; grad <- grad/sqrt(sum(grad^2))
-	maxradius <- .face.maxradius(drawing,faceName)
-	chord.to.xy <- amidpoint- maxradius*grad
-
-	npoints <- .probe.chord.intersections(drawing,faceName,chord.from.xy,chord.to.xy)
-
-	cix <- which(rownames(npoints)=="centroid")	
-	if (cix-2 > 0) {
-		q1 <- npoints[cix-2,,drop=FALSE];
-		q2 <- npoints[cix-1,,drop=FALSE]
-	} else if (cix+2 <= nrow(npoints) ){
-		q1 <- npoints[cix+1,,drop=FALSE];
-		q2 <- npoints[cix+2,,drop=FALSE]
-	} else{ stop(sprintf("Error in finding a point in face %s",faceName))}
-	qmid <- (q1+q2)/2
-	rownames(qmid) <- faceName
-		return(qmid)
-	} # old method
 	ear.triangle <- .find.triangle.within.face(drawing,faceName)
 	earCentroid <- .polygon.centroid(ear.triangle)
 	if (!	.is.point.within.face(drawing,faceName,earCentroid )) {

Modified: pkg/Vennerable/inst/doc/Venn.Rnw
===================================================================
--- pkg/Vennerable/inst/doc/Venn.Rnw	2009-09-26 20:15:07 UTC (rev 61)
+++ pkg/Vennerable/inst/doc/Venn.Rnw	2009-09-27 15:52:50 UTC (rev 62)
@@ -189,7 +189,7 @@
 
 
 \begin{figure}[H]\begin{center}
-<<pwabVmonth3,echo=TRUE,fig=TRUE>>=
+<<pwabVmonth3x2,echo=TRUE,fig=TRUE>>=
 grid.newpage()
 SetLabels <- VennGetSetLabels(C3)
 SetLabels[SetLabels$Label=="February","y"] <- SetLabels[SetLabels$Label=="March","y"]
@@ -478,7 +478,7 @@
 
 
 \begin{figure}[H]\begin{center}
-<<S47battle,fig=TRUE,echo=TRUE,eval=FALSE>>=
+<<S47battle,fig=TRUE,echo=TRUE,eval=TRUE>>=
 plot(Venn(n=9),type="battle",show=list(SetLabels=FALSE,FaceText=""))
 @
 \caption{The battlement variant of the Edwards construction on 9 sets with the \texttt{type=battle} argument}
@@ -560,12 +560,6 @@
 separated by these (possibly modified) distances.
 
 
-<<Vdemo,echo=FALSE,eval=FALSE>>=
-V3 <- Venn(SetNames=month.name[1:3])
-Weights(V3) <- c(0,81,81,9,81,9,9,1)
-@
-
-
 \newpage
 
 \subsubsection{Squares}

Modified: pkg/Vennerable/inst/doc/Venn.pdf
===================================================================
--- pkg/Vennerable/inst/doc/Venn.pdf	2009-09-26 20:15:07 UTC (rev 61)
+++ pkg/Vennerable/inst/doc/Venn.pdf	2009-09-27 15:52:50 UTC (rev 62)
@@ -31,42 +31,191 @@
 (Graphical parameters)
 endobj
 25 0 obj
-<< /S /GoTo /D [26 0 R  /Fit ] >>
+<< /S /GoTo /D (section.3) >>
 endobj
-29 0 obj <<
-/Length 360       
+28 0 obj
+(Unweighted Venn diagrams)
+endobj
+29 0 obj
+<< /S /GoTo /D (subsection.3.1) >>
+endobj
+32 0 obj
+(Unweighted 2-set Venn diagrams)
+endobj
+33 0 obj
+<< /S /GoTo /D (subsection.3.2) >>
+endobj
+36 0 obj
+(Unweighted 3-set Venn diagrams)
+endobj
+37 0 obj
+<< /S /GoTo /D (subsection.3.3) >>
+endobj
+40 0 obj
+(Unweighted 4-set Venn diagrams)
+endobj
+41 0 obj
+<< /S /GoTo /D (subsection.3.4) >>
+endobj
+44 0 obj
+(Unweighted Venn diagrams on more than four sets)
+endobj
+45 0 obj
+<< /S /GoTo /D (section.4) >>
+endobj
+48 0 obj
+(Weighted Venn diagrams)
+endobj
+49 0 obj
+<< /S /GoTo /D (subsection.4.1) >>
+endobj
+52 0 obj
+(Weighted 2-set Venn diagrams for 2 Sets)
+endobj
+53 0 obj
+<< /S /GoTo /D (subsubsection.4.1.1) >>
+endobj
+56 0 obj
+(Circles)
+endobj
+57 0 obj
+<< /S /GoTo /D (subsubsection.4.1.2) >>
+endobj
+60 0 obj
+(Squares)
+endobj
+61 0 obj
+<< /S /GoTo /D (subsection.4.2) >>
+endobj
+64 0 obj
+(Weighted 3-set Venn diagrams)
+endobj
+65 0 obj
+<< /S /GoTo /D (subsubsection.4.2.1) >>
+endobj
+68 0 obj
+(Circles)
+endobj
+69 0 obj
+<< /S /GoTo /D (subsubsection.4.2.2) >>
+endobj
+72 0 obj
+(Squares)
+endobj
+73 0 obj
+<< /S /GoTo /D (subsubsection.4.2.3) >>
+endobj
+76 0 obj
+(Triangles)
+endobj
+77 0 obj
+<< /S /GoTo /D (subsection.4.3) >>
+endobj
+80 0 obj
+(Chow-Ruskey diagrams for 3 or more sets)
+endobj
+81 0 obj
+<< /S /GoTo /D (section.5) >>
+endobj
+84 0 obj
+(Euler diagrams)
+endobj
+85 0 obj
+<< /S /GoTo /D (subsection.5.1) >>
+endobj
+88 0 obj
+(2-set Euler diagrams)
+endobj
+89 0 obj
+<< /S /GoTo /D (subsubsection.5.1.1) >>
+endobj
+92 0 obj
+(Circles)
+endobj
+93 0 obj
+<< /S /GoTo /D (subsubsection.5.1.2) >>
+endobj
+96 0 obj
+(Squares)
+endobj
+97 0 obj
+<< /S /GoTo /D (subsection.5.2) >>
+endobj
+100 0 obj
+(3-set Euler diagrams)
+endobj
+101 0 obj
+<< /S /GoTo /D (subsubsection.5.2.1) >>
+endobj
+104 0 obj
+(Circles)
+endobj
+105 0 obj
+<< /S /GoTo /D (subsubsection.5.2.2) >>
+endobj
+108 0 obj
+(Triangles)
+endobj
+109 0 obj
+<< /S /GoTo /D (subsection.5.3) >>
+endobj
+112 0 obj
+(4-set Euler diagrams)
+endobj
+113 0 obj
+<< /S /GoTo /D (subsubsection.5.3.1) >>
+endobj
+116 0 obj
+(Chow-Ruskey diagrams)
+endobj
+117 0 obj
+<< /S /GoTo /D (section.6) >>
+endobj
+120 0 obj
+(Some loose definitions)
+endobj
+121 0 obj
+<< /S /GoTo /D (section.7) >>
+endobj
+124 0 obj
+(This document)
+endobj
+125 0 obj
+<< /S /GoTo /D [126 0 R  /Fit ] >>
+endobj
+129 0 obj <<
+/Length 359       
 /Filter /FlateDecode
 >>
 stream
-xÚmRKOÃ0¾÷Wø¸JÔË»É
-M€Än°Šâme-Ðvl‘ö÷qúEB‘­<¾ÏþìxU$ËŁç(¸VP¼ƒ5w`ŒBa
-{x]¼¤œóEÙ¶i&4[ìk8ùæ<œêñö9}+֐IƒÚ
-ÈGÇíÀ¿Ô¡@¡*#Œ²ŠyVÃPh	욎’‘kKr'2¿%÷5QÿvsÇ'êÑï>ýa$Z‹ÌCçrRfÑ:1à×]ëCåÇ6—º
-]û«pƦz¬²q‰NåûƒTuQ¨䪸‰§Û3¹YO¡‹•q*)ü§3§Q›QžÐW¤EGÒ{(”Ò
-0êî
*#!›
7å1”Ͷ<¥Š-n†¢c.Ò“û"‰}d at Q´CžK9ÅpvMò04ÒPÓ#d¾ï'æx±|l8ÜuÉ­é)›¢f³°«q•'L?N!79Ðw)9Ÿþ ÄVŸ1
+xÚmRÉNÃ@½ç+|l$Ɲ}¹¡
+è
+qAÒ64
’”6RO–$4²5Ë{ö³Ç«,Y>h
¡FCöRz4"€µ¥·íáuñ’
+!EÓ¤L¾ØWùá”×çáT·Ïé[¶¦,/IAø©ºr uea”UγZŽÒ(à×t”Œ\S;‘å[r_õà Ñ1Qùî3?Ì€¤Â,pÁ‘2>È
¿n›¼+ó±„Í¥jº¶ùU8cS=^{`BaÐn`ª6
+Í;reÜÄÓí™Ü…¬Š§®•q*©ûOæ:6Î ±£<é®Hþ¤öШT`ÔÝÿrÔV
›
7ű+êmqJ5_ÜEKÎC¤'÷Yûȁ¢˜€Â)Žb»:ùN8Ze©é2ß÷s¼X>ÖîÚä‰ÖôĦ¨lv5Ž` ò¤í'0hÖ
}—Vã ‰IàÆvŸ3
 endstream
 endobj
-26 0 obj <<
+126 0 obj <<
 /Type /Page
-/Contents 29 0 R
-/Resources 28 0 R
+/Contents 129 0 R
+/Resources 128 0 R
 /MediaBox [0 0 595.276 841.89]
-/Parent 34 0 R
+/Parent 134 0 R
 >> endobj
-27 0 obj <<
+127 0 obj <<
 /Type /XObject
 /Subtype /Form
 /FormType 1
 /PTEX.FileName (Vennfig-front.pdf)
 /PTEX.PageNumber 1
-/PTEX.InfoDict 35 0 R
+/PTEX.InfoDict 135 0 R
 /BBox [0 0 432 432]
 /Resources <<
 /ProcSet [ /PDF /Text ]
 /Font << >>
 /ExtGState <<
 >>>>
-/Length 36 0 R
+/Length 136 0 R
 >>
 stream
 q
@@ -1183,135 +1332,364 @@
 Q
 endstream
 endobj
-35 0 obj
+135 0 obj
 <<
-/CreationDate (D:20090925231407)
-/ModDate (D:20090925231407)
+/CreationDate (D:20090927152826)
+/ModDate (D:20090927152826)
 /Title (R Graphics Output)
 /Producer (R 2.9.0)
 /Creator (R)
 >>
 endobj
-36 0 obj
+136 0 obj
 17018
 endobj
-30 0 obj <<
-/D [26 0 R /XYZ 124.802 740.998 null]
+130 0 obj <<
+/D [126 0 R /XYZ 124.802 740.998 null]
 >> endobj
-31 0 obj <<
-/D [26 0 R /XYZ 124.802 716.092 null]
+131 0 obj <<
+/D [126 0 R /XYZ 124.802 716.092 null]
 >> endobj
-28 0 obj <<
-/Font << /F41 32 0 R /F42 33 0 R >>
-/XObject << /Im1 27 0 R >>
+128 0 obj <<
+/Font << /F41 132 0 R /F42 133 0 R >>
+/XObject << /Im1 127 0 R >>
 /ProcSet [ /PDF /Text ]
 >> endobj
-39 0 obj <<
-/Length 91        
+169 0 obj <<
+/Length 761       
 /Filter /FlateDecode
 >>
 stream
-xÚ%Ë1@@ Àþ^‘’BH.Ò2®P§3:”üúÝÞC
	FQ߁X°kÚF‘ØÀW˜‹á<îí¸¯rñ©ÎB`hÊúy5Œš RJ¨FàW†ÑÃY_ž
+xÚå™Ër›0†÷y
+–b
•ŽîË6“v¦›Î4´Y¤]0±b3µ!Å8™¾}%$ð
+;îL§õecd}‡ÿH¿äwÙÕ›÷G„¥”	ˆ²Çˆ K†Hb‘ÐQ6ŠîÑuU6¦læñ÷ìc{ƒNµ á®ÇQ‚þJ'cŒ>=Ç#S»Ïç¼Ä	(fÛÔ…ho"©&á&7]W³§E“7EUÚë9Fy9ò·eYu?­”DÜ÷…‘•¾XÍX”›‹;m»Ä»èE9ö!¿Æ„dÊð¨QÇ„£ûû<N$£(n;uœpùâ]2[`Þ
C ^MšC|Êë|fS[@EŽp WãÒ€û¡ÎŸ&ÅC>ݦ€O‰vZÔ\Ò	½-"åAC})_L1ž4fÔëÜž]ê¼ÈÇ61sl
üZ!…DÓ¾6Ÿ ÉÜ4ÃEÕ?Œjy4y%îè¹7ÕDûâÙ„¤'	I†!éHv’0Év@î$sߺ±rVÕÆ·šIÎ=V‹Ú·l–ܪÕ_c`‡–9e~Ž,tR ",tÖú]¬0úãR÷©
+™¸mF5ûòðÓ†5)šlxKÚ²‚óEý05¶“Ö•œà\ñ*?ÞzÉíPçÐo.òÚ¡sÅÎ=Y{÷}`§Êë%ÈãdVÛr_"_€ÜÕ°Üáä®w¡Ó€žÅ”£ºÈËqûî%WçAd ÐûA¾s;ד*»ÄK>/æ?Úå©[ñýÚ;Ñ`êM[à- ÿWô˜ðªK+j\ÂÍbjêm@*‚CWм÷+³ÿ``
+ìdÄw›ü\î%ðKp	°Ç%ðÞ%Ð3Ö¾Ú£ý°°nÄÎ|Þ¤xŸô»y“¯ô)ì‘>]Jÿ0ç 	#Þ¦a 2U\­o+ˆ`n«Y08Óªš‡æÈ|ÃÊÂm%;ÿ Âíä¯oå‡82ÄÉ&E°R£êa13e+ A¢lÈwRÁíPÂ:Õý/`¯¼ºÉ®~°
 endstream
 endobj
-38 0 obj <<
+168 0 obj <<
 /Type /Page
-/Contents 39 0 R
-/Resources 37 0 R
+/Contents 169 0 R
+/Resources 167 0 R
 /MediaBox [0 0 595.276 841.89]
-/Parent 34 0 R
+/Parent 134 0 R
+/Annots [ 137 0 R 138 0 R 139 0 R 140 0 R 141 0 R 142 0 R 143 0 R 144 0 R 145 0 R 146 0 R 147 0 R 148 0 R 149 0 R 150 0 R 151 0 R 152 0 R 153 0 R 154 0 R 155 0 R 156 0 R 157 0 R 158 0 R 159 0 R 160 0 R 161 0 R 162 0 R 163 0 R 164 0 R 165 0 R 166 0 R ]
 >> endobj
-40 0 obj <<
-/D [38 0 R /XYZ 124.802 740.998 null]
+137 0 obj <<
+/Type /Annot
+/Border[0 0 1]/H/I/C[1 0 0]
+/Rect [123.806 682.747 181.489 691.723]
+/Subtype /Link
+/A << /S /GoTo /D (section.1) >>
 >> endobj
-42 0 obj <<
-/D [38 0 R /XYZ 124.802 695.646 null]
+138 0 obj <<
+/Type /Annot
+/Border[0 0 1]/H/I/C[1 0 0]
+/Rect [123.806 658.926 266.4 669.805]
+/Subtype /Link
+/A << /S /GoTo /D (section.2) >>
 >> endobj
-37 0 obj <<
-/Font << /F51 41 0 R /F41 32 0 R >>
+139 0 obj <<
+/Type /Annot
+/Border[0 0 1]/H/I/C[1 0 0]
+/Rect [138.75 646.836 270.326 657.74]
+/Subtype /Link
+/A << /S /GoTo /D (subsection.2.1) >>
+>> endobj
+140 0 obj <<
+/Type /Annot
+/Border[0 0 1]/H/I/C[1 0 0]
+/Rect [138.75 634.881 254.684 645.785]
+/Subtype /Link
+/A << /S /GoTo /D (subsection.2.2) >>
+>> endobj
+141 0 obj <<
+/Type /Annot
+/Border[0 0 1]/H/I/C[1 0 0]
+/Rect [138.75 622.926 249.135 633.83]
+/Subtype /Link
+/A << /S /GoTo /D (subsection.2.3) >>
+>> endobj
+142 0 obj <<
+/Type /Annot
+/Border[0 0 1]/H/I/C[1 0 0]
+/Rect [123.806 601.143 258.191 612.022]
+/Subtype /Link
+/A << /S /GoTo /D (section.3) >>
+>> endobj
+143 0 obj <<
+/Type /Annot
+/Border[0 0 1]/H/I/C[1 0 0]
+/Rect [138.75 589.053 296.188 599.957]
+/Subtype /Link
+/A << /S /GoTo /D (subsection.3.1) >>
+>> endobj
+144 0 obj <<
+/Type /Annot
+/Border[0 0 1]/H/I/C[1 0 0]
+/Rect [138.75 577.098 296.188 588.002]
+/Subtype /Link
+/A << /S /GoTo /D (subsection.3.2) >>
+>> endobj
+145 0 obj <<
+/Type /Annot
+/Border[0 0 1]/H/I/C[1 0 0]
+/Rect [138.75 565.143 296.188 576.047]
+/Subtype /Link
+/A << /S /GoTo /D (subsection.3.3) >>
+>> endobj
+146 0 obj <<
+/Type /Annot
+/Border[0 0 1]/H/I/C[1 0 0]
+/Rect [138.75 553.188 365.916 564.091]
+/Subtype /Link
+/A << /S /GoTo /D (subsection.3.4) >>
+>> endobj
+147 0 obj <<
+/Type /Annot
+/Border[0 0 1]/H/I/C[1 0 0]
+/Rect [123.806 531.404 247.581 542.283]
+/Subtype /Link
+/A << /S /GoTo /D (section.4) >>
+>> endobj
+148 0 obj <<
+/Type /Annot
+/Border[0 0 1]/H/I/C[1 0 0]
+/Rect [138.75 519.315 326.105 530.218]
+/Subtype /Link
+/A << /S /GoTo /D (subsection.4.1) >>
+>> endobj
+149 0 obj <<
+/Type /Annot
+/Border[0 0 1]/H/I/C[1 0 0]
+/Rect [161.664 509.417 223.76 518.263]
+/Subtype /Link
+/A << /S /GoTo /D (subsubsection.4.1.1) >>
+>> endobj
+150 0 obj <<
+/Type /Annot
+/Border[0 0 1]/H/I/C[1 0 0]
+/Rect [161.664 495.404 227.078 506.308]
+/Subtype /Link
+/A << /S /GoTo /D (subsubsection.4.1.2) >>
+>> endobj
+151 0 obj <<
+/Type /Annot
+/Border[0 0 1]/H/I/C[1 0 0]
+/Rect [138.75 483.449 285.428 494.353]
+/Subtype /Link
+/A << /S /GoTo /D (subsection.4.2) >>
+>> endobj
+152 0 obj <<
+/Type /Annot
+/Border[0 0 1]/H/I/C[1 0 0]
+/Rect [161.664 473.551 223.76 482.398]
+/Subtype /Link
+/A << /S /GoTo /D (subsubsection.4.2.1) >>
+>> endobj
+153 0 obj <<
+/Type /Annot
+/Border[0 0 1]/H/I/C[1 0 0]
+/Rect [161.664 459.539 227.078 470.443]
+/Subtype /Link
+/A << /S /GoTo /D (subsubsection.4.2.2) >>
+>> endobj
+154 0 obj <<
+/Type /Annot
+/Border[0 0 1]/H/I/C[1 0 0]
+/Rect [161.664 447.584 232.816 458.487]
+/Subtype /Link
+/A << /S /GoTo /D (subsubsection.4.2.3) >>
+>> endobj
+155 0 obj <<
+/Type /Annot
+/Border[0 0 1]/H/I/C[1 0 0]
+/Rect [138.75 435.628 331.944 446.532]
+/Subtype /Link
+/A << /S /GoTo /D (subsection.4.3) >>
+>> endobj
+156 0 obj <<
+/Type /Annot
+/Border[0 0 1]/H/I/C[1 0 0]
+/Rect [123.806 413.845 206.883 424.724]
+/Subtype /Link
+/A << /S /GoTo /D (section.5) >>
+>> endobj
+157 0 obj <<
+/Type /Annot
+/Border[0 0 1]/H/I/C[1 0 0]
+/Rect [138.75 401.755 246.106 412.659]
+/Subtype /Link
+/A << /S /GoTo /D (subsection.5.1) >>
+>> endobj
+158 0 obj <<
+/Type /Annot
+/Border[0 0 1]/H/I/C[1 0 0]
+/Rect [161.664 391.857 223.76 400.704]
+/Subtype /Link
+/A << /S /GoTo /D (subsubsection.5.1.1) >>
+>> endobj
+159 0 obj <<
+/Type /Annot
+/Border[0 0 1]/H/I/C[1 0 0]
+/Rect [161.664 377.845 227.078 388.749]
+/Subtype /Link
+/A << /S /GoTo /D (subsubsection.5.1.2) >>
+>> endobj
+160 0 obj <<
+/Type /Annot
+/Border[0 0 1]/H/I/C[1 0 0]
+/Rect [138.75 365.89 246.106 376.794]
+/Subtype /Link
+/A << /S /GoTo /D (subsection.5.2) >>
+>> endobj
+161 0 obj <<
+/Type /Annot
+/Border[0 0 1]/H/I/C[1 0 0]
+/Rect [161.664 355.992 223.76 364.839]
+/Subtype /Link
+/A << /S /GoTo /D (subsubsection.5.2.1) >>
+>> endobj
+162 0 obj <<
+/Type /Annot
+/Border[0 0 1]/H/I/C[1 0 0]
+/Rect [161.664 341.98 232.816 352.883]
+/Subtype /Link
+/A << /S /GoTo /D (subsubsection.5.2.2) >>
+>> endobj
+163 0 obj <<
+/Type /Annot
+/Border[0 0 1]/H/I/C[1 0 0]
+/Rect [138.75 330.024 246.106 340.928]
+/Subtype /Link
+/A << /S /GoTo /D (subsection.5.3) >>
+>> endobj
+164 0 obj <<
+/Type /Annot
+/Border[0 0 1]/H/I/C[1 0 0]
+/Rect [161.664 318.069 291.058 328.973]
+/Subtype /Link
+/A << /S /GoTo /D (subsubsection.5.3.1) >>
+>> endobj
+165 0 obj <<
+/Type /Annot
+/Border[0 0 1]/H/I/C[1 0 0]
+/Rect [123.806 298.189 234.29 307.165]
+/Subtype /Link
+/A << /S /GoTo /D (section.6) >>
+>> endobj
+166 0 obj <<
+/Type /Annot
+/Border[0 0 1]/H/I/C[1 0 0]
+/Rect [123.806 276.271 204.124 285.247]
+/Subtype /Link
+/A << /S /GoTo /D (section.7) >>
+>> endobj
+170 0 obj <<
+/D [168 0 R /XYZ 124.802 740.998 null]
+>> endobj
+172 0 obj <<
+/D [168 0 R /XYZ 124.802 695.646 null]
+>> endobj
+167 0 obj <<
+/Font << /F70 171 0 R /F41 132 0 R >>
 /ProcSet [ /PDF /Text ]
 >> endobj
-48 0 obj <<
-/Length 1716      
+179 0 obj <<
+/Length 1699      
 /Filter /FlateDecode
 >>
 stream
-xÚÍXÝoÛ6ï_a{Z)Q²‹aCÓ6k‡-0£Ðõ–˜X,/ÿýŽ¼Ó‡%¥KÛEòîxäñG‘—Ûg/®[°È£˜/¶7Æ#ðEÄ>ã›Å6[|òØrÅ‚ ð>Ü-Yà)m¿w¹:-?o|q±ÅÆßÄ<¶ãƒÅŠsŸÇ	ŽÜîÕ±÷qÉóTY*-w…#&ÞQ¦È[’8êjÉèÍT]5&/±—x¦BjZŽ¡A²ÌHU±d^e°ÓC¡,—·ZêçÐ
-™——iÑd+ë¼u—1#º›—·V&öŒó;L¼´u§D=ÙÈ«²Ð¶ÖJ­Ò\§j-"·ä×UÔÖSê ÀÝ’Oê\™{¤W7ȨÀ]#í”›=R³üƸQZ•f.˜Ê£Ò&Ç©í,ÅÞM¥‘Ò±n'µVVã] U"«V¦ö—«0àÞ{"É,ËM^Q/7´ ’Ç@ぜø§}žîÉn›R+‰$ˆy&%ݐ8ð´²ÞÝ¢yèç5Ö6ØJ[·d”­‘˜AÊh­êcUf¸ÀÀ+›ÃNil»Ù†"&ÕFH{ÕÊØ•ÀæIå·{;73în÷έ`MYæV Øxo›Â
-Æ0YÜM
-áD‚ÈNamöU¦ë¼¢$Ã$ö`ʁyoII?oõœÇã¹4P«ÃÑ%$4óÒ@"ªÔ85Ž´—6­1e²S.w„]«nfÇÍpª e6QDÖc´~•ß6ÎÑ$´(c«z_Ù\<ÕØ•XöP†ñC—âÇŽ›+7Ê	s¯†AÀÇ¡*‹{ìÝTM™Ù,O6Þv¹ÜÆ´Ú´´®;„‡ž·PaìòÒÁ.dâ5µkÐ1‹X»ùÿSŽ	X¯r‚®9!?ayœú_
$ì ¼¦váÊw£Ðß \ÓèL‰ÆÝL€ÍËÊB×½KBë“!Ÿ\*K"?^G­²ïgÌ%Ðb­@›Â ¯ÈkS÷Q:Ú­*©UʃÂ$[û<Í)@m•æÒ¨Óˆ Ϧ"€ Í
-5¬œ¦tÕ²¬S	š,Ó+SSéšÂ[ŸŸQzœ¬~·\	º™Í¡ì À	‰‡õ=”ß@õ‘¡¤¢¢;Z…âln¯‘¥Œ†ªIû×—|Fk|¦µ¦áúéG™hÏpÐÏèÿ‰&
-8[L0Ç®9—„Ïù¹Wß û™ÝB‰ô«({ç¯ë~‚&ƒòJ…C	¡|Fö4_Q±a½òÊÅ9û’L]’†û5•kçÍ,ûMOö¡‰ef-)>닍ñ7gð‘ñ1ò.²9Ñ²ÖÄ^A¹‚òÊ/So1¯©-f_’Ñàiq_“škŠÿÚc)Âdx8XƒÖ@BôÿSðoi®ž’ÔÃE%vBÓ2Zä„”=þϧŖœ›‹i„ä+ܺnïÛCY׆˜ŽöŽ}£›”È’p¶Ú}Q-­f÷Ç<w¾E`©?àαtêüõš·Ò/g`|Åb¸£DbÍ?v€ÕŸ#ë¶U'1óŠÂg÷a|¥é~5çO³ö\ùB¬ôË;üWd¹FRÍXÙœãçͼç4	=ª!mnÇ[úùf˜9ŸÚ`XœclJ
-[q ŦR½ä™.6ÕŦºØTJOübS¿ØÔ/6õ‹MýbS¿ØÔ/Ì+&üþ­ÎÖ(°ð(étn¨R_ at _$¸~‚x1­gD¼˜Úí81èó“±ßž@ŒÆ¢l'NÖÞ9èìý“eç{^8àÅŽ7Dmàg{£À;ýŒfàÏoMÀMáÒ‹-úo„V´ÂKÈ
-ïÀ^Ã8£›1ˆ•xû E¤P«¬IÉž»
Mb…“¹…–{”|ìèBìÎÁ×Xê“Û’ÝADˆvAv¸É/zÉ‹™ý>bÏmý‹íIö<´Áüë˜þW˜8£ìAìáË[F¸2”žŒ°dÆ‹Á–neCDœ/€6­è%“dž =yðÿ•÷JD¿¾“wÁÁú^W†þ,öÝ~틍èÞXÚŽ&²<Ú×m¯ˆ½L4ÇÌ^gžDkª50|Mà€EØÍÓd±mºûïq&ûÓÔÝñÙ”s'j4Blø4Áñ1ˆýË×Þ½|àCÐû¹
î
pàçYöR]SLZá:‰ýXlÎ_|î½ët—é¯^—BÐ_0‹7~Û­ „8ŽªÝ2?{»}ö‡’¿
+xÚÍXÝoÛ6ï_a{Z%‘²‹a@Ó6[‡-0£õA–˜X,”/ÿýîx§KJ—¶ŠäÝñ¾Hþ(òrûâÕUä-Dè¡òÛÛ…ðCwíù‹ÈS®ð7‹mº¸qÄr%<Ïs>Þ/…çhƒßûLŸ–Ÿ·?¾º
+Åbãn”¯p¼·Xù¾ë«ˆFn÷z	å|Z
+!]ÚÄ»Ü#ç'Äw,q4åRHЛêŠ(¦lê¬ ^äÔ%Q“òplj)«Ê—Â)kêtÆH(Íâ;ª—Ð
+„“IÞ¤+tÝÂÝHIîfÅÊ(§¶~‘“äqUe	SOy¹"Ù¶ÂFëU’™$çQ­Eâï–¾ç45Ê+ô”;$p¿ô¥›L×D/o‰Q‚¦"Ú)«÷DM³[p«.ê¹0 •GmêŒR'Û,)ç¶4DiŽT·I­4j¼Ç	б*]Wîrx¾óIqšfuVr/«yBb&sš 9Œ2æŸöY²g»íºˆŽ‰1Ï„¢c;DyŽÑèÝ™‡~VQÁ–ÝŠs¢Ø °¶F”€%cŒ®Že‘Ò¯h;m¨m³
+5D̪k}`íe+ƒ3AÍ“Îîö˜›w·{ë–·æUfgÀÛ8ï›ÜÆp5
+Õ%„(‘ ²ÓT×û²
Sĵ^1fÃEìAʁyoYIŸ·jÎãqn$çj}8Ú	ͬ¨a!ꤶj,i㲦%C”¶kGâ\h3[nJ©”Ù„![Wdý*»k¬£Q€(ƒUµ/q-ž*êÆTöP†ñC—㧎͕e…}§‚B$€CYäÔ»-›"ÅUmœíríٍ‰ÚLŒ®[„‡ž·PQ¿¤a'0ÈÀi*Ûðí!
gk›ÿ?ãÃ1gIôÊ"gSøÂõ#	ócõÿ
+(QCÑÎ
Ê[nç¶L7”0zÓŽNã:&c˜
+¬/KÄ®\…Ö©šÌÝñ™Ú¼1†<«êª÷Ö6ît¡9J¹RŽRÄÍK ³L²¸Ö)õºpIÑv–¼é †0¼ìL\T‰ÉŽ1ÈDŸã¤.MÅSçg€žÏ|·\I?°	Ê ì ÀIˆê(¿{Òƒêç²à¢¢;α&q1·gØRÊCj®Yû×gnF«:ÓZñpó|£…g1è|ÿĉ!Ö¬	ȱm†Ö%XDþ¹Wßû#›ÝB	‰ôšª({ë¯íÞ@S at y
+EAñ¡P>ûšo¸`Xï ü åâœ}ɦ.YÈý–˵õf–ý®'»Ð¤23—ú‚1þf
+>1>ÁÞEP6ç1"kÍì”+( ü2õö	©xËmù8û’zÏ‹ûšÕ\süßÛО¸â£iàÁ`ZÓÿOÁ¿ç	ºz΢NúhaGœ–Ñ$G¬ì‘ð~|YlÙ¹¹˜Fø¿¢­k7üº=\MU3óÀñ]›&arÌ8[î¾è–Ö³ýó;§ð¤QA{ÒœcéÔ/ßs×k¿•~=ãö8
­³hþ©¬þ,ù[»­:‰!˜ÿSþ;»ã+§ûÍœ?Ìâ¹ò…YÉ9-wø¯ÙrE¤‚˜³Ò9ÇÏZ8/9	=ªmnÇ#ý|3ÌœOo0*Ö11%yƒ­8S©^òL—˜êS]bª‹¤'~‰©_bê—˜ú%¦~‰©_bê­+!]¥Äùyx‘£Nç†û
÷%ôeDó'™§x>Cæ)n·ãä ïw˜Lýö<–ìP;²²xw ³÷‹N.’!œïyÁ€§,oˆÚÀÏöFNw¼ó„3
ð‡L·à&py¥ÿ7B+\Ñåä†ÿýÀ^§|Á7\+èÁŠX¡Ñi“°={Ë
ZL]0æ6YîQò©?¢SÁÎÁ×XêÆnÉî bD»à
+;Üä½äÅÌ~±ç¶þE‹…x’=1˜ƒÿ
+g”=Š}#|aËWF˜2“–Ìx1ØÒ­l at HBù" xÓÊ^2ê~È{lðÚ“‡þ_ý^‰ìçwò¾7˜ßë²æ?‹}·ßdûò"»·’¶c˜ñÕÆà1ç†æ˜â…qæ©@¶¦Z‘ W
0#ω »yº¥rÃMØþ{gÂÁŸ&Ñ
+Ðó(ç'*2bøÄàÓ£ûA/~÷‚A*@ïsÜàÀϱðR]qL†¯×‘r•Üœ¾ôl1zŸé.Ó_½:/¥ä¿`¡6n ðGËàÎ'Õvš_¼ß¾øFòR
 endstream
 endobj
-47 0 obj <<
+178 0 obj <<
 /Type /Page
-/Contents 48 0 R
-/Resources 46 0 R
+/Contents 179 0 R
+/Resources 177 0 R
 /MediaBox [0 0 595.276 841.89]
-/Parent 34 0 R
-/Annots [ 43 0 R 44 0 R ]
+/Parent 134 0 R
+/Annots [ 173 0 R 174 0 R 175 0 R ]
 >> endobj
-43 0 obj <<
+173 0 obj <<
 /Type /Annot
 /Border[0 0 1]/H/I/C[1 0 0]
 /Rect [167.481 608.978 174.455 619.882]
 /Subtype /Link
 /A << /S /GoTo /D (figure.1) >>
 >> endobj
-44 0 obj <<
+174 0 obj <<
 /Type /Annot
+/Border[0 0 1]/H/I/C[0 1 0]
+/Rect [373.763 599.18 380.737 607.927]
+/Subtype /Link
+/A << /S /GoTo /D (cite.boyer2005) >>
+>> endobj
+175 0 obj <<
+/Type /Annot
 /Border[0 0 1]/H/I/C[1 0 0]
 /Rect [341.758 202.448 348.732 213.407]
 /Subtype /Link
 /A << /S /GoTo /D (figure.1) >>
 >> endobj
-49 0 obj <<
-/D [47 0 R /XYZ 124.802 740.998 null]
+180 0 obj <<
+/D [178 0 R /XYZ 124.802 740.998 null]
 >> endobj
 6 0 obj <<
-/D [47 0 R /XYZ 124.802 716.092 null]
+/D [178 0 R /XYZ 124.802 716.092 null]
 >> endobj
-46 0 obj <<
-/Font << /F51 41 0 R /F41 32 0 R /F55 50 0 R /F58 51 0 R >>
+177 0 obj <<
+/Font << /F70 171 0 R /F41 132 0 R /F74 181 0 R /F76 182 0 R >>
 /ProcSet [ /PDF /Text ]
 >> endobj
-57 0 obj <<
-/Length 821       
+189 0 obj <<
+/Length 820       
 /Filter /FlateDecode
 >>
 stream
-xڝVmoÓ0þÞ_ñ)ÄóÙq^&@bb“@iZµ} $ÒÔkMR’Œ©ÿž³}iÓ­LU'Û÷î'wçžÍg'*õ2–Å"öæ·ˆˆ¥\x	Ï$‰7_z_ü·A¨„ô7
øk¤i@úÊÇå©'–Fª‘$Ò+gµ$‹WH+¤’Lz§öÆ-Èy‡ô	é
-éÜŁàÛüãì|>ã<P&?éE‘WÔ³_3Îb«ÈªL÷V8ZãäC-¼÷íì£(½†·g£&	ÁY‘'3Ôæ±Ãè¢ZÝu:…â>œ¡Ž±Ç¡ì´‹ª+Ö¤€
¢Ñ4òU—×æŽ^˜bæqê…2Æ2çüò®Œ©ä~ÑÖuÛ¬·A¬ÂBJÿžDu¾u›2÷ |õz@œ…Èüû²í‰Y5ƒîz]UÛôŽe]¡–`9?›6Ê¿w§ÅÖɇ’|4wuèò†ˆeQ„+°L(Ý™
-¿½u«^ëZ7CÏ@±?/µM%EÞ¸Íbdt:ôÒòÞÁZUÓZ%KdŒŸÎ»¦k,YõÃÏ&™ÌĨÝ.~àÍ{Š¹uk·Ù¬·U³¢¨niòzÌÃaZíþ^ó
-!Mˆ”°P.àñúœ¦&Å.Íþ”L›4$'ÔA“–“N4­'œè5nýÖ«]+_Ûôåg¤œœèG}Zì^ ÝR¤–ÎÔûf» ?‰l7ï4Ž£r4’Ã!›~ÑL0É«ïG ¢LG¹IŽ¸
lçžò‚‚ï4(±ÄÞÂÖ¾„uÕáy$ÔáÇý[»HðTÆÿœp:&üÆǘx.Š&'þß(>H	luîŠbœôZ"žâPLþ¦¬
-C8œ\WbKJ	8©pòšIhfN=nÐXŠoÛsçFÄ =ÎyÕ»•&V´Ä‘`F¨åšf6›uK“±oŽ4öÉKe¹h_š^(Jw¢ð=PÉá|Í1²{BÜ€å¾Î¥ÙM§;qz·nºvÓv†Ÿ¯é…jÇ—Ê=ʼÕªÈ"ïGŸn>v‚Ù!Θ´-bµÄôÏ!ßí?‹Sû
+xڝVmoÓ0þÞ_ñ)ÄóÙy ‰‰M!¤iÕö
HS¯	4IIR¦þ{Îö¥MÖ2
+Tlß»ŸÜ{1Ÿ]Å‘“²4‘3¿w@,á‰yÊ ŽùÒùâ¾õüPHwほFjz¤¯<ä¸Ü"uÄRH’Dze­–dqGâi…TIgÕÞØå
+9ï>!Ý ]Ú8à}›œ]Îgàpü¡ÎO: ÆEàäÕì׌³HFa`TÆ{#,‰qö¡Îûfv¿Aä^ý‘ۍQ #Œ„à,€À‘)jóÈbtU®¶­ò|rÎ=_Ç‹˜c_´JùyÙækR@È Ñ¨k{\–ÙªÍ*}GÇO0ó(q|a©u~½-{m*¹›7UÕÔ띅a!¥û@¢*ÛÙM‘y‚»¿=]uªGœ…H݇¢éˆYÖ½j;•÷eSw–e\¡–‰`8?ëÆ¡û`O‹•÷ù¨·•o󆀥A€+°4$PªÕ7nsoWµV•ªûŽi€"w^(“Jò¬¶›ÅÀhUÖ«¥=d‚µŒk5’,–~:ì–
+¬6dÔ§ŸM2™ŠA»YüÀ›wsg×n»Ù¬we½¢¨v©³jÈÃbš÷Íá^ÇyùÄDBX„6àéú?NS“bŸfwN
ÆMê“ŽÈá¤I5
+ËQ'êÖVô·þAë€Õ¾•oˆ­ûò3RFNÔQŸæ£H÷©¡3õ¾Þ.ÈOK"ÓÍ{Ó¨œŒdqˆÇ_4LrÀêû	¨°(“A®“…n Û9€§¼ †à{
+J,6·0µ/!FÝpúÁ_ž5ý¸Kx	žÊøŸN†„ÃáÏEQçÄÿÅG)©Î}Q“þQKøÀŠñ´àïŠ2Ç1„ÃÉv%¶¤”€“
+'¯ž„ú çÔqƒ&ÀÌý¹s#`Ldžu^vv¥I…-q$èj¸z éÍfݐÁhìë#}òR.Úºòžè|Âx:_3ŒlŸ;`¹«2m©wãéNœÎ®›¶Ù4­ægkz¡šá¥²C¨_‚rUôd‘uƒO»Ž;ÁL‚¥LšH°Z"úçïö—Ìû
 endstream
 endobj
-56 0 obj <<
+188 0 obj <<
 /Type /Page
-/Contents 57 0 R
-/Resources 55 0 R
+/Contents 189 0 R
+/Resources 187 0 R
 /MediaBox [0 0 595.276 841.89]
-/Parent 34 0 R
-/Annots [ 53 0 R ]
+/Parent 134 0 R
+/Annots [ 185 0 R ]
 >> endobj
-45 0 obj <<
+176 0 obj <<
 /Type /XObject
 /Subtype /Form
 /FormType 1
 /PTEX.FileName (Vennfig-pVmonth3.pdf)
 /PTEX.PageNumber 1
-/PTEX.InfoDict 60 0 R
+/PTEX.InfoDict 192 0 R
 /BBox [0 0 432 432]
 /Resources <<
 /ProcSet [ /PDF /Text ]
-/Font << /F2 61 0 R>>
+/Font << /F2 193 0 R>>
 /ExtGState <<
 >>>>
-/Length 62 0 R
+/Length 194 0 R
 >>
 stream
 q
@@ -1956,58 +2334,58 @@
 Q
 endstream
 endobj
-60 0 obj
+192 0 obj
 <<
-/CreationDate (D:20090925231417)
-/ModDate (D:20090925231417)
+/CreationDate (D:20090927152851)
+/ModDate (D:20090927152851)
 /Title (R Graphics Output)
 /Producer (R 2.9.0)
 /Creator (R)
 >>
 endobj
-61 0 obj
+193 0 obj
 <<
 /Type /Font
 /Subtype /Type1
 /Name /F2
 /BaseFont /Helvetica
-/Encoding 63 0 R
+/Encoding 195 0 R
 >>
 endobj
-62 0 obj
+194 0 obj
 10550
 endobj
-63 0 obj
+195 0 obj
 <<
 /Type /Encoding
 /BaseEncoding /WinAnsiEncoding
 /Differences [ 45/minus]
 >>
 endobj
-53 0 obj <<
+185 0 obj <<
 /Type /Annot
 /Border[0 0 1]/H/I/C[1 0 0]
 /Rect [401.053 272.252 408.027 283.156]
 /Subtype /Link
 /A << /S /GoTo /D (figure.2) >>
 >> endobj
-58 0 obj <<
-/D [56 0 R /XYZ 124.802 740.998 null]
+190 0 obj <<
+/D [188 0 R /XYZ 124.802 740.998 null]
 >> endobj
-52 0 obj <<
-/D [56 0 R /XYZ 259.756 411.062 null]
+183 0 obj <<
+/D [188 0 R /XYZ 259.756 411.062 null]
 >> endobj
-55 0 obj <<
-/Font << /F58 51 0 R /F41 32 0 R /F55 50 0 R /F59 59 0 R >>
-/XObject << /Im2 45 0 R >>
+187 0 obj <<
+/Font << /F76 182 0 R /F41 132 0 R /F74 181 0 R /F77 191 0 R >>
+/XObject << /Im2 176 0 R >>
 /ProcSet [ /PDF /Text ]
 >> endobj
-68 0 obj <<
+200 0 obj <<
 /Length 1178      
 /Filter /FlateDecode
 >>
 stream
-xÚ­VMÏÛ6¾çW=9À×–?3`Úµ¶Û¶¬;¬;(¶’hu$W²ß4ÿ~¤Hç£oì0Š%Š¢È‡(½Ý,^(›h¬+QE›]”‰"iRÕé:Éê:ÚtÑŸñËU)òxXfqÍB¡}JË>¡uд#OhO´ªcѬ¢¡í¡ØŠ'µïé³
ɯÐ~‡öþjÏІ`ävÁ+´lÖq¿ç­<´Wäh¶ükóóâýf‘E)ü²(+1À<*D–¤¢ˆÚãâË"Mª¼*‹ rÛ“óJ¼þé˜GïìâøÍS«ÙêêÆì[¹Èn@i“¬kåkÐN+ùƒÞObe‹ï–«<Kã74OKØ•W#	NJï£êh	È `chØi¹wòˆ
G«jØt•WàΚwZfelhçe<”WÔÝJ¯[ìVñÐÛÑ?a¿‰§yÞî.KÐ80§¼cN•TM
+xÚ­VMÏÛ6¾çW=9À×–?3`Úµ¶Û¶¬;¬;(¶’hu$W²ß4ÿ~¤Hç£oì0Š%Š¢È‡(½Ý,^¨«h¬+QE›]”‰"iRÕé:Éê:ÚtÑŸñËU)òxXfqÍB¡}JË>¡uд#OhO´ªcѬ¢¡í¡ØŠ'µïé³
ɯÐ~‡öþjÏІ`ävÁ+´lÖq¿ç­<´Wäh¶ükóóâýf‘E)ü²(+1À<*D–¤¢ˆÚãâË"Mª¼*‹ rÛ“óJ¼þé˜GïìâøÍS«ÙêêÆì[¹Èn@i“¬kåkÐN+ùƒÞObe‹ï–«<Kã74OKØ•W#	NJï£êh	È `chØi¹wòˆ
G«jØt•WàΚwZfelhçe<”WÔÝJ¯[ìVñÐÛÑ?a¿‰§yÞî.KÐ80§¸cN•TM
 8„M>r7Åù‘ж—3wØ”ER+ƒl?Ë=ï”gêx{T£>*OÎZŒçÿ”û¬ûžýÞ.EO#ᐭ+HL,Y—¹FÄ*`­
 ÀC¯µÇ¡Whê+
 Dìõ8ÉQ[ãIAô=H :»©§¾Üê^ZùÒWRçÇûu²ïíR”ñ‰—#–³Ú1 ŒšôyFmé´Ï$€yŒ(åPJ
@@ -2017,34 +2395,33 @@
  C‚
 Q
%Á	̏hÖDJøÊ®óÜ£Ï%	ÐIhšà 
ŐçÑY\ˆGo
 †MÛOä.%’_ôΏüD²aõjmo'G}
-á!ßžu7…}AvÙ“À«ABfU•q•	
-|‘äE%°¦ÀVyžTPŽÃVb¹ÊÒ4„Ã>át“©p°óÆËsÁ×ÙÜ’¢är*’ìÎ …Mu„׺ìä	æüƒ¢‡X4P=Éà&d
+á!ßžu7…}AvÙ“À«ABfU•q•	ªq‘äE%°¦ÀVyžTPŽÃVb¹ÊÒ4„Ã>át“©p°óÆËsÁ×ÙÜ’¢är*’ìÎ …Mu„׺ìä	æüƒ¢‡X4P=Éà&d
 €Ý{ê</Kn™%èÒ\+ï®ç—› Ïy6kKÇ› ¡!†p‘ò‘2Z™6(ÁÁ€äʱ3ÄZôŠ.&̉`É´\7qH'+”âºLê&¿Ï~C–Ô3]j<´Xèݙāˆ·Ó (:z"ÀaæSš
-¨¸H¦„ÀÆÉž¬!¹lfû·jÇ[“uÜöÒû ‹¦JÄ¿ßiïnî´¿ALxÞ¼D5Ûº».Œƒ ÌLpÓ¤I,ùÊ'·z\op˜¹)Bó
-µ`$Êÿú”ó,šŸsùÿõ”›_a¸ã æÈÕ—‰Î~¸ÿúpßDÂAˆ2xØÀó8iR6|°Ëù‘÷¹É%
+¨¸H¦„ÀÆÉž¬!¹lfû·jÇ[“uÜöÒû ‹¦JÄ¿ßiïnî´¿ALxÞ¼D5Ûº».Œƒ ÌLpÓ¤I,ùÊ'·z\op˜¹)Bõ
+µ`$Êÿú”ó,šŸsùÿõ”›_a¸ã æÈÕ—‰Î~¸ÿúpßDÂAˆ2xØÀó8iR6|°Ëù‘÷õÉ*
 endstream
 endobj
-67 0 obj <<
+199 0 obj <<
 /Type /Page
-/Contents 68 0 R
-/Resources 66 0 R
+/Contents 200 0 R
+/Resources 198 0 R
 /MediaBox [0 0 595.276 841.89]
-/Parent 34 0 R
+/Parent 134 0 R
 >> endobj
-54 0 obj <<
+186 0 obj <<
 /Type /XObject
 /Subtype /Form
 /FormType 1
 /PTEX.FileName (Vennfig-pVS23.pdf)
 /PTEX.PageNumber 1
-/PTEX.InfoDict 70 0 R
+/PTEX.InfoDict 202 0 R
 /BBox [0 0 432 432]
 /Resources <<
 /ProcSet [ /PDF /Text ]
-/Font << /F2 71 0 R>>
+/Font << /F2 203 0 R>>
 /ExtGState <<
 >>>>
-/Length 72 0 R
+/Length 204 0 R
 >>
 stream
 q
@@ -3474,13 +3851,13 @@
 ET
 BT
 0.000 0.000 0.000 rg
-/F2 1 Tf 20.00 0.00 0.00 20.00 318.17 208.82 Tm (7) Tj
+/F2 1 Tf 20.00 0.00 0.00 20.00 336.77 208.82 Tm (7) Tj
 ET
 BT
-/F2 1 Tf 20.00 0.00 0.00 20.00 121.26 208.82 Tm (12) Tj
+/F2 1 Tf 20.00 0.00 0.00 20.00 95.48 208.82 Tm (12) Tj
 ET
 BT
-/F2 1 Tf 20.00 0.00 0.00 20.00 228.48 208.82 Tm (8) Tj
+/F2 1 Tf 20.00 0.00 0.00 20.00 227.37 208.82 Tm (8) Tj
 ET
 Q q
 Q q
@@ -3488,90 +3865,91 @@
 Q
 endstream
 endobj
-70 0 obj
+202 0 obj
 <<
-/CreationDate (D:20090925231419)
-/ModDate (D:20090925231419)
+/CreationDate (D:20090927152854)
+/ModDate (D:20090927152854)
 /Title (R Graphics Output)
 /Producer (R 2.9.0)
 /Creator (R)
 >>
 endobj
-71 0 obj
+203 0 obj
 <<
 /Type /Font
 /Subtype /Type1
 /Name /F2
 /BaseFont /Helvetica
-/Encoding 73 0 R
+/Encoding 205 0 R
 >>
 endobj
-72 0 obj
-24236
+204 0 obj
+24235
 endobj
-73 0 obj
+205 0 obj
 <<
 /Type /Encoding
 /BaseEncoding /WinAnsiEncoding
 /Differences [ 45/minus]
 >>
 endobj
-69 0 obj <<
-/D [67 0 R /XYZ 124.802 740.998 null]
+201 0 obj <<
+/D [199 0 R /XYZ 124.802 740.998 null]
 >> endobj
-64 0 obj <<
-/D [67 0 R /XYZ 248.314 411.062 null]
+196 0 obj <<
+/D [199 0 R /XYZ 248.314 411.062 null]
 >> endobj
 10 0 obj <<
-/D [67 0 R /XYZ 124.802 273.498 null]
+/D [199 0 R /XYZ 124.802 273.498 null]
 >> endobj
 14 0 obj <<
-/D [67 0 R /XYZ 124.802 244.498 null]
+/D [199 0 R /XYZ 124.802 244.498 null]
 >> endobj
-66 0 obj <<
-/Font << /F58 51 0 R /F41 32 0 R /F55 50 0 R /F51 41 0 R >>
-/XObject << /Im3 54 0 R >>
+198 0 obj <<
+/Font << /F76 182 0 R /F41 132 0 R /F74 181 0 R /F70 171 0 R >>
+/XObject << /Im3 186 0 R >>
 /ProcSet [ /PDF /Text ]
 >> endobj
-77 0 obj <<
-/Length 993       
+209 0 obj <<
+/Length 992       
 /Filter /FlateDecode
 >>
 stream
-xÚ•V[¯£6~ϯà¤Åë6Pµ•ºÛ=RûЪUÚ>´}ð
Ÿ@p
-d³ù÷Û	çdµ[E–ÇÆžË7ߌóf¿{ý ‹¨$¥â*Ú?EŒg¤ <ÊiIXžGû:ú3þ6I%ñÛ„Å"ˆ_ƒ˜±ÑÂèaaœ`Ì0ãw”QIq{º9Ú{å,~´Ö¨õüÜÂ8ÀhðÊŽ}¦=ìü
-ã7ï‚
-–ü½ÿ1¢QÊ)¥Ü⍨´F74tÆ044W—?£ÕÝêÐíùzë-¶ÜÞ½Ûï¨ ‹˜t(‹H”9a,‹ª~÷ïŽ%”Ìü‘[Ù\nâÆëú,úÞî~ßò)]´¦7j߸Lgì&ÓœRRÒ"¹$¬T!”‡öpM’rIcñU’
-FãïÂòlÚC3›:¬æf4&­Ú±êð8$”
\Öu«£î=^©b„))BE°ô“ÝE
-X5(œ&ìS˜u˜žNC5·vÀÕhûëEP–·´(¼m®ýñ-œE¶žõ±i«)èÚÇQ—°8êê½> …2Ö]·õub4CmÆ„S(<Ëa"ßr¦Έ Mo¡âj4:໧	N܉®(ˆ¤Ù'çùrÚ>þcªy"V*ãý]ô$#²äˍÿWÛ/í«Œ”%[´Ýä"¬ôâžõûhfŽ°ù!ášÖÌ—°8{49‡ô§7hj ¡ˆ§Þ³ƒ5ÏâéT5AÒӝ8!'4_‘ù|·y[V’œÉ);Ì£í:—5o5ð
„ƒ±½™=‹œ3CßíÑvö€ÛžE¹¼ÞªGh at 2>ƒ¾WH#.I©Ù~nÚ¥þîWƒ(	¿æsÛ¢îòEäëip»±X‚ Ã4œúG`¹—½óîÓ³,ÀÖwf쬑~]/ýb:vú’(	Ì
-q@ô¡rçZª8Q
-òù—¬r“”Q
-Mê™Þ£†æcf3ÞKëßQ¨ÄB*$ bäg·Zré>¶C˜v¼ržku…—Û)ÌKÄá/¨ünz8“ÀÃbAü
ž
-y¸Çùã'ò•IÂåÊbÓ}°ç’">I 3+×62!Õ­ÿ^šI…ë’¼Üro…W®YNsf{ÏbN¤Ê¿˜ˆºòJD×±2ÿ± 1u
-+O@µô`Åž»†9	‹sc¼žŒºÿ\eñ“]´úüëþØ,:h·Y¶Äoädf¬
°±TÅòhÞ°Æ—–È•çÇÛ¡n]§ûÐÖ'xR.KÕtžaßÑ#¦Jÿ
À‡Œ‘þx'ÔòWâ?Ÿ©l4
+xÚ•V[¯ã4~ï¯Èc"m¼¾'A€Ä.{$x 
+< >‰O6‰K’n·ÿžñ-mÎéjU–ÇŽ=—o¾÷Í~÷ú¡I…*Ie²Jå¨Ä4)p…HQ$û&ù3ý6ËeéÛŒ¤Ì‹_ƒ˜{±ÑÀ`aœ`,04ã÷ aü…ÛóÍÑÁ)'é+¯µ	ZÿŸ;m¸2ûcßøi;¿Âø
+Æ;oƒdïLp’‚*!6XESPÚ7Ç`èÂPÁ ¾ºü­öVÜ^®·Þ†ÀâíÝ»ýŽ€
+œ„‹2KXU BxR»wI&wGne÷1Þ¯xò½Ùý¿ø)Zóµol¦9¹É4ÅU¸LX!©¤å¡;œ&åTà”}•åŒàô;¿<ëîÐ.ºñ«¥´ÎënªûpJ ®qô˦S‡I
+¯\D$‡$ÂÌ[úÉ,ö"¬Ú œæ ˜'?+?=ÆzéÌV“®A=0˜ß2˜•ˆá
+ pv¶¹vÇ·0PT–|==©cÛÕ³7Ðw“š.~qTõ{uÐ 
+-Eªú~ëëŤÇFOÅP .xRHDX±åL7¬šÞL¦õ¤•ÇvO3œ¸]Y"ùÇ¥E<mÿÑõ2#H+éþ.z‚ QÑxãÿÕöKû’£ª"QÛM!ÂZ>îE½Ï€f:Àá7?dÔBÓéåâ÷
g‡&¥^àôM ”éá4èq±°<Ouë%5߉r‚‹™Ïw›—±ñ
+D¬H™q™LßÛ¬9«ž ´ôâXd›ðÝMoaÛ±¨×[Í
+H¤gÐ÷*Ј
+T at j6ŸÛ.Ößýj`¢×|n[Ô]¾°b=
+n·&Ô{«f/(?§áXîdç¼ýô,°µ…ÅžG³¨À·nb¿˜½ºdR ³|ÐÌ\¨Ôº–KŠ¤„¼Cþ)½‡Ñ,'C“z¦÷¨ ùèEO÷Rgûw‰dPb!gÑò‹]­Ù‚´»ÑÏZY^ÙO–µª—»ÙÏ1b§— ünz(ÀÃ2"þž:ðp揟ȈŠ•Åº×zoÏ&…}’ &¯Ö62ª÷þ½4“3Û%iµåÞ
+1 .m³œ/-æžÅ	Y|11t啈¶cq–þ±c!ÔÙ¯
eìÁ’<w-äÄ/έvz8¶ÿ5¨ä铉Z]þÕpìu(:h·œÇ¸Ã9ë%Ô ØˆUÍÖ¸Ò%¹òüx76ítºæOÊ%VMoàv=!²Bð |àð_À9!ã_‰ÿ Ä
l=
 endstream
 endobj
-76 0 obj <<
+208 0 obj <<
 /Type /Page
-/Contents 77 0 R
-/Resources 75 0 R
+/Contents 209 0 R
+/Resources 207 0 R
 /MediaBox [0 0 595.276 841.89]
-/Parent 34 0 R
+/Parent 134 0 R
 >> endobj
-65 0 obj <<
+197 0 obj <<
 /Type /XObject
 /Subtype /Form
 /FormType 1
 /PTEX.FileName (Vennfig-pwVmonth3.pdf)
 /PTEX.PageNumber 1
-/PTEX.InfoDict 80 0 R
+/PTEX.InfoDict 212 0 R
 /BBox [0 0 432 432]
 /Resources <<
 /ProcSet [ /PDF /Text ]
-/Font << /F2 81 0 R>>
+/Font << /F2 213 0 R>>
 /ExtGState <<
 >>>>
-/Length 82 0 R
+/Length 214 0 R
 >>
 stream
 q
@@ -21867,88 +22245,86 @@
 Q
 endstream
 endobj
-80 0 obj
+212 0 obj
 <<
-/CreationDate (D:20090925231422)
-/ModDate (D:20090925231422)
+/CreationDate (D:20090927152857)
+/ModDate (D:20090927152857)
 /Title (R Graphics Output)
 /Producer (R 2.9.0)
 /Creator (R)
 >>
 endobj
-81 0 obj
+213 0 obj
 <<
 /Type /Font
 /Subtype /Type1
 /Name /F2
 /BaseFont /Helvetica
-/Encoding 83 0 R
+/Encoding 215 0 R
 >>
 endobj
-82 0 obj
+214 0 obj
 310458
 endobj
-83 0 obj
+215 0 obj
 <<
 /Type /Encoding
 /BaseEncoding /WinAnsiEncoding
 /Differences [ 45/minus]
 >>
 endobj
-78 0 obj <<
-/D [76 0 R /XYZ 124.802 740.998 null]
+210 0 obj <<
+/D [208 0 R /XYZ 124.802 740.998 null]
 >> endobj
-79 0 obj <<
-/D [76 0 R /XYZ 240.25 387.151 null]
+211 0 obj <<
+/D [208 0 R /XYZ 240.25 387.151 null]
 >> endobj
 18 0 obj <<
-/D [76 0 R /XYZ 124.802 286.519 null]
+/D [208 0 R /XYZ 124.802 286.519 null]
 >> endobj
-75 0 obj <<
-/Font << /F58 51 0 R /F41 32 0 R /F55 50 0 R /F51 41 0 R >>
-/XObject << /Im4 65 0 R >>
+207 0 obj <<
+/Font << /F76 182 0 R /F41 132 0 R /F74 181 0 R /F70 171 0 R >>
+/XObject << /Im4 197 0 R >>
 /ProcSet [ /PDF /Text ]
 >> endobj
-87 0 obj <<
-/Length 1084      
+219 0 obj <<
+/Length 1085      
 /Filter /FlateDecode
 >>
 stream
-xÚ­WKÛ6¾ûW9ÉhÅð!êQ4òÚ"ÅæPÔHM\I–‰èáHr6ûï;$G¶d)Û¤c‘ÃáðÓÌ7Cí‹ÝæéL¼”¤¼ÝÞc<$	å^LSÂâØÛåÞßþoÛ@rá—[æw $! 
-H
rrQ %ê>PI݃mÿÙýáQ/`Œ¤Rμš]H2\v½ ?;«†´ºwªgîQ!¢~¾ÿÁdf‡Ï/Ölêà	nÖ½ÁÆÙ	_Ùì|rAóªŒÉ-šß¡®²î¦(ÏÑÒì|m­Dä§mÀ#–.°‹;»ô
-7ÈAÞN^e at gÝ:³	»ämóz·a •zÌcÒÐBx"
6ó²zóiCI$"Z“éØ.Ž;QñôM-½WíæOø—‚Ñk0qûÂP3dSjF’HXqD¨.d7º<uÄMR?üeFýÝ
½ªqôn˼~Ó¸i®UÙ©ÚMîõpÕû-—þ¾èŠf0¯Å!§RI˜ˆ ´={ÎIk>Ì1­
-N,†¢ëÑ3DÓæž[8?%\Æ^šbáq"¶
£”ú¿wêxЙªÒkg³s
-«%·† ödU‰“Z
?¨_ônª´& ÷›äE¦{Ý6¸¦îÚÓà†gç&CëžY[µ§Î+ÝŒ¾U“»ÁÞœ¨²QŸÇ¢ÉuSÎJ!r¨[“©$õ›Kdm}¬€¿Òÿ¢‡§k÷WF˜W²
-BžÀ›ë7+tw‡†­qôÙü]§ó¼Àuäú\2€ÇœP™Ž9-±ëÝÎzÐ2#"$œŠq—‚òLüòT#Ë€÷4"<âón a]¡ %<dgNÍzç
-)I’3ÉUyä…ËÈ©œ";´Ú¦ÇLÔXVŧ“6Ùþl~Te@[ýßôþ€ãPÊt\.îe´ìÒ¯0Üðö©e‡Uftõ¹!.î‰rË<‚ðÙc—ãWJqˆ[W6
™üƒŠ!d›ë”òL
-XqaèxkV
-oâÔ›z±ªu‚2 (ƒöñýÁÏ
-A!2"JüááhºOõ€xƒzÿ0ÖpÀÇIÊç¥ìª3LGW¶zA­ÜÃx¿"ÖôÅ
rn½ßF’å{J….¢Cˆ¶aÀ³n»s‘JWNk›RøµÞÀÜçÿb­;½Ô
-Ï<šÖÍB.›öf.9Æ[
-ßvµB%{‰8†+G|7U—]6„±ÿã%üƒ.×ü6 ü6Æ®/êíËÆJåèÇ0ÌhúÓñX]Æ 
J)®:åz> Ñ™Ó/±øÇ&0~Ù=G]‰úñwÀtÕ+!H(‰ÓsµÝzŸŽ“ó=¡‘ÙäsRM>;p;™›÷“¯mh	†QF¢8]«Ýþ‘zšQùcêI^ÈàrÂÿ°9‚¤Øâñ[ò_N¦ø
+xÚ­WKÛ6¾ûW9ÉhÅð!êQ4òÚ"ÅæPÔHM\I–‰èáHr6ûï;$G¶d)Û¤c‘ÃáðãÌ7#í‹ÝæéMy)I#y»½ÇxHʽ˜¦„ű·Ë½¿ý߶äÂ/·Ìï@4HB@ää¢@JÔ} ’ºÛþ³ûã^ÀI¥œy5»*d¸ìz	"@~vV=huïTÏÜ£BDý|ÿ
+‚ÉÌŸ_¬ÙÔÁܬzƒ;³^Ùì|rAóªŒÉ-šß¡®²î¦(ÏÑÒì|m­Dä§mÀ#–.°‹;»ô
+7ÈAÞN®2 ³î?Ù„]ò¶y½Û0€J=æ1ih!<‘Æ ›yY½ù´¡$‘­Étlǝ¨xú¦–Þ«vó'üKÁè5˜¸}a¨²)5#I$,Š8"T²]žºâ&©þ²
+£þ^Õ8z·e®ß4nškUvªv“{=Fõ~Ë¥¿/º¢ÌÕ¡8Â)‚T&" mÏžsÒšÏ sADÌG룂‹¡èzôW·¹çÆÎO	—±„&„XxœˆmÀ(¥þï:t¦*‡ôÚÙì\ê„D‰óa£!¨„=ÙGUâ¤VÀê½›ê
­	À}ã&y‘é^·
+®©»ö4¸áÁÙ¹ÉкgÖVí©sãJ7£oÕän°7'ªlÔçűhrÝ”³RˆêÖd*IýÁæY[+à¯ô¿èáÁéÚý•æ•lƒ'psÝãf…îîа5Ž>›Ÿ¢ëtž¸Ž\@ŸKð˜*Ó1§%v½ÛYZfD„„S1îRPž‰_žjdðžF„G|Þ
+ ¬+¤„‡ìÌ©Yï\a %Irf ¹*¼p9UƒSd‡VÛô˜‰˪øtÒ&۟͏ªh«?㛾?àÂ8”2—‹÷Ç2ZvéWnøûTƒ²Ã*3ºúÜï‰ò–yá³Ç,.ǯ”â$·®l 2ù-B(È6×(å™°âÂÐñÖ¬ÞÅ©7õbUëe at Píãû	CÄV
[TRUNCATED]

To get the complete diff run:
    svnlook diff /svnroot/vennerable -r 62