# es. 6.1 sullo spazio tridimensionale (copia il file e incollalo in R)
f1 <- c(
-.414213562373095,-.414213562373095,
-.424791685539169,-.451517313086983,
-.434948208221595,-.489894945022477,
-.444651025618363,-.529472745182015,
-.453858796868471,-.570389929673295,
-.462519192583735,-.612800788139932,
-.470566689873235,-.656877222401279,
-.477919789171676,-.702811771240357,
-.484477486146866,-.750821238038765,
-.490114775815017,-.801151070558751,
-.494676888411297,-.854080685463467,
-.497971848242584,-.909929988177737,
-.499760793830234,-.969067417193793,
-.499745279209483,-1.03191994928049,
-.497550460246976,-1.0989856505363,
-.492702606439789,-1.17084956611254,
-.484598689084513,-1.24820403635305,
-.472464754141287,-1.3318749515026,
-.455298184444733,-1.42285607743187,
-.431786442281325,-1.52235450689613,
-.400190861368125,-1.63185168712879,
-.358177474166283,-1.75318663247224,
-.30256581164091,-1.88867134163107,
-.228947543988329,-2.0412539671217,
-.131092877510552,-2.21475449781336,
-6.41286419346375e-17,-2.41421356237309,
.177677346842635,-2.64642321028663,
.422330694503042,-2.92076098929882,
.766244727307833,-3.25055080129983,
1.262766517733,-3.65538435465226,
2.00478065863361,-4.16529977009041,
3.1649605791131,-4.82881735219276,
5.09261401118959,-5.7297416467243,
8.57927248163255,-7.02636622904135
)
f2 <- c(
10.8223556579139,5.7297416467243,
7.99377793130584,4.82881735219275,
6.17008042872403,4.16529977009042,
4.91815087238526,3.65538435465226,
4.01679552860767,3.25055080129983,
3.34309168380186,2.92076098929881,
2.82410055712926,2.64642321028663,
2.41421356237309,2.41421356237309,
2.08366162030281,2.21475449781336,
1.81230642313337,2.0412539671217,
1.58610552999016,1.88867134163107,
1.39500915830595,1.75318663247224,
1.23166082576066,1.63185168712879,
1.09056806461481,1.52235450689613,
.967557892987137,1.42285607743187,
.85941019736131,1.3318749515026,
.763605347268536,1.24820403635305,
.67814695967275,1.17084956611254,
.601435190289325,1.0989856505363,
.532174670071013,1.03191994928049,
.469306623363559,.969067417193793,
.411958139935153,.909929988177737,
.35940379705217,.854080685463466,
.311036294743734,.801151070558751,
.266343751891898,.750821238038764,
.224891982068681,.702811771240357,
.186310532528045,.656877222401279,
.150281595556196,.612800788139932,
.116531132804824,.570389929673295,
.0848217195636521,.529472745182015,
.0549467368008824,.489894945022477,
.0267256275478136,.451517313086983,
3.30082064485434e-17,.414213562373095,
-.0253695910641712,.377868511775821,
-.0495063157931475,.342376525728683,
-.0725192966729581,.307640169659898,
-.0945054731256488,.273569043082237,
-.11555116781958,.240078759080116,
-.135733406160739,.207090044427938,
-.155121030189139,.174527938894365,
-.173775640001218,.142321075702943,
-.191752389356393,.110401027815819,
-.209100656923414,7.87017068246185e-2,
-.225864610389051,.0471588028774803,
-.242083677162461,.0157092553236651,
-.257792932486126,-.015709255323665,
-.273023413266531,-.0471588028774807,
-.287802363748032,-.0787017068246184,
-.302153417172212,-.110401027815819,
-.316096715704161,-.142321075702943,
-.329648969083504,-.174527938894365,
-.342823450588678,-.207090044427939,
-.355629926899696,-.240078759080116,
-.368074516207886,-.273569043082237,
-.380159466332856,-.307640169659898,
-.391882841521831,-.342376525728683,
-.403238102839992,-.377868511775821,
-.414213562373095,-.414213562373095
)
f3 <- c(
-.666666666666667,-.666666666666667,
-.695374546879575,-.739123805113161,
-.725876612116767,-.817576153354045,
-.758578073751482,-.903284580498885,
-.793990082412236,-.997852086140473,
-.832770230837601,-1.10335368127316,
-.875782784177311,-1.22252971805596,
-.9241909216291671,-1.35908215836849,
-.979602856647865,-1.51814408439136,
-1.04431260962594,-1.70705354436325,
-1.12171573596997,-1.93668992248499,
-1.21706890314691,-2.22391586303584,
-1.3389783442482,-2.59636270343327,
-1.50258877059258,-3.10268329176028,
-1.73727260650604,-3.83727444382671,
-2.10850853925547,-5.01062157184577,
-2.79806766714831,-7.20711680570474
)
f4 <- c(
2.17557050458495,8.8712880305100,
1.13095722612153,5.53574480178966,
.635393498810028,3.96624286581801,
.341710922127813,3.04663139534605,
.144267683261367,2.43733684437973,
5.31259064517897e-17,2,
-.111962532817932,1.66763096588943,
-.202985914251879,1.4038130484967,
-.279812020887897,1.18701396080873,
-.346715783837871,1.00365303795608,
-.40656198385668,.844707140700334,
-.461366178120385,.703911771073898,
-.512612616824817,.576744644853103,
-.561444975023261,.459819643263938,
-.608787049038563,.350507840660583,
-.655423483244744,.246689549345563,
-.702057330523125,.146584200162219,
-.749354478459037,.0486269911628311,
-.797981469621868,-.0486269911628318,
-.848641530685345,-.146584200162219,
-.902113032590306,-.246689549345563,
-.959294889699146,-.350507840660583,
-1.0212646182872,-.459819643263938,
-1.08935726167792,-.5767446448531039,
-1.16527794919428,-.703911771073898,
-1.25126912455701,-.844707140700334,
-1.35036882179395,-1.00365303795608,
-1.46682598169663,-1.18701396080873,
-1.60679896274858,-1.4038130484967,
-1.77959349870736,-1.66763096588943,
-2,-2,
-2.29306916111836,-2.43733684437973,
-2.70492047321824,-3.04663139534605,
-3.33084936700799,-3.96624286581802,
-4.40478757566814,-5.53574480178967,
-6.69571752592515,-8.87128803051009
)
f5 <- c(
4.40904913855643,7.20711680570474,
2.90211303259031,5.01062157184577,
2.10000183732067,3.83727444382671,
1.6000945211677,3.10268329176028,
1.25738435918507,2.59636270343327,
1.00684695988893,2.22391586303584,
.814974186515017,1.93668992248499,
.66274093473731,1.70705354436325,
.538541227743491,1.51814408439136,
.434891236739318,1.35908215836849,
.346746933878648,1.22252971805596,
.270583450435561,1.10335368127316,
.203862003728237,.997852086140473,
.144706506747404,.903284580498885,
.0916995412372778,.817576153354044,
.0437492582335855,.73912380511316,
5.31259064517897e-17,.666666666666667,
-.0402292578528835,.59919648512519,
-7.7488264605993e-2,.5358945095287621,
-.112226652928834,.476086064417986,
-.144816741526333,.419207227807575,
-.175570504584946,.364779946989695,
-.204752400041369,.312393130185508,
-.232589214471684,.261688026190305,
-.25927773176305,.21234671148429,
-.284990798439138,.16408284231209,
-.309882199541455,.116634057383244,
-.334090649777449,.0697555720169068,
-.357743129046665,.0232146100073878,
-.380957739054053,-.0232146100073876,
-.403846221794355,-6.97555720169074e-2,
-.426516256924699,-.116634057383244,
-.449073640751228,-.164082842312091,
-.47162444324734,-.212346711484289,
-.494277240661989,-.261688026190305,
-.517145530226878,-.312393130185509,
-.540350451574641,-.364779946989695,
-.564023969333908,-.419207227807575,
-.58831271734682,-.476086064417986,
-.6133827741347549,-.5358945095287621,
-.639425742978074,-.599196485125191,
-.666666666666667,-.666666666666667
)
# riduco i margini
par( mai = c(0.5,0.5,0.1,0.1) )
plot(c(-5,5),c(-5,5),type="n", asp=1)
abline(h=seq(-5,5,1), v=seq(-5,5,1), lty=3, col="grey")
abline(h=0,v=0)
n <- length(f1)/2; f11<-vector(length=n); f12<-vector(length=n)
for(i in 1:n) {f11[i] <- f1[i*2-1]; f12[i] <- f1[i*2]}
lines(f11,f12,col="blue")
n <- length(f2)/2; f11<-vector(length=n); f12<-vector(length=n)
for(i in 1:n) {f11[i] <- f2[i*2-1]; f12[i] <- f2[i*2]}
lines(f11,f12,col="blue")
n <- length(f3)/2; f11<-vector(length=n); f12<-vector(length=n)
for(i in 1:n) {f11[i] <- f3[i*2-1]; f12[i] <- f3[i*2]}
lines(f11,f12,col="green4")
n <- length(f4)/2; f11<-vector(length=n); f12<-vector(length=n)
for(i in 1:n) {f11[i] <- f4[i*2-1]; f12[i] <- f4[i*2]}
lines(f11,f12,col="green4")
n <- length(f5)/2; f11<-vector(length=n); f12<-vector(length=n)
for(i in 1:n) {f11[i] <- f5[i*2-1]; f12[i] <- f5[i*2]}
lines(f11,f12,col="green4")
symbols(0, 0, circles=1, inches=FALSE, add=TRUE, fg="red")
# Scegli tra 1/2 e sqrt(2) i valori da dare a q affinche' la trasf. x' = x/(y-x-q),
# y' = (x+y)/(y-x-q) mandi il cerchio nell'una e nell'altra curva disegnata.