3 Date 20131122 Author Bernard Desgraupes University of Paris Ouest Lab ModalX Maintainer Bernard Desgraupes Description plot conics ellipses hyperbolas parabolas License GPL 2 URL httpwwwrprojectorg Collate mainR Encoding latin1 Imports graphics t ID: 70493
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2conicAsymptotes conicAsymptotesAsymptotesofaconic DescriptionFindtheslopesoftheasymptoticdirectionsofaconic.UsageconicAsymptotes(x)Argumentsxa6-lengthvectororasymmetric3x3matrixDetailsTheconicAsymptotesfunctioncalculatestheslopesoftheasymptoticdirectionsofaconicspeci-edbyitscoefcientsorbyitssymmetricmatrix.Iftheequationoftheconicisv_1x_1^2+v_2x_1x_2+v_3x_2^2+v_4x_1+v_5x_2+v_6=0theslopesoftheasymptotesaretherootsoftheequationatinnityoftheconic:v_1+v_2t+v_3t^2=0wheret=x_2/x_1.ValueAvectorcontainingtheslopes:twovaluesinthecaseofahyperbolaorofintersectinglines,onevalueinthecaseofaparabolaorofparallellines.Inthecaseofanellipse(whichhasnopointsatinnity),thefunctionreturnsanemptyvector.Author(s)BernardDesgraupes¾rn; rd.;Þsg;&#xraup;s@u;&#x-par;&#xis10;&#x.fr0;UniversityofParisOuest-NanterreLabModal'X(EA3454)SeeAlsoconicAxes,conicCenter,conicMatrix,conicPlot 4conicCenterExamples#Ellipse#Equation:2*x_1^2+2*x_1*x_2+2*x_2^2-20*x_1-28*x_2+10=0vc(2,2,2,-20,-28,10)conicAxes(v)#Hyperbola#Equation:2*x_1^2+2*x_1*x_2-2*x_2^2-20*x_1+20*x_2+10=0vc(2,2,-2,-20,20,10)conicAxes(v) conicCenterCenterofaconic DescriptionFindthecenterofaconic.UsageconicCenter(x)Argumentsxa6-lengthvectororasymmetric3x3matrixDetailsTheconicCenterfunctioncalculatesthecoordinatesofthecenterofaconicspeciedbyitscoef-cientsorbyitssymmetricmatrix.ValueAtwo-elementsvectorcontainingthecoordinatesofthecenter.Iftheconichasnocenterthefunctionraisesanerror.Author(s)BernardDesgraupes¾rn; rd.;Þsg;&#xraup;s@u;&#x-par;&#xis10;&#x.fr0;UniversityofParisOuest-NanterreLabModal'X(EA3454)SeeAlsoconicAsymptotes,conicAxes,conicMatrix,conicPlot 6conicPlotExamples#Equation:2*x_1^2+2*x_1*x_2+2*x_2^2-20*x_1-28*x_2+10=0vc(2,2,2,-20,-28,10)conicMatrix(v) conicPlotPlotaconic DescriptionPlotaconic(ellipse,hyperbola,orparabola)speciedbyaquadraticpolynomialorbyasymmetric3x3matrix.UsageconicPlot(x,type=l,npoints=100,sym.axes=FALSE,center=FALSE,asymptotes=FALSE,add=FALSE,xlim=NULL,ylim=NULL,ax.lty=1,ax.col=palette()[1],as.lty=1,as.col=palette()[1],...)Argumentsxa6-lengthvectororasymmetric3x3matrixtype(character)thetypeofplottodraw(samemeaningaswiththeplotfunction)npoints(numeric)numberofpointstodrawsym.axes(logical)ifTRUE,displaytheaxesoftheconiccenter(logical)ifTRUE,displaythecenteroftheconic(ifany)asymptotes(logical)ifTRUE,displaytheasymptotes(hyperbolas)add(logical)ifTRUE,plotoverthecurrentgraphicaldevicexlim(vector)intervalforthex-coordinateylim(vector)intervalforthey-coordinateax.lty(characterornumeric)linetypeoftheaxesax.col(characterornumeric)coloroftheaxesas.lty(characterornumeric)linetypeoftheasymptotesas.col(characterornumeric)coloroftheasymptotes...otherparameterspassedtotheplotfunctionDetailsTheconicPlotfunctionidentiesthetypeoftheconicandplotsitinthecurrentgraphicaldevice.Theconicisspeciedeitherbya6-lengthvectorrepresentingthecoefcientsofthequadraticpolynomial,orbythesymmetricmatrixrepresentingtheassociatedquadraticform.SeethefunctionconicMatrixtobuildthismatrixgiventhecoefcientsofthepolynomial.Itisusuallyagoodideatosetexplicitelytheaspectratioto1(asanadditionalargumentasp=1intheconicPlotfunction)inordertoavoiddistorsionsbetweentheunitsofthex-axisandthey-axis.Seeexamplesbelow. conicPlot7ValueThereturnvalueisinvisible,i-eitisnotprintedontheconsolebydefaultbutcanbestoredinavariable.Itisalistofrelevantcomputedvaluescorrespondingtovariouselementsoftheconic.Thefollowingelementscanbefoundinthereturnlist,dependingonthekindoftheconic:kindthekindoftheconic:"ellipse","hyperbola","parabola",or"lines".axesthesymmetryaxes.SeealsothefunctionconicAxes.centerthecenteroftheconic.SeealsothefunctionconicCenter.asymptotestheslopesoftheasymptotes.SeealsothefunctionconicAsymptotes.verticestheverticesoftheconic.focithefocalpointsoftheconic.eccentricitytheeccentricityoftheconic.interceptstheinterceptsinthecaseofparallellines.pointsthecoordinatesofthepointsusedtoplottheconic.Thepointscomponentisreturnedonlyifthetypeoptionisequaltonandiftheconicisnon-degenerate.Inthatcase,nothingisdrawn.Author(s)BernardDesgraupes¾rn; rd.;Þsg;&#xraup;s@u;&#x-par;&#xis10;&#x.fr0;UniversityofParisOuest-NanterreLabModal'XSeeAlsoconicAsymptotes,conicAxes,conicCenter,conicMatrixExamples#Ellipse#-------#Equation:2*x_1^2+2*x_1*x_2+2*x_2^2-20*x_1-28*x_2+10=0vc(2,2,2,-20,-28,10)conicPlot(v)v[6]20conicPlot(v,type=p,col="red",add=TRUE)#Symmetricmatrixmrbind(c(5,-3,-21),c(-3,5,-19),c(-21,-19,93))conicPlot(m)#Hyperbola#---------#Equation:2*x_1^2+2*x_1*x_2-2*x_2^2-20*x_1+20*x_2+10=0vc(2,2,-2,-20,20,10)conicPlot(v,center=TRUE,sym.axes=TRUE,asp=1)conicPlot(v,asymptote=TRUE,as.col="grey30",as.lty=2,sym.axes=TRUE,ax.col="red",ax.lty=6,col="blue",asp=1) conics9P(x_1,x_2)=v_1x_1^2+v_2x_1x_2+v_3x_2^2+v_4x_1+v_5x_2+v_6=0Non-degenerateconicsincludetheellipses,thehyperbolasandtheparabolas.Degenerateconicsarepairsoflines.AuthorBernardDesgraupes¾rn; rd.;Þsg;&#xraup;s@u;&#x-par;&#xis10;&#x.fr0;UniversityofParisOuest-NanterreLabModal'XReferencesFormoreinformationaboutthealgebraicbackgroundofconicsandtheirmatrixrepresentation,seethevignetteaccompanyingthispackage.Todisplaythevignette,typethefollowinginstructionintheRconsole:¾rn; rd.;Þsg;&#xraup;s@u;&#x-par;&#xis10;&#x.fr0;vignette("conics")SeeAlsoThefollowingfunctionsareavailable:conicAsymptotes,conicAxes,conicCenter,conicMatrix,conicPlot