I'm trying to plot two parametric graphs as follows:
alpha3[t_] := {Sin[2t]Cos[t],Sin[2t]Sin[t]}
evoluta[t_] := alpha3[t]+(1/kappa[alpha3][t]) normal[alpha3][t]
graph1 = ParametricPlot[alpha3[t]//Evaluate,{t,-2Pi,2Pi},PlotStyle->{{PlotRange -> 1}}]
graph2 = ParametricPlot[evoluta[t]//Evaluate,{t,-2Pi,2Pi},PlotStyle->{{RGBColor[0.8,0.2,0.2],PlotRange ->1}}]
Show[graph1,graph2]
The result obtained is:
I would like that the whole plot appears on the screen, however, PlotRange->All is not working for me?
How can I do so?
Extra (code for drawing evolute)
tangent[alpha_][t_]:=D[alpha[u],u]/Simplify[Factor[D[alpha[u],u].D[alpha[u],u]]]^(1/2) /. u->t
J:={{0,-1},{1,0}}
normal[alpha_][t_]:=J.tangent[alpha][t]
kappa[alpha_][t_]:=Det[{D[alpha[u],u],D[alpha[u],{u,2}]}]/
Simplify[D[alpha[u],u].D[alpha[u],u]]^(3/2)/.u->t
ParametricPlot[{alpha3[t], evoluta[t]} // Evaluate, {t, -2 Pi, 2 Pi}, PlotRange -> All, PlotStyle -> {{}, Directive[RGBColor[0.8, 0.2, 0.2], Thick]}]
. $\endgroup$ – J. M.'s ennui♦ Mar 30 '18 at 0:32PlotStyle
just to show how to change styles for a specific curve. Remember to useDirective[]
if you want to apply more than one style (e.g. color and thickness at the same time). $\endgroup$ – J. M.'s ennui♦ Mar 30 '18 at 0:38kappa
ornormal
. Questions should include executable code. $\endgroup$ – Bob Hanlon Mar 30 '18 at 1:34