某曲线的旋转版本及其它

某曲线的旋转版本

list=Table[ParametricPlot[Table[#,{k,0,3}]&@(RotationTransform[k Pi/2,{7,0}]@{7+Cos[\[Theta]] (-7+6 Cos[Cos[22 t]] Sin[2.94` t])-6 Cos[2.94` t]^2 Sin[\[Theta]] Sin[Sin[22 t]],(-7+6 Cos[Cos[22 t]] Sin[2.94` t]) Sin[\[Theta]]+6 Cos[2.94` t]^2 Cos[\[Theta]] Sin[Sin[22 t]]})//Evaluate,{t,-8,8},Axes->False,PlotPoints->500,PlotRange->{{-6,20},{-13,13}},ImageSize->350],{\[Theta],0,2Pi,2Pi/49}];Export["testSpecialCurve.gif",list]

五星

ClearAll["Global`*"];curve={-9Sin[2t]-5Sin[3t],9Cos[2t]-5Cos[3t]};x[t_]:=Evaluate@curve[[1]]y[t_]:=Evaluate@curve[[2]]deltaT=t/.Solve[{x[\[Pi]+t]-x[\[Pi]-t]==0,0<t<Pi},t];t0=deltaT[[1]]-2 \[Pi]/5//Simplify;ParametricPlot[curve u,{t,0,2Pi},{u,0,1},MeshFunctions->{Boole@((Or[Pi/5<=#3<=(Pi/5+t0),3Pi/5-t0<=#3<=3Pi/5,Pi<=  #3<=(Pi+t0),7Pi/5<=#3<=(7Pi/5+t0),9Pi/5-t0<=#3<=9Pi/5] )&&0<= #4<=1)&},Mesh->{{.2}},MeshShading->{{Yellow},{Red}},PlotPoints->120,Axes->False]/.Line[_]:>Sequence[]

ParametricPlot[curve u,{t,0,2Pi},{u,0,1},MeshFunctions->{Boole@(Or[((Pi-t0)<=  #3<= (Pi+t0)),((7Pi/5-t0)<=  #3<= (7Pi/5+t0))]&&0<= #4<=1)&},Mesh->{{.2}},MeshShading->{{Green},{Red}},PlotPoints->90,Axes->False]/.Line[_]:>Sequence[]

这样更清凉，有夏天来了的感觉：

ClearAll["Global`*"];curve={-9Sin[2t]-5Sin[3t],9Cos[2t]-5Cos[3t]};x[t_]:=Evaluate@curve[[1]]y[t_]:=Evaluate@curve[[2]]Solve[x[\[Pi]+t]-x[\[Pi]-t]==0,t]/.C[1]->0;t0=%[[4,1,2]]-2 \[Pi]/5//FullSimplify;ParametricPlot[curve u,{t,0,2Pi},{u,0,1},MeshFunctions->{Boole@((Or[(Pi/5-t0)<=#3<=(Pi/5+t0),(9Pi/5-t0)<=#3<=(9Pi/5+t0)])&&0<=#4<=1)&},Mesh->{{.2}},MeshShading->{{Green},{Red}},PlotPoints->90,Axes->False]/.Line[_]:>Sequence[]