Math 2325 
Project 3 (Chapter 9) - Parametric Curve Representation

Helmut Knaust, Department of Mathematical Sciences, UTEP, El Paso TX 79968
hknaust@utep.edu
10/8/2012.

Curve Salad

We can think of the curve (({{x[t]}, {y[t]}}))=(({{Sin[p t]+Cos[q t]}, {Sin[r t]+Cos[s t]}})) as the sum of the two curves (({{Cos[q t]}, {Sin[r t]}}))and (({{Sin[p t]}, {Cos[s t]}})):

{p,q,r,s}={3,2,2,3};
x[t_]=Sin[p t]+Cos[q t];
y[t_]=Sin[r t]+Cos[s t];
endtime=2*Pi;
win=2;
(*Do not change anything below this line*)
Animate[Show[
ParametricPlot[{Cos[q u],Sin[r u]},{u,0,t},PlotStyle->Green,PlotRange->{{-win,win},{-win,win}},Epilog->{Green,AbsolutePointSize[5],Point[{Cos[q t],Sin[r t]}]}],
ParametricPlot[{z(x[t]-Cos[q t])+Cos[q t],z(y[t]-Sin[r t])+Sin[r t]},{z,0,1},PlotStyle->Dashed,PlotRange->{{-win,win},{-win,win}}],
ParametricPlot[{Cos[q t]+Sin[p v],Sin[r t]+Cos[s v]},{v,0,endtime},PlotRange->{{-win,win},{-win,win}}],
ParametricPlot[{x[u],y[u]},{u,0,t}, PlotRange -> {{-win,win},{-win,win}},
PlotStyle->Directive[Thick,Black]],Graphics[{Red,Thickness[.01],Circle[{x[t],y[t]},.02]}],
Graphics[Text[StringJoin["t = ",ToString[NumberForm[t/Pi,{2,1}]],ToString[Pi,StandardForm]],{.75win,.95win}]]],
{t,endtime/10.^5,endtime},AnimationRepetitions->1,AnimationRate->0.02]