What are the issues with the dynamic image code generated by sine curves? How to modify and improve it?

BX[t_] := 
  Module[{g1, g2, g3, g4, r}, 
   g1 = ParametricPlot[{{Cos[2 \[Pi] r], 
       Sin[2 \[Pi] r]}, {2 + \[Pi] t r/64, Sin[\[Pi] t r/64]}}, {r, 0,
       1}, PlotStyle -> {RGBColor[0, 0, 1]}, 
     Ticks -> {{-1, 0, 1, 2, 2 + \[Pi]/2, 2 + \[Pi], 2 + 3 \[Pi]/2, 
        2 + 2 \[Pi]}, {-1, 0, 1}}, 
     PlotRange -> {{-1, 2 + 2 \[Pi]}, {-1, 1}}]; 
   g2 = ParametricPlot[{{r + Cos[\[Pi] t/64], 
       r Sin[\[Pi] t/64]}, {r (2 + \[Pi] t/64) + (1 - 
           r) Cos[\[Pi] t/64], Sin[\[Pi] t/64]}}, {r, 0, 1}, 
     PlotStyle -> {RGBColor[0, 1, 0]}]; 
   g3 = Graphics[{PointSize[0.04], RGBColor[1, 0, 0], 
      Point[{2 + \[Pi] t/64, Sin[\[Pi] t/64]}]}]; 
   g4 = Graphics[{PointSize[0.04], RGBColor[1, 0, 0], 
      Point[{Cos[\[Pi] t/64], Sin[\[Pi] t/64]}]}]; 
   Show[g1, g2, g3, g4, AspectRatio -> Automatic]];
Animate[BX[t], {t, 0, 128, 1}]