如何用动画画出曲线或曲面的生成过程

Question

就是类似这样的效果

或者是类似马鞍面的生成动画（双曲线平移得到）

Comments

http://tieba.baidu.com/p/2178750344

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说白了就是一笔一划的画出来。就像怎么写汉字，先写一横，再写一竖，再写一撇，再....。

Answer 1

我画最简单的一个来抛砖引玉一下吧

pics = Table[
   Show[Graphics[{Circle[], Line[{{0, 0}, pst = {Cos[t], Sin[t]}}], 
      Arrow[{pst, {2, Last[pst]}}]}, ImageSize -> {Automatic, 200}], 
    Plot[Sin[4 (x - 2 + t/4)], {x, 2, 2 + Pi/2}]], {t, 0, 2 Pi, .05}];
Export["test.gif", pics]

Comments

想问一下，旁边对应的Sin函数是怎么确定的

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本来应该是Sin的，但2Pi太长了，为了好看，所以缩了4倍

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我的意思是要是变成了两个圆，怎么知道生成的函数是什么，两个圆旋转速度不一样生成的函数也是不一样的

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我抛的是砖而已，你问的是玉 :)

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oo,我自己再去看看，主要现在是我可以让两个圆动，但是不知道对应的函数是什么

Answer 2

http://blog.csdn.net/WinsenJiansbomber/article/details/50769511

Module[{x, y, t, s}, t = 0; s = 1.2;
 Column[{Slider[Dynamic[s], {1, 2}];
   Dynamic[Graphics[{
      {LightBlue, 
       Rectangle[{-Dynamic[s], -Dynamic[s]}, {Dynamic[s], 
         Dynamic[s]}]},
      Point[{1.2, y}], 
      Text[Style["by Jimbowhy", 18], { 2.6, -1}],
      Text[Style["(x,y) Sin(θ)=y/r", 18], {1.1 x, 1.1 y}], 
      Text[Style["r", 18], { 2 x/5, y/2}],
      Text[Style["θ", 18], {Cos[t/2]/4, Sin[t/2]/4}],
      Circle[{0, 0}, 0.3, {0, t}],
      {Thin, Dashed, Line[{{x, y}, {1.2, y}}]},
      Plot[Sin[-2 (z - 1.2) + t], {z, 1.2, 2 π + 1.2}][[1]],
      {Thin, Arrowheads[0.05], Arrow[{{0, 0}, {x, y}}]},
      {Thin, Dashed, Line[{{0, y}, {x, y}}]}, {Thin, Dashed, 
       Line[{{x, 0}, {x, y}}]},
      {Thin, Line[{{-1, 0}, {3.8, 0}}]}, {Thin, 
       Line[{{0, 1}, {0, -1}}]},
      Circle[{x = Cos[t], y = Sin[t = If[t >= 2 π, 0, t + 0.02]]},
        0.0]
      }, PlotRange -> {{-1.2, 4}, {-1.2, 1.2}}, 
     ImageSize -> {480, 220}]]
   }]]

 

Answer 3

n = 5;
colors = RandomColor[n];
calAngle[p_] := ArcCos[p.{1, 0}] Sign[Cross[p].(p - {1, 0})];
DynamicModule[{p = {1, 0}},
 LocatorPane[Dynamic[p, (p = Normalize@#) &], 
  Dynamic[r[n_][p_] := 
    1/(2 n - 1) {Cos[(2 n - 1) calAngle@p], Sin[(2 n - 1) calAngle@p]};
   positions = Accumulate[r[#][p] & /@ Range[n + 1]];
   arrowseries = Partition[positions, 2, 1];
   pointseries = Accumulate[r[#][p] & /@ Range[n]];
   radios = 1/(2 # + 1) & /@ Range[n];
   Show[
    Graphics[{Red, PointSize[0.015], Point[Last@positions]}],
    Graphics[{Arrow[{{0, 0}, p}], Circle[{0, 0}, 1]}],
     Graphics[{Arrowheads[0.025], Arrow /@ arrowseries}],
    Graphics[MapThread[Circle][{pointseries, radios}]]]
   ]]]

n = 10;
calAngle[p_] := ArcCos[p.{1, 0}] Sign[Cross[p].(p - {1, 0})];
DynamicModule[{p = {1, 0}}, 
 LocatorPane[Dynamic[p, (p = Normalize@#) &], 
  Dynamic[r[n_][p_] := 
    1/(2 n - 1) {Cos[(2 n - 1) calAngle@p], Sin[(2 n - 1) calAngle@p]};
   f[n_][\[Theta]_] := 1/(2 n - 1) Sin[(2 n - 1) \[Theta]];
   positions = Accumulate[r[#][p] & /@ Range[n + 1]];
   arrowseries = Partition[positions, 2, 1];
   pointseries = Accumulate[r[#][p] & /@ Range[n]];
   radios = 1/(2 # + 1) & /@ Range[n];
   fun[\[Theta]_] := Total[f[#][\[Theta]] & /@ Range[n + 1]];
   Show[Graphics[{Red, 
      Line[{Last@positions, {3, Last@Last@positions}}]}], 
    Plot[fun[\[Theta] + calAngle[p] - 3], {\[Theta], 3, 10}, 
     PerformanceGoal -> "Quality"], 
    Graphics[{Red, PointSize[0.015], Point[Last@positions]}], 
    Graphics[{Arrow[{{0, 0}, p}], Circle[{0, 0}, 1]}], 
    Graphics[{Arrowheads[0.015], Arrow /@ arrowseries}], 
    Graphics[MapThread[Circle][{pointseries, radios}]], 
    ImageSize -> Full]]]]