四人追逐问题的模拟

minjiecow

这里写了一个小段子模拟四人追逐问题，即四个人各处于正方形的一顶点，以相同的速度相互追逐。

chungyuandye

n人追逐

1. 
   
2. equiangular[ntemp_Integer,ttemp_]:=
   
3. Block[{n=ntemp,t=ttemp,myarrow,mypoint},
   
4. myarrow={Exp[-#(2Pi/n)-Pi*(t-0.005)+#(2Pi/n)]*{Cos[-#(2Pi/n)-Pi*(t-0.005)],Sin[-#(2Pi/n)-Pi*(t-0.005)]},
   
5. Exp[-#(2Pi/n)-Pi*t+#(2Pi/n)]*{Cos[-#(2Pi/n)-Pi*t],Sin[-#(2Pi/n)-Pi*t]}}&/@Range[0,n-1];
   
6. mypoint=Flatten[{Exp[-#(2Pi/n)-Pi*t+#(2Pi/n)]*{Cos[-#(2Pi/n)-Pi*t],Sin[-#(2Pi/n)-Pi*t]}}&/@Range[0,n-1],1];
   
7. Show[Graphics[{Red,PointSize[0.02],Arrow[#]&/@myarrow},
   
8. PlotRange->{{-3/2,3/2},{-3/2,3/2}}],
   
9. Graphics[Line/@Partition[mypoint,2,1,1]],PolarPlot[{Exp[x+#(2Pi/n)]},{x,-#(2Pi/n),-#(2Pi/n)-Pi*t}]&/@Range[0,n-1],Frame->True]]
   
10. 
    
11. Animate[equiangular[5, t], {t, 0.001, 3}]
    

复制代码

file:///Users/chungyuandye/2.gif

minjiecow

呵呵，做得不错！

FreddyMusic

搞的有点意思，写个演示项目嘛，+2 分技术分。
http://demonstrations.wolfram.com/participate.html

FreddyMusic

I made some edit to implement in Manipulate.
It's looks pretty like "Pursuit Curve".
http://mathworld.wolfram.com/PursuitCurve.html

1. 
   
2. equiangular[n_Integer,t_]:=
   
3. Module[{arrow,point},
   
4. arrow={Exp[-#(2Pi/n)-Pi*(t-0.005)+# (2Pi/n)]*{Cos[-#(2Pi/n)-Pi*(t-0.005)],Sin[-#(2Pi/n)-Pi*(t-0.005)]},Exp[-#(2Pi/n)-Pi*t+# (2Pi/n)]*{Cos[-#(2Pi/n)-Pi*t],Sin[-#(2Pi/n)-Pi*t]}}&/@Range[0,n-1];
   
5. point=Flatten[{Exp[-#(2Pi/n)-Pi*t+# (2Pi/n)]*{Cos[-#(2Pi/n)-Pi*t],Sin[-#(2Pi/n)-Pi*t]}}&/@Range[0,n-1],1];
   
6. Show[
   
7. Graphics[{Red,PointSize[0.02],Arrow[#]&/@arrow,Blue,Line/@Partition[point,2,1,1]},PlotRange->{{-3/2,3/2},{-3/2,3/2}}],PolarPlot[{Exp[x+# (2Pi/n)]},{x,-#(2Pi/n),-#(2Pi/n)-Pi*t}]&/@Range[0,n-1],Frame->True]];
   
8. 
   
9. Manipulate[equiangular[n,t],{n,2,10,1},{t,.01,1.5}]

复制代码

It can be very cool graphics if you are able to change the inital velocity for any direction.

minjiecow

版主一加工，就都变漂亮了！

minjiecow

但存在一点问题，这似并不能模拟真正的n人追逐，因为代表当前人的点并不在代表追逐他的人的轨迹的切方向上，所以不正确！

minjiecow

版主一加工，就都变漂亮了！

HyperGroups

我拿去研究一下，最近可能研究这种模型，生成引擎动画:D