GraphingCalculator 4;
Window 47 8 765 988;
PaneDivider 242;
SignificantDigits 14;
FontSizes 18;
BackgroundType 0;
T 0 5;
2D.BottomLeft -2.859375 -3.421875;
2D.Axes 0;
2D.GraphPaper 0;
2Dp.BottomLeft -2.84375 -1.265625;
2Dp.Axes 0;
2Dp.GraphPaper 0;
Text "Relativistic Doppler Effect – Headlight Effect.
Version 0.3
To do:
i) Shading of rays/plane according to relativistic Doppler effect, f_obs=f_src/[gamma(1-betacostheta)] is currently quite crude, giving the gist only that forward rays are blueshifted.   In particular, it doesn't preserve the source frequency.  Also doesn't deal properly with receding rays.


b – v/c; g – rapidity; d – offset for rays at π/2 to direction of motion.
Let t=-5..5 to get rear-facing fan of rays.

f – source frequency in rest frame; F(V,x) – Doppler-shifted frequency in observer frame; 
";
Color 4;
Expr b=slider([sn(1,-6),0.9999]);
Color 6;
MathPaneSlider 38;
Expr f=slider([0,1]);
Color 4;
Expr function(g,V)=1/sqrt(1-V^2);
Color 5;
Expr function(F,V,a)=f/([1-(V*cos(a))]*function(g,V));
Color 3;
MathPaneSlider 8;
Expr d=slider([0.01,0.1]);
Color 3;
Expr function(m,a)=tan(a);
Color 2;
Expr function(Y,x,m,b)=m*x+b;
Color 6;
Expr function(Y,x,function(m,T),0),in(T,set([-5]*pi/12,[-4]*pi/12,[-3]*pi/12,[-2]*pi/12,[-1]*pi/12,1*pi/12,2*pi/12,3*pi/12,4*pi/12,5*pi/12,0));
Expr function(Y,x,function(m,pi/2-d),0),x>0;
Color 8;
Expr function(Y,x,function(m,-pi/2+d),0),x>0;
Color 5;
Expr function(A,a)=acos([(cos(a)+b)/(1+b*cos(a))]);
Color 7;
Expr function(M,a)=sgn([a])*function(m,function(A,a));
Color 2;
Grain 1;
Expr vector(prime(x),prime(y))=vector(t,function(Y,t,function(M,T),0)),in(T,set([-5]*pi/12,[-4]*pi/12,[-3]*pi/12,[-2]*pi/12,[-1]*pi/12,1*pi/12,2*pi/12,3*pi/12,4*pi/12,5*pi/12,0));
Grain 1;
Expr vector(prime(x),prime(y))=vector(t,function(Y,t,function(M,T),0)),in(T,set(-pi/2+d,pi/2-d));
Expr vector(h,s,v)=vector(f,1,1);
Color 8;
Expr function(H,x,y,V)=1/(2*b*function(g,V))*[function(F,V,atan([y/x]))-function(F,V,pi)];
Color 7;
Expr function(K,x,y,V)=1/(2*b*function(g,V))*[function(F,V,0)-function(F,V,atan([y/x]))];
Color 2;
Expr function(D,x,y,V)=(function(F,V,atan([y/x]))-f)/(function(F,V,0)-f);
Color 3;
Expr function(E,x,y,V)=(function(F,V,atan([y/x]))-f)/(function(F,V,pi)-f);
Expr function(W,x,y)=branch(if(1,abs(atan(y/x))<function(A,pi/2-d)),if(0,abs(atan(y/x))>function(A,pi/2-d)));
Color 2;
Expr vector(h,s,v)=vector(function(D,prime(x),prime(y),b),1,function(W,prime(x),prime(y)));
Color 17;
Expr vector(h,s,v)=vector(function(D,prime(x),prime(y),b),1,1);
Text "

<size=14>Author: David A. Craig <<http://web.lemoyne.edu/~craigda/>";