dottedline := proc(x,y,np);

       RETURN(plot([x[1]*(1-t)+y[1]*t,x[2]*(1-t)+y[2]*t,t=0..1],

                    numpoints=np,style=POINT,symbol=POINT,

                    args[4..nargs]));

       end:  





ZetaArc := proc()

    local X1,X2,s,u,d,m,y,z,s0,t0,t,a1,a2,ay,R,al,a,b;

    X1 := args[1];

    X2 := args[2];

    s := args[3];

    u := [X2[1]-X1[1],X2[2]-X1[2]];

    d := sqrt(u[1]^2+u[2]^2);

    s0 := s*d/2;

    u := [u[1]/d,u[2]/d];

    m := [(X1[1]+X2[1])/2,(X1[2]+X2[2])/2];

    y := [m[1]-s0*u[2],m[2]+s0*u[1]];

    t0 := solve(t^2+d^2/4=(s0-t)^2,t);

    z := [m[1]-t0*u[2],m[2]+t0*u[1]];

    z := evalf(z); 

    R := sqrt((z[1]-X1[1])^2 +(z[2]-X1[2])^2);

    a1 := arctan((X1[2]-z[2]),(X1[1]-z[1]));

    a2 := arctan((X2[2]-z[2]),(X2[1]-z[1]));

    ay := arctan((y[2]-z[2]),(y[1]-z[1]));

    al := sort(evalf([a1,a2,ay]));

    if ay = al[1] 

       then a :=al[3]-2*Pi;

            b := al[2];

       elif ay = al[3]

       then a :=al[1]+2*Pi;

            b := al[2];

       else a := al[1];

            b := al[3];

       fi;

    RETURN(arc(z,R,a..b,args[4..nargs]))

    end:

 

midZetaArc := proc(X1,X2,s,v)

    local u,d,m,y,z,s0,t0,t,a1,a2,ay,R,al,a,b,v0;

    u := [X2[1]-X1[1],X2[2]-X1[2]];

    d := sqrt(u[1]^2+u[2]^2);

    s0 := s*d/2;

    u := [u[1]/d,u[2]/d];

    m := [(X1[1]+X2[1])/2,(X1[2]+X2[2])/2];

    y := [m[1]-s0*u[2],m[2]+s0*u[1]];

    t0 := solve(t^2+d^2/4=(s0-t)^2,t);

    z := [m[1]-t0*u[2],m[2]+t0*u[1]];

    z := evalf(z); 

    R := sqrt((z[1]-X1[1])^2 +(z[2]-X1[2])^2);

    a1 := arctan((X1[2]-z[2]),(X1[1]-z[1]));

    a2 := arctan((X2[2]-z[2]),(X2[1]-z[1]));

    ay := arctan((y[2]-z[2]),(y[1]-z[1]));

    al := sort(evalf([a1,a2,ay]));

    if ay = al[1] 

       then a :=al[3]-2*Pi;

            b := al[2];

       elif ay = al[3]

       then a :=al[1]+2*Pi;

            b := al[2];

       else a := al[1];

            b := al[3];

       fi;

    v0 := a*(1-v)+b*v; 

     RETURN([z[1]+R*cos(v0), z[2]+R*sin(v0)]);

     end:

    

midline := proc(X1,X2,s)

    RETURN([X1[1]*(1-s)+X2[1]*s,X1[2]*(1-s)+X2[2]*s]);

    end: