# new version of drdtplot
drdtp := proc(rboundary,trange)
local line,f,g,a,b,i,theta;
    f := op(1,op(2,rboundary));
    g := op(2,op(2,rboundary));
    a := op(1,op(2,trange));
    b := op(2,op(2,trange));
    theta := 'theta';
    tst := false;
    tst := type(trange,string = range) and op(1,rboundary) = 'r' and
        op(1,trange) = 'theta' and type(evalf(a),numeric) and 
         type(evalf(b),numeric);

#    if not tst then ERROR(`input expression is not of drdt type`) fi;
    line := {[f*cos(theta),f*sin(theta),theta = a .. b],
        [g*cos(theta),g*sin(theta),theta = a .. b],[0,0,0,0]};
    for i from 0 to 5 do
        if evalf(subs(theta = 1/5*(5-i)*a+1/5*i*b,g))-
            evalf(subs(theta = 1/5*(5-i)*a+1/5*i*b,f)) < -.1*10^(-3) then
            ERROR(`the positions of the radiall functions are not correct`)
        fi;
        line := line union {[
            subs(theta = evalf(1/5*(5-i)*a+1/5*i*b),f*cos(theta)),
            subs(theta = evalf(1/5*(5-i)*a+1/5*i*b),f*sin(theta)),
            subs(theta = evalf(1/5*(5-i)*a+1/5*i*b),g*cos(theta)),
            subs(theta = evalf(1/5*(5-i)*a+1/5*i*b),g*sin(theta))]}
    od;
    plot(line)
end;