%
%  macm 202 -- 27 dec 02 -- djm
%
%  w1curve.m:  complex curve demo, plots z(t)
%               & integrates of f(z) along z(t)
%    - to run, type "w1curve" at the matlab prompt
%

%  clear workspace & graphics ("help clear", etc)

clear;  close all;  disp(' ')

% 'a' can be any COMPLEX value
%1 global a;  a = 0.0 + 0.0*i;

%  parameter vector

T = 1;  dt = 1/108;  t = 0:dt:T;

%  plot curve of complex points

zp = w1curve1(t,0);

figure(1);  %clf;
plot(real(zp),imag(zp),'k.')
hold on
plot(real(zp(  1)),imag(zp(  1)),'ro')
plot(real(zp(end)),imag(zp(end)),'rx')

title('\bf my first complex-valued contour (with tangents)')
xlabel('\bf real[z(t)]')
ylabel('\bf imag[z(t)]')

%  tangent check

tc = 0:0.1*T:T;
z = w1curve1(tc,0);  dzdt = w1curve1(tc,1); 
quiver(real(z),imag(z),real(dzdt),imag(dzdt),0.2)

%  complex contour integral

zquad = quad(@w1curve2,0,T,1e-6);
%1 disp(['a = ' num2str(a)])
%1 plot(real(a),imag(a),'b*')
disp(['complex quadrature = ' num2str(zquad,'%2.4f')])
axis equal
