MATLAB: Filling a region between parametric curves

fillzgrid

Hi! I am trying to fill a region between parametric curves, defined by the following code (in a zgrid):
figure; zgrid; hold on;
Ts = .1; wn = [.4*pi/Ts .6*pi/Ts]; FillColor = 'r';
wn_lb = wn(1); wn_ub = wn(2);
    % Values of zeta that correspond to start and end of wn curves:
    zeta = linspace(0,1);
    
    % Create vector of complex numbers to plot:
    mag_lb = exp(-zeta.*wn_lb*Ts);
    ang_lb = sqrt(1-zeta.^2).*wn_lb*Ts;
    z_lb = mag_lb.*exp(ang_lb*1j);
    
    mag_ub = exp(-zeta.*wn_ub*Ts);
    ang_ub = sqrt(1-zeta.^2).*wn_ub*Ts;
    z_ub = mag_ub.*exp(ang_ub*1j);  
    
    % Create unit circle arc for appropriate shading:
    theta_lb = linspace(angle(conj(z_lb(1))),angle(z_lb(1)));
    unit_circle_lb = cos(theta_lb) + sin(theta_lb)*1j;
    theta_ub = linspace(angle(conj(z_ub(1))),angle(z_ub(1)));
    unit_circle_ub = cos(theta_ub) + sin(theta_ub)*1j;
    
    theta = [linspace(angle(conj(z_ub(1))),angle(conj(z_lb(1)))) linspace(angle(z_lb(1)),angle(z_ub(1)))];
    unit_circle = cos(theta) + sin(theta)*1j;
% This is a plot of the region I want to get!
scatter([real(z_ub) flip(real(z_ub)) real(unit_circle) real(z_lb) flip(real(z_lb))],...
    [imag(z_ub) flip(-imag(z_ub)) imag(unit_circle) imag(z_lb) flip(-imag(z_lb))])
% This is all I've gotten so far... :(
hold off; figure; 
fill([real(z_ub),flip(real(z_ub)),(real(unit_circle)),real(z_lb),flip(real(z_lb)),real(unit_circle)], ...
     [imag(z_ub),flip(-imag(z_ub)),(imag(unit_circle)),imag(z_lb),flip(-imag(z_lb)),imag(unit_circle)],...
     FillColor,'FaceAlpha',.3);
zgrid
However, I can't seem to figure out how to fill the center region of figure 1. Thus far, figure 2 is the best I've gotten to using fill.
(Perhaps using patch?)
Thanks so much!

Best Answer

The actual issue is the order of the point. The patch function fails because the points are not distributed as a closed-loop. The following uses a very simple way to order the vertices and then call the patch function.
figure; zgrid; hold on;
Ts = .1; wn = [.4*pi/Ts .6*pi/Ts]; FillColor = 'r';
wn_lb = wn(1); wn_ub = wn(2);
    % Values of zeta that correspond to start and end of wn curves:
    zeta = linspace(0,1);
    
    % Create vector of complex numbers to plot:
    mag_lb = exp(-zeta.*wn_lb*Ts);
    ang_lb = sqrt(1-zeta.^2).*wn_lb*Ts;
    z_lb = mag_lb.*exp(ang_lb*1j);
    
    mag_ub = exp(-zeta.*wn_ub*Ts);
    ang_ub = sqrt(1-zeta.^2).*wn_ub*Ts;
    z_ub = mag_ub.*exp(ang_ub*1j);  
    
    % Create unit circle arc for appropriate shading:
    theta_lb = linspace(angle(conj(z_lb(1))),angle(z_lb(1)));
    unit_circle_lb = cos(theta_lb) + sin(theta_lb)*1j;
    theta_ub = linspace(angle(conj(z_ub(1))),angle(z_ub(1)));
    unit_circle_ub = cos(theta_ub) + sin(theta_ub)*1j;
    
    theta = [linspace(angle(conj(z_ub(1))),angle(conj(z_lb(1)))) linspace(angle(z_lb(1)),angle(z_ub(1)))];
    unit_circle = cos(theta) + sin(theta)*1j;
% This is a plot of the region I want to get!
scatter([real(z_ub) flip(real(z_ub)) real(unit_circle) real(z_lb) flip(real(z_lb))],...
    [imag(z_ub) flip(-imag(z_ub)) imag(unit_circle) imag(z_lb) flip(-imag(z_lb))])
% ordering the vertices
x = [real(z_ub) flip(real(z_ub)) real(unit_circle) real(z_lb) flip(real(z_lb))];
y = [imag(z_ub) flip(-imag(z_ub)) imag(unit_circle) imag(z_lb) flip(-imag(z_lb))];
X_original = [x' y'];
X_ordered = zeros(size(X_original));
X_ordered(1,:) = X_original(1,:);
x_temp = X_original(1,:);
X_original(1,:) = [];
count = 2;
while ~isempty(X_original)
    [~,idx] = min(pdist2(X_original, x_temp));
    X_ordered(count,:) = X_original(idx, :);
    x_temp = X_original(idx, :);
    X_original(idx, :) = [];
    count = count + 1;
end
hold off; figure; 
p = patch(X_ordered(:,1), X_ordered(:,2), 'r');
p.FaceAlpha = 0.2;
p.EdgeColor = 'none';
zgrid
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