# How to separately color regions R1, R2, R3, R4 in the 1st quadrant of (delta,theta) plane

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Atom on 20 Dec 2022
Edited: Karim on 21 Dec 2022
How to separately color regions R1, R2, R3, R4
• R_1={(δ,θ)│DD>0, δ>0.3414, θ<1.8758}
• R_2={(δ,θ)│DD=0, δ>0.3414}
• R_3={(δ,θ) | 0<δ<0.3414}
• R_4={(δ,θ) | DD<0} ∪ {(δ,θ) | δ≤-0.7} ∪ {(δ,θ) | DD>0, δ>0.3414, δ+0.5θ>1.2793}}
where DD=(delta+.5*theta-1.2793)^2-(4*(1+theta))*(.5*delta-.1707)?
• DD=0 is the Black curve
• δ=0.3414 is the Blue line
• θ=1.8758 is the Red line
• δ+0.5θ=1.2793 is the Green line
delta=0:0.01:5;
fimplicit(@(delta,theta) (delta+.5*theta-1.2793).^2-(4*(1+theta)).*(0.5*delta-.1707),'Color', 'k', 'linewidth',2);
axis([0 7 0 5])
line([0.3414, 0.3414], [0, 5], 'Color', 'b', 'linewidth',2);
line([0, 7], [1.8758, 1.8758], 'Color', 'r', 'linewidth',2); theta=-2*delta+2.5586;
hold on;
plot(delta,theta,'g', 'LineWidth',2)
xlabel('$\delta\rightarrow$','FontSize',20,'interpreter','latex','FontWeight','normal','Color','k')
ylabel('$\theta\rightarrow$','FontSize',20,'interpreter','latex','FontWeight','normal','Color','k')

Karim on 20 Dec 2022
Edited: Karim on 21 Dec 2022
Hi, below i demonstrated how to fill in the region using the patch command.
% evaluate the function to set up the grid points
delta = ((24544953/12500000)/14379)*2500 : 0.01 : 7;
theta_m = 2*delta - 2*sqrt(14379*delta/2500 - 24544953/12500000) + 1193/1000;
theta_p = 2*delta + 2*sqrt(14379*delta/2500 - 24544953/12500000) + 1193/1000;
% combine the data
delta = [fliplr(delta) delta];
theta = [fliplr(theta_p) theta_m];
% create a test plot to see if the function looks ok
figure
plot(delta,theta)
ylim([0 5])
xlim([0 7])
grid on
title('plot function to test the grid')
% set up a patch command to fill in the region
figure
hold on
plot(delta,theta,'Color', 'k', 'linewidth',2);
patch('Faces',1:numel(delta),'Vertices',[delta' theta'],'FaceColor','k','FaceAlpha',0.4)
ylim([0 5])
xlim([0 7])
grid on
xlabel('$\delta\rightarrow$','FontSize',20,'interpreter','latex','FontWeight','normal','Color','k')
ylabel('$\theta\rightarrow$','FontSize',20,'interpreter','latex','FontWeight','normal','Color','k')
EDIT: added a blue box to demonstrate the concept of the patch region.
Assume we want to color a rectangular region. To define the region we need 4 points:
Grid = [0 5;
0 0;
0.3414 0;
0.3414 5];
Next we need a way to tell the patch command which points (i.e. the rows from the points matrix) he needs to connect. The number of the point is the row from the points matrix (Grid in this example).
Region = [1 2 3 4];
Now we can simply call the patch command to plot the region:
figure
hold on
plot(delta,theta,'Color', 'k', 'linewidth',2);
patch('Faces',Region,'Vertices',Grid,'FaceColor','blue','FaceAlpha',0.75)
ylim([0 5])
xlim([0 7])
grid on
xlabel('$\delta\rightarrow$','FontSize',20,'interpreter','latex','FontWeight','normal','Color','k')
ylabel('$\theta\rightarrow$','FontSize',20,'interpreter','latex','FontWeight','normal','Color','k')
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Karim on 21 Dec 2022