How to Add Constraint Lines with Ticks to Both Plot and Legend in MATLAB?

Hi! I’ve created a graphical solution for an optimization problem. To present this properly, I need to use proper constraint lines, meaning a line with ticks that symbolize the area I need to stay within. I’ve managed to manually add ticks to the constraint lines in the plot, but I can’t get them to appear correctly in my legends.

Does anyone know the best way to solve this?

I’m attaching an image of my plot and another one showing how I want it to look, drawn in Paint. I’m also attaching my code.

I feel like there should be a function in MATLAB to do this automatically, but I haven’t been able to find one.

Any suggestions?

xh=linspace(0.005, H - 0.005, 1000);
xb=linspace(0.005, B - 0.005, 1000);
[bg,hg]=meshgrid(xb,xh);

I = (B.*H.^3-bg.*hg.^3)/12;

volym=L*(B.*H-bg.*hg);  % Volume
massa=Density*volym;    % Mass

sigma = (Mmax * C) ./ I;    % Bending stress

contour(bg,hg,massa,[2.5,3,3.5,4,4.5,5],'LineWidth',1.2,'ShowText','on'); % Mass in kg
colormap("cool");
hold on

bbb=((B*H^3)./xh.^3)-((12*Mmax*C)./(ReLSF*xh.^3))
ht=(((B*H^3)/(B-0.005))-(12*Mmax*C)/(250e6*(B-0.005)))^(1/3);
bt=(B*H^3)/(ht)^3-(12*Mmax*C)/(ReLSF*(ht)^3)

line([B-0.005,B-0.005],[0,H], 'Color', 'black', 'LineStyle', '-', 'LineWidth', 1); % Vertical line for b
line([0,B],[H-0.005,H-0.005], 'Color', 'black', 'LineStyle', '-', 'LineWidth', 1); % Horizontal line for h
% Fixed axis limits
x_min = 0.005; x_max = 0.017;
y_min = 0.005; y_max = 0.04;

% Proportion between x and y axes
aspect_ratio = (x_max - x_min) / (y_max - y_min);

% Tick length (adjusted for proportions)
base_length = 0.0003; % Base length
x_length = base_length; % Length in x
y_length = base_length / aspect_ratio; % Length in y

% Vertical line for b
line([B-0.005, B-0.005], [0, H], 'Color', 'black', 'LineStyle', '-', 'LineWidth', 1); % Vertical line

% Add ticks to the vertical line
yv = linspace(0, H, 30); % Ticks for the vertical line
xv = ones(size(yv)) * (B - 0.005); 
for i = 1:length(yv)
    line([xv(i) xv(i) + x_length], [yv(i) yv(i)], 'Color', 'red', 'LineWidth', 1); % Horizontal ticks
end

% Horizontal line for h
line([0, B], [H-0.005, H-0.005], 'Color', 'black', 'LineStyle', '-', 'LineWidth', 1); % Horizontal line

% Add ticks to the horizontal line
xh_k = linspace(0, B, 50); % Ticks for the horizontal line
yh_k = ones(size(xh_k)) * (H - 0.005);
for i = 1:length(xh_k)
    line([xh_k(i) xh_k(i)], [yh_k(i) yh_k(i) + y_length], 'Color', 'red', 'LineWidth', 1); % Vertical ticks
end

plot(bbb,xh)
scatter(bt, ht);
xlabel("Lilla b (m)")
ylabel("Lilla h (m)")
legend("Funktionen","Bivillkor (b)","Bivillkor (h)","Objektsfunktion",Location="best")
plot(NaN, NaN, 'or', 'DisplayName', 'Optimal solution')
axis([0.005 0.017 0.005 0.04])
INData: 
P=5200; %Newton
L=0.82; %Meter
B=0.021; %Meter
b=0.011; %Meter
H=0.041; %Meter
h=0.031; %Meter
E=205*10^9; %Pascal
Vmax=P/2;
t=B-b; %Livets tjocklek
k=(H-h)/2; %Flänsens tjocklek
I=((B*H^3)-(b*h^3))/12; %I-värde balk
ypl=h/4; %Y' fläns
ypf=((H-h)/4)+(h/2); %Y' liv
apl=(h*t)/2; %A' liv
apf=B*k; %A' fläns
apt=apl+apf; %A' tot

ReL=450*10^6;
SF=1.8;
ReLSF=ReL/SF;
Density=7.81*1000; %omvandla till kg/m3

Without ticks:

With ticks (handmade)

Answer 1

[Jacob Mathew]

Hey Filip,

You can use the Vertical ( | ) and Horizontal ( _ ) marker types to achieve this effect. The example code below creates the same:

% Example number of points
numPoints = 10;

% Horizontal line parallel to x-axis
x_horizontal = linspace(0, 9, numPoints);
y_horizontal = ones(1, numPoints) * 5; % y = 5

% Vertical line parallel to y-axis
y_vertical = linspace(0, 9, numPoints);
x_vertical = ones(1, numPoints) * 3; % x = 3

% Plot the horizontal line with black color and red '|' markers
h1 = plot(x_horizontal, y_horizontal, 'k-|', 'MarkerEdgeColor', 'r', 'DisplayName', 'Boundary');
hold on;

% Plot the vertical line with black color and red '|' markers
h2 = plot(x_vertical, y_vertical, 'k-_', 'MarkerEdgeColor', 'r');

% Hide the second plot from the legend
set(get(get(h2, 'Annotation'), 'LegendInformation'), 'IconDisplayStyle', 'off');

% Add labels and title
title('Lines Parallel to Axes');
xlabel('x');
ylabel('y');
legend;
grid on;
hold off;

[Filip]

Hello! Thanks for your suggestion. Looks almoast as i would like it, however, the markings should only be at one side of the lines. As in my constraints. if the red line cross the constraintfunction it would suggest its ok to be on both sides.

Any suggestions on how to adjust it ?

Thanks !!

Answer 2

[Benjamin Kraus]

If you have access to the Aerospace Toolbox (and MATLAB R2021b or later), you can use the boundaryline command to draw something like this:

boundaryline([0.02 0],[0.035 0.035], Hatches='|');
boundaryline([0.016 0.016],[0 0.04], Hatches='|');
xlim([0.005 0.02])
ylim([0.005 0.04])
legend