How to tick the parameter in the plot of a parametric function?

I have a plot of a parametric function, as in the following simple example:

t = linspace(0, 1, 1000);
x = t.^2;
y = t.^3; 
figure
plot(x, y, '-')
axis([0 1 0 1])
axis square
xticks(0:.1:1)
yticks(0:.1:1)
xlabel('x')
ylabel('y')
title('Parametric Plot: x = t^2; y = t^3')

How can I add ticks for the parameter value along the curve, similar to the x- and y-ticks?

Thank you!

Bernhard

[Adam Danz]

I updated your question by running your code using the Run Feature (green triangle in the "RUN" section of the editor.

[Adam Danz]

What does it mean to add ticks for the parameter values along the curve?

[Bernhard]

I mean something like this (three ticks inserted manually):

[Adam Danz]

Moving my answer to here in support of the other answers added later.

What about using Grid lines?

t = linspace(0, 1, 1000);
x = t.^2;
y = t.^3; 
figure
plot(x, y, '-')
axis([0 1 0 1])
axis square
xticks(0:.1:1)
yticks(0:.1:1)
xlabel('x')
ylabel('y')
title('Parametric Plot: x = t^2; y = t^3')

grid on

Or text objects

figure
plot(x, y, '-')
axis([0 1 0 1])
axis square
xticks(0:.1:1)
yticks(0:.1:1)
xlabel('x')
ylabel('y')
title('Parametric Plot: x = t^2; y = t^3')

idx = 800;  %for the 500th point
hold on
plot(x(idx),y(idx), 'bo')
text(x(idx), y(idx), sprintf('[%.2f, %.2f]',x(idx),y(idx)), ...
    'VerticalAlignment', 'Bottom', 'HorizontalAlignment', 'right')

Answer 1

[Voss]

t = linspace(0, 1, 1000);
x = t.^2;
y = t.^3; 

tick_length = 0.04;
t_tick = linspace(0,1,21);
x_tick = t_tick.^2;
y_tick = t_tick.^3; 
dxdt_tick = 2.*t_tick;
dydt_tick = 3.*t_tick.^2;

theta_tick = atan2(dydt_tick,dxdt_tick)+pi/2;
xx = x_tick+cos(theta_tick)*tick_length/2.*[-1; 1];
yy = y_tick+sin(theta_tick)*tick_length/2.*[-1; 1];
xx(end+1,:) = NaN;
yy(end+1,:) = NaN;

figure
hold on
line(xx(:),yy(:), ...
    'Color','k', ...
    'LineWidth',1, ...
    'Clipping','off')
plot(x, y, '-')
axis([0 1 0 1])
axis square
xticks(0:.1:1)
yticks(0:.1:1)
xlabel('x')
ylabel('y')
title('Parametric Plot: x = t^2; y = t^3')

[Voss]

If you want labels too, you can do this (here I've increased the t-tick spacing):

t = linspace(0, 1, 1000);
x = t.^2;
y = t.^3; 

tick_length = 0.04;
t_tick = linspace(0,1,11);
x_tick = t_tick.^2;
y_tick = t_tick.^3; 
dxdt_tick = 2.*t_tick;
dydt_tick = 3.*t_tick.^2;

theta_tick = atan2(dydt_tick,dxdt_tick)+pi/2;
xx = x_tick+cos(theta_tick)*tick_length/2.*[-1; 1];
yy = y_tick+sin(theta_tick)*tick_length/2.*[-1; 1];
xx(end+1,:) = NaN;
yy(end+1,:) = NaN;

figure
hold on
line(xx(:),yy(:), ...
    'Color','k', ...
    'LineWidth',1, ...
    'Clipping','off')
plot(x, y, '-')
axis([0 1 0 1])
axis square
xticks(0:.1:1)
yticks(0:.1:1)
xlabel('x')
ylabel('y')
title('Parametric Plot: x = t^2; y = t^3')

text(xx(1,:),yy(1,:),sprintfc('%.1f',t_tick), ...
    'VerticalAlignment','top', ...
    'Clipping','on')
set(gca(),'ClippingStyle','rectangle')

[Les Beckham]

Nice answer @Voss! +1

[Voss]

Thanks!

Answer 2

[Les Beckham]

Try this (or something similar):

% Your original code
t = linspace(0, 1, 1000);
x = t.^2;
y = t.^3; 
figure
plot(x, y, '-')
axis([0 1 0 1])
axis square
xticks(0:.1:1)
yticks(0:.1:1)
xlabel('x')
ylabel('y')
title('Parametric Plot: x = t^2; y = t^3')

% New code
tdisp = [0 .3:.1:1]; % times to mark
hold on
plot(tdisp.^2, tdisp.^3, '+') % mark the points
text(tdisp.^2 + .02, tdisp.^3, split(num2str(tdisp))) % add labels

Answer 3

[Bernhard]

Thank you @AdamDanz, @Voss, @LesBeckham for your helpful answers.

Frankly speaking, I had hoped for a neat, fully automated algorithm for adding annotated ticks to the curve, but reflecting on your answers, I see now that this would not be feasable for the general case.

Voss' code, providing ticks orthogonal to the curve, gives the prettiest result, but it depends on calculating the derivatives uf x(t) and y(t), which might be not always possible.

So Les Beckham's proposal of adding '+' Markers, and annotating them with a smart use of the "split" function, might be favorable for most of the practical cases.