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

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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
  4 Comments
Adam Danz
Adam Danz on 29 Jul 2022
Edited: Adam Danz on 29 Jul 2022
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')

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Accepted Answer

Voss
Voss on 29 Jul 2022
Edited: Voss on 29 Jul 2022
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')
  3 Comments

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More Answers (2)

Les Beckham
Les Beckham on 29 Jul 2022
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

Bernhard
Bernhard on 31 Jul 2022
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.

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