Quite often we need to plot mathematical expressions or values, which are function of angles, which might be measured in degrees (°) or radians (π). By default, in Scilab, the axes tick labels are set in decimal values, even if the angle is given in radians.

For example we want to plot a trigonometric equation function of an angle between 0 and 4π. For this we’ll write the following Scilab script:

t = 0:0.01:4*%pi; f = sin(t).^2+cos(t); plot(t,f,'LineWidth',2)

where `t`

is our angle in radians and `f`

our trigonometric function.

By running this piece of code we get the following graphical window:

Without any formatting the plot doesn’t look very professional. Let’s add a grid, axes labels, title and limit the horizontal axis to the maxim value of the function argument. This formatting is performed with the following Scilab instructions:

xgrid() xlabel('t [decimal]','FontSize',2) ylabel('f(t)','FontSize',2); title('$f(t)=sin^2(t)+cos(t)$','FontSize',3); ha=gca(); ha.tight_limits = ["on","on","on"] ha.data_bounds=[min(t),min(f)-0.1;max(t),max(f)+0.1];

By running this additional piece of code our graphical window is updated accordingly:

This is better but not complete. As you can see, the ticks on the x-axis are labeled with decimal numbers. The values correspond to the angle (e.g. `3.1416 = π`

) but it’s not what we expected. For a better understanding of the behaviour of the function we need to have the x-axis in radians, exactly as the function argument (variable `t`

).

To understand how the axis tick labels are set, we’ll use the `gca()`

function handle. For our example, the tick labels of the x-axis are displayed by entering the instruction `ha.x_ticks`

at the Scilab console:

--> ha.x_ticks

ans =

ans(1)

!ticks locations labels !

ans(2)

0.

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

ans(3)

!0 !

!1 !

!2 !

!3 !

!4 !

!5 !

!6 !

!7 !

!8 !

!9 !

!10 !

!11 !

!12 !

-->

This means that the axis tick labels are formatted as a `Tlist`

variable, which contains two arrays: first with the `locations`

of the ticks, second with the `labels`

of the ticks.

To format both the locations and the labels we need to use this Scilab format:

`ha.x_ticks=tlist(["ticks","locations","labels"],locations_array,labels_array);`

For out particular case, we are going to setup the locations in **decimal** equivalent of the radians, starting with `0`

and incrementing with `π/2`

up to `4π`

. The labels are going to be setup with the same values but in Latex **string** format, as:

ha.x_ticks=tlist(["ticks","locations","labels"],.. [0;%pi/2;%pi;3*%pi/2;2*%pi;5*%pi/2;3*%pi;7*%pi/2;4*%pi],.. ["$\Large{0}$";.. "$\Large{\frac{\pi}{2}}$";.. "$\Large{\pi}$";.. "$\Large{\frac{3\pi}{2}}$";.. "$\Large{2\pi}$";.. "$\Large{\frac{5\pi}{2}}$";.. "$\Large{3\pi}$";.. "$\Large{\frac{7\pi}{2}}$";.. "$\Large{4\pi}$"]); xlabel('t [rad]','FontSize',2)

The size of both arrays must match, otherwise the formatting by not be applied. In our example we used double dots `..`

to be able to continue the instruction on the following row. Running the above Scilab instructions will output the following graphical window:

As you can see the vertical grid is now setup function of the position of the x-axis ticks. Also, the labels of the ticks are now represented in radians using Latex format. The same formatting method can be applied as well to the y-axis.

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