# 2D & 3D Plots

## 2D Plots

### Gnuplot on Mac

Octave uses gnuplot when plotting. If you use Mac, you must make sure gnuplot works. You might need to reinstall gnuplot with x11 support by using homebrew:

brew uninstall gnuplot;brew install gnuplot --with-x

Then start Octave and write:

setenv("GNUTERM","X11")

For troubleshooting check out this.

## Plot using Octave

When plotting in Octave you plot points having their `x`-values stored
in one vector and the `y`-values in another vector. The two vectors
must be the same size.

You can use a `x`-vector to store the `x`-values; then you
use element by element operations on the `x`-vector to store the function
values in a `y`-vector. Having two vectors like this, you then use
the command

plot(x_vector, y_vector)

>>> x=-2:2 x = -2 -1 0 1 2 >>> y=x.^2 y = 4 1 0 1 4 >>> plot(x,y)

Octave inserts lines between the points. If you want a smoother
graph, make a longer `x`-vector.

>>> x=-2:0.5:2; >>> y=x.^2; >>> plot(x,y)

If you know how many points you want to plot in an interval, you can let Octave space the points linearly by using the command

linspace(first x-value, last x-value, number of evenly spaced points)

>>> x=linspace(-2, 2, 500); >>> y=x.^2; >>> plot(x,y)

## 3D - the grid

If we have a function of two variables \(z=f(x,y)\), we need three axes to display the graph.

When plotting in 2D we use evenly spaced `x`-values and function values
of these stored in a `y`-vector.

When plotting in 3D we need evenly spaced `x`- and `y`-values,
spaced on a grid where each function value `z` is taken of a point
(`x`, `y`) on the grid. In order to achieve this we use the
command `meshgrid`

.

>>> x=linspace(-2,2,5) x = -2 -1 0 1 2 >>> y=linspace(-2,2,5) y = -2 -1 0 1 2 >>> [xx,yy]=meshgrid(x,y) xx = -2 -1 0 1 2 -2 -1 0 1 2 -2 -1 0 1 2 -2 -1 0 1 2 -2 -1 0 1 2 yy = -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 0 0 1 1 1 1 1 2 2 2 2 2

Each point on the grid is made by taken an element from the `xx`

-matrix as the
`x`-value and the corresponding element from the `yy`

-matrix as the `y`-value. All
in all there are 25 points in this grid.

## Plot a 3D graph

After having made a grid you can plot a 3D graph using the command `mesh(xx,yy,z)`

,
where `xx`

and `yy`

are the matrices made by `meshgrid`

and where `z` is a function of `x` and `y`. You get
the function values of `z` by using element by element operations on
matrices `xx`

and `yy`

.

>>> x=linspace(-2,2,5); >>> y=linspace(-2,2,5); >>> [xx,yy]=meshgrid(x,y); >>> mesh(xx,yy,4-(xx.^2+yy.^2))

If you want a smoother graph, make a longer `x`-vector and a longer
`y`-vector.

>>> x=linspace(-2,2,50); >>> y=linspace(-2,2,50); >>> [xx,yy]=meshgrid(x,y); >>> mesh(xx,yy,4-(xx.^2+yy.^2))

You can get a contour plot by using the command `meshc`

.

>>> x=linspace(-2,2,50); >>> y=linspace(-2,2,50); >>> [xx,yy]=meshgrid(x,y); >>> meshc(xx,yy,4-(xx.^2+yy.^2))

by Malin Christersson under a Creative Commons Attribution-Noncommercial-Share Alike 2.5 Sweden License