# How to plot Surface Plots

JTK 2010.5.3

## Contents

## The Function

For our example function, we'll be plotting z = x^2 + y^2. This is essentially a two dimensional parabola.

## Generating the X,Y Grid

The first thing to do is to generate an X,Y grid for our plot. Think of this grid as the equivalent of the latitude/longitude on Earth - and that we'll be later be plotting something (say topographic elevation) for each point on this grid.

x = -4:.1:4; % The range of x values. y = -4:.1:4; % The range of y values. [X,Y] = meshgrid (x,y); % This generates the actual grid of x and y values.

## Generating the Z Data

To generate the actual Z data, all we need to do is create a function relating "X" and "Y" (the variables from the meshgrid --- not the ranges, 'x' and 'y').

Z=Y.^2+X.^2; % The function we're plotting. % Remember to use the correct vector notation for all operations (such as % using the '.^' operator to do piecewise powers).

## Generating the Surface Plot

Next, all we need to do is to generate a contour plot!

figure(1); % Generating a new window to plot in. contour(X,Y,Z) % The surface plotting function. % Without any further qualifiers, MATLAB will automatically pick a scale % for the contours. You can, however, tell MATLAB how many contours you'd % like: figure(2); contour(X,Y,Z,20)

## Combining Contour and Surface Plots

(Please read the surface plot introduction before proceeding) To plot a contour plot ontop of a surface plot, all we do is plot the surface plot, tell MATLAB to wait, and then use the "contour3" plotting routine to plot a 3D contour ontop of the surface plot:

figure(3); surf(X,Y,Z,'EdgeColor','none') hold on contour3(X,Y,Z,20,'k') hold off % The color of the contour lines are by default a rainbow --- which will % make them blend into the underlying surface plot. We specified the color % to be black with the 'k' qualifier in the contour3 routine.

## Contour Plots ontop of Surface Plots ontop of Contour Plots... oh my!

A further nifty command is "meshc" which plots a mesh surface plot, and generates a contour plot beneath it on the X,Y plane.

figure(4); meshc(X,Y,Z) % We can make arbitrarily complicated plots by merely combining different % plotting functions and using the "hold" function from previous: figure(5); shading interp meshc(X,Y,Z); hold on surf(X,Y,Z,'EdgeColor','none') contour3(X,Y,Z,20,'k') hold off