Tutorial · Beginner · 8 min

Surfaces in 3D

From a formula to a shaded, rotatable 3D surface — and the same data as a contour map.

1. A grid of points

   meshgrid turns two vectors into grids X and Y, so you can compute Z for every point at once.

   [X, Y] = meshgrid(-2:1:2, -1:1:1)

   Try it ↗

   X = 3×5
     -2  -1   0   1   2
     -2  -1   0   1   2
     -2  -1   0   1   2
   Y = 3×5
     -1  -1  -1  -1  -1
      0   0   0   0   0
      1   1   1   1   1

2. Your first surface

   Compute Z with element-wise operations and pass all three to surf. Drag the figure to rotate it, scroll to zoom, double-click to reset.

   [X, Y] = meshgrid(linspace(-2, 2, 50));
   Z = X .* exp(-X.^2 - Y.^2);
   surf(X, Y, Z)
   colorbar

   Try it ↗

3. Colours and camera

   Choose a colormap (viridis, plasma, coolwarm …), remove the grid lines with shading flat, and set the camera angle with view(azimuth, elevation).

   [X, Y] = meshgrid(linspace(-3, 3, 70));
   surf(X, Y, peaks(X, Y))
   colormap plasma
   shading flat
   view(-60, 35)
   title('peaks, from another angle')
   xlabel('x'), ylabel('y'), zlabel('z')

   Try it ↗

4. The same data as a map

   Contours are often clearer in a paper than a 3D view. contourf fills between levels; axis equal keeps distances true.

   [X, Y] = meshgrid(linspace(-3, 3, 150));
   contourf(X, Y, peaks(X, Y), 14)
   colormap viridis
   axis equal
   title('peaks as filled contours')

   Try it ↗