Plotting a function over surface of a cube in Octave

Question

I have a function which is defined for a set of points over the surface of a cube. I know the value of the function for the coordinates. How to generate a plot which will assign a color to every point on the surface of the cube, depending on the value of the function at that point?

On 2D, I can generate colorful contour plots, but how to do something similar in 3D?

Suppose, the function which I want to plot is f(x,y,z) = x^2 + yz. And, the points on the cube are defined as xvar = linspace(-1,1,20), yvar = linspace(-1,1,20), zvar = linspace(-1,1,20).

Answer 1

From:
https://octave.sourceforge.io/octave/function/scatter3.html

scatter3 (x, y, z, s, c)

Draw a 3-D scatter plot.

A marker is plotted at each point defined by the coordinates in the vectors x, y, and z.

The size of the markers is determined by s, which can be a scalar or a vector of the same length as x, y, and z. If s is not given, or is an empty matrix, then a default value of 8 points is used.

The color of the markers is determined by c, which can be a string defining a fixed color; a 3-element vector giving the red, green, and blue components of the color; a vector of the same length as x that gives a scaled index into the current colormap; or an Nx3 matrix defining the RGB color of each marker individually.

If you use colors, you can try different color profiles. colormap(rainbow), colormap(jet) etc. These color profiles assign darker color to higher values (which the default colormap does not do), which might make the plots look better.