# ListPlot3D: Multiple Values at One Data Point

Setup: I am using ListPlot3D[] to plot a data set of three independent variable and one output value, $f(x,y,z) \to w$.

Because ListPlot3D[] only takes two independent variables, there will be multiple values at each point in the domain.

Question: When viewing the plot, only one surface appears, so what is Mathematica doing with the multiple data points? Taking the average, minimum, a random value?

Example: Plotting $x$ on one axis and $y$ on the other axis, means there will be as many data points at each $(x,y)$ as there are $z$ values corresponding to $(x,y)$. For instance if we have three $z$-values for each $(x,y)$ pair we would expect 3 data points to appear at each point.

I.e. with the data at $(x=5, y=5)$ as $$f(5,5,1) = 1,\, f(5,5,2) = 3,\, f(5,5,5) = -2$$ We would expect to see 3 data points at $(x=5,y=5)$ in the plot, one at -2, 1, and 3. However, only one value appears.

Note: The number of multiple values at each data point is the same. E.g. There are three $z$-values for each $(x,y)$ pair.

• Probably you need ListDensityPlot3D. – swish Apr 14 '17 at 19:18
• It seems that you're plotting four-dimensional data: $f(x,y,z)$ which gives a value that could be plotted on a fourth axis. In your example, what do the third entries in the function—1, 2, 5—represent? – David G. Stork Apr 15 '17 at 0:39