I have $4$ variables $X$, $Y$, $Z$ and $C$, and I want to plot these on a graph. Usually I would just plot the surface $X$, $Y$, $Z$ and then use color to represent the $4$th dimension, as shown bellow:
However, my $X$, $Y$, and $Z$ co-ordinates make up a $3$-dimensional meshgrid, so when I do the $4$ dimensional plot it is hard to see what is going on, as shown below:
$X$, $Y$ and $Z$ represent spatial dimensions and $C$ represents a value that depends on its place its $3$-dimensional space. I need $X$, $Y$, and $Z$ to be shown in all places because these are the independent variables. In this simplified version of my function, $C=X+Y+Z$. I want to be able to pick any $3$ numbers for $X$, $Y$, and $Z$, and then look at my graph, and be able to get a good idea of what $C$ is. You can sort of do this with this current graph but it is hard to use.
What I want to know is: Is there a better way to plot this information? For example, is there a different co-ordinate system I could use that would be better? Or is there a way I could represent the 3 spatial dimensions so they look like a curved surface, but still include every point?
To reiterate that last question: Is there a way to represent every point in $3$ dimensions within $0 \leq X,Y,Z \leq 10$, all on one surface?