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There are essentially two ways for plotting three-dimensional data:

  • Colour maps (or heat maps)¹:
    enter image description here
  • Surface plots:
    enter image description here

While surface plots are quite nice to visualise data if you can interactively move the perspective, they often obfuscate aspects of the data if you only have one perspective at hand – as it is mostly the case in papers or presentations. And even if the data is benign for surface plots, I have not yet met an example where it adds anything to the colour map, at least in my opinion. This holds for the case where the two are combined, i.e., the surface is coloured (as in the above example).

As surface plots are still used, even by people who are otherwise making very good plots, I wonder whether I am missing something here. Thus my question is: Given that I have evenly sampled, three-dimensional data and that I can only show one image to visualise it², is there any argument or situation due to which I should use a surface plot instead of a colour map? In both cases, assume optimally chosen plotting parameters, such as the colour scheme or the viewing angle. Also, you can assume that the plot is being used in an academic context, e.g., a paper, presentation or poster. In particular, the audience can be expected to be able to read such a plot and things like fanciness should not be an argument.


¹ This example is just to illustrate the types of plot. I am not asking about how they specifically should be presented. ² And thus, showing a video or multiple perspectives is not an option.

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This question appears to be off-topic because it is about graphs. –  Dave Clarke May 6 at 8:47
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The question is not about academica. –  Dave Clarke May 6 at 9:01
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The question is not about how to do a graph but how to represent data. We accept questions on writing along the same lines so although I agree it is on the fringes of the topic authoring and presenting data in publications should be on topic. –  Peter Jansson May 6 at 9:11
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Cross Validated deals with data visualisation. User Experience deals with the ergonomics of visualisation –  EnergyNumbers May 6 at 9:55
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Preparing figures for manuscripts is on-topic here. –  aeismail May 6 at 10:46
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3 Answers 3

As everything, it depends. Here is a 3d plot of a mass-spectroscopic peak in time and mass to charge: zoomin

You can get a pretty good idea of its shape and how important noise is. Also, as it is a wireframe, you can see what is behind. If you want to see several of them I can show you too:

zoomout

Now the thickness is not so obvious, but still, you get a nice idea of the whole thing. You can immediately see the relative intensities, and patterns like the uppermost corner, where there are several peaks parallel to each other (which is an important feature of my data), with falling intensities.

For the show off, I generated a bigger slice with Blender, that gives a nice feeling of how the data looks like, including the long "ridges", parallel peaks, noise, and profiles:

blender

In this case, I don't care some peaks are covering each other because the exact positioning is quite random. If I do a heatmap I get this:

heatmap

I can overlay more information, like the red lines on top, but now we have lost track of the relative intensities, actual shapes, and level of noise.

In my case, the 3D works because the position of the peaks is quite random, and the exact shape varies from experiment to experiment. Also, intensities and noise are important, and one needs to keep them in mind. But if you want to plot a function (say, a kernel density), where the exact shape is important, and relative values are not so much, a heatmap or a contour plot are usually a better choice.

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+1 - using color can not effectively show magnitudes in numeric data - it is mostly only effective for showing ordinal changes in ranks. In terms of the occlusion problem I have seen people provide multiple perspectives of the same plot rotated as static images. –  Andy W May 6 at 12:44
    
To definitely solve the occlusion problem and add a WOW factor, when possible, show a video: youtube.com/watch?v=PeAUDzMr_Fg –  Davidmh May 6 at 15:09
    
With your second 3d graph, I would almost recommend taking the slice between 402 and 403, averaging each point along that axis and display a 2d graph. That's where the interesting data is. –  Cruncher May 6 at 20:48
    
@Cruncher in my application, the separation is also important, the gap between the peaks are actual zeroes (they are the same thing with an extra neutron or two). Averaging along an axis doesn't work here, because separations in both x and y are very relevant, and the presence of small features, very important. –  Davidmh May 7 at 9:12
    
While I agree with @AndyW that this a good example where there is an advantage to surface plots (and thus what I have been asking for), namely better visualising details of the relative magnitudes, this is not a generalisable feature. In fact, this is the first such example, I have seen, while in other cases, this information is not well-accessible in either type of plot. Also, I would guess that the colour map can be drastically improved by tweaking the colour scheme and scale. –  Wrzlprmft May 7 at 23:12
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There are four questions, in the order as below:

  • what you want to show or put the emphasis on?
  • which visualization makes the data as clear as possible to read and interpret?
  • what is typical way of showing data in your field (to reduce confusion)?
  • (optional) does it make sense in black and white? (some people print papers; sometimes displays have poor color display)

In the case you have shown, heat map looks much more clear; surface plot may have some visual appeal (arguably), but obfuscates the data (some places are hidden, it is harder to read numerical values and see symmetries). Also, it may be good to consider contour plot with values on contours as it is printable in black and white.

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I think the choice here is mainly a question of taste. Personally, I always prefer the the colour map type plots but I know some people who strongly prefer surface plots. The brief arguments for each are as follows:

Colour map:

Pros:

  • Less possibility of hiding or misleading data by obstruction.

  • More accurate representation of the data (no perspective effects).

Cons:

  • Can be hard to plot selected areas and similar things (although not impossible).

Surface plot:

Pros:

  • Look nicer (I strongly disagree)

  • Can be useful if you want to show multiple things on one plot, e.g. height with one area selected (you colour the selected area but put the height surface)

Cons:

  • Very easy to hide some data behind something or make it unclear.

  • I find it sometimes difficult to "unwrap" the image to get back to the height.

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I've downvoted for the comment "a question of taste". Both the other answers and yourself have provided instances of situations to prefer one over the other. These don't have to do with "taste" but with accurately presenting information to your audience. –  Andy W May 6 at 15:16
    
@AndyW I think it is a question of taste. I don't think any of the arguments for surface plots are really valid and given the choice I would never use them. Other people have a different opinion and quite like them. Also I'm not really convinced by any of the other arguments as to why I would want to use a surface plot other than its what everyone else does in the field, which doesn't actually make one way better objectively. –  nivag May 6 at 15:30
    
There is a field of study related to data visualization; mostly occupied by statisticians, psychologists, geographers, and computer scientists. For but one reference on the topic and where 3d can be useful, I would refer you to Illuminated Choropleth Maps (Stewart & Kennelly, 2010). Online PDF preprint here. –  Andy W May 6 at 16:28
    
For a more general reference I would recommend Thematic Cartography and Geovisualization (Slocum et al. 2005 - although there are newer versions which I have not read). There certainly are objective criteria to guide us as to what graphics will convey information more accurately to our audience than simply aesthetic preferences. –  Andy W May 6 at 16:31
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