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One of the most crucial requirements for rich, interactive scientific graphics is being able to "annotate" individual graphic elements (e.g. the data points of a scatterplot, the individual curves in a plot of multiple curve fits to data, individual subregions of a density plot) with additional information. I'm using the term "annotate" very broadly here to stand for "associate additional information with". Minimally, one would like to be able to assign unique identifiers to each feature of interest, that can be used as keys in auxiliary data structures.

(For example, one way to make a scatterplot interactive is to equip each data point in the scatterplot with a tooltip that will display additional information about that point when the user hovers the cursor over the point. Another way would be to give the user the ability to "light up" a subset of the data points based on some shared metadata value.)

Can the Mathematica Graphics object accommodate such annotations within it?

(NB: I don't doubt that it would be possible to implement this sort of capability "on top of" Mathematica. At the moment I am interested only in whether such functionality is already built into Mathematica.)

EDIT: added one more example of possible modes of interactivity.

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Have you seen Tooltip[]? What limitations do you see there? – belisarius has settled Sep 29 '13 at 17:18
@belisarius: thanks, that's what I was looking for. Mathematica's way of doing this sort of thing is, as usual, orthogonal to the first approach that comes to my mind, but it is always interesting... – kjo Sep 29 '13 at 17:25
Why do you say it is "orthogonal" to your approach? You were the one that suggested placing the info in a tooltip, which is exactly what Tooltip does! :) – R. M. Sep 29 '13 at 17:30
@rm-rf: what's orthogonal is the idea of wrapping the object (line, point, whatever) in the metadata, whereas my first instinct would have made it a property of the object... – kjo Sep 29 '13 at 17:32
@rm-rf: also, the Mathematica approach is far more specific than the approach I had in mind, namely, to associate metadata with individual elements, irrespective of whether the downstream use of it is based on tooltips or anything else. For example, a different interactive functionality would be one that lights up certain points depending on their associated metadata. This has nothing to do with tooltips. (I've added this example to my post.) – kjo Sep 29 '13 at 17:40

1 Answer 1

up vote 5 down vote accepted

I suggest the dictionary data structure, to create semantic and maintainable code.

The most common approach that I've seen on here for handling related data is to stick it all in a list, so people end up with code like this:

{city[[54, 1]], Tooltip[Disk[Reverse@city[[54, 2]], 0.1], city[[54, 3]] <> " (" <> ToString@city[[54, 4]] <> ")"]}

Which is utterly nonsense to the rest of us, who haven't got a clue about what those indices represents. With the dictionary data structure on the other hand we can associate with each object several key/value pairs. For example, to get the population of a certain city we may write:


This is a lot easier to remember than if we had some index for the city and some index for population:


To implement the dictionary data structure, all you have to do is to load the package that I've posted previously here.

<< "~/Documents/Mathematica/datadictionary.m"

Here's an example I've created. It uses tooltips to display the name of a city and its population on mouse over, and it colors each city according to which region it belongs to. It also uses MouseAnnotation to color the cities in the same region as the city you're hovering over white. So it's meant to both exemplify how one can do the things mentioned in the post, and at the same time the dictionary data structure.

getKeys[symbol_] := DownValues[symbol][[All, 1, 1, 1]];

colors = MapIndexed[# -> ColorData[3][First@#2] &, CountryData["Sweden", "Regions"]];

addCity[{name_, region_, country_}] := (
  city[name] = makeDictionary[];
  dictStore[city[name], "Name", name];
  dictStore[city[name], "Region", region];
  dictStore[city[name], "Coordinates", CityData[{name, country}, "Coordinates"]];
  dictStore[city[name], "Population", CityData[{name, country}, "Population"]];
  dictStore[city[name], "Color", region /. colors]

addCity /@ CityData[{All, "Sweden"}];

    RGBColor[0.896`, 0.8878`, 0.8548`], EdgeForm[GrayLevel[0]],
    CountryData["Sweden", "FullPolygon"], {
        MouseAnnotation[] === city[#]["Region"],
        Tooltip[Disk[Reverse@city[#]["Coordinates"], 0.1], 
         city[#]["Name"] <> " (" <> ToString@city[#]["Population"] <> 
        , city[#]["Region"], "Mouse"]
       } & /@ getKeys[city]
    }, AspectRatio -> Full]


As you may have noticed, the first example of how horribly unreadable code with related data may become if you keep the data in a list is just a converted version of the code I'm actually using to draw the disks. Only with the dictionary data structure it looks like this:

{city["Goteborg"]["Color"], Tooltip[Disk[Reverse@city["Goteborg"]["Coordinates"], 0.1], city["Goteborg"]["Name"] <> " (" <> ToString@city["Goteborg"]["Population"] <> ")"]}

Which is much more intuitive.

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