IS6335 Chap.7 Spatial Data, Maps and Three Dimensional Views
Spatial Data, Maps and Three Dimensional Views
The week position stops being yours to choose
Week six covers the three dimensional data structure, the lattice, surface and contour plot, the map data structure and map visualization, with an R tutorial on both. It is also the heaviest week of the semester for deadlines, because the group milestone report falls here alongside a weekly lab exercise.
The distinction drawn in week two starts paying now.
A continuous field is a grid of positions, each cell carrying attributes: temperature over a region, elevation, a satellite index. Its positions are regular and its values are samples, so resolution is a property you inherit. Geometry is discrete shape given in advance: a coastline, a district boundary, a building footprint. Its positions are not samples and cannot be resampled.
The consequence is the sentence from week two read in reverse.
On spatial data geometry is very largely not a design decision, and that removes the strongest channel from your budget, so everything the reader needs beyond location has to be carried by colour, size or a second view.
Ask first whether the question is spatial at all
Because a map is easy to produce from any file carrying a place name, a great many maps are built for questions that are not about place.
The test is simple. Would the answer change if the regions were rearranged into a sorted list? If it would not, the reader is asking a ranking question and a map is the most expensive available way to answer it.
Spatial position earns the page only when adjacency, distance or extent is part of what the reader has to see.
What a choropleth can and cannot answer
A choropleth colours regions by a value and it is the most commonly built and most commonly misread spatial idiom.
It answers where a value is high, because colour is read against a legend and location is given directly, and it answers whether there is a spatial pattern, because adjacent regions are adjacent on the page. It does not answer which region has the largest total, because area encodes land rather than the attribute and large sparse regions dominate the page.
It answers differences between two regions only weakly, since colour is a low capacity ordered channel and the regions are rarely adjacent. And it says nothing at all about how many people are affected unless population has been encoded somewhere.
The rule that repairs most choropleths follows from that list.
Mapping a count is almost always wrong, because the eye reads area and the largest regions usually have the most of anything. Map a rate instead, a count divided by the population or the area it belongs to, which removes the confound. This is the derive instruction again: the column the map needs usually does not exist in the file you were given.
A second decision hides inside the legend.
Choosing where the colour classes break decides which regions look alike, and equal intervals, quantiles and natural breaks give three different maps from one dataset. None is neutral.
State the scheme you used, and if a single extreme region is driving the classes, say so rather than letting it flatten everything else into one colour.
Three idioms for a third dimension
The week names the lattice, the surface and the contour plot together.
They encode the same information and support different tasks, which makes them the clearest small example in the course of an idiom being chosen by the task rather than by the data. A surface shows shape immediately and hides values behind one another. A contour plot makes values readable and shape harder to grasp.
A lattice makes every cell addressable and shape hardest of all.
Projecting a third dimension onto a flat page costs occlusion, because near objects hide far ones, and perspective distortion, because equal quantities at different depths are not the same size on the page. Both costs fall on the reader and neither is visible in the chart.
The honest default for a field is therefore a contour plot or a heatmap, with a surface reserved for the case where the shape of the whole is genuinely the question being asked.
What this chapter covers
- 01
Continuous fields against given geometry
- 02
Why position leaves the channel budget on spatial data
- 03
The test for whether a question is spatial at all
- 04
What a choropleth answers, and what it cannot
- 05
Map a rate, not a count
- 06
Class breaks as an argument rather than a setting
- 07
Lattice, surface and contour as three answers
- 08
Occlusion and perspective distortion as reader costs
Choose between a surface and a contour plot
- 1Name the dataset type and what it fixes.
- 2Rule on the first reader and justify it.
- 2Rule on the second reader and justify it.
- 1Decide the single-view case.
Key terms
- Choropleth
- A map colouring regions by a value. It answers where a value is high and whether a pattern exists, and it cannot answer which region has the largest total, because area already encodes size.
- Geometry dataset
- Spatial data given as discrete shape rather than as a sampled grid. Its positions are part of the data, so they may not be reassigned to carry something else.
- Class breaks
- The boundaries between colour classes on a map legend. Equal intervals, quantiles and natural breaks produce three different maps from one dataset, so the scheme has to be stated.
- Contour plot
- A field drawn as lines of equal value. It makes individual values readable, which is what a projected surface cannot do, at the cost of showing overall shape less immediately.
- Occlusion
- Near objects hiding far ones in a projected three dimensional view. It is a cost borne entirely by the reader and it is invisible in the chart itself.
Spatial Data, Maps and Three Dimensional Views FAQ
My map of totals looks convincing. Why should I change it?
Because two separate things are already encoded before your attribute arrives. Area on the page carries land size, and a count of almost anything grows with the population that produced it, so a big populous region will dominate a total map whatever the underlying rate. That is why a map of national renewable generation makes large countries look like leaders.
Divide by the population or by the region's own total to get a rate, map that, and if the absolute totals still matter operationally, put them in a sorted bar chart beside the map where length can be compared on a common baseline.
How do I show where incidents concentrate when I only have point locations?
Not by plotting every point, because that reports overlap rather than density and the densest area becomes indistinguishable from a merely busy one. Bin the points, either into a regular grid or into the administrative geometry you already hold, and derive a count per cell. Then derive again, into a rate against the population exposed in that cell, so that a busy city centre is not automatically the answer.
Encode the rate on luminance, which is the ordered colour channel that survives printing. The derived column is the whole answer here, and the idiom follows from it.
Assessment move
Before building any map this term, write one sentence answering the sorted-list test: would the reader's question change if the regions were rearranged into a list? Keep the maps that survive it and turn the others into sorted bar charts.
For the ones that survive, write down the denominator you divided by and the class break scheme you chose, because those two sentences are what turns a map into a defensible figure in the report rather than a decorative one.
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