Why 3-D?

Why Visualize Property Value in 3-D?

Once we recognize the importance of property taxes to a local government and having established the importance of normalizing tax value by the space it consumes, why is it that we display this data in three dimensions? In addition to creating a compelling and attractive visualization, using all three dimensions allows us to more effectively identify patterns and overcome some mapping barriers. Given the nature of urban development the most efficient, and thus most important to show, properties tend to be very small. The visual paradox we run into with the “miles-per-tank” total value map is that larger less efficient parcels are much easier to spot compared to small downtown parcels. The most direct way to account for this is to display our maps at various scales but this sacrifices context and makes direct comparisons awkward

Value per acre in Buffalo, NY. In visualizing the entire community our view is dominated by the physically largest properties. The most efficient and most important properties, such as downtown, are quite small and hard to make out.

In addition to these visual limitations a two dimensional map presents some data limitations. In order to convey the data clearly we tend to summarize continuous data such as value per acre or population into classes though there are plenty of other innovative solutions. This makes it much easier to interpret the data, especially for those less familiar with maps or with the particular area, but we can no longer distinguish the magnitude of difference between values within the same class. How much more “purple” is one property than another? One often overlooked limitation of chloropleth maps is the difficulty in making them legible to those with color blindness

If we distort the image so that the size of property reflects its value we can distinguish the relative tax value of different locations. In blue are boundaries of municipalities, distorted along with the property to reflect relative weight. The yellow boxes reflect the expanded contribution of downtown.

One way to try and compensate for the small size but high value of downtown parcels is to create a cartogram. Typically, a map depicts shape and size with respect to realistic shape and area. A cartogram distorts the size of a feature to reflect its value while attempting to minimize shape distortion. This can be a powerful tool for visualizing the relative importance of different features but makes its own set of informational sacrifices. The resulting distortion can be difficult for the viewer to interpret since familiar shapes and locations have shifted.

To overcome these barriers we visualize value per acre as elevation. In addition to quickly revealing the pattern of tax production, depicting value in this way provides a continuous representation of each individual property without altering their shape or position. We can then fully recognize the proportional differences between different parts of the community, examine the distribution of value production, and explore outstanding properties. The resulting image approximates a scene which is familiar to us: a city skyline or mountain range. The peaks and distribution of each 3-D image become a fingerprint, of sorts, identifying each city and telling us about its development history.

Another way to visualize 3-D data is to create a 3-D surface.  It facilitates visualizing large areas at the expense of fine grain details.