# Shapeshifting Tile Maps in Tableau

In the past
few days, we’ve seen a resurgence of innovation with hex maps in Tableau. The
technique was first developed by Matt Chambers in his post, How To: Hex Tile Maps in Tableau and was based on the square tile map technique
developed by Brittany Fong in her post, Periodic Table Map AKA Tile Map. In the two years since Matt developed the technique, it
has become ubiquitous in the Tableau community, but recent innovation by Rody
Zakovich has turned the hex map into polygons in order to avoid problems with
sizing of the shapes (Polygon Hex Map in Tableau) and Joshua Milligan has converted Rody’s polygons to a spatial
file in his post, Hex Map Spatial File.

I just love how
the community takes one idea and builds upon it. Paired with a platform like
Tableau Public, which enables this type of collaboration, it is truly what
makes our community great. But, I have to admit that after seeing these four
people work together to innovate this technique, I was a bit jealous that I wasn’t
part of it. So, I’m going to attempt to add something to the conversation. In
all honesty, I’m not entirely sure my technique will be of much value, but it
was fun to create, so I’m going to share it with you.

**Regular Polygon Maps**

Here’s my
idea: What if we could create a template that allows you to build a tile map
using any type of regular polygon, be it triangles, diamonds, squares,
hexagons, octagons, or circles (circles are just polygons with lots of sides).

*Note: A regular polygon is one that is both equilateral (the lengths of all the sides are equal) and equiangular (the angles are all equal).*So that’s what I set out to do.
The basic idea
would be that you would use five parameters to build your map:

1.

**Number of Points**– This will specify the number of points on the polygon.
2.

**Rotation**– This will rotate the polygon. So, if you chose 4 points, you’d get a square, but if you rotate it, you’ll have a diamond.
3.

**Row Offset**– In order to aid in tessellation (fitting the polygons together nicely), you may need to move some of your rows to the left or right. For example, on Matt’s hex map, every other row is moved in by ½ in order to make the hexagons fit together. This row offset will allow you to adjust the offset as desired.
4 & 5.

**Horizontal and Vertical Padding**– Sometimes your polygon may seem too large or too small or you may wish to have some padding between them, so these parameters will allow you to adjust the padding so you can get it just right.*Note: This is not the same as the issue Rody was trying to address. Once you set these parameters, everything will look the same when you place the sheet on a dashboard.*
I’m pleased to
say that, after hacking away at it, I was able to get everything working as
desired. Here’s a short gif showing the functionality of the tool.

**How Does it Work?**

I’ve built my
sample workbook to act as a template. So, if you’re not interested in the
internals of how it was built, feel free to download the workbook, add in your data,
and use it in your own projects. You can find the workbook here: Configurable Regular Polygon Maps. But, if you’re interested in the details, keep
reading.

If you read my
post on creating Geometric Art in Tableau, you’ll remember that I had originally created some artwork using
circle shapes (if you haven’t read it, then why not??). But, I ran into similar
problems as Rody encountered with the hex map shapes. First, shapes have a
maximum size, so that limited the size of my overall artwork. Second, you have
to manually size the shapes to get it just right and then make adjustments when
you put your sheet on a dashboard. To overcome this problem, I decided to draw
each bubble as separate polygons (with 100 points to make it look like a smooth
circle) using the parametric equation for a circle. As a bonus, I had used an
adjustable bins technique to allow you to change the number of points on each
polygon. So, instead of circles, you could change the polygons to squares or
triangles or hexagons. Here’s an example showing

*The Great Wave Off Kanagawa*with triangles:
The polygon
map uses the exact same technique. Essentially, each shape will be an
approximation of a circle with the number of points specified. While you may
not think of a square as a circle, strictly speaking, it is an approximation of
one, just with 4 points. Thus, the parametric equation for a circle will be all
we need to calculate the points of each polygon. Obviously, we’ll be using
parametric equations in this process so, if you’re unfamiliar with them, I’d
suggest reading my blog, Beyond Show Me Part 3: Parametric Equations.

**The Data**

Let’s start by
taking a look at our data set (you can find the template here: Poly Map Template.xlsx). The data includes two worksheets:

1)

**Polygons**– Defines the center point of each state. This is based on Matt’s original hex map data, with some slight modifications of my own. The center x point is in a field called**CX**and the center y point is in**CY**.
2)

**Range**– This has one column with two rows with values of 0 and 100. This will be used to create our bins, which we’ll use for determining the points of each polygon.**Onto Tableau**

Now let’s
build it in Tableau using the following steps:

**1) Connect to the Data**

Connect to the
spreadsheet then join

**Polygons**and**Range**using a join calculation, 1 = 1.**2) Create Parameters**

Create the parameters
I discussed earlier:

**Number of Points**– Integer with values ranging from 3 to 100. If you like, you could limit the number of options further using a list, as polygons with more than 20 or so points look pretty much like a circle. In my case, I’ve limited it to 3, 4, 5, 6, 8, 10, 15, 20, and 100.

**Rotation**– This will be the rotation in degrees, so this should be an Integer with values from 0 to 360.

**Row Offset**– Float with all allowed values. Typically, you’ll want this to be either 0 or 0.5.

**Horizontal Padding**– Float with all allowed values.

**Vertical Padding**– Float with all allowed values.

**3) Calculations for Adjusted Center Points**

**CX**and

**CY**define the default center points of each polygon, but we’ll need to adjust them to account for the row offset and the padding. So, create the following calculated fields:

**Center X Adj**

IF [CY] % 2 =
1 THEN [CX]+[Row Offset]+([Horizontal Padding]*([CX]+[Row Offset])) ELSE
[CX]+([Horizontal Padding]*[CX]) END

The map will
have a reversed y-axis, so our first row at the top will be row 0 (Alaska &
Maine). Every other row, starting with 1 (Vermont and New Hampshire) will be
affected by the Row Offset, so the calculation above will make those
adjustments for odd numbered rows. All rows will receive the adjustment for horizontal
padding.

**Center Y Adj**

[CY]+([Vertical
Padding]*[CY])

There is no
offset for the y-axis, so the calculation to adjust the Y center point is a bit
simpler.

**4) Create Adjusted Bins**

**Range**, which will have values 0 and 100 will be used to create bins, which will then be leveraged in the plotting of each polygon point. However, we want the number of points to be adjusted based on what we’ve specified in the

**Number of Points**parameter, so we’ll need to first create a calculated field called

**Range Adjusted**with the following calculation:

[Range]/(100/[Number of Points])

Then we’ll
create bins on this field with a size of 1.

**4) Parametric Equations Calculations**

Next, we’ll need to deal
with the parametric equations. For this, we’ll need to determine our value of
T, then use it to calculate X and Y. First, we’ll create a field called

**Index**with the formula:
Index()

As discussed in my post
on Parametric equations, the ideal range of values for

**T**when creating a circle are 0 to 2Ï€. So, our formula for**T**will be:
[Index]*6.28318/[Number of Points]

Next, we’ll
use

**T**to calculate our**X**and**Y**coordinates:
X = WINDOW_AVG(AVG([Center X Adj])) + COS([T])*COS(RADIANS([Rotation])) -
SIN([T])*SIN(RADIANS([Rotation]))

Y = WINDOW_AVG(AVG([Center Y Adj])) + COS([T])*SIN(RADIANS([Rotation])) + SIN([T])*COS(RADIANS([Rotation]))

These
calculations use the standard parametric equation for a circle with some slight
adjustments to account for the rotation and each polygon’s center point.

**5) Plot It**

Now we’ll plot it in
Tableau:

A) Drag

**State**and**Range Adjusted (bin)**to the Detail card.
B) Remove the
auto-generated Latitude and Longitude from the Rows and Columns shelf.

C) Drag

**X**to the Columns shelf and**Y**to the Rows shelf. They will become table calcs. Change them both to compute using**Range Adjusted (bin)**.
D) Reverse the
y-axis. You should now have something that looks like this:

E) Change the
chart to Polygon.

F) Drag

**T**to the Path card.
From here, you
can add your sheet to a dashboard, adjust your parameters as desired, and blend
the data with your own data set. And that’s all there is to it!! Here’s my
final version using the Superstore data set. Click on the image to interact
with the visualization and play with the different options.

Again, I’m not
sure that there’s a lot of utility to this, but if you use it, I’d love to see
what you create.

**Update, 12/23/2017**: Using this methodology and the coordinates I developed for a square tile map of Africa, I also generated a version of this tool for Africa. You can see the visualization here: Africa Shapeshifting Tile Map
Ken Flerlage, December
22, 2017

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