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How-To's Totally Useless Charts

Totally Useless Charts & How to Build Them – “Hand-drawn” Bar Charts

Welcome to our 2nd installment of Totally Useless Charts & How to Build Them, where we do…exactly what the name implies. Look at some totally useless charts and walk through, step by step, how to build them. If you missed the first installment, the goal of this series isn’t necessarily to teach you how to build these specific useless charts, but more to talk through the techniques, the approach, and the thought process behind each chart, so you can apply those concepts to your own custom charts.

In this installment we’re going to learn how to build “hand-drawn” bar charts in Tableau. These of course aren’t actually hand-drawn, but using some interesting techniques, and a lot of random numbers, we can kind of make them look that way. If you would like to follow along, you can download the workbook here, and the data here.

“Hand-Drawn” Bar Charts

First, let’s look at an example of what we’re talking about. Here is a viz that I published recently about relationships on the show “The Office”. You can check out the interactive viz here.

My goal was to make the entire viz look like an office desk belonging to everyone’s favorite receptionist/office manager, Pam Halpert. To do that, I had to make all of the visualizations appear to be “hand-drawn”, including the bar charts. Let’s zoom in one those.

Here we have two different bar charts, one for the Longest Relationship, and one for the Most Time in Relationships (by number of episodes). Today we’re going to be using different data, but the goal is still the same…build some bar charts that look “hand-drawn”.

Building Your Data Source

Let’s start with our data. For this example we’re going to look at the top 10 highest grossing films of all time. If you downloaded the sample data, you can find these in the “Data” tab.

Next, we need to do some densification. The first thing we need to do is to create a record for every line needed in each bar. If you look at one of these bars closely, you’ll see that it’s actually made up of a bunch of lines…one outer line (orange), and a number of cross lines (blue).

So we are going to densify our data with our first densification table, called “Lines” in the sample data. In this table, we have 1 record for our Outer Line, and 50 records for our Cross Lines

Then we’re going to join our “Data” table, and our “Lines” table using a join calculation with a value of 1 on each side.

But we’re not quite done yet. Now we have a record for each of our lines, but each of those lines is made up of multiple points. Our “Outer Line’ is made up of 4 points, and each of our “Cross Lines” is made up of two points

So we’re going to use one more densification table to create additional records for each of these points, for each of the lines. This table is called “Points” in the sample data

And we’re going to join this to our “Lines” table on the [LineType] Field.

Now for each of our 10 films, we have 4 records for our “Outer Line” and 100 records for our “Cross Lines”, 2 for each of the 50 lines in the “Lines” table.

Drawing the “Outer Lines”

Now we have our data, let’s start building our Totally Useless Chart. We’re going to start with the Outer Lines. To do this, and to make it a bit dynamic so you can play around with how the chart looks, we’re going to build 4 Parameters. Each of these is going to have a Data Type of “Float” and the Default values are below

  • Bar_Width = .6 (used for the height of each bar and the spacing between the bars)
  • Scale_Bar_Outer_Height = .03 (used along with a random number to jitter points vertically)
  • Scale_Bar_Outer_Length = .1 (used along with a random number to jitter points horizontally)
  • Cross Lines = 50 (used to limit the number of cross-lines in each bar. This is optional)

Next, we’ll start building our calculations. The first, and arguably most important of these calcs is going to be our [Jitter] calculation. We want a random number between -1 and 1. The Random() function will give us a random number between 0 and 1, so we can modify that by multiplying the random number by 2 and then subtracting 1 (so a random number of .6 would become .2, and a random number .4 would become -.2)

Jitter = Random()*2-1

Next, we need to calculate the length of each of our “bars”. We’re going to do this by comparing each value to the maximum value and then multiplying it by the Max Length, which in our case will be the number of “Cross” lines we have. So the highest grossing film, Avatar, will have a length of 50, since we have 50 “Cross” lines. ((2.847B/2.847B)*50). Number 10 on the list will have a length of around 26.6 ((1.515B/2.847B(*50). So first, let’s calculate our Max length.

Max Length = {MAX([Line ID]}

Next, we’ll want to divide the Box Office Gross for each movie by the value for the highest grossing movie. The result of this will be a percentage which we’ll then multiply by our [Max Length] field to get our [Outer Bar Length]

Outer Bar Length = ([Box Office Gross]/{MAX([Box Office Gross])})*[Max Length]

Now, we need to calculate the X and Y coordinates for the 4 points of each “Outer Line”. So under normal circumstances, point 1 and point 4 would start at 0, and point 2 and point 3 would just be the [Outer Bar Length]. So if you connected those points, it would start at 0 for point 1, go to the end of the line for point 2, stay at the end of the line for point 3, and then return to 0 for point 4. But we want this to look “hand-drawn”, and if I was drawing bar charts by hand, there is no way they would align that neatly. That’s where our [Jitter] and “Scale” parameters come in.

Outer_Bar_X

CASE [Points]

WHEN 1 then 0+([Jitter]*[Scale_Bar_Outer_Length])

WHEN 2 then [Outer Bar Length]+([Jitter]*[Scale_Bar_Outer_Length])

WHEN 3 then [Outer Bar Length]+([Jitter]*[Scale_Bar_Outer_Length])

WHEN 4 then 0+([Jitter]*[Scale_Bar_Outer_Length])

END

We just want to move these points slightly to get that “hand-drawn” effect, which is why we are using the “Scale” parameters. For that first point, if we just did 0+[Jitter], that value could fall anywhere between -1 and 1, which is a pretty significant shift. But using the [Scale_Bar_Outer_Length] parameter, we can increase that value to get more jitter, or decrease the value to get less jitter. Using a value of .1 in the parameter, means that the value for that first point would now fall somewhere between -.1 and .1.

Next, we need to calculate our Y coordinates for those same 4 points. Again, under normal circumstances, for point 1 we would add half of the bar width to our starting point (the middle of the bar), same for point 2, and then for points 3 and 4, we would subtract half of the bar width from the starting point. So, along with the X coordinates, it would look something like this.

This is where the [Bar_Width] parameter comes into play. We need to know how thick these bars should be. We’re using the [Rank] field as our starting point, so the first bar will start 0,1, the second bar will start at 0,2, and so on. But we don’t want the bars to overlap, or be right up against each other, so we can control that with the parameter. A larger value in this parameter will result in wider bars and less spacing, a smaller value will result in skinnier bars, and more spacing. A value of 1 will result in no spacing between the bars.

Also, similar to the calculation for the X coordinates, we are using that [Jitter] field along with a “Scale” parameter to control how much jitter there will be. So a larger number in the [Scale_Bar_Outer_Height] parameter will result in more vertical jitter, and a lower number will result in less. Here is the calculation for the Y coordinates.

Outer_Bar_Y

CASE [Points]

WHEN 1 then [Rank]+([Bar_Width]/2)+([Jitter]*[Scale_Bar_Outer_Height])

WHEN 2 then [Rank]+([Bar_Width]/2)+(([Jitter]*[Scale_Bar_Outer_Height])2)

WHEN 3 then [Rank]-([Bar_Width]/2)+(([Jitter]*[Scale_Bar_Outer_Height])2)

WHEN 4 then [Rank]-([Bar_Width]/2)+([Jitter]*[Scale_Bar_Outer_Height])

END

Now we have all of the calculations needed to draw our “Outer” lines. So let’s do that

  • Drag [Line Type] to the filter shelf and filter on “Outer Lines”
  • Right click on [Outer_Bar_X], drag it to Columns, and when prompted, choose [Outer_Bar_X] without aggregation
  • Right click on [Outer_Bar_Y], drag it to Rows, and when prompted, choose [Outer_Bar_Y] without aggregation
  • Change the Mark Type to “Line”
  • Right click on [Rank], select “Convert to Dimension” and then drag [Rank] to Detail
  • Right click on [Points], drag it to Path, and when prompted, choose [Points] without aggregation
  • Right click on the Y-axis, select “Edit Axis”, and check the box labelled “Reverse” under Scale

When that’s finished, you should have something that looks like this. There are 10 “bars”, with all 4 points in each bar slightly jittered to give it that “hand-drawn” look.

Next, we need to add the “Cross Lines”

Drawing the “Cross Lines”

To help understand the approach we’re going to take, think about taking each of these bars and breaking them into individual segments. So, for example, our first bar has a length of 50 (think back to the Max Length calculation). So we want to break that into 50 individual segments and draw a diagonal line from the top left of the segment to the bottom right of the segment.

The image above is roughly what it would look like if we draw perfect lines across those segments. But we don’t want perfect lines. We want “hand-drawn” lines. So we’re going to leverage our [Jitter] field and our “Scale” parameters once again.

So let’s build our X and Y calculations. Remember when we built our data source, for our “Cross Lines”, we needed two points, 1 and 2. So Point 1 is going to start the line at the top left of our segment, and Point 2 is going to end the line at the bottom right of our segment. Here is the calculation

Cross_X = if [Points]=1 then [Line ID]-1 + ([Jitter]*[Scale_Bar_Outer_Length]*2) else [Line ID]+([Jitter]*[Scale_Bar_Outer_Length]*2) END

Here we are calculating the position for both points on the X axis. For the first point, when [Points]=1, we want to use our [Line ID] value and subtract 1, so we’re starting at the beginning of our segment (ex. line 1 will start at 0, line 2 will start at 1, line 3 will start at 2, and so on). When [Points]=2, we are going to use just the [Line ID] value (ex. line 1 will end at 1, line 2 will end at 2, line 3 will end at 3). And then we’re just using our [Jitter] field and our “Scale” parameter to jitter these points a little bit, similar to what we did with the “Outer” lines. You may notice that there is a “*2” in these calculations. I added these so I could re-use my same parameters, but could add a little extra jitter to the Cross Lines. I figured if these were actually being done by hand there would be a lot more variation in these lines, compared to the “Outer” lines.

Now let’s calculate our Y coordinates. Similar to how we calculated the Y coordinates for the “Outer” lines, we want one of our points to be half the width of the bar above our starting point, and the other one, half the width of the bar below the starting point. And then we want to jitter them. Here’s the calculation for the Y coordinates.

Cross_Y = if [Points]=1 then [Rank]-([Bar_Width]/2)+([Jitter]*[Scale_Bar_Outer_Height]*2) else [Rank]+([Bar_Width]/2)+([Jitter]*[Scale_Bar_Outer_Height]*2) END

Now this is a little bit confusing because we reversed our axis in an earlier step. So, for Point 1, instead of adding half of the width of the bar to our starting point, the [Rank] field, we need to subtract it from the starting point, to get it to appear above the bar (because the axis is reversed). So when [Points]=1 we’ll subtract half of the width of the bar ([Bar_Width]/2) from the starting point, [Rank]. When [Points]=2, we’ll add half of the width of the bar to the starting point. And then once again we’re using the [Jitter] field, the “Scale” parameter, and then multiplying by 2 to get a little extra jitter. If you wanted to reverse the direction of these lines, so they go from top right to bottom left, just change the calc so when [Points]=1 you add, and when [Points]=2 you subtract.

Now let’s build it.

  • Drag [Line Type] to the filter shelf and filter on “Cross Lines”
  • Right click on [Cross_X], drag it to Columns, and when prompted, choose [Cross_X] without aggregation
  • Right click on [Cross_Y], drag it to Rows, and when prompted, choose [Cross_Y] without aggregation
  • Change the Mark Type to “Line”
  • Right click on [Line ID], select “Convert to Dimension” and then drag [Line ID] to Detail
  • Right click on [Rank], select “Convert to Dimension” and then drag [Rank] to Detail
  • Right click on [Points], drag it to Path, and when prompted, choose [Points] without aggregation
  • Right click on the Y-axis, select “Edit Axis”, and check the box labelled “Reverse” under Scale

Once complete, you should have 50 “Cross Lines” for each of your “bars”.

Now we just need to bring it all together

Combining the Lines

We have our “Outer” lines, and we have our “Cross” lines, and because we have separate data points for each of these (because of the way we structured our data) we can bring them together in the same view pretty easily. We just need to 2 more “Final” calculations for the X and Y coordinates.

Final_X = if [Line Type]=’Outer Lines’ then [Outer_Bar_X] else [Cross_X] END

Final_Y = if [Line Type]=’Outer Lines’ then [Outer_Bar_Y] else [Cross_Y] END

These are pretty straightforward, but basically, if the [Line Type]=”Outer Lines” use the X and Y values from the “Outer_Bar” fields. Otherwise, use the X and Y values from the “Cross” fields. Now let’s build our “bars” with these “Final” calcs.

  • Right click on [Final_X], drag it to Columns, and when prompted, choose [Final_X] without aggregation
  • Right click on [Final_Y], drag it to Rows, and when prompted, choose [Final_Y] without aggregation
  • Change the Mark Type to “Line”
  • Right click on [Line ID], select “Convert to Dimension” and then drag [Line ID] to Detail
  • Right click on [Rank], select “Convert to Dimension” and then drag [Rank] to Detail
  • Drag [Line Type] to Detail
  • Right click on [Points], drag it to Path, and when prompted, choose [Points] without aggregation
  • Right click on the Y-axis, select “Edit Axis”, and check the box labelled “Reverse” under Scale

And now you should have everything together on the same view!

Wait…that doesn’t look right. We don’t want all of those extra “Cross” lines on our shorter bars. Luckily, we can filter those out pretty easily with a calculated field. This is just a boolean calc that checks to see if the Line ID is less than the length of the bar. Remember from earlier that the Line ID corresponds to the right side, or the end of each of these “Cross” lines. So we only want to keep the lines where that value is less than the length of the bar.

Extra Lines Filter = [Line ID]<=[Outer Bar Length]

Now just drag the [Extra Lines Filter] field onto the Filter shelf, and filter on TRUE and voila!

There is one more step that’s completely optional. The way we set up this data source, we can have up to 50 “Cross” lines for the largest bar. But maybe you want less than that. I like to make my visualizations as dynamic as possible so I can play around with how it looks. Earlier we created a parameter called [Cross Lines]. We can use that parameter to determine how many lines we want to use. We’re just going to create one additional calculated field.

Max Cross Lines Filter = [Line ID]<=[Cross Lines]

Just drag that field onto the Filter shelf, filter on TRUE, and then right click on the pill and choose “Add to Context”. Now you can adjust the number of lines, and in doing so, the spacing between the lines. Here’s what it looks like with 30 lines instead of 50.

If you want to use more than 50 lines, just add some additional rows to the “Lines” densification table.

Final Touches

So now our view is built, but there is one critical piece of information missing from our chart…Row Labels. There are a few different ways you can add these, but I’m going to cover two quick options; Shapes and Labels.

For the viz that I shared earlier, I was publishing it to Tableau Public, which has pretty limited options when it comes to fonts, and I really wanted a “hand-drawn” font. What I ended up doing was creating custom shapes for each of my labels in PowerPoint. If you decide to go this route, one thing you want to make sure that you do is to set the size of each of the text boxes equal. If the text boxes are different sizes when you save them as images, it will look like the text is a different size for each value because Tableau will attempt to “normalize” them.

So first, create your shapes in PowerPoint. Here, I inserted 10 text boxes, typed my movie names, set the alignment to “Right”, and then set the Font to “Caveat”. Then I clicked and dragged to highlight all 10 text boxes, and in the top right corner of PowerPoint, in the Shape Format options, I set the “Width” so that they would all be the same size. regardless of how long the text in each box actually is.

Then I right-clicked on each image, saved them to a folder in my “Shapes” repository. Finally, I created a new sheet using the “Shapes” mark type, positioned them by Rank, and then fixed and reversed the axis so they would align with the bars. Then you can throw these two sheets in a container on your final dashboard and have something like this.

So that’s an option if your data is static and you don’t have a lot of values. This would be nearly impossible to maintain if new values were constantly being introduced, and would be way too much work if there were a lot of values in your data source. In those cases, you may need to go with more traditional labels and be limited to the available fonts. But even that can be a little bit tricky because these are lines, not bars.

For this we need one more calculated field. We only want to label 1 point for each of our bars but we can’t filter out any points. We also can’t use a calculation that results in some null values and some populated values for a given Line Type (because it can inadvertently remove sections of the lines we worked so hard to draw).

Label Name = if [Line Type]=’Outer Lines’ then [Name] END

Now just drag the [Label Name] field to Label and then set the Label options as follows.

You can choose whichever font type and size you prefer, but make sure to set the Alignment to “Top Left’, select “Line Ends” under Marks to Label, and under Options, de-select “Label end of line”. Between the calculated field and these options, only 1 Label will appear per bar, and it will appear to the top left of Point 1 of the “Outer” line (which is the bottom left point in each bar). It should end up looking something like this.

Those are a couple of ways to add Row Labels to your “hand-drawn” bar charts. If you want to add value labels as well you can follow a pretty similar process, but it’s a little trickier. This post is already long enough so I’m not going to go into that, but if you make it this far and want to add value labels, please reach out and I’d be happy to help you. Or you can take the easy way out and do what I did, and just create an image of a “hand-drawn” axis and add it to your dashboard.

Thank you so much for reading, and keep an eye on the blog for more ‘Totally Useless Charts & How to Build Them’!

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How-To's Tableau Techniques Totally Useless Charts

Totally Useless Charts & How to Build Them – Lotus Flowers

Welcome to our new series, Totally Useless Charts & How to Build Them. In each installment of this series we’ll look at one very custom chart, something with almost no real use cases, and we’ll walk through, step by step, how to build it. The purpose of this series isn’t necessarily to teach you how to build these specific useless charts, it’s more about talking through the techniques, the approach, and the thought process behind each chart. Our hope is that seeing how we went about building these will help you with your own custom charts. But if you do somehow find a great use case for one of these charts, by all means, please download the workbook and use it as your own.

In this first installment we’re going to learn how to build Lotus Flowers in Tableau. It’s not a requirement, but it may be a good idea to review Part 1 and Part 2 of the Fun With Curves Series before proceeding. To follow along, you can download the workbook here, and the data here.

Lotus Flower

First, let’s take a look at what we’re trying to build. Below is a lotus flower with 10 petals, which means we have a total of 11 polygons; 1 circle and 10 petals. The circle is fairly easy to build using the techniques in Part 1 mentioned above. The petals are a little more complicated. But first thing’s first…we need some data.

Building Your Data Source

Let’s start with our data. For this example we’re going to build 12 lotus flowers and we’re going to use the value from our data source to size the flowers appropriately. We’ll start with the tab titled ‘Source Data’.

Next, we’re going to do some densification to get the number of polygons needed for each of the flowers. Below I have 1 record for the Circle and 24 records for the petals. We’re going to build this in a way that will let you choose how many petals you want to display (up to 24). This data can be found in the ‘Polygons’ tab in the sample data.

Now we’re going to join these two sources together using a join calculation (value of 1 on each side). The result will be 25 records for each of our 12 ‘Base’ records.

Next, we need to do a little more densification, but this time it’s a little trickier. For our circle, we want at least 50 points for a relatively smooth curve. For our petals, we actually need to draw 2 lines for each petal, one for the left side of the petal (Min) and one for the right side of the petal (Max), and then join those together. Pretty confusing right? We’ll talk about this in a lot more detail. This table is a little too large to include a screenshot, but take a look at the ‘Densification’ tab in the sample data.

For our circles, we have 50 records. We have two numerical fields, [Points] and [Order], that both run from 1 to 50 and a [Type] field to identify that these points are for our circles. For our petals, we have 100 records. We still have the same two numerical fields, but the values are a little different. We have an [Order] field that runs from 1 to 100, and a [Points] field that runs from 1 to 50 and then back down from 50 to 1. We also have a [Side] field with values of Min or Max. The Min records will be used to draw the left side of our petals. The Max records will be used to draw the right side of our petals. And then we have a [Type] field to identify that these records are for our petals. Now we just need to join this table to our data source on the [Type] Field.

Building Your Circles

If you have read through Part 1 of the Fun With Curves series, then you may remember that in order to draw a circle in Tableau, we only need 2 inputs; the distance of each point from the center of the circle (the radius), and the position of each point around the circles (represented as a percentage).

Let’s start with the first input, the radius. We are going to size our circles based on the Value field in the Source Data. We want the area of our circles to represent the value in the data. So we have the area of each circle, we just need to use those values to calculate the radius of each circle. We can do this with the simple calculation below.

Radius = SQRT([Value]/PI())

Next, we need to calculate the position of each point around the circle. I’m not going to go into too much detail on this, but you can read more about it in the post mentioned above. To calculate this, we need the maximum number of points for our Circles (50), and we need the [Points] field (values 1 thru 50). For the max point calculation I am going to use an LOD because the max number of points for our circles, may not always align with the max number of points in our data source (but in this case it does).

Max_Point = {FIXED [PolygonType] : MAX([Points])}

Circle_Position = ([Points]-1)/([Max_Point]-1)

Next, we just need to plug the [Radius] and the [Circle_Position] values into our X and Y formulas for plotting points around a circle.

Circle_X = [Radius]* SIN(2*PI() * [Circle_Position])

Circle_Y = [Radius]* COS(2*PI() * [Circle_Position])

Now, let’s draw our circles

  • Right click on [Circle_X] and drag it to columns. When prompted, choose [Circle_X] without any aggregation
  • Right click on [Circle_Y] and drag it to rows. When prompted, choose [Circle_Y] without any aggregation
  • Right click on [Base_ID], change it to a Dimension, and drag it to Detail
  • Right click on [Order], change it to a Dimension, and drag it to Path
  • Drag [Type] to Filter Shelf and filter to ‘Circle’
  • Change the Mark Type to Polygon

Now you should have something that looks like this.

Although it looks like one big circle, we actually have all 12 circles in this view. They’re just stacked on top of each other. So next we need to space these out a little bit. There are a lot of different techniques to do this, but here’s one I like to use to create Trellis Charts. This technique works great when you have a sequential ID field, which we do (Base_ID).

First, we’re going to create a numeric parameter that will allow us to choose the number of columns we want to create. We’ll call the parameter [Column Count] and set the value to 3. Next, we’re goin to use the [Base_ID] field to break our circles into columns and rows, starting with row.

Row = CEILING([Base ID]/[Column Count])

Column = [Base ID]-(([Row]-1)*[Column Count])

Now right click on both of these fields, change them to Dimensions, and then drag them to the appropriate shelf (Row to Rows, Column to Columns). The result should look something like this.

Building Your Petals

Alright, so this part is a little more complicated. I’m going to start by reviewing the basics of how you build these shapes, but I’m going to skim over the calculations since those will change significantly once we try to build these petals around our circle. No need to follow along with the workbook during this section.

So here are the basics. Let’s start by drawing a Bezier Curve with 4 control points. Our line is going to start at 0,0 and end at 5,10. Wow, this is easy, we already have the coordinates for 2 of the points!

Let’s take a look at our inputs. Our line will have a height of 10 and a width of 5. I’ve also built 2 parameters that we’ll use to calculate the 2nd and 3rd set of points. You can experiment with different values here, but these seem to work pretty well. We need a total of 8 values (4 sets of X and Y).

  • Point 1 will be the start of the line. In this case, it’s 0,0
  • Point 2 will appear on the same X axis as Point 1, but will be somewhere between the start and end of the line on the Y axis. I like to place it two thirds of the way, or .67 (the value in the P2 Parameter Input above). So the coordinates for Point 2 will be 0 and 6.7 (P2 Parameter x Height of the line)
  • Point 3 will appear on the same X axis as Point 4, and will appear somewhere between the start and end of the line on the Y axis (similar to P2). I like to place it halfway, or .5 (the value in the P3 Parameter Input above). So the coordinates for Point 3 will be 5 and 5 (P3 Parameter x Height of the line).
  • Point 4 will be the end of the line. In this case, it’s 5,10

If you were to plot these 4 points, you would have a jagged line like you see in the image above. But look what happens when we plug those values into our Bezier calculations

X = (1-[T])^3*[P1_X] + 3*(1-[T])^2*[T]*[P2_X] + 3*(1-[T])*[T]^2*[P3_X] + [T]^3*[P4_X]

Y = (1-[T])^3*[P1_Y] + 3*(1-[T])^2*[T]*[P2_Y] + 3*(1-[T])*[T]^2*[P3_Y] + [T]^3*[P4_Y]

Alright, we are halfway there! Kind of. So now we have a line that will create 1/2 of one of our petals. But in order to turn this into a petal shaped polygon, we need another line that’s a mirror image of this one.

This is where the Min and Max records come in. We need to calculate our 4 sets of coordinates for both sides. Luckily, most of the values are actually the same. P3 and P4 are going to be identical for both lines. And the Y values for P1 and P2 are the same. The only differences are the X values for P1 and P2. And to calculate those we just add the width of the whole petal (width x2) to our starting point. And if we were to plug these coordinates into the same calculations, we have this.

Now this is where the [Order] field comes into play. To make this one single polygon instead of two separate lines, we can use the [Order] field on Path and change the Mark Type to polygon

On the Left (Min) side, we have points 1 thru 50, running from the bottom left up to the top middle. On the right (Max) side, we have points 1 thru 50 running from the bottom right up to the top middle. But then we have the [Order] field (on label in the image above). This field runs from the bottom left to the top middle to the bottom right, in one continuous flow, from value 1 to 100. This is what makes it a single continuous polygon.

Ok, so that’s how we would build 1 single petal shaped polygon, perfectly positioned facing directly upward. But that’s not what we’re trying to do. We’re trying to build a dynamic number of petals, evenly spread around a circle and facing outward in the appropriate directions. So let’s do that.

Building Your Petals (for real this time)

We’re going to use a similar approach to what was described above, but everything needs to be plotted around a circle. So any calculations we use to determine our 4 points are going to have to run through those X and Y calculations for plotting points around a circle. That means, for all of our points, P1 thru P4 for both sides, we need to calculate two things; the distance from the center of the circle, and the position around the circle. But before we calculate those specific points there are a few other calculations that we’ll need. We also need a parameter, called [Petal Count] that will allow us to select how many petals we want. This should be a numeric parameter, and let’s set the value to 10 (I recommend using a range, allowing values from 4 to 24)

T = ([Points]-1)/([Max_Point]-1) – this is the same as the [Position] calc used earlier. It’s used to evenly space points between 0% and 100%

Petal_Count_Filter = [Polygon ID]<=[Petal Count] – this will be used as a filter to limit the number of petals displayed to what is selected in the [Petal Count ] parameter

Petal_Width = 1/[Petal Count] – this calculates the total position around the circle that will be occupied by each petal. For example, if there were 10 petals, each one would occupy 1/10 of the space around the circle, or .10

Petal_Side_Position = IF [Side]=’MIN’ THEN ([Polygon ID]-1)*[Petal_Width] ELSE [Polygon ID]*[Petal_Width]
END
– this calculates the position of the start of each Min line and Max line. If there were 10 petals, the Min side of the 2nd petal would be at position .1 or (2-1)*.1, and the Max side of the petal would be at position .2, or 2*.1. The Min value will share the same position as the Max value of the previous petal. The max value will share the same position as the Min value of the next petal

Petal_Middle_Position = ([Polygon ID]/[Petal Count]) – ([Petal_Width]/2) – this calculates the position of the center of each petal. If there were 10 petals, the center of petal 3 would be at .25, or (3/10) – (.1/2). This is also halfway between the position of the Min line and the Max line.

Alright, now we can calculate all of our coordinates. Let’s start with P1. For the first input, we want this point to start right at the edge of our circle. So the distance from the center is going to be equal to the radius of the inner circle. So the first input is just [Radius]. For the second input, we’ll use the the [Petal_Side_Position] we calculated above.

P1_X = [Radius]* SIN(2*PI() * [Petal_Side_Position])

P1_Y = [Radius]* COS(2*PI() * [Petal_Side_Position])

If we were to plot these points for 12 petals, we would end up with 24 points, but it would appear that we only 12 because each is overlapping with another point. But this gives us the outside edges of each of our petals

Now onto P2. This one is a little more complicated. We’re going to use P1 as a starting point for this calculation, instead of the center of the inner circle. Now we need to calculate the distance from P1 where we want our next point to appear. First, we need to determine the length of the entire petal. I like to use a parameter for this so I can dynamically adjust the look of the flowers. So let’s create a parameter called [Petal_Length_Ratio]. This is going to be a number relative to the radius, so a ratio of 1 would set the length of the petal equal to the radius of the circle. A value of .8 would set the length of the petal equal to 80% of the radius, and so on. I usually go with a value somewhere between .5 and 1. We’ll use this along with the radius, so that the petals of each flower are sized appropriately based on the size of their inner circle. Next, we need to position this point somewhere between the start of the line and the end of the line. As I mentioned earlier, I like to place it two thirds of the way (P2_Parameter from the previous section). So the first input, the distance from P1, is going to be the radius x the length ratio x the P2 parameter. For the second input, we’re going to use the [Petal_Middle_Position] because we want this side of the line to follow the same path as the line with P3 and P4. If we were to use the [Petal_Side_Position] field, we would end up with really wide, strange looking petals. This will probably make more sense a little further along. For now, let’s plug those values into our X and Y calcs.

P2_X = [P1_X] + (([Radius] * [Petal_Length_Ratio] * [P2_Parameter]))* SIN(2*PI() * [Petal_Middle_Position])

P2_Y = [P1_Y] + (([Radius] * [Petal_Length_Ratio] * [P2_Parameter]))* COS(2*PI() * [Petal_Middle_Position])

P3 is a little more straight forward. For the first input, we’re going to calculate the distance from the center of the inner circle. And then we’ll use a similar approach to what we did for P2. The first input will be the radius + (the radius x the length ratio x the P3 parameter). As I mentioned in the earlier section, I like to set this parameter to .5. And once again, we’re going to use the [Petal_Middle_Position] field for the second input.

P3_X = ([Radius]+([Radius] *[Petal_Length_Ratio] * [P3_Parameter]))* SIN(2*PI() * [Petal_Middle_Position])

P3_Y = ([Radius]+([Radius] *[Petal_Length_Ratio] * [P3_Parameter]))* COS(2*PI() * [Petal_Middle_Position])

P4 is almost identical to P3, except we don’t need the length ratio. We want this point to appear at the end of the line. So we can just remove that from the calc.

P4_X = ([Radius]+([Radius] * [Petal_Length_Ratio])) SIN(2*PI() * [Petal_Middle_Position])

P4_Y = ([Radius]+([Radius] * [Petal_Length_Ratio])) COS(2*PI() * [Petal_Middle_Position])

We’re almost there! If we were to plot these points for the first petal in our lotus flower, it would look like this. It looks very similar to what we reviewed in the previous section, but with one very important difference…everything is at an angle…which is what we wanted.

All that’s left to do is to plug all of these points in our Bezier calcs and then build our polygons!

Petal_X = (1-[T])^3*[P1_X] + 3*(1-[T])^2*[T]*[P2_X] + 3*(1-[T])*[T]^2*[P3_X] + [T]^3*[P4_X]

Petal_Y = (1-[T])^3*[P1_Y] + 3*(1-[T])^2*[T]*[P2_Y] + 3*(1-[T])*[T]^2*[P3_Y] + [T]^3*[P4_Y]

Now the polygons. Let’s build this as a Trellis chart, just like we did with the Circles. So drag [Row] on to Rows and [Column] onto Columns. And then;

  • Right click on [Petal_X] and drag to Columns. When prompted, select [Petal_X] without aggregation
  • Right click on [Petal_Y] and drag to Rows. When prompted, select [Petal_Y] without aggregation
  • Drag [Type] to Filter Shelf and filter to ‘Petal’
  • Drag [Petal_Count_Filter] to Filter Shelf and filter to TRUE. Right click and ‘Add to Context’
  • Drag [Polygon_ID] to Detail
  • Drag [Order] to Path
  • Change Mark Type to Polygon

We’re so close! Your sheet should look like this

The only thing left to do is to combine the Circle polygons with the Petal Polygons. We have separate data for them, all we need to do is get them on the same sheet. So we’ll create two more simple calcs to bring it all together.

Final_X = IF [Type]=’Circle’ THEN [Circle_X] ELSE [Petal_X] END

Final_Y = IF [Type]=’Circle’ THEN [Circle_Y] ELSE [Petal_Y] END

Now just replace [Petal_X] and [Petal_Y] with [Final_X] and [Final_Y] and drag [Type] from the filter shelf on to Color and you should have your lotus flowers!

The Final Touches

The hard part is done, now to make it look pretty. Play around with some of the parameters until you get the look that you like. Adjust the [Petal Count], the [Column_Count], the [Petal_Length_Ratio], and even the [P2_Parameter] and [P3_Parameter] if you wanna get crazy.

Next, throw some color on there. You could make the color meaningful to encode some data, or you could do what I just did and color it randomly. I used the calc below and then just assigned one of the color palettes I have saved.

Color = [Type] + STR([Base ID])

And that’s it! If you made it this far, please reach out and let me know what you thought, and what you came up with. Thank you so much for reading, and keep an eye on the blog for more ‘Totally Useless Charts & How to Build Them’