#TweakThursday 23: Creating Trochoids with 2 Rows of Data

Following previous post on Creating Sigmoid with 2 Rows of Data which is inspired by Rody Zakovich's post, I was looking for some interesting curves to apply the same trick. Then I fell on this one:
http://www.tableau.com/stories/gallery/theta-analysis
This viz is created by the technical product marketing people at Tableau. The trochoids are defined here which belong to a family of math functions.

The twbx file weighs over 12MB and there are 880K+ rows in the data set. Looks like a good case for me to try. The result is pretty good. To create the same chart, I only needed 2 rows of data in a single column. The workbook size is reduced to 118K, that is, less than 1% of the original size.

The key for the data reduction is the use of data densification.

Click image to view the interactive version.

Some details of the implementation are as follows.

1.The two rows of data are in a single column:

2.I created "gear ratio" and "cycloidality ratio" as parameters, instead of dimensions. This saves quite a few rows

3.Used Padded and Index() to create data densification as did in the previous post.

4.Created 5 calculated fields for the coordinates:

That's the tweak of the week.