A closed form solution for the intersections of two ellipses

There intersections of two ellipses are determined using the following steps Rewrite each ellipse as a second degree equations in x and y coordinates Convert the intersection of the two second degree equations into a fourth degree polynomial which can be solved using closed form methods Compute the x values for each y. In theory … Continue reading

Spacing circles in a 2-item Venn Diagram

Venn diagrams display the overlap of two set. One can adjust the size of the circles and their overlap so the areas of the circles and the overlap are proportional to the three values. The radii of the circles can be adjusted so their area is proportionate to their respective values. The placement of the … Continue reading

The geometry of a colorful Venn Plot

The following steps are needed to build a colorful Venn Plot. I will first identify the overlap of two circles followed by the steps needed to construct the 4-item plot. Identifying the overlap between two circles of different sizes Coloring the intersection of two circles requires identification of the the number of degrees of arc … Continue reading

Plotting a colorful Venn Diagram with R

Update: the CRAN package now includes routines to plot intersections for 2-item and 4-item sets in addition to the 3-items sets. The user specifies the values and colors for each of the 15 intersections in a 4-item plot. To find our more about the methods used to customize the colors for regions within the Venn … Continue reading