NYCJUG/HexagonAspects

Effect of "Aspect" Parameter in Plot

Recently I noticed that the plot of a regular hexagon looks slightly distorted when plotted with a normal aspect ratio. Since this is a bit subjective, I came up with a method to demonstrate this distortion.

I plotted three hexagons to PDF with three different aspect ratios of 1, 0.9, and 0.8. I imported a screenshot of each into a paint program and selected the top (horizontal) side, leaving a little bit of the corner at each end to ensure I was getting the entire length. I then drew perpendiculars from each of these corners, rotated the image 60 degrees, then pasted this back into the original image by lining it up with the side to the right of the top.

Here's what I got:

Aspect 1	Aspect 0.9	Aspect 0.8

From this it seems clear that only the one plotted with "aspect 0.9" has sides that appear to be the same length. For the other two, it's clear that the top edge is a different length than the top right edge. Not only that, it's clear that the 60 degree rotation lines up only for the 0.9 example as the other two are clearly not parallel.

Also, they are each different sizes even though I was fairly careful to select them the same way, using the screen capture tool built into Windows 10.