Glad you fellows liked that way of producing an ellipse. Seems a lot better than most of the other methods i've come across.
I backtracked slightly from ellipses and looked at how to make curved miters where piece meet with a in-curved corner:
- Elements de Geometrie plain a'-small.jpg (35.78 KiB) Viewed 7585 times
Following on from ellipses, my study has since moved through the construction of "les anses de panier", which literally means the basket handles. These are curved vaults formed from an odd number of centers (3, 5, 7, etc.) and are entirely plotted by circular arcs. That's where I learned the French have a word for the versed sine/versine, aka
sagitta, which is
flèche. It's funny that we don't seem to have a word for that aspect of basic geometry in English. We have chord, but nothing to describe a perpendicular line raised from the middle of the chord to touch the circle perimeter line.
Here's one of the drawings to produce such a vault, as might be found on a bridge, or interior vaulting work in wood:
- Elements de Geometrie plain b'-small.jpg (89.61 KiB) Viewed 7585 times
After
anse de panier, it was a look at converting a drawing of a circular arc on a horizontal over to the same displacement atop a sloped, or
rampant line. Here's an illustration:
- Elements de Geometrie plain-small.jpg (114.58 KiB) Viewed 7585 times
There were method for working out the shape in situations where you know the width but not the height, or where you had the height and width as constraints and needed to determine which curve would work.
Then it was onto 'Le Chapeau de Gendarme', a shape which evokes the head covering of a Napoleonic-era policeman. Several methods were explored, here's one of them:
- Elements de Geometrie plain b-small.jpg (46.19 KiB) Viewed 7585 times
After that, the study turns to a look at spirals, first with the Archimedean spiral:
- Elements de Geometrie plain c-small.jpg (204.46 KiB) Viewed 7585 times
That was followed by 2-, 3-, 4-, and 6-point spirals. They were easy enough and I find this sort of stuff fun to draw. Up next is volutes, but that can wait for another day as I feel I covered some good ground today. The section ends with volutes, so not much further to go, and then it will be on descriptive geometry for various solids.
If anyone is interested in details about how to do any of the geometrical forms mentioned above, I'd be happy to post up a step-by-step.