Bézier moi
cormullion.github.io
cormullion.github.io
It also mentions the concept of the osculating circle, probably the only risque mathematical term (anyone know of any other ones?), which led me of the following poem (from this post https://motherboard.vice.com/en_us/article/ezvq9n/the-kissin...) that summarizes Descartes's Theorem (https://en.wikipedia.org/wiki/Descartes%27_theorem):
"For pairs of lips to kiss maybe
Involves no trigonometry.
This not so when four circles kiss
Each one the other three.
To bring this off the four must be
As three in one or one in three.
If one in three, beyond a doubt
Each gets three kisses from without.
If three in one, then is that one
Thrice kissed internally. "
Not a term, but there's the "Hairy Ball Theorem":
Now, who has an article about 3D wireframes?
https://www.youtube.com/watch?v=4abvrxNj89s
And then there is this movie which I'll never watch.
And it shouldn't be the place to police writings with prudish 19th century ideas of "sexuality" as sin.
A more traditional choice might be the cubic curve where the maximum distance between a curve point and the circle is minimized. Or it might instead be desirable to preserve the arclength of the circle and minimize curvature deviation. Or it might be desirable to preserve the circle’s area. Or ...
Depending on the application different choices might be better. For some purposes it is not strictly essential that the endpoints of the curve directly fall on the circle.
It's call the CX because it refers to the coefficient of drag (Cd in English, but CX in French). I have the definitive book on the CX, de originale Citroën CX (it's in Dutch)[0], and they spend a lot of time discussing the mathematics of the design.
It's only unfortunate that I don't own a CX (although I used to have a '85 TRS 22, but it was in too bad shape to keep).
[0] See here for an English article discussing the book: https://citroenvie.com/new-citroen-cx-book-available/
But the TRS I had was also badly maintained by the previous owner, which is why I eventually abandoned it and got a '98 Xantia Activa V6 instead.
That being said, I still want a CX, just a good one. And they do exist (good ones). As for the DS being indestructible, the engine definitely was, but the body work would often erode in northern climates like mine (Denmark). And particularly at 40+ years of age, there are signs of its age. Fortunately, mine runs fine, so I hope to keep it at least for another 20 years.
I've never seen a DS Berline made in 75, the one I drove a lot was made Nov '74 and it was the newest that I've seen, my other one was from '68 (officially an ID 19B). There are however a lot of Breaks from '75.
As for the rust problem, the 'good' DSs were all striped down to bare metal, sandblasted and welded up then coated in tectyl or some other rust protector inside and out, an original, unrestored DS in good condition is something I haven't seen in many years. Maybe there are a couple in storage somewhere. Here in NL we still have several DS specialists, most notably Auto Renaissance in Amsterdam. There is also a company that converts Breaks into Decapotables, but that's not really my cup of tea. Though in convertible form it still is the most beautiful car there is to me.
Much good luck with your goddess, if you ever need parts that you can't get let me know and I'll see how warm my contacts in that scene are.
Edit: Amazing, I just checked, the license of my other DS/ID (not the one I took on long trips abroad) is still alive a good 20 years after I last saw the car, but it appears to be taken of the road when I sold it in 1998. DE-70-72 sits in a storage space somewhere. Let's hope one day someone puts it back on the road, I'd be happy to buy it today if I knew who the owner was.
I am also fortunate to know a great DS specialist here in Denmark, who mostly imports his spare parts from the Netherlands and Germany, since that's where the good parts come from these days (Chinese parts have only gotten better in looking good, not actually working). In appreciation (and for helping working on my cars), I build him a website.
That being said, I do like actually working on the cars myself, but there are limits to what I can do when I live in a flat in the city. But don't worry, my cars are both parked in garages, as I want these to last a few more decades. The previous owner of my DS actually sandblasted it.
Here is a picture of it at a car park: https://i.imgur.com/KJXYtOX.jpg And here next to a Aston Martin Vanquish: https://i.imgur.com/pPMDoEg.jpg
As you can see, it has been decorated as a Pallas, but it probably was not an original Pallas.
The biggest advantage of the half-automatic was that people that would ask to drive it were easily put off by the exotic gearbox :) You had to start it by pressing the gear shift lever to the left after making contact to avoid starting it in gear, clever interlock.
The engine that went with the 5-speed manual was different than the other engines, because the transmission was bigger. It was therefore not possible to get an engine with the manual starter at the front of the car, if it was 5-speed.
The reason I ask is that I've inherited a 1950 Jaguar, which also has a hole for crank starting the engine, but it's only these very early models that have the hole in the radiator for the crank. Apparently, the force required to start the XK engine manually is too much to be feasible for mere humans to achieve, and I've been told the best way to start it if the starter fails is to find a hill you can push the car down and putting it in gear.
The problem is that if it misfires while you crank it (which is very easy because you are revolving the engine very slowly) then it will kick back against the direction of turn. Alternatively, the hole and the freeing mechanism will be so rusty that once it does catch it will continue to turn with the crank it. 2 chances for $1. It is supposed to free up once it starts running by pushing the crank forward against a slant cut into the receiver on the engine but that works as often as it doesn't.
I've done it, once. Even if you know what you are doing it is still dangerous and I would definitely not recommend it. Young, stupid, and so on. The good part is that the sleeve is long enough that it likely will not throw the crank out the way some other cars will do, it goes in quite far.
As for pushstarting it, that will work with the manual gearboxes, but it does not work with the semi-automatics.
Oh, that's funny. The owners of the hostel we stayed at in the Netherlands used to do that, too. Apparently it was one of the V12 Jags from the 70s or 80s (Daimler Sovereign or XJ I think), and for good measure they had an after market trailer hitch attached, so they could bring their caravan along for the trip! I don't dare thinking about how much money that must've cost in fuel alone...
I've been toying with the idea (not new) of triangular NURBS which could do away with the need for trimming entirely. Questions remain about which type of triangular surface patch will meet the requirements.