Fantastic article and well written, too. For those of you, like me, who don't know French and miss the pun of the title: <a href="https://en.wikipedia.org/wiki/Baise-moi" rel="nofollow">https://en.wikipedia.org/wiki/Baise-moi</a>.<p>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 <a href="https://motherboard.vice.com/en_us/article/ezvq9n/the-kissing-circles-the-time-nature-published-a-poem-as-a-scientific-paper" rel="nofollow">https://motherboard.vice.com/en_us/article/ezvq9n/the-kissin...</a>) that summarizes Descartes's Theorem (<a href="https://en.wikipedia.org/wiki/Descartes%27_theorem" rel="nofollow">https://en.wikipedia.org/wiki/Descartes%27_theorem</a>):<p><pre><code> "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. "
</code></pre>
EDIT: Turns out there are many other such math terms, e.g. see <a href="https://math.stackexchange.com/questions/1102872/unusual-mathematical-terms" rel="nofollow">https://math.stackexchange.com/questions/1102872/unusual-mat...</a>:
Off-topic, but the title (Bézier moi) sounds like "Baisez-moi", which in French pretty much means "Fuck me". Seeing how most people involved in the article are French I assume the title was chosen on purpose, in case any reader was wondering about it.
Deciding which is the “best” approximation to a quarter circle depends on your choice of error metric. Just choosing the one with the correct endpoints and endpoint tangents which intersects the circle halfway along is not the best you can do by most choices of error metric.<p>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 ...<p>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.
The inclusion of a Citroën DS is nice (as an owner of '74 model, I am a little biased), but it's weird that he doesn't mention the Citroën CX, the fruits of de Casteljau's labours.<p>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, <i>de originale Citroën CX</i> (it's in Dutch)[0], and they spend a lot of time discussing the mathematics of the design.<p>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).<p>[0] See here for an English article discussing the book: <a href="https://citroenvie.com/new-citroen-cx-book-available/" rel="nofollow">https://citroenvie.com/new-citroen-cx-book-available/</a>