Barycentric coordinates

Stream: maths

[Yaël Dillies]

@Oliver Nash, do you think we could use your new docs#barycentric_coord to solve this kind of problems?

• Two cevians intersect
• For a b c d : E a vector space (I assume convex space is enough), u ∈ [a, b],v ∈ [b, c], w ∈ [c, d], [u, w] and the triangle avd intersect.

The second comes up in Stone's separation theorem. This is exactly this sorry.

[Oliver Nash]

Reading ...

[Oliver Nash]

Not sure, sorry!

[Yaël Dillies]

Plain calculations work, but are very annoying given that weights can be 0, which forces unnatural manipulations to get the sum of the weights to be 1.

[Oliver Nash]

Agreed, though in recent examples in my work this has turned out not so bad.

[Yaël Dillies]

Hmm... do you have another idea then? Also, I haven't yet figured out what's the condition about these arrangements that make them work.

[Oliver Nash]

I'm afraid I've just finished a bottle of wine. Ask me again tomorrow morning ;-)

[Oliver Nash]

I've just logged in to do some quick easy stuff!

[Yaël Dillies]

:rofl: I can wait

[Oliver Nash]

Incidentally have your lectures resumed yet?

[Yaël Dillies]

They will, tomorrow supposedly.

[Oliver Nash]

Ah right. I'm sure you'll enjoy it! Lots of fun stuff to learn :-)

[Yaël Dillies]

And not-so-fun example sheets to hand in! But sure enough it will be fine :smile:

[Yaël Dillies]

Take care!

[Oliver Nash]

Likewise! Off to recharge now.