15387Re: [EMHL] Cevian Trace Equal Area Points
- Aug 1, 2007Anh Tuan oi
Now, I criticize your formula:
We construct point Q = X(6)*c(P)*c(U)*t(cd(P, U))
I find it too much complex for X(6) is not needed.
You deduct it from the formula:
a). Barycentrics of Q = (q + r)*(v + w)/(q*w - r*v) : :
I look at ETC glossary the meaning of the point:
M = q*w - r*v::
where P = (p:q:r) and Q = (u:v:w)
M is the cross difference of P and Q only in case of using trilinears.
But here, you are using barycentrics so X(6) appareance is artificial though
needed to get a correct formula.
I don't find in ETC glossary the point M = q*w -r*v:: where P =(p:q:r) and Q
= (u:v:w) in using barycentrics;
M is simply the dual point of the line through P and Q.
Is there a special name for this point with such a projective definition?
Calling it AT(P,Q) for the moment, then we will have:
Q = c(P)*c(U)*t(AT(P,U))
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