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15387Re: [EMHL] Cevian Trace Equal Area Points

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  • Francois Rideau
    Aug 1, 2007
      Anh 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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