
Re: Conway on Trilinear vs Barycentric
Posted:
Jul 2, 1998 10:59 AM


> >I read all of this and still can't fathom which of >these coordinate system types is this: > > (0,0,1) >  >  * P >  > / \ > / \ > / \ > (1,0,0) (0,1,0) > > >Any point P is reachable by linear combination of >basis vectors. Only positive scalars required >(vector reversal operation not required to span >plane, only grow/shrink and tiptotail addition). >
I do not think your system is either. Neither trilinears nor barycentric coordinates represent distances from a common origin. Yours looks like the regular basis vectors in 3D space. If yours is in 2D space then I think it is different from the other two.
Whenever you describe a two dimensional idea (a point) interms of 3 numbers, you are giving up something important, namely that your basis vectors are orthogonal with an operation (the dot product) representing that orthogonality. With barycentrics and trilinears (both homogeneous) we gain something by doing this. Many of the properties of a triangle do not depend on scale, for which homogeneous systems are nice. Also the dual nature of points and lines comes out nicely with this. What advantages does your system have?
steve

