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Re: Conway on Trilinear vs Barycentric
Posted:
Jul 2, 1998 10:59 AM
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>
>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 tip-to-tail 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
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