Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » Math Topics » geometry.research.independent

Topic: Conway on Trilinear vs Barycentric coordinates
Replies: 13   Last Post: Feb 16, 1999 8:05 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
steve sigur

Posts: 139
Registered: 12/6/04
Re: Conway on Trilinear vs Barycentric
Posted: Jul 2, 1998 10:59 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

>
>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





Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.