Talk:Barycentric coordinate system
|WikiProject Mathematics||(Rated Start-class, Low-importance)|
Barycentric coordinates on triangles
I would like to discuss the appropriateness of this example to illustrate the use of barycentric coordinates relative to a triangle. I have been using barycentric coordinates off-and-on for some time, and there are many geometric uses which are much more accessible. Moreover, the use of baycentric coordinates is independent of calculus. I feel the example does not really aid the understanding of barycentric coordinates relative to a triangle.
"Trilinear coordinates" redirects to "barycentric coordinates", but they're not the same thing. Essentially, if I put three masses (m,p,q) at the vertices of a given triangle, the point described by those barycentric coordinates is the center of mass of that system. On the other hand, trilinear coordinates describe the relative distances from the three sides of a given triangle. See for example, the Mathworld page on trilinear coordinates.
Another example: the centroid in barycentric coords is (1,1,1). On the other hand, the incenter in trilinear coordinates is (1,1,1). Lunch 23:22, 1 September 2006 (UTC)
- Errr, nevermind. I changed the redirect myself. But there's still a stub there if anyone wants to embellish it... Lunch 23:48, 1 September 2006 (UTC)
"Affine Coordinates" redirects to this page but do not appear in the article. --220.127.116.11 11:58, 2 November 2007 (UTC)
I'm interested in the reliability of barycentric coordinates, both the two variable and three variable forms and alternatives when applied to texture mapping for example. Does the accuracy fall for extremely narrow triangles? 18.104.22.168 (talk) 05:14, 10 July 2008 (UTC)
In accurate, theoretic math no, it doesn't. In the real world of approximated floating-point math, obviously yes, as FP can only work on a fixed footprint to store values. As the triangle approaches degeneration, that is det(A) appoaches 0 this algo will be less and less tolerant to error. 22.214.171.124 (talk) 10:12, 29 June 2010 (UTC)
Generalised Barycentric Coordinates
This section states:
- More abstractly, generalized barycentric coordinates express a polytope with n vertices, regardless of dimension, as the image of the standard -simplex, which has n vertices – the map is onto:
Hi! I just wanted to say that in section 'Barycentric coordinates on triangles' points ABC and P are extensively referenced to explain something, but that these points are not drawn on any schematic. This leads to understanding the text to be a piece of guesswork at best... Thanks! 126.96.36.199 (talk) 09:36, 17 October 2013 (UTC)