# Questions tagged [barycentric-coordinates]

This tag is for questions relating to Barycentric coordinate systems which describe the place of certain points in a triangle. They do not use distances of points, but only ratios of segments. Thus, they belong to the geometry of the affine plane, which deals with parallels and ratios of collinear segments without to use a notion of distance between two points, as it does euclidean geometry. The system was introduced in 1827 by August Ferdinand Möbius.

138 questions
Filter by
Sorted by
Tagged with
139 views

• 4,196
1 vote
26 views

### Expressing a 'zero-sum' ratio as a point in space? ( Eg. $1:-9:8$ )

I have a collection of ratios (they are all the same degree) where the sum of their parts equate to $0$; and I need a way to represent these ratios as points in space (to perform k-means clustering on ...
1 vote
51 views

1 vote
212 views

### How can I describe a triangle or tetrahedron with barycentric coordinates?

How would I, for example, describe a triangle given by the vertices $(2,1),(4,2),(2.5,2)$ with barycentric coordinates? My guess would be $(a:b:1-a-b)$ where $0\leq a,b\leq 0.75$ and $a+b\leq 0.75$ ...
• 2,482
Example problem: Compute $\int _A 3x^2+y \, \mathrm{d}A$, where $A$ is a triangle with vertices $(0,0),(2,0),(1,1)$. Can this be computed using barycentric coordinates? I found a Wikipedia article on ...