# Questions tagged [barycentric-coordinates]

Barycentric coordinates describe the place of certain points in a triangle.

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### Given two cevians in a tetrahedron, how do I know if they intersect?

Given two cevians in the format of barycentric coordinates on the surface triangle of a n-scale tetrahedron. Next multiplying each cevian's barycentric coordinate by the lcm (value for two cevians' ...
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### Barycentric subdivision and chain maps

In Rotman's An Introduction to Algebraic Topology, 4th printing, pp. 113, he provided a definition of barycentric subdivision in a convex set $E$: Let $E$ be a convex set. Then barycentric ...
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1answer
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### formula for rational length cevians in an equilateral triangle

I wrote a computer program that iterates through progressively larger scale triangles. The program seeks whole numbers m & n that represent distances from the base vertices, and when a whole ...
1answer
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### Is the integral of a linear function over a triangle always the average of the vertices?

Say I have a triangle with vertices$\ r_0$,$\ r_1$and$\ r_2$. At each vertex the value of some function$\ f(r)$ is known. I know that I can use barycenter coordinates to describe any point$\ t$ in ...
1answer
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### Barycentric Coordinates: How do I keep track of Ratios

I am trying to write a java Program wich essentially lets a Point inside a given triangle move only in a straight line to one of the three corners (the specific corner being chosen randomly at every ...
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### Barycentric coordinate of the excenter proof?

I'm trying to show that the barycentric coordinate of excenter of triangle ABC, where BC=a, AC=b, and AB=c, and excenter opposite vertex A is Ia, is Ia=(-a:b:c). I've gotten to the point where after a ...
2answers
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### Barycentric Coordinates of Incenter

I'm trying to prove the fact that the incenter has the barycentric coordinates $(a,b,c)$. My reasoning goes like this; consider the triangle $\Delta ABC$ with barycentric coordinates $(1,0,0)$, \$(0,1,...
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### The difference between barycentric and parallel coordinates

I am studying for an exam tomorrow and there are some topics which I do not understand from the slides of the professor. If anyone could give me a clear explanation, I would be eternally grateful. ...