What is a scenario where this would be useful? I feel like having the areas of different subsections of a triangle would yield a solution to finding the position of the (x, y) point in the triangle without using barycentric coordinates (that would probably be easier). Moreover what scenarios exist where you know the areas of sub-triangles but do not know how to find information about the geometry of the triangle?
ninjab3381
I found a cool application of barycentric coordinates in something called Voronoi diagrams:
https://builtin.com/data-science/voronoi-diagram
In this you draw each edge in between two points such that both points are equidistant from each edge. This uses all space in a plane and can be used to model a bunch of things like animal coats.
ninjab3381
I also read about how you can move from barycentric coordinates to quadratic Barycentric Coordinates to also include information about the edges rather than just the vertices to coat the triangle. However for some reason, I'm not able to find good resources about possible formulas . I was also just curious if using the areas is equivalent to calculating the weights of adding each pints done from the other point of view.
What is a scenario where this would be useful? I feel like having the areas of different subsections of a triangle would yield a solution to finding the position of the (x, y) point in the triangle without using barycentric coordinates (that would probably be easier). Moreover what scenarios exist where you know the areas of sub-triangles but do not know how to find information about the geometry of the triangle?
I found a cool application of barycentric coordinates in something called Voronoi diagrams:
https://builtin.com/data-science/voronoi-diagram
In this you draw each edge in between two points such that both points are equidistant from each edge. This uses all space in a plane and can be used to model a bunch of things like animal coats.
I also read about how you can move from barycentric coordinates to quadratic Barycentric Coordinates to also include information about the edges rather than just the vertices to coat the triangle. However for some reason, I'm not able to find good resources about possible formulas . I was also just curious if using the areas is equivalent to calculating the weights of adding each pints done from the other point of view.