Barycentric coordinates

Stream: Is there code for X?

[Yakov Pechersky]

Do we have the isometry or any form of equivalence for barycentric coordinates? Even for interpolating in a simple triangle.

[Bhavik Mehta]

There's finset.center_mass, where the weights can be thought of as the barycentric coordinates for the point in question

[Yakov Pechersky]

That will give the center. I'm hoping for the affine transform that can help me interpolate for any point in the interior

[Yakov Pechersky]

I guess it's just some matrix.mul

[Bhavik Mehta]

Yakov Pechersky said:

That will give the center. I'm hoping for the affine transform that can help me interpolate for any point in the interior

It's not restricted to the center. You can specify any weights you wish and get any point in the interior.

[Bhavik Mehta]

There's also docs#set.finite.convex_hull_eq_image and https://leanprover-community.github.io/mathlib_docs/linear_algebra/affine_space/combination.html

[Bhavik Mehta]

More specifically docs#affine.finset.affine_combination