Jan 16, 2018 · The word barycentric literally means “weight-centered.” The barycentric coordinates of a point relative to a polygon are the masses that you’d have to place at the vertices of the polygon for …

To calculate the barycentric cooordinates of a point wrt a given triangle, the wikipedia formulae are fine. You can write the formulae in terms of triangle areas or vector cross products, instead, if you want.

Jan 3, 2019 · Prove triangle area formula for barycentric coordinates Ask Question Asked 7 years ago Modified 6 years, 11 months ago

Jun 10, 2022 · You can derive the coordinates of isotomic conjugate, in nicer ways, without using the area definition of barycentric coordinates.

Wikipedia's "Altitude (triangle)" entry describes the barycentric coordinates of $\triangle ABC$ 's orthocenter as $$ (\tan A : \tan B : \tan C)$$ How would you prove this using solely the areal …

Oct 3, 2017 · The normalized barycentric coordinates $m_b$ and $m_c$ of a point $p$ are just the coordinates of $p$ in a coordinate system that has $a$ as its origin and $c-a$ and $b-a$ as its bases.

Mar 30, 2023 · Is there any easy way to calculate the signs of the barycentric coordinates for coordinates that may need to represent a point located outside of the triangle? Once again, I don't …

Jul 27, 2025 · 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. …

Feb 13, 2025 · Suppose there is a line given, and a point is also given. Can we find the equation of a line perpendicular to the given line, passing through that point (in barycentric coordinates)? …

I understand that mapping from the Cartesian coordinate system to an arbitrary polygon results in the Generalized Barycentric Coordinate. However, I am not sure how the inverse can be done properly, …