Convert cartesian coordinates to baricentric coordinates

Grasshopper
1

i have a (regular) triangle populated with points. is it possible to convert the cartesian coordinates of the points into baricentric coordinates relativ to the trinagle?

cartesian2baricentric
cartesian2baricentric1761×812 88.2 KB

cartesian2baricentric.gh (17.3 KB)

2

It is an odd omission that GH includes a native component to convert from barycentric to cartesian but not the other way around.
However, you can get the MeshParameter value of a point relative to a mesh, which includes the barycentric coordinate, so one way without scripting or plugins is to make a single mesh triangle and evaluate the closest point on that, then parse the values.
cartesian_to_barycentric.gh (14.7 KB)
You could also use this function:

double[] Barycentric(Point3d p, Point3d a, Point3d b, Point3d c)
  {
    Vector3d v0 = b - a, v1 = c - a, v2 = p - a;
    double d00 = v0 * v0;
    double d01 = v0 * v1;
    double d11 = v1 * v1;
    double d20 = v2 * v0;
    double d21 = v2 * v1;
    double denom = d00 * d11 - d01 * d01;
    double u,v,w;
    v = (d11 * d20 - d01 * d21) / denom;
    w = (d00 * d21 - d01 * d20) / denom;
    u = 1.0 - v - w;
    return new double[3]{u, v, w};
  }

(from the first answer here)

3

thanks a lot, david!
for the explanation, examples and link …