`cartesianToBarycentric`

Converts Cartesian points to barycentric coordinates relative to given triangles or tetrahedra.

Category: Mathematics > Computational Geometry

Syntax

B = cartesianToBarycentric(TR, T, X)

Returns the barycentric coordinates of each row of X with respect to the simplex listed in T.

Description

Barycentric coordinates express a point as weights on the vertices of a simplex. To find them, the function solves a small linear system built from the simplex's vertices. The coordinates are all in [0, 1] exactly when the point lies inside the simplex, which makes this a convenient inside test and the base of linear interpolation over a mesh.

The query points do not have to lie inside the chosen simplex; they are then extrapolated.

Input arguments

TR: A triangulation or delaunayTriangulation (2-D, 3-D tetrahedral or 3-D surface triangles).
T: Column vector of simplex indices, one per query point.
X: Query points, one per row.

Output arguments

B: Barycentric coordinates, one row per query point. Rows sum to 1; a negative entry means the point lies outside that simplex.

Examples

Point outside the chosen triangle

x = [0 1 1 0 0.5]';
y = [0 0 1 1 0.5]';
DT = delaunayTriangulation(x, y);
B = cartesianToBarycentric(DT, 1, [0.1 0.2])

Output

B = 1×3

    1.8000   -0.1000   -0.7000

Tetrahedron

tet = delaunayTriangulation([0 0 0; 1 0 0; 0 1 0; 0 0 1]);
B = cartesianToBarycentric(tet, 1, [0.1 0.1 0.1])