# cartToBary

Class: TriRep

(Will be removed) Convert point coordinates from cartesian to barycentric

 Note:   `cartToBary(TriRep)` will be removed in a future release. Use `cartesianToBarycentric(triangulation)` instead.`TriRep` will be removed in a future release. Use `triangulation` instead.

## Syntax

`B = cartToBary(TR, SI, XC)`

## Description

`B = cartToBary(TR, SI, XC)` returns the barycentric coordinates of each point in `XC` with respect to its associated simplex `SI`.

## Input Arguments

 `TR` Triangulation representation. `SI` Column vector of simplex indices that index into the triangulation matrix `TR.Triangulation`. `XC` Matrix that represents the Cartesian coordinates of the points to be converted. `XC` is of size `m`-by-`n`, where `m` is of `length(SI)`, the number of points to convert, and `n` is the dimension of the space where the triangulation resides.

## Output Arguments

 `B` Matrix of dimension `m`-by-`k` where `k` is the number of vertices per simplex.

## Definitions

A simplex is a triangle/tetrahedron or higher dimensional equivalent.

## Examples

Compute the Delaunay triangulation of a set of points.

```x = [0 4 8 12 0 4 8 12]'; y = [0 0 0 0 8 8 8 8]'; dt = DelaunayTri(x,y)```

Compute the barycentric coordinates of the incenters.

```cc = incenters(dt); tri = dt(:,:); ```

Plot the original triangulation and reference points.

```figure subplot(1,2,1); triplot(dt); hold on; plot(cc(:,1), cc(:,2), '*r'); hold off; axis equal; ```

Stretch the triangulation and compute the mapped locations of the incenters on the deformed triangulation.

```b = cartToBary(dt,[1:length(tri)]',cc); y = [0 0 0 0 16 16 16 16]'; tr = TriRep(tri,x,y) xc = baryToCart(tr, [1:length(tri)]', b); ```

Plot the deformed triangulation and mapped locations of the reference points.

```subplot(1,2,2); triplot(tr); hold on; plot(xc(:,1), xc(:,2), '*r'); hold off; axis equal; ```