# Documentation

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# baryToCart

Class: TriRep

(Not recommended) Convert point coordinates from barycentric to Cartesian

### Note

`baryToCart(TriRep)` is not recommended. Use `barycentricToCartesian(triangulation)` instead.

`TriRep` is not recommended. Use `triangulation` instead.

## Syntax

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

## Description

`XC = baryToCart(TR, SI, B)` returns the Cartesian coordinates `XC` of each point in `B` that represents the barycentric coordinates 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` `B` `B` is a matrix that represents the barycentric coordinates of the points to convert with respect to the simplices `SI`. `B` is of size `m`-by-`k`, where `m` = `length(SI)`, the number of points to convert, and `k` is the number of vertices per simplex.

## Output Arguments

 `XC` Matrix of Cartesian coordinates of the converted points. `XC` is of size `m`-by-`n`, where `n` is the dimension of the space where the triangulation resides. That is, the Cartesian coordinates of the point `B(j)` with respect to simplex `SI(j)` is `XC(j)`.

## 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; ```

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