baryToCart - Class: TriRep

Converts point coordinates from barycentric to Cartesian

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.

Inputs

`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.

Outputs

`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)`.

Definitions

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

Example

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(:,:);
subplot(1,2,1);
triplot(dt); hold on;
plot(cc(:,1), cc(:,2), '*r'); hold off;
axis equal;
title(sprintf('Original triangulation and ...
     reference points.\n'));

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);
subplot(1,2,2);
triplot(tr); hold on;
plot(xc(:,1), xc(:,2), '*r'); hold off;
axis equal;
title(sprintf('Deformed triangulation and mapped\n ...
    locations of the reference points.\n'));