cartToBary - Class: TriRep
Convert point coordinates from cartesian to barycentric
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.
Inputs
| 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. |
Outputs
| 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(:,:);
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'));
See Also
 | camzoom | | cart2pol |  |
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