Weighted Delaunay Triangulation

This repository contains MATLAB and python codes for computing weighted delaunay triangulation.

Weighted delaunay triangulation is computed by exploiting the duality between Delaunay triangulation and a convex hull of one dimension higher.

In Python

An example is provided in weighted_delaunay.ipynb that contains a function to compute weighted delaynay triangulation.

Here's a snippet of the code:

num_points = 10
points = np.random.rand(num_points, 2)
weights = np.random.rand(num_points,1)
delaunay = WeightedDelaunay(points,weights)
delaunay = np.asarray(delaunay)
print(delaunay)

In MATLAB

The matlab function provided as WeightedDelaunay.m takes points in num_points X dimensions and weights as num_points X 1 MATLAB arrays and produces triangulated faces compatible to be plotted with MATLAB triplot.m.

Here's an example script for the same.

num_points = 10;
points = rand(num_points,2);
weights = 10*rand(num_points,1);

[cells, lifted] = WeightedDelaunay(points,weights);

close all;
figure('units','normalized','position',[0.2,0.2,0.6,0.4])
subplot(121)
scatter(points(:,1),points(:,2),100*(weights./max(weights)),'k','filled');
hold on;
text(points(:,1),points(:,2),cellstr(num2str((1:num_points)')))
triplot(cells,points(:,1),points(:,2));
hold off;
fig_labels(2,'title','Weighted Delaunay')

DT = delaunay(points(:,1),points(:,2));
subplot(122)
plot(points(:,1),points(:,2),'ro');
hold on;
text(points(:,1),points(:,2),cellstr(num2str((1:num_points)')))
triplot(DT,points(:,1),points(:,2));
hold off;
fig_labels(2,'title','Delaunay')

This produces the following figure as an output.