Convex hull of Delaunay triangulation
2-D Delaunay Triangulation
Compute and plot the convex hull of a 2-D Delaunay triangulation.
Create a Delaunay triangulation from a set of 2-D points.
rng default; x = rand([10,1]); y = rand([10,1]); DT = delaunayTriangulation(x,y);
Compute the convex hull.
C = convexHull(DT);
Plot the triangulation and highlight the convex hull in red.
plot(DT.Points(:,1),DT.Points(:,2),'.','MarkerSize',10) hold on plot(DT.Points(C,1),DT.Points(C,2),'r')
3-D Delaunay Triangulation
Compute and plot the convex hull of a 3-D Delaunay Triangulation.
Create a Delaunay triangulation from a 3-D set of points.
rng('default'); P = rand([25,3]); DT = delaunayTriangulation(P);
Compute the convex hull and the volume bounded by the convex hull.
[C,v] = convexHull(DT);
Display the volume and plot the convex hull.
v = 0.3943
trisurf(C,DT.Points(:,1),DT.Points(:,2),DT.Points(:,3), ... 'FaceColor','cyan')
C — Convex hull vertices
column vector | matrix
Convex hull vertices, returned as a column vector or matrix of vertex IDs.
DTis a 2-D triangulation,
Cis a column vector containing the sequence of vertex IDs around the convex hull. The vertex IDs are the row numbers of the vertices in the
DTis 3-D triangulation,
Cis a 3-column matrix containing the connectivity list of triangle vertices in the convex hull.
v — Area or volume
Area or volume of the convex hull, returned as a scalar.