convexHull

Convex hull of Delaunay triangulation

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Syntax

C = convexHull(DT)
[C,v] = convexHull(DT)

Description

C = convexHull(DT) returns the vertices of the convex hull of a Delaunay triangulation.

example

[C,v] = convexHull(DT) also returns the area or volume bounded by the convex hull.

example

Examples

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Open Live Script

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')

Figure contains an axes object. The axes object contains 2 objects of type line. One or more of the lines displays its values using only markers

Open Live Script

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
v = 
0.3943

trisurf(C,DT.Points(:,1),DT.Points(:,2),DT.Points(:,3), ...
       'FaceColor','cyan')

Figure contains an axes object. The axes object contains an object of type patch.

Input Arguments

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Delaunay triangulation, specified as a scalar delaunayTriangulation object.

Data Types: delaunayTriangulation

Output Arguments

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Convex hull vertices, returned as a column vector or matrix of vertex IDs.

  • When DT is a 2-D triangulation, C is 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 Points property.

  • When DT is 3-D triangulation, C is a 3-column matrix containing the connectivity list of triangle vertices in the convex hull.

Data Types: double

Area or volume of the convex hull, returned as a scalar.

Data Types: double

Extended Capabilities

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Thread-Based Environment
Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

Version History

Introduced in R2013a

See Also