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convhull

Convex hull

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Syntax

k = convhull(P)
k = convhull(x,y)
k = convhull(x,y,z)
k = convhull(___,'Simplify',tf)
[k,av] = convhull(___)

Description

k = convhull(P) computes the 2-D or 3-D convex hull of the points in matrix P.

example

k = convhull(x,y) computes the 2-D convex hull of the points in column vectors x and y.

k = convhull(x,y,z) computes the 3-D convex hull of the points in column vectors x, y, and z.

example

k = convhull(___,'Simplify',tf) specifies whether to remove vertices that do not contribute to the area or volume of the convex hull. tf is false by default.

example

[k,av] = convhull(___) also computes the area (for 2-D points) or volume (for 3-D points) of the convex hull.

example

Examples

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Open Live Script

Create a matrix of 2-D points. Compute the convex hull and its area.

P = [0 0; 1 1; 1.5 0.5; 1.5 -0.5; 1.25 0.3; 1 0; 1.25 -0.3; 1 -1];
[k,av] = convhull(P);

Plot the original points and the convex hull.

plot(P(:,1),P(:,2),'*')
hold on
plot(P(k,1),P(k,2))

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

Display the area.

av
av = 
1.7500
Open Live Script

Simplify a 3-D convex hull by removing points that do not affect its volume.

Create a set of 3-D points. Compute the convex hull and its volume. Plot the convex hull. 

[x,y,z] = meshgrid(-2:1:2,-2:1:2,-2:1:2);
x = x(:);
y = y(:);
z = z(:);

[k1,av1] = convhull(x,y,z);

trisurf(k1,x,y,z,'FaceColor','cyan')
axis equal

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

Compute and plot a simplified version of the convex hull that contains fewer points, but preserves the volume.

[k2,av2] = convhull(x,y,z,'Simplify',true);

trisurf(k2,x,y,z,'FaceColor','cyan')
axis equal

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

Display the volumes of both convex hulls. The volumes are the same, but the simplified convex hull uses fewer points. 

av1
av1 = 
64.0000

av2
av2 = 
64

Input Arguments

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Points, specified as a matrix whose columns are the x-coordinates, y-coordinates, and (in three dimensions) z-coordinates.

x-coordinates, specified as a column vector.

y-coordinates, specified as a column vector.

z-coordinates, specified as a column vector.

Simplify indicator, specified as a numeric or logical 0 (false) or 1 (true).

Output Arguments

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Indices, returned as a vector or matrix.

  • For 2-D points, k is a column vector containing the row indices of the input points that make up the convex hull, arranged counterclockwise.

  • For 3-D points, k is a 3-column matrix representing a triangulation that makes up the convex hull. Each row represents a facet of the triangulation. The values represent the row indices of the input points.

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

  • For 2-D points, av is the area of the convex hull.

  • For 3-D points, av is the volume of the convex hull.

Tips

  • To plot the output of convhull in two dimensions, use the plot function. To plot the output of convhull in three dimensions, use trisurf or trimesh.

Extended Capabilities

Version History

Introduced before R2006a

See Also