find convex hull enclosing the given points - Maple Help

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simplex[convexhull] - find convex hull enclosing the given points

Calling Sequence

convexhull(P)

convexhull(P, output=area)

convexhull(P, output=hull)

convexhull(P, output=plot)

Parameters

P

-

list or set of points in 2 dimensions

Description

• 

The command convexhull(P) returns a list of points defining the convex hull of the points in P in counter-clockwise order.

• 

Every point in P must be a list of an x and y coordinate, both of which must be numbers (of type numeric).

• 

If the option output=area is specified, the area of the convex hull of the points is returned.

• 

If the option output=hull is specified, the convex hull is is returned as a list of points.  This is the default return value.

• 

If the option output=plot is specified, a plot of the points and the convex hull is returned.

• 

Multiple outputs can be specified, for example, output=[hull,area] returns a sequence of two values.

• 

An nlogn algorithm computing tangents of pairs of points is used.

• 

For a slightly more geometrical interpretation of the same command, see geometry[convexhull].  The points input and output are geometric points, and the output is considered to be a convex polygon.

• 

The command with(simplex,convexhull) allows the use of the abbreviated form of this command.

Examples

withsimplex:

P:=0,0,12,12,1,1,2,0,1,0,1,12

P:=0,0,1,0,1,1,1,12,2,0,12,12

(1)

convexhullP

0,0,2,0,1,1

(2)

convexhullP,output=area

1

(3)

H,A:=convexhullP,output=hull,area

H,A:=0,0,2,0,1,1,1

(4)

Execute the following to get a plot of the points and the convex hull.

convexhullP,output=plot

This creates 50 points uniformly distributed at random on [0,1).

R:=rand1010:

U01 := proc() Float( R(), -10 ) end proc:

P:=seqU01,U01,i=1..50:

convexhullP,output=area

0.7570693924

(5)

Execute the following to get a plot of the points and the convex hull.

convexhullP,output=plot

See Also

geometry[convexhull]


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