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PolyhedralSets

  

Volume

  

volume of polyhedral set

  

Area

  

area of polyhedral set

  

Length

  

length of polyhedral set

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

Volume(polyset)

Volume(polyset, d)

Area(polyset)

Length(polyset)

Parameters

polyset

-

polyhedral set

d

-

(optional) non-negative integer, dimensionality of the set in which the volume should be computed; default is the dimension of polyset's coordinate space

Description

• 

The Volume command computes the volume of a polyhedral set in the generalized sense of a Lebesgue measure, defining a d-volume of a set in higher dimensions.  For sets in 3, 2, and 1 dimensional spaces, this corresponds to the standard definitions of volume, area, and length, respectively.

• 

The optional parameter d specifies which d-volume to compute for the set, where d is less than or equal to the number of polyset's coordinates.  For sets of dimension greater than d, the sum of the volumes for the d-faces is computed.

• 

The Area and Length commands are used to compute the 2-volume and 1-volume of polyset, respectively, and are equivalent to Volume(polyset, 2) and Volume(polyset, 1).

Examples

withPolyhedralSets:

For the standard cube

cExampleSets:-Cube

c{Coordinates:x1,x2,x3Relations:x31,x31,x21,x21,x11,x11

(1)

the edges of the cube all have length 2

c_edgesEdgesc:mapLength,c_edges

2,2,2,2,2,2,2,2,2,2,2,2

(2)

the cube has a volume of 8

Volumec

8

(3)

and the total surface area of the cube is

Areac

24

(4)

The polyhedral set ps is a three-dimensional polytope in four-dimensional space.

psPolyhedralSet1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,x,y,z,u

ps{Coordinates:x,y,z,uRelations:u0,z0,y0,u+z+y1,u+z+y+x=1

(5)

Its four-dimensional volume is 0, but its three-dimensional volume is positive.

Volumeps

0

(6)

Volumeps,3

13

(7)

Compatibility

• 

The PolyhedralSets[Volume], PolyhedralSets[Area] and PolyhedralSets[Length] commands were introduced in Maple 2015.

• 

For more information on Maple 2015 changes, see Updates in Maple 2015.

See Also

PolyhedralSets[Faces]

PolyhedralSets[Dimension]

PolyhedralSets[PolyhedralSet]

PolyhedralSets