RegionMeasure

RegionMeasure[reg]
gives the measure of the region reg.

RegionMeasure[reg,d]
gives the d-dimensional measure of the region reg.

Details and OptionsDetails and Options

  • RegionMeasure is also known as count (0D), length (1D), area (2D), volume (3D), and Lebesgue measure.
  • Example cases where rows correspond to embedding dimension and columns to geometric dimension:
  • If the region reg is of dimension d0 then the d-dimensional measure is used.
  • The zero-dimensional measure counts the number of points in the region.
  • RegionMeasure takes an Assumptions option that can be used to specify assumptions on parameters.

ExamplesExamplesopen allclose all

Basic Examples  (4)Basic Examples  (4)

RegionMeasure corresponds to count for zero-dimensional regions:

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RegionMeasure corresponds to curve length for one-dimensional regions:

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RegionMeasure corresponds to surface area for two-dimensional regions:

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RegionMeasure corresponds to volume for three-dimensional regions:

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Introduced in 2014
(10.0)