gives the measure of the region reg.
gives the d-dimensional measure of the region reg.
- 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 d≥0, 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.
RegionMeasure corresponds to count for zero-dimensional regions:
RegionMeasure corresponds to curve length for one-dimensional regions:
RegionMeasure corresponds to surface area for two-dimensional regions:
RegionMeasure corresponds to volume for three-dimensional regions: