These functions provide approximate measures of length, area, and volume of geometries where relevant. The reason for approximation is that some measures require square root operations or multiplication by π, both operations where exactness is necessarily lost. Not all geometries have meaningful measures, e.g. a direction is dimensionless, a line is without area, and a circle has no volume. Some geometries are infinite in some measures, e.g. a plane has an infinite area. The return value will reflect this.

## Usage

approx_length(x)

approx_area(x)

approx_volume(x)

approx_radius(x)

## Arguments

x

A geometry vector

## Value

A numeric vector

Other Measures: approx_angle(), distance_squared()

## Examples


approx_length(vec(point(1:4, 4:7)))
#> [1] 4.123106 5.385165 6.708204 8.062258
approx_area(circle(point(0, 0), 5:9))
#> [1] 15.70796 18.84956 21.99115 25.13274 28.27433
approx_volume(sphere(point(0, 0, 0), 5:9))
#> [1]  46.83210  61.56239  77.57748  94.78150 113.09734