The conic intrinsic volumes of (products of) circular cones

circ_ivols computes the conic intrinsic volumes of circular cones, whose dimensions and angles are given in the vectors d and alpha (vectors must be of same lengths); if the length of the vectors is one, a single vector is returned; if the length of the vectors is greater than one and product==FALSE, a list of vectors is returned; if the length of the vectors is greater than one and product==TRUE, a single vector with the intrinsic volumes of the product cone is returned.

circ_ivols(d, alpha, product = FALSE)

Arguments

d	vector of dimensions; must be same length as alpha.
alpha	vector of angles; must be same length as d.
product	logical; if TRUE, intrinsic volumes of product cone are returned.

Value

If length(d)==1 or (length(d)>1 & product==TRUE) then a single vectors will be returned. If (length(d)>1 & product==FALSE) then a list of vectors will be returned.

See also

Package: conivol

Examples

circ_ivols(5, pi/4)
#> [1] 0.05805826 0.17677670 0.26516504 0.26516504 0.17677670 0.05805826
circ_ivols(c(5,5), c(pi/4,pi/8))
#> [[1]]
#> [1] 0.05805826 0.17677670 0.26516504 0.26516504 0.17677670 0.05805826
#> 
#> [[2]]
#> [1] 0.226998099 0.394290254 0.244980556 0.101474269 0.028021346 0.004235477
#> 
circ_ivols(c(5,5), c(pi/4,pi/8), product = TRUE)
#>  [1] 0.0131791150 0.0630197805 0.1441164338 0.2139422254 0.2292054019
#>  [6] 0.1799475769 0.1012851037 0.0407148130 0.0119680411 0.0023756043
#> [11] 0.0002459045