Vectorised solid-angle computation over a list of cones

Applies compute_solid_angle to each element of a list of generator matrices and returns the vector of normalized solid angles.

Usage

compute_solid_angles(cone_list, ...)

Arguments

cone_list

A list whose elements are numeric matrices of cone generators, each suitable as the V argument of compute_solid_angle.

...

Further arguments forwarded to compute_solid_angle (method, max_terms, tol, normalize).

Value

A numeric vector of normalized solid angles, of length equal to length(cone_list).

Details

The wrapper is a thin sapply() over cone_list; each element is processed independently with the same method and tolerance settings. The cost is the sum of the per-cone costs and is dominated by the chosen backend.

References

Fitisone, A., & Zhou, Y. (2023). Solid angle measure of polyhedral cones. arXiv:2304.11102 (math.CO). https://arxiv.org/abs/2304.11102

See also

compute_solid_angle for the single-cone dispatcher; diagnose_cone to inspect spectral conditioning before a large batch run.

Examples

# Two 3D cones: the orthant and a non-orthogonal triple
cone1 <- diag(3)
cone2 <- cbind(c(1, 0, 0),
               c(0, 1, 0),
               c(1, 1, 0) / sqrt(2))
compute_solid_angles(list(cone1, cone2))
#> Warning: ⚠ Vectors are not linearly independent - solid angle may be 0
#> [1] 0.125 0.000