Towards rapid computing of high order spherical harmonics and their use in meteor radiant mapping

The computation of spherical harmonics of high order can be inconveniently slow, due mainly to the need to evaluate lengthy recurrence relations for associated Legendre polynomials. It is shown that significant savings in computing time can be achieved by letting the polynomials be represented by model functions obtained either (i) in closed-form, or (ii) from numerical processing of data retrieved from storage. The speed and accuracy of some models that have been developed are assessed in the context of applications involving the spherical transform, with particular reference to its use in meteor radiant mapping. The results show that options (i) and (ii) above both yield model harmonics which closely approximate those derived rigorously for all orders up to at least 256. In case (i) the effective computing speed may be increased by a factor of up to ∼ 6, depending on the maximum order involved, while in case (ii) a factor of ∼ 40 is attainable but this option is subject to the availability of sufficient storage (up to ∼ 4.5 Mbytes). Other models discussed are either slower, or yield less satisfactory results.