.. _rays: Defining Spheres and Rays ========================= The first step in ray tracing steric hindrance is to define the molecule as a set of spheres with given radii, and to define the rays as a number of vectors emanating (evenly) from a given location. To define the spheres with which the rays interact, ``atom_access`` first shifts the cartesian coordinates of the molecule such that the atom interest is centred at the origin. Then, each atom is assigned a spherical radius from a list of known van der Waals atomic radii.\ :footcite:`crc` Finally, we discard all atoms which have no intersection with a spherical region of radius :math:`r_\text{cutoff}` centered on the central atom from the subsequent :ref:`ray tracing ` process. An angular Zaremba-Conroy-Wolfsberg (ZCW) grid with variable density index :math:`\rho`,\ :footcite:`zcw_z,zcw_c,zcw_w` is used to define a set of rays emanating from the origin (atom of interest) which evenly sample the surface of a sphere. The number of rays is controlled by the density index, as given in Table 1. .. table:: Table 1: Number of rays for each ZCW density index value. +-------------------+----------------+ | ZCW density index | Number of rays | | :math:`\rho` | | +===================+================+ | 0 | 21 | +-------------------+----------------+ | 1 | 34 | +-------------------+----------------+ | 2 | 55 | +-------------------+----------------+ | 3 | 89 | +-------------------+----------------+ | 4 | 144 | +-------------------+----------------+ | 5 | 233 | +-------------------+----------------+ | 6 | 377 | +-------------------+----------------+ | 7 | 610 | +-------------------+----------------+ | 8 | 987 | +-------------------+----------------+ | 9 | 1597 | +-------------------+----------------+ | 10 | 2584 | +-------------------+----------------+ | 11 | 4181 | +-------------------+----------------+ | 12 | 6765 | +-------------------+----------------+ | 13 | 10946 | +-------------------+----------------+ | 14 | 17711 | +-------------------+----------------+ | 15 | 28657 | +-------------------+----------------+ .. footbibliography::