  Creating spherical initial conditions in smoothed particle hydrodynamics
simulations that are spherically conformal is a difficult task. Here, we
describe two algorithmic methods for evenly distributing points on surfaces,
that when paired can be used to build 3D spherical objects with optimal
equipartition of volume between particles, commensurate with an arbitrary,
radial density function. We demonstrate the efficacy of our method against
stretched lattice arrangements on the metrics of hydrodynamic stability,
spherical conformity, and the harmonic power distribution of gravitational
settling oscillations. We further demonstrate how our method is highly
optimized for simulating multi-material spheres, such as planets with
core-mantle boundaries.
