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Monte Carlo simulations in nuclear medicine, with accurately modeled photon transport and high-quality random number generators, require precisely defined and often detailed phantoms as an important component in the simulation process. Contemporary simulation models predominantly employ voxel-driven algorithms, but analytical models offer important advantages. The authors discuss the implementation of ray-solid intersection algorithms in analytical superquadric-based complex phantoms with additional speed-up rejection testing for use in nuclear medicine imaging simulations, and we make comparisons with voxelized counterparts. Comparisons are made with well-known cold rod:sphere and anthropomorphic phantoms. For these complex phantoms, the analytical phantom representations are nominally several orders of magnitude smaller in memory requirements than are voxelized versions. Analytical phantoms facilitate constant distribution parameters. As a consequence of discretizing a continuous surface into finite bins, for example, time-dependent voxelized phantoms can have difficulties preserving accurate volumes of a beating heart. Although virtually no inaccuracy is associated with path calculations in analytical phantoms, the discretization can negatively impact the simulation process and results. Discretization errors are apparent in reconstructed images of cold rod:sphere voxel-based phantoms because of a redistribution of the count densities in the simulated objects. These problems are entirely avoided in analytical phantoms. Voxelized phantoms can accurately model detailed human shapes based on segmented computed tomography (CT) or magnetic resonance imaging (MRI) images, but analytical phantoms offer advantages in time and accuracy for evaluation and investigation of imaging physics and reconstruction algorithms in a straightforward and efficient manner.