Simulated optical polarizing microscopy (OPM) textures can be used to help compare a director ansatz with an associated experimental OPM texture. Here, we present a pedagogical treatmement of a simulation formalism based on the method of Jones matrices. We focus on toroidal geometries as an example and perform computer simulations of the nematic textures seen between crossed-polarizers. For tangentially-anchored nematic tori, we compare qualitative and quantitative features between experimental and simulated OPM textures and discuss the influence of twist in the director field. In addition, we quantify the effect of averaging over multiple wavelengths, the effect of voxel size, how refraction affects the comparison between experimental and simulated OPM textures, and the effect of deviations from the toroidal shape. For homeotropically-anchored nematic tori, we adapt the classic escaped-radial director field found in homeotropically-anchored capillaries to a toroidal geometry to produce simulated OPM textures. Lastly, we show that the same signatures of twist in the tangentially-anchored nematic toroids persist in the homeotropically-anchored nematic toroids. [ABSTRACT FROM AUTHOR]