Nematic liquid crystals confined to cylindrical cavities, and polymer networks constrained by the presence of an oriented liquid crystal are studied. Frank elastic theory is used to predict stable nematic structures and to calculate their corresponding interference patterns (textures) for structures observed with a polarizing microscope. The comparison of theoretical and experimental textures are used to investigate nematic ordering which result in the measurement of the bend-to-splay (K-33/K-11) bulk elastic constant ratio, the saddle-splay-to-splay (K-24/K-11) surface elastic constant ratio, and the degree of orientational order of polymer networks induced by the nematic liquid crystal during the formation of these networks.