Deformable models are widely used in many disciplines such as engineering and medicine. Real objects are usually scanned to create models in such applications. In many cases the shape of the object is extracted from volumetric data acquired during the scanning phase. At the same time, this volume can be used to define the model's appearance. In order to achieve a visualization that unifies the shape (physical model) and appearance (scanned volume) specially adapted volume rendering techniques are required. One of the most common volumetric visualization techniques is ray casting, which also enables the use of different corrections or improvements such as adaptive sampling or stochastic jittering. This paper presents an extensive study about a ray casting method for tetrahedral meshes with an underlying structured volume. This allows a direct visualization of the deformed model without losing the information contained in the volume. The aim of this study is to analyse and compare the different methods for ray traversal and illumination correction, resulting in a comprehensive relation of the different methods, their computational cost and visual performance.