Abstract: The modeling and rendering of textile materials has already been investigated in detail in the computer graphics literature. Modeling the 3D microstructure of textiles as volume data sets allows a more realistic image generation. Textiles, e.g., knitwear, are typically characterized by high repetitive structures. These repetitive features enable time and memory efficient rendering through object instancing even when using the ray-tracing technique. This paper concentrates on the rendering of more general textiles whose macrostructures are defined by free-form surfaces. We show how object instancing and tracing curved rays through object space efficiently produce realistic looking images. Concerning realism our approach of approximating the 3D microstructure of textiles with volume data sets compares favorably with previous techniques which used the mapping of 2D textures onto textile surfaces. This is especially true when a close-up inspection of synthetic textiles is required.