Abstract: This paper presents new algorithms and techniques for rendering parametric free-form surfaces in pen and ink. In particular, we introduce the idea of "controlled-density hatching" for conveying tone, texture, and shape. The fine control over tone this method provides allows the use of traditional texture mapping techniques for specifying the tone of pen-and-ink illustrations. We also show how a planar map, a data structure central to our rendering algorithm, can be constructed from parametric surfaces, and used for clipping strokes and generating outlines. Finally, we show how curved shadows can be cast onto curved objects for this style of illustration.