Abstract. Surgical simulations with the aid of computers is a topic of increasingly extensive research. Realtime response and interactivity are crucial components of any such system and a major effort has been invested in finding ways to improve the performance of existing systems. In this paper, we propose the use of a new variant of Free Form Deformations that supports discontinuities (DFFD) in complex real time surgical simulations. The proposed scheme can benefit from an a priori or, alternatively, interactive low resolution, physical simulation of the incision procedure that is encoded into the DFFD. The DFFD is then applied to the geometry of the tissue in hand, a two-dimensional skin shape or a three-dimensional volumetric representation, capturing the incision’s shape as well as the behavior of the neighborhood geometry over time.