Abstract: Nonuniform rational B-splines (NURBS) are a powerful tool to model deformable objects. Their shapes can be easily modified by moving the control points. A common method used to render these objects is polygonization. However, the polygonization process is computationally very expensive. If the object deforms, we need to execute this process in every frame to reflect the geometric change of the object. This limitation makes real-time rendering of deforming objects very difficult. In this paper, we present an incremental method for polygonizing deforming objects modeled by NURBS surfaces. Some incremental techniques are introduced here to further improve the performance of the method. They include an efficient mechanism for determining the deformation region when the surface deforms, an incremental crack prevention technique, and an updating method for multiple control point movement.