Abstract: This paper presents an efficient data structure that facilitates high-speed haptic (force feedback) interaction with detailed digital models. Models are partitioned into coarse slabs, which collectively define a piecewise continuous vector field over a thick volumetric region surrounding the surface of the model. Within each slab, the surface is represented as a displacement map, which uses the vector field to define a relationship between points in space and corresponding points on the model's surface. This representation facilitates efficient haptic interaction without compromising the visual complexity of the scene. Furthermore, the data structure provides a basis for interactive local editing of a model's color and geometry using the haptic interface. We describe implementation details and demonstrate the use of the data structure with a variety of digital models.