There are strict time constraints with regard to the update rates for applications incorporating the sense of touch. Therefore, it is essential to employ efficient algorithms for haptic rendering to ensure stable and realistic force feedback is perceived. A major part in any haptic rendering algorithm is the collision detection between the virtual representation of the haptic interface and the objects in the scene. The first part of this paper describes an efficient collision detection algorithm, which is derived from spatial partitioning and bounding volume hierarchy approaches. The pair of closest points is obtained between two polygonal models which may be non-convex. The second part of the paper describes a haptic rendering algorithm that allows three-dimensional polygonal objects to represent deformable tools in the virtual environment.