In this paper, we propose a new ray-based haptic rendering method for displaying 3D objects in virtual environments. We have developed a set of software algorithms that work with a force reflecting haptic interface and enable the user to touch and feel arbitrary 3D polyhedral virtual objects. Using the interface device and the suggested model, the user feels as if exploring the shape and surface details of objects such as textures. The components of the model include a hierarchical database for storing geometrical and material properties of objects, collision detection algorithms, a simple mechanistic model for computing the forces of interaction between the 3D virtual objects and the force-reflecting device, and a haptic filtering technique for simulating surface details of objects such as smoothness and texture. The developed algorithms together with a haptic interface device have several applications in areas such as medicine, education, computer animation, teleoperation, entertainment, and rehabilitation.