Haptic Rendering in Virtual Environments

1. Introduction The goal of haptic rendering is to enable a user to touch, feel, and manipulate virtual objects through a haptic interface. With the introduction of high fidelity haptic devices (ref. **Biggs and Srinivasan Chapter**), it is now possible to simulate the feel of even fine surface textures on rigid complex shapes under dynamic conditions. Starting from the early nineties, significant progress has occurred in our ability to model and simulate haptic interactions with 3D virtual objects in real-time (Salisbury and Srinivasan, 1997; Srinivasan and Basdogan, 1997). The rapid increase in the number workshops, conference sessions, community web pages, and electronic journals on haptic displays and rendering techniques 1 indicates growing interest in this exciting new area of research, which we call computer haptics. Just as computer graphics is concerned with synthesizing and rendering visual images, computer haptics is the art and science of developing software algorithms that synthesize computer generated forces to be displayed to the user for perception and manipulation of virtual objects through touch. We have already seen various applications of computer haptics in the areas of medicine (surgical simulation, tele-medicine, haptic user interfaces for blind people, rehabilitation of patients with neurological disorders) entertainment (3D painting, character animation, morphing and sculpting), mechanical design (path planning and assembly sequencing), and scientific visualization (geophysical data analysis, molecular manipulation). We anticipate that more applications are on the way as the devices and rendering techniques improve and the computational power increases. This chapter will primarily focus on the fundamental concepts of haptic rendering with some discussion of implementation details. Although, it is impossible to cite all the relevant work within the constraints of this chapter, we have made attempts to cover the major references. Given that the current technology is mature for net force and torque feedback (as in tool usage in the real world) and not tactile feedback (as in actual distribution of force fields on the skin during contact with real objects), we restrict ourselves to techniques concerning the former. In general, the concepts discussed in the chapter include: (1)

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