This is the first book to describe how Autonomous Virtual Humans and Social Robots can interact with real people, be aware of the environment around them, and react to various situations. Researchers from around the world present the main techniques for tracking and analysing humans and their behaviour and contemplate the potential for these virtual humans and robots to replace or stand in for their human counterparts, tackling areas such as awareness and reactions to real world stimuli and using the same modalities as humans do: verbal and body gestures, facial expressions and gaze to aid seamless human-computer interaction (HCI). The research presented in this volume is split into three sections: *User Understanding through Multisensory Perception: deals with the analysis and recognition of a given situation or stimuli, addressing issues of facial recognition, body gestures and sound localization. *Facial and Body Modelling Animation: presents the methods used in modelling and animating faces and bodies to generate realistic motion. *Modelling Human Behaviours: presents the behavioural aspects of virtual humans and social robots when interacting and reacting to real humans and each other. Context Aware Human-Robot and Human-Agent Interaction would be of great use to students, academics and industry specialists in areas like Robotics, HCI, and Computer Graphics.

Research into the methods and techniques used in simulating crowds has developed extensively within the last few years, particularly in the areas of video games and film. Despite recent impressive results when simulating and rendering thousands of individuals, many challenges still exist in this area.

The comparison of simulation with reality, the realistic appearance of virtual humans and their behavior, group structure and their motion, and collision avoidance are just some examples of these challenges. For most of the applications of crowds, it is now a requirement to have real-time simulations which is an additional challenge, particularly when crowds are very large.

"Crowd Simulation "analyses these challenges in depth and suggests many possible solutions. Daniel Thalmann and Soraia Musse share their experiences and expertise in the application of:

. Population modeling

. Virtual human animation

. Behavioral models for crowds

. The connection between virtual and real crowds

. Path planning and navigation

. Visual attention models

. Geometric and populated semantic environments

. Crowd rendering

The second edition presents techniques and methods developed since the authors first covered the simulation of crowds in 2007. "Crowd Simulation" includes in-depth discussions on the techniques of path planning, including a new hybrid approach between navigation graphs and potential-based methods. The importance of gaze attention individuals appearing conscious of their environment and of others is introduced, and a free-of-collision method for crowds is also discussed."

Deformable avatars are virtual humans that deform themselves during motion. This implies facial deformations, body deformations at joints, and global deformations. Simulating deformable avatars ensures a more realistic simulation of virtual humans. The research requires models for capturing of geometrie and kinematic data, the synthesis of the realistic human shape and motion, the parametrisation and motion retargeting, and several appropriate deformation models. Once a deformable avatar has been created and animated, the researcher must model high-level behavior and introduce agent technology. The book can be divided into 5 subtopics: 1. Motion capture and 3D reconstruction 2. Parametrie motion and retargeting 3. Musc1es and deformation models 4. Facial animation and communication 5. High-level behaviors and autonomous agents Most of the papers were presented during the IFIP workshop "DEFORM '2000" that was held at the University of Geneva in December 2000, followed by "A V AT ARS 2000" held at EPFL, Lausanne. The two workshops were sponsored by the "Troisu me Cycle Romand d'Informatique" and allowed participants to discuss the state of research in these important areas. x Preface We would like to thank IFIP for its support and Yana Lambert from Kluwer Academic Publishers for her advice. Finally, we are very grateful to Zerrin Celebi, who has prepared the edited version of this book and Dr. Laurent Moccozet for his collaboration."

This edited book is one of the first to describe how Autonomous Virtual Humans and Social Robots can interact with real people and be aware of the surrounding world using machine learning and AI. It includes: * Many algorithms related to the awareness of the surrounding world such as the recognition of objects, the interpretation of various sources of data provided by cameras, microphones, and wearable sensors * Deep Learning Methods to provide solutions to Visual Attention, Quality Perception, and Visual Material Recognition * How Face Recognition and Speech Synthesis will replace the traditional mouse and keyboard interfaces * Semantic modeling and rendering and shows how these domains play an important role in Virtual and Augmented Reality Applications. Intelligent Scene Modeling and Human-Computer Interaction explains how to understand the composition and build very complex scenes and emphasizes the semantic methods needed to have an intelligent interaction with them. It offers readers a unique opportunity to comprehend the rapid changes and continuous development in the fields of Intelligent Scene Modeling.

This edited book is one of the first to describe how Autonomous Virtual Humans and Social Robots can interact with real people and be aware of the surrounding world using machine learning and AI. It includes: * Many algorithms related to the awareness of the surrounding world such as the recognition of objects, the interpretation of various sources of data provided by cameras, microphones, and wearable sensors * Deep Learning Methods to provide solutions to Visual Attention, Quality Perception, and Visual Material Recognition * How Face Recognition and Speech Synthesis will replace the traditional mouse and keyboard interfaces * Semantic modeling and rendering and shows how these domains play an important role in Virtual and Augmented Reality Applications. Intelligent Scene Modeling and Human-Computer Interaction explains how to understand the composition and build very complex scenes and emphasizes the semantic methods needed to have an intelligent interaction with them. It offers readers a unique opportunity to comprehend the rapid changes and continuous development in the fields of Intelligent Scene Modeling.

This is the first book to describe how Autonomous Virtual Humans and Social Robots can interact with real people, be aware of the environment around them, and react to various situations. Researchers from around the world present the main techniques for tracking and analysing humans and their behaviour and contemplate the potential for these virtual humans and robots to replace or stand in for their human counterparts, tackling areas such as awareness and reactions to real world stimuli and using the same modalities as humans do: verbal and body gestures, facial expressions and gaze to aid seamless human-computer interaction (HCI). The research presented in this volume is split into three sections: *User Understanding through Multisensory Perception: deals with the analysis and recognition of a given situation or stimuli, addressing issues of facial recognition, body gestures and sound localization. *Facial and Body Modelling Animation: presents the methods used in modelling and animating faces and bodies to generate realistic motion. *Modelling Human Behaviours: presents the behavioural aspects of virtual humans and social robots when interacting and reacting to real humans and each other. Context Aware Human-Robot and Human-Agent Interaction would be of great use to students, academics and industry specialists in areas like Robotics, HCI, and Computer Graphics.

This book contains invited papers and a selection of research papers submitted to Computer Animation '91, the third international work shop on Computer Animation, which was held in Geneva on May 22-24. This workshop, now an annual event, has been organized by the Computer Graphics Society, the University of Geneva, and the Swiss Federal Institute of Technology in Lausanne. During the international workshop on Computer Animation '91, the fourth Computer-generated Film Festival of Geneva, was held. The book presents original research results and applications experience of the various areas of computer animation. This year most papers are related to character animation, human animation, facial animation, and motion contro!. NA DIA MAGNENAT THALMANN DANIEL THALMANN v Table of Contents Part I: Facial Animation Contral Parameterization for Facial Animation F. I. PARKE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Linguistic Issues in Facial Animation C. PELACHAUD, N. !. BADLER, M. STEEDMAN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Facial Animation by Spatial Mapping E. C. PATTERSON, P. c. LITWINOWICZ, N. GREENE . . . . . . . . . . . . . . . . . . . . . . . . . 31 A Transformation Method for Modeling and Animation of the Human Face fram Photographs T. KURlHARA, K. ARAI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 Techniques for Realistic Facial Modeling and Animation D. TERZOPOULOS, K. WATERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 Part ll: Human Modeling and Animation Generation of Human Motion with Emotion M. UNUMA, R. TAKEUCHI . . . . . . . . . . *. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 Creating Realistic Three-Dimensional Human Shape Characters for Computer-Generated Films A. PAOURl, N. MAGNENATTHALMANN, D. THALMANN . . . . . . . . . . . . . . . . . . . 89 Design of Realistic Gaits for the Purpose of Animation N. VASlLONIKOLIDAKIS, G. J CLAPWORTHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

This book contains the invited papers and a selection of research papers submitted to Computer Animation '93, the fifth international workshop on Computer Animation, which was held in Geneva on June 16-18, 1993. This workshop, now an annual event, has been organized by the Computer Graphics Society, the University of Geneva, and the Swiss Federal Institute of Technology in Lausanne. During the international workshop on Computer Animation '93, the sixth Computer-generated Film Festival of Geneva, was also held. The volume presents original research results and applications experience to the various areas of computer animation. Most of the contributions are related to motion control, visualization, human animation, and rendering techniques.

An overview of biomechanical modeling of human soft tissue using nonlinear theoretical mechanics and incremental finite element methods, useful for computer simulation of the human musculoskeletal system.

Deformable avatars are virtual humans that deform themselves during motion. This implies facial deformations, body deformations at joints, and global deformations. Simulating deformable avatars ensures a more realistic simulation of virtual humans. The research requires models for capturing of geometrie and kinematic data, the synthesis of the realistic human shape and motion, the parametrisation and motion retargeting, and several appropriate deformation models. Once a deformable avatar has been created and animated, the researcher must model high-level behavior and introduce agent technology. The book can be divided into 5 subtopics: 1. Motion capture and 3D reconstruction 2. Parametrie motion and retargeting 3. Musc1es and deformation models 4. Facial animation and communication 5. High-level behaviors and autonomous agents Most of the papers were presented during the IFIP workshop "DEFORM '2000" that was held at the University of Geneva in December 2000, followed by "A V AT ARS 2000" held at EPFL, Lausanne. The two workshops were sponsored by the "Troisu!me Cycle Romand d'Informatique" and allowed participants to discuss the state of research in these important areas. x Preface We would like to thank IFIP for its support and Yana Lambert from Kluwer Academic Publishers for her advice. Finally, we are very grateful to Zerrin Celebi, who has prepared the edited version of this book and Dr. Laurent Moccozet for his collaboration.

This volume presents the proceedings of COMPUTER GRAPHICS INTERNATIONAL '93 (COl '93), the Eleventh International Conference of the Computer Graphics Society (CGS), COl '93 has been held in Lausanne, Switzerland from June 21-25,1993 under the theme Communicating with Virtual Worlds. Since its foundation in 1983, COl conference has continued to attract high qUality research articles in all aspects of computer graphics and its applications. Previous conferences in this series were held in Japan (1983-1987), in Switzerland (1988), in the United Kingdom (1989), in Singapore (1990), in the United States (1991), and in Japan (1992). Future CG International conferences are planned in Australia (1994), and in the United Kingdom (1995). COS also organizes each year Computer Animation in Geneva, an international workshop and Computer Generated Film Festival. Two new CGS events are planned in 1993: Pacific Graphics '93 in Seoul and MMM '93, an International Conference on Multi-Media MOdeling in Singapore."

New Trends in Computer Graphics contains a selection of research papers submitted to Computer Graphics International '88 (COl '88). COl '88 is the Official Annual Conference of the Computer Graphics Society. Since 1982, this conference ha~ been held in Tokyo. This year, it is taking place in Geneva, Switzerland. In 1989, it will be held in Leeds, U. K. , in 1990 in Singapore, in 1991 in U. S. A. and in 1992 in Montreal, Canada. Over 100 papers were submitted to CGI '88 and 61 papers were selected by the International Program Committee. Papers have been grouped into 6 chapters. The flrst chapter is dedicated to Computer Animation because it deals with all topics presented in the other chapters. Several animation systems are described as well as speciflc subjects like 3D character animation, quaternions and splines. The second chapter is dedicated to papers on Image Synthesis, il1 particular new shading models and new algorithms for ray tracing are presented. Chapter 3 presents several algorithms for geometric modeling and new techniques for the creation and manipulation of curves, surfaces and solids and their applications to CAD. In Chapter 4, an important topic is presented: the specification of graphics systems and images using l~nguages and user-interfaces. The last two chapters are devoted to applications in sciences, medicine, engineering, art and business.

Research, development, and applications in computer graphics have dramatically expanded in recent years. Because of decreasing prices, superior hardware is now being used and image quality is better than ever. Many people now require image-synthesis techniques and software for their applicaions. Moreover, the techniques of computer ani mation have become very popular. In this book, we present a wide range of applications of computer graphics. This book is a collection of 44 papers in various areas of computer graphics selected from papers presented at Graphics Interface '85. Graphics Interface '85, held from May 27 to 31 in Montreal, was the first truly international computer graphics conference in Canada. This year, for the first time, the conference was presented jointly by the Com puter Graphics Society and the Canadian Man-Computer Communications Society. This new arrangement gave the conference international scope. The conference was spon sored by the Department of Communications in Ottawa, the Department of Science and Technology in Quebec, Supply and Services Canada, the Natural Sciences and Engineer ing Research Council of Canada, Hydro-Quebec, the "Association Canadienne Fran"aise pour I' Avancement des Sciences", and the Canadian Broadcasting Corpora tion. Graphics Interface '85 was organized by "1'Ecole des Hautes Etudes Commerciales" of the University of Montreal. Over 100 papers were submitted to the conference , but 64 were selected by the inter national program committee for presentation. This book contains new expanded versions of the papers.

Computer Animation '90, the second international workshop on computer animation, was held in Geneva, Switzerland, on April 25-27, 1990. This book contains invited papers and a selection of research papers submitted to this workshop. The contributions address original research as well as results achieved in a number of fields of computer animation including scientific visualization, human animation, behavioral animation, and motion control.

"Image Synthesis: Theory and Practice" is the first book completely dedicated to the numerous techniques of image synthesis. Both theoretical and practical aspects are treated in detail. Numerous impressive computer-generated images are used to explain the most advanced techniques in image synthesis. The book contains a detailed description of the most fundamental algorithms; other less important algorithms are summarized or simply listed. This volume is also a unique handbook of mathematical formulae for image synthesis. The four first chapters of the book survey the basic techniques of computer graphics which play an important role in the design of an image: geometric models, image and viewing transformations, curves and surfaces and solid modeling techniques. In the next chapters, each major topic in image synthesis is presented. The first important problem is the detection and processing of visible surfaces, then two chapters are dedicated to the central problem of light and illumination. As aliasing is a major problem in image rendering, the fundamental antialiasing and motion blur techniques are explained. The most common shadow algorithms are then presented as well as techniques for producing soft shadows and penumbrae. In the last few years, image rendering has been strongly influenced by ray tracing techniques. For this reason, two chapters are dedicated to this important approach. Then a chapter is completely dedicated to fractals from the formal Mandelbrot theory to the recursive subdivision approaches. Natural phenomena present a particularly difficult challenge in image synthesis. For this reason, a large portion of the book is devoted to latest methods to simulate these phenomena: particle systems, scalar fields, volume density scattering models. Various techniques are also described for representing terrains, mountains, water, waves, sky, clouds, fog, fire, trees, and grass. Several techniques for combining images are also explained: adaptive rendering, montage and composite methods. The last chapter presents in detail the MIRALab image synthesis software.

This book contains several invited papers and a selection of research papers submitted to Computer Animation '92, the fourth international workshop on Computer Animation, which was held in Geneva on May 20-22. This workshop, now an annual event, has been organized by the Computer Graphics Society, the University of Geneva, and the Swiss Federal Institute of Technology in Lausanne. During the international workshop on Computer Animation '92, the fifth Computer-generated Film Festival of Geneva, was held. The book presents original research results and applications experience in various areas of computer animation. This year most papers are related to physics-based animation, human animation, and geometric modelling for animation. NADIA MAGNENAT THALMANN DANIEL THALMANN Table of Contents Part I: Physics-based Animation The Control of Hovering Flight for Computer Animation David Haumann, Jessica K. Hodgins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Inverse Problems in Computer Graphics Michael Kass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . " . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 NPSNET: Physically-based Modeling Enhancements to An Object File Format Michael J. Zyda, James G. Monahan, David R. Pratt. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 A New Method for Approximative Interactive Dynamics Ulrich Leiner, Bernhard Preim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 Part ll: Human animation Extraction of 3D Shapes from the Moving Human Face Using Lighting Swjtch Photometry Hitoshi Saji, Hirohisa Hioki, Yoshihisa Shinagawa, Kensyu Yoshida, Tosiyasu L. Kunii . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 An Interactive Tool for the Design of Human Free-Walking Trajectories Laurent Bezault, Ronan Boulic, Nadia Magnenat Thalmann, Daniel Thalmann . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 Achilles - A System for Visualizing Non Standard Human Gait Homero L. Piccolo, Kentaro Takahashi, Marcus G. de Amorim, Andre C. de Sa Carneiro . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

This book presents the making of computer-generated films using three-dimensional synthetic actors. It is based mainly on the production of the film Rendez-vous a Montreal, an animated film that uses advanced computer techniques to achieve such effects as reincarnating film stars Humphrey Bogart and Marilyn Monroe. The main purpose of Rendez-vous a Montreal is to show that true synthetic actors can be created. This fllm represents a technological breakthrough which opens up new vistas in motion pictures, television, and advertising. With this technique, it will now be possible to produce short fllms or motion pictures featuring any celebrity in any situation. The book explains in detail how such a film can be produced using numerous drawings and color pictures. In particular, the following topics are presented: - Preparation of object construction: documentation search, and plaster models preparation - Object construction: digitizing and modeling - Body animation - Hand animation and object grasping - Facial animation: expressions, phonemes and emotions - Choreography: decors, actors, cameras, and lights - Realism: colors, lights, shading, shadows, and textures - Image recording: special effects Finally, an extensive appendix describes in detail the HUMAN FACTORY system.

Computer Science Workbench is a monograph series which will provide you with an in-depth working knowledge of current developments in computer technology. Every volume in this series will deal with a topic of importance in computer science and elaborate on how you yourself can build systems related to the main theme. You will be able to develop a variety of systems, including computer software tools, computer gra phics, computer animation, database management systems, and compu ter-aided design and manufacturing systems. Computer Science Work bench represents an important new contribution in the field of practical computer technology. TOSIYASU L. KUNII Preface to the Second Edition Computer graphics is growing very rapidly; only computer animation grows faster. The first edition of the book Computer Animation: Theory and Practice was released in 1985. Four years later, computer animation has exploded. Conferences on computer animation have appeared and the topic is recognized in well-known journals as a leading theme. Computer-generated film festivals now exist in each country and several thousands of films are produced each year. From a commercial point of view, the computer animation market has grown considerably. TV logos are computer-made and more and more simulations use the technique of computer animation. What is the most fascinating is certainly the development of computer animation from a research point-of-view."

The book contains 16 papers and one invited talk presenting the latest research in computer animation and simulation. Special focus is given on the modelling and animation of complex phenomena. This includes the modelling of virtual creatures-from their body-parts to the control of their behaviour-and the nomination of natural phenomena such as water, smoke, fire, and vegetation.

The 20 research papers in this volume demonstrate novel models and concepts in animation and graphics simulation. Special emphasis is given on innovative approaches to Modelling Human Motion, Models of Collision Detection and Perception, Facial Animation and Communication, Specific Animation Models, Realistic Rendering for Animation, and Behavioral Animation.

The CAPTECH'98 workshop took place at the University of Geneva on November 26-27, 1998, sponsored by FIP Working Group 5.10 (Computer Graphics and Virtual Worlds) and the Suisse Romande regional doctoral seminar in computer science. The subject of the conference was ongoing research in data capture and interpretation. The goals of capturing real world data in order to perceive, understand, and interpret them and then reacting to them in a suitable way are currently important research problems. These data can be very diverse: sounds, emotions, shapes, motions, forces, muscles, actions, etc. Once captured, they have to be treated either to make the invisible visible, or to understand a particular phenomenon so as to formulate an appropriate reaction, or to integrate various information in a new multimedia format. The conference included six sessions of presented papers and three panel discussions. Invited speakers treating various aspects of the topic were: Professor R. Earnshaw from Bradford University, Professor T. L. Kunii from Hosei University, and Professor P. Robert from EPFL. Professor K. Bauknecht, of the University of Zurich, President of IFIP, offered the welcoming address. Mr. E. Badique, project officer for the EU in Brussels, discussed recent results of the EU ACTS research program. Finally, the Geneva Computer Animation '98 Film Festival highlighted the evening of November 26."

This volume contains the research papers presented at the Eighth Eurographics Workshop on Computer Animation and Simulation which took place in Budapest, Hungary, September 2-3, 1997. The workshop is an international forum for research in human animation, physically-based modeling, motion control, animation systems, and other key aspects of animation and simulation. The problem of realistically and efficiently modeling the motion of people, ob- jects, fluids, etc. remains a significant challenge in computer graphics. This workshop is representative of the continuing interest in this field of study. This year, animation and simulation of human shape and motion is of particular interest. In fact, nine of the papers in this volume deal with techniques which are applicable to human animation. Others are concerned with equally interesting dy- namic natural phenomena, such as clouds, plant development, and coastal scenes. The call for papers required submission of the full papers for review, and each paper was reviewed by at least 3 members on the international program committee, consisting of: Bruno Arnaldi (IRISA/INRIA Rennes, France) Norman Badler (University of Pennsylvania, U. S. A. ) Ronan Boulic (Swiss Federal Institute of Technology, Switzerland) Michael Cohen (Microsoft, U. S. A. ) Sabine Coquillart (INRIA, France) David Forsey (University of British Columbia, Canada) Marie-Paule Gascuel (iMAGIS-IMAG, France) Gerard Hegron (Ecoles des Mines de Nantes, France) Jessica Hodgins (Georgia Institute of Technology, U. S. A.

This volume contains research papers that were presented at the Sixth Eurographics Workshop on Animation and Simulation which took place at Maastricht, The Nether lands, September 2-3, 1995. A core area within computer graphics, animation is concerned with the computer synthesis of dynamic scenes. The creation of realistic animation based on the simulation of physical and biological phenomena is a unify ing and rapidly evolving research theme. This series of workshops, an activity of the Eurographics Working Group on Animation and Simulation, is an international forum where researchers representing the animation and simulation communities convene to exchange knowledge and experience related to this theme and to physics-based mod elling, human modelling, motion control, visualization, etc. Of keen interest at this sixth workshop were novel animation techniques and animation systems that simulate the dynamics and interactions of physical objects-solid, fluid, and gaseous-as well as the behaviors of living systems such as plants, lower animals, and humans. The workshop continued to promote the confluence of animation and simulation as a leading edge of computer graphics research that is providing animators with sophisticated new algorithms for synthesizing dynamic scenes. The call for extended abstracts for the workshop, issued in February 1995, elicited an enthusiastic response."

MODULA-2 is a new programming language which was created by Niklaus Wirth of the Swiss Federal Institute of Technology (ETH) in Zurich. The lan guage is derived from PASCAL: it includes all aspects of PASCAL and some times improves on them. Moreover, MODULA-2 includes the important "mod ule" concept, as well as multiprogramming capabilities and a way of implemen ting low-level software in an elegant manner. In summary, MODULA-2 may be used equally well as a general-purpose programming language and as a system implementation language. MODULA-2 provides the programmer with a good way of writing high quality software. In particular, modules are powerful tools for achieving modularity, reliability, readability, extensibility, reusability and ma chine-independence. This book presents the complete MODULA-21anguage from the beginning. Each topic is presented by means of numerous examples and each concept is justified. The syntax of the language is explained using syntactic diagrams. This book is not a reference manual for MODULA-2, but a textbook from which the student can learn the language progressively. The most important con cepts (i.e. procedures, modules and data structures) are explained in great detail and methodological aspects are also emphasized. Beginning in the first chapter, the student may execute his/her own pro grams. Program examples in this book have been executed on several machines (APPLE II, IBM PC and VAX 11/780) and they may be taken as a basis for stu dents."

Virtual reality techniques are increasingly becoming indispensable in many areas. This book looks at how to generate advanced virtual reality worlds. It covers principles, techniques, devices and mathematical foundations, beginning with basic definitions, and then moving on to the latest results from current research and exploring the social implications of these. Very practical in its approach, the book is fully illustrated in colour and contains numerous examples, exercises and case studies. This textbook will allow students and practitioners alike to gain a practical understanding of virtual reality concepts, devices and possible applications.