By Steven M. LaValle, Copyright 2015, 2016

   This free VR book covers the fundamentals of virtual reality systems, including geometric modeling, transformations, graphical rendering, optics, the human vision, auditory, and vestibular systems, tracking systems, interface design, human factors, developer recommendations, and technological issues.

See my accompanying MOOC (free on-line course), produced by NPTEL and IIT Madras, 2016.

Why am I writing this? Click here.

Book cover art by Anna Yershova.


This book is not yet finished! It is based on my lectures from the virtual reality course at the University of Illinois. Notes, slides, and other materials from the course appear at the bottom of this page. These might hold you over until the book is finished.

You are welcome to download drafts of the chapters below, or even the entire book so far. However, please understand that this is a work-in-progress, with many missing pieces, errors, inconsistencies, and so on. The purpose of posting it at this point is to reach people who are interested in VR as soon as possible, while also providing me with some feedback as I complete the book (send me comments, references, suggested topics). In case you are wondering, the entire book will remain online for free after I finish it (as was the case with my first book).

To help you judge whether it might be worth your time to look at various parts, I have coded each chapter with a European road symbol to indicate its completion status:
Just barely started. Probably not worth much attention, other than to see what is coming soon.
Complete drafts of some parts may appear, but other parts may be missing altogether. Significant revisions may also be required.
A complete draft is finished; however, it may require more refinement and proofreading. A paragraph or figure could be missing here and there.
This should be ready to go, but there will undoubtedly be typos and minor missing items. Feel free to send me errata or suggestions for improvement.

Download drafts of chapters

Chapter 1: Introduction
6 Oct 2015 Definition of VR, modern experiences, historical perspective.
Chapter 2: Bird's Eye View
6 Oct 2015 Hardware, sensors, displays, software, virtual world generator, game engines, human senses, perceptual psychology, psychophysics.
Chapter 3: The Geometry of Virtual Worlds
31 Oct 2015 Geometric modeling, transforming rigid bodies, yaw, pitch, roll, axis-angle representation, quaternions, 3D rotation inverses and conversions, homogeneous transforms, transforms to displays, look-at and eye transforms, canonical view and perspective transforms, viewport transforms.
Chapter 4: Light and Optics
1 Dec 2015 Light propagation, lenses and images, diopters, spherical aberrations, optical distortion; more lens aberrations; spectral properties; the eye as an optical system; cameras.
Chapter 5: The Physiology of Human Vision
8 Jan 2016 Parts of the human eye, photoreceptors and densities, scotopic and photopic vision, display resolution requiments, eye movements, neural vision structures, sufficient display resolution, other implications of physiology on VR.
Chapter 6: Visual Perception
30 Jan 2016 Depth perception, motion perception, vection, stroboscopic apparent motion, color perception, combining information from multiple cues and senses, implications of perception on VR.
Chapter 7: Visual Rendering
3 Mar 2016 Graphical rendering, ray tracing, shading, BRDFs, rasterization, barycentric coordinates, VR rendering problems, anti-aliasing, distortion shading, image warping (time warp), panoramic rendering.
Chapter 8: Motion in Real and Virtual Worlds
27 Apr 2016 Velocities, acceleration, vestibular system, virtual world physics, simulation, collision detection, avatar motion, vection.
Chapter 9: Tracking
30 May 2016 Tracking systems, estimating rotation, IMU integration, drift errors, tilt and yaw correction, estimating position, camera-feature detection model, perspective n-point problem, sensor fusion, lighthouse approach, attached bodies, eye tracking, inverse kinematics, map building, SLAM.
Chapter 10: Interaction
23 Jun 2016 Remapping, locomotion, manipulation, social interaction, specialized interaction mechanisms.
Chapter 11: Audio
4 Oct 2015 Sound propagation, ear physiology, aural perception, auditory localization; audio simulation and rendering; HRTFs.
Chapter 12: Evaluating VR Systems
4 Oct 2015 Design of experiments, perceptual training, adaptation, best practices, VR sickness.
Chapter 13: Frontiers
4 Oct 2015 Haptics, taste, smell, brain-machine interfaces, robotic interfaces.

Download a draft of the whole book

[pdf file] -- Two pages per one. Recommended for printing on US Letter paper.
[pdf file] -- Two pages per one. Recommended for printing on A4 paper
[pdf file] -- One page per one (larger print). May be easier for on-line viewing.

Related resources

The book above is expanded from the VR lectures and course materials below. It was taught by Steve LaValle in Spring 2015 and Anna Yershova in Fall 2015. These might be useful, especialy before a complete draft of the book is completed: