Augmented & Virtual Reality (AD-803 (B)) Unit 1 Notes

How unit 1 is examined

This unit covers what VR is, its history, paradigms, systems and interaction, and the geometry (models, translation, rotation, viewing, chaining) behind virtual worlds; no topic was asked recently, so learn each definition and formula.

Introduction to Virtual Reality

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Definition. <mark>Virtual reality is a computer-generated, three-dimensional environment that a user can enter and interact with in real time through sensory devices, so that the user feels present in it.</mark>

Key points.

VR replaces the real world's sensory input with synthetic input, mainly sight and sound.
It rests on three ideas: immersion, interaction and imagination.
Head tracking updates the view as the user moves, which creates presence.
Uses include training, medicine, games, design and education.

VR Basics

Definition. VR basics are the core concepts that make a virtual world convincing: immersion, presence, interactivity and real-time response.

Key points.

Immersion is the degree to which the system shuts out the real world and surrounds the senses.
Presence is the user's feeling of actually being inside the virtual world.
Interactivity lets the user change the world and see the result immediately.
Real-time rendering must be fast, about 60-90 frames per second, or the user gets latency and motion sickness.

History of VR

Definition. The history of VR is the development of devices that simulate an environment, from early simulators to modern head-mounted displays.

Key points.

Morton Heilig built the Sensorama (1950s), a multisensory cinema booth.
Ivan Sutherland created the first head-mounted display, the "Sword of Damocles", in 1968.
The term "virtual reality" was popularised by Jaron Lanier in the 1980s (VPL Research, DataGlove).
Cheap, high-quality headsets such as the Oculus Rift (2012 onwards) made VR consumer-ready.

VR paradigms

Definition. A VR paradigm is a style of delivering a virtual experience, chosen by how the display and user are arranged.

Key points.

Non-immersive (desktop) VR shows the world on an ordinary monitor.
Semi-immersive VR uses large screens or projection, as in flight simulators.
Fully immersive VR uses a head-mounted display with tracking.
Augmented and mixed reality overlay virtual objects on the real world.

Collaboration

Definition. Collaborative VR lets several users share one virtual world at the same time, seeing each other as avatars.

Key points.

Users at distant places work together in one shared space.
Each user is shown as an avatar, so others see their position and gestures.
Network delay and state consistency between users are the main technical problems.
Applications are joint design review, remote training and virtual meetings.

Virtual reality systems

Definition. A VR system is the combination of hardware and software that generates the virtual world and links it to the user.

Key points.

Input devices such as trackers, gloves and controllers capture the user's position and actions.
The computer (VR engine) simulates the world and renders images for each eye.
Output devices, such as a head-mounted display, speakers and haptics, present the world to the senses.
Software includes the world database, the physics and the rendering engine.

User -> Input devices -> VR engine (simulate + render) -> Output devices -> User

Representation

Definition. Representation is how the objects, users and behaviour of the virtual world are described inside the computer.

Key points.

Objects are stored as geometric models (points, polygons, meshes) with colour and texture.
Each object has a position and orientation in the world's coordinate frame.
A scene graph organises objects hierarchically so a parent's movement moves its children.
Level of detail reduces model complexity for far objects to keep rendering fast.

User interaction

Definition. User interaction is the way the user navigates, selects and manipulates objects in the virtual world.

Key points.

Navigation moves the user's viewpoint, by walking, flying or teleporting.
Selection picks an object, for example by pointing a ray from the controller.
Manipulation grabs, moves and rotates the selected object.
Feedback (visual, audio, haptic) confirms each action to the user.

The Geometry of Virtual Worlds, Geometric Models

Definition. A geometric model describes the shape of a virtual object using points (vertices), edges and faces in a 3D coordinate system.

Key points.

The world is a 3D space with x, y, z axes, and every point has coordinates $(x,y,z)$.
Surfaces are built from triangles, because three points always lie in one plane.
A mesh is a set of triangles sharing vertices; it is the standard model in VR and graphics.
Models are defined in their own local frame and then placed in the world.

Changing Position and Orientation

Definition. Position is where an object is (translation) and orientation is how it is turned (rotation); together they are its pose.

Key points.

Translation by $(t_x,t_y,t_z)$ gives $x'=x+t_x,\ y'=y+t_y,\ z'=z+t_z$.
In 2D, rotation by angle $\theta$ about the origin is $x'=x\cos\theta-y\sin\theta,\ y'=x\sin\theta+y\cos\theta$.
Rotation preserves lengths and angles; it is a matrix with determinant 1.
Example: rotate $(1,0)$ by $90^\circ$ to get $(0,1)$, then translate by $(2,3)$ to get (2, 4).

Axis, Angle Representations of Rotation

Definition. Any 3D rotation can be described by a unit axis vector $\mathbf{v}$ and an angle $\theta$ turned about that axis.

Key points.

This avoids gimbal lock, which affects yaw-pitch-roll (Euler angle) rotations.
Rodrigues' formula: $R = I\cos\theta + (1-\cos\theta)\,\mathbf{v}\mathbf{v}^T + \sin\theta\,[\mathbf{v}]_\times$.
A unit quaternion $q=(\cos\frac{\theta}{2},\ \mathbf{v}\sin\frac{\theta}{2})$ stores the same rotation compactly.
Quaternions are easy to interpolate, so VR engines use them for smooth head motion.

Viewing Transformations

Definition. A viewing transformation converts world coordinates into the coordinates of the viewer's eye, so the scene is drawn from the user's viewpoint.

Key points.

Moving the eye is equivalent to moving the whole world in the opposite way.
The view matrix is the inverse of the eye's pose: $T_{view}=T_{eye}^{-1}$.
For eye rotation $R$ and position $\mathbf{e}$, the view transform is $R^{T}(\mathbf{p}-\mathbf{e})$.
VR draws it twice, once per eye, with the eyes about 6.4 cm apart.

Chaining the Transformations

Definition. Chaining is combining several transformations into one by multiplying their matrices, so a point passes through all of them in a single step.

Key points.

Transformations are applied as $p' = T_n\cdots T_2T_1\,p$; the rightmost matrix acts first.
Matrix multiplication is not commutative, so rotate-then-translate differs from translate-then-rotate.
A homogeneous $4\times4$ matrix holds both rotation and translation, which makes chaining possible.
The full VR pipeline is model, world, view (eye) and then projection.

Last-minute revision

Virtual reality is a computer-generated 3D world that the user interacts with in real time.
The three I's: immersion, interaction, imagination.
Sutherland built the first head-mounted display in 1968.
Paradigms: non-immersive, semi-immersive, fully immersive.
Triangles form the meshes used as geometric models.
Translation adds $(t_x,t_y,t_z)$; 2D rotation uses $\cos\theta$ and $\sin\theta$.
Axis-angle avoids gimbal lock; quaternion is $(\cos\frac{\theta}{2},\ \mathbf{v}\sin\frac{\theta}{2})$.
View matrix is the inverse of the eye pose.
Chained transforms: $p'=T_n\cdots T_1p$, order matters.
VR needs 60-90 fps to avoid motion sickness.

Memory hooks

3 I's: Immersion, Interaction, Imagination.
Triangle rule: three points, always flat, so meshes use triangles.
Chain right to left: the matrix nearest the point acts first.
Eye inverse: move the world, not the eye.

Coverage checklist

Introduction to Virtual Reality: definition, three I's (no past questions).
VR Basics: immersion, presence, interactivity (no past questions).
History of VR: Sensorama, Sutherland, Lanier (no past questions).
VR paradigms: non-, semi-, fully immersive (no past questions).
Collaboration: shared avatars (no past questions).
Virtual reality systems: input, engine, output (no past questions).
Representation: models, scene graph (no past questions).
User interaction: navigate, select, manipulate (no past questions).
The Geometry of Virtual Worlds, Geometric Models: meshes (no past questions).
Changing Position and Orientation: translation, rotation (no past questions).
Axis, Angle Representations of Rotation: Rodrigues, quaternion (no past questions).
Viewing Transformations: view matrix (no past questions).
Chaining the Transformations: matrix product (no past questions).

Account

Augmented & Virtual Reality (AD-803 (B)) - Unit 1 Short Notes

How unit 1 is examined

Introduction to Virtual Reality

VR Basics

History of VR

VR paradigms

Collaboration

Virtual reality systems

Representation

User interaction

The Geometry of Virtual Worlds, Geometric Models

Changing Position and Orientation

Axis, Angle Representations of Rotation

Viewing Transformations

Chaining the Transformations

Last-minute revision

Memory hooks

Coverage checklist