Augmented & Virtual Reality (AD-803 (B)) - Unit 2 Short Notes

How unit 2 is examined

This unit covers how motion is described physically, how the body senses it, how a VR engine simulates it, and why mismatched cues cause sickness. No topic was asked in the supplied papers, so each is taught compactly but completely in case it appears this year.

Velocities and Accelerations

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Definition. <mark>Velocity is the rate of change of position with time, and acceleration is the rate of change of velocity with time.</mark>

Key points.

1. Linear velocity is a vector, so it has both speed and direction, and it is written $v = \dfrac{dx}{dt}$ in metres per second.
2. Linear acceleration is $a = \dfrac{dv}{dt}$ in metres per second squared, and it is nonzero whenever speed or direction changes.
3. Angular velocity $\omega = \dfrac{d\theta}{dt}$ (rad/s) and angular acceleration $\alpha = \dfrac{d\omega}{dt}$ (rad/s$^2$) describe rotation of the head or of an object about an axis.
4. A VR tracker measures position and orientation at each frame, and velocity is estimated as the change between two samples divided by the time step: $v \approx \dfrac{x_2 - x_1}{\Delta t}$.
5. An inertial measurement unit (IMU) with a gyroscope and an accelerometer measures angular velocity and linear acceleration directly, and integrating them gives orientation and position.
6. Velocity is not felt by the body but acceleration is, which is why steady motion in a smooth train feels like standing still.

Example. A head turns from $0^\circ$ to $30^\circ$ in $0.3$ s. Then $\omega = \dfrac{30}{0.3} = 100^\circ/\text{s}$. Answer: $\omega = 100^\circ/\text{s}$. If the display has $20$ ms latency, the image lags the head by $100 \times 0.02 = 2^\circ$.

Answer frame. Open with the definition of velocity and acceleration; write the four formulas; then develop points 1-6 in order; close with the head-turn example and the remark that only acceleration is sensed.

Pitfall: Do not say that the body feels velocity; it senses only acceleration.

The Vestibular System

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Definition. <mark>The vestibular system is the inner-ear sensory system that detects head rotation and linear acceleration, giving the sense of balance and spatial orientation.</mark>

Diagram. <figure class="ds-fig" style="margin:1.4rem 0;overflow-x:auto"><svg xmlns="http://www.w3.org/2000/svg" id="dsfig-u2-01" viewBox="0 0 1126 194" width="1126" height="194" role="img" aria-label="Vestibular system, canals sense rotation and otoliths sense linear acceleration"><style>#dsfig-u2-01 .e{stroke:#454C5A;stroke-width:1.4;fill:none}#dsfig-u2-01 .e.hi{stroke:#2340B8;stroke-width:2.6}#dsfig-u2-01 .n{fill:#FFFFFF;stroke:#16181D;stroke-width:1.4}#dsfig-u2-01 .n.hi{fill:#E3E9FC;stroke:#2340B8;stroke-width:2.2}#dsfig-u2-01 .n.rb-b{fill:#16181D;stroke:#16181D}#dsfig-u2-01 .n.rb-r{fill:#BD3227;stroke:#BD3227}#dsfig-u2-01 text{font-family:"JetBrains Mono",ui-monospace,Menlo,Consolas,monospace;font-size:13px}#dsfig-u2-01 .t{fill:#16181D;font-weight:500}#dsfig-u2-01 .t.inv{fill:#FFFFFF;font-weight:700}#dsfig-u2-01 .kd{stroke:#16181D;stroke-width:1.2}#dsfig-u2-01 .dot{fill:#16181D}#dsfig-u2-01 .ann{fill:#2340B8;font-size:11px;font-weight:700}#dsfig-u2-01 .lbl{fill:#6F7787;font-family:system-ui,-apple-system,sans-serif;font-size:12px;font-weight:700}#dsfig-u2-01 .ptr{fill:#2340B8;font-size:12px;font-weight:700}#dsfig-u2-01 .ah{fill:#454C5A}#dsfig-u2-01 .ah.hi{fill:#2340B8}#dsfig-u2-01 .wl rect{fill:#FFFFFF;stroke:#DCE0E7}#dsfig-u2-01 .wl .t{font-size:12px;font-weight:700}#dsfig-u2-01 .wl.hi rect{fill:#2340B8;stroke:#2340B8}#dsfig-u2-01 .wl.hi .t{fill:#FFFFFF}html.dark #dsfig-u2-01 .e{stroke:#B1B7C3}html.dark #dsfig-u2-01 .e.hi{stroke:#8FA3FF}html.dark #dsfig-u2-01 .n{fill:#161920;stroke:#E6E8ED}html.dark #dsfig-u2-01 .n.hi{fill:#1E2748;stroke:#8FA3FF}html.dark #dsfig-u2-01 .n.rb-b{fill:#E6E8ED;stroke:#E6E8ED}html.dark #dsfig-u2-01 .n.rb-r{fill:#FF7E71;stroke:#FF7E71}html.dark #dsfig-u2-01 .t{fill:#E6E8ED}html.dark #dsfig-u2-01 .t.inv{fill:#0F1115}html.dark #dsfig-u2-01 .kd{stroke:#E6E8ED}html.dark #dsfig-u2-01 .dot{fill:#E6E8ED}html.dark #dsfig-u2-01 .ann{fill:#8FA3FF}html.dark #dsfig-u2-01 .lbl{fill:#858D9C}html.dark #dsfig-u2-01 .ptr{fill:#8FA3FF}html.dark #dsfig-u2-01 .ah{fill:#B1B7C3}html.dark #dsfig-u2-01 .ah.hi{fill:#8FA3FF}html.dark #dsfig-u2-01 .wl rect{fill:#161920;stroke:#2A2E37}html.dark #dsfig-u2-01 .wl.hi rect{fill:#8FA3FF;stroke:#8FA3FF}html.dark #dsfig-u2-01 .wl.hi .t{fill:#0F1115}</style><defs><marker id="ah1" viewBox="0 0 10 10" refX="9" refY="5" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path class="ah" d="M0,1 L9,5 L0,9 z"/></marker><marker id="ahh1" viewBox="0 0 10 10" refX="9" refY="5" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path class="ah hi" d="M0,1 L9,5 L0,9 z"/></marker></defs><line class="e" x1="461.5" y1="37" x2="282.5" y2="101"/><line class="e" x1="461.5" y1="37" x2="819.5" y2="101"/><line class="e" x1="282.5" y1="101" x2="103.5" y2="165"/><line class="e" x1="819.5" y1="101" x2="640.5" y2="165"/><line class="e" x1="819.5" y1="101" x2="998.5" y2="165"/><rect class="n" x="385" y="22" width="153" height="30" rx="8"/><text class="t" x="461.5" y="37" dy=".35em" text-anchor="middle">Vestibular system</text><rect class="n" x="198" y="86" width="169" height="30" rx="8"/><text class="t" x="282.5" y="101" dy=".35em" text-anchor="middle">Semicircular canals</text><rect class="n" x="62" y="150" width="83" height="30" rx="8"/><text class="t" x="103.5" y="165" dy=".35em" text-anchor="middle">Rotation</text><rect class="n" x="754.5" y="86" width="130" height="30" rx="8"/><text class="t" x="819.5" y="101" dy=".35em" text-anchor="middle">Otolith organs</text><rect class="n" x="603" y="150" width="75" height="30" rx="8"/><text class="t" x="640.5" y="165" dy=".35em" text-anchor="middle">Utricle</text><rect class="n" x="961" y="150" width="75" height="30" rx="8"/><text class="t" x="998.5" y="165" dy=".35em" text-anchor="middle">Saccule</text></svg><figcaption style="font-size:.82em;opacity:.72;margin-top:.45rem">Vestibular system, canals sense rotation and otoliths sense linear acceleration</figcaption></figure>

Key points.

1. The vestibular organs sit in the inner ear next to the cochlea, one set in each ear, and they work as the body's built-in motion sensor.
2. Three semicircular canals, set at right angles to each other, detect angular acceleration of the head about the yaw, pitch and roll axes.
3. Each canal is filled with fluid, and when the head rotates the fluid lags behind and bends hair cells, which send nerve signals to the brain.
4. The two otolith organs, the utricle and the saccule, detect linear acceleration and gravity, using small crystals that shift over hair cells.
5. The utricle mainly senses horizontal motion and the saccule vertical motion, so together they tell the brain which way is down.
6. The brain fuses these signals with vision and body sensing, and the vestibulo-ocular reflex moves the eyes opposite to the head so that the gaze stays steady.
7. The system responds to acceleration and not to constant velocity, so during steady motion the canal fluid settles and the signal fades.

Answer frame. Open with the definition; draw the tree of canals and otoliths; then develop points 2-4 for the two organs, then points 6 and 7; close with the sentence that this system explains why VR motion cues must match what the inner ear expects.

Pitfall: Canals sense rotation and otoliths sense linear acceleration; do not swap them.

Physics in the Virtual World

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Definition. <mark>Physics in the virtual world is the simulation of natural laws such as gravity, collision and motion so that virtual objects behave in a believable way.</mark>

Key points.

1. A physics engine advances the world in small time steps $\Delta t$, normally one per frame, and updates every object at each step.
2. Motion follows Newton's second law $F = ma$, so acceleration is computed from the net force acting on the object.
3. Velocity and position are then updated by numerical integration, $v \leftarrow v + a\,\Delta t$ followed by $x \leftarrow x + v\,\Delta t$ (Euler method).
4. Collision detection finds when two objects overlap, and collision response changes their velocities, for example by reflecting a bouncing ball.
5. Rigid-body simulation treats objects as non-deforming, and it is favoured in VR because it is cheap enough for real time.
6. The simulation must run at a steady high frame rate, about 90 Hz, since jitter or delay breaks the feeling of presence.
7. The virtual world need not obey real physics exactly, but any departure, such as low gravity, should be consistent so the user is not confused.

Example. A ball dropped from rest with $a = 9.8$ m/s$^2$ at $90$ Hz ($\Delta t = 1/90$ s) has $v = 9.8$ m/s after $90$ frames, and Euler integration gives $x \approx 4.95$ m against the exact $4.9$ m. Answer: about $4.95$ m fallen in $1$ s.

Answer frame. Open with the definition; list the update loop of force, acceleration, velocity, position; then develop points 4-6; close with the falling-ball example and the remark that small steps keep the error small.

Mismatched Motion and Vection

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Definition. <mark>Vection is the illusion of self-motion produced by visual motion alone, and when vision disagrees with the vestibular system the mismatch causes VR sickness.</mark>

Diagram. <figure class="ds-fig" style="margin:1.4rem 0;overflow-x:auto"><svg xmlns="http://www.w3.org/2000/svg" id="dsfig-u2-02" viewBox="0 0 434.5 252" width="434.5" height="252" role="img" aria-label="Eyes report motion, ears report none, conflict causes sickness"><style>#dsfig-u2-02 .e{stroke:#454C5A;stroke-width:1.4;fill:none}#dsfig-u2-02 .e.hi{stroke:#2340B8;stroke-width:2.6}#dsfig-u2-02 .n{fill:#FFFFFF;stroke:#16181D;stroke-width:1.4}#dsfig-u2-02 .n.hi{fill:#E3E9FC;stroke:#2340B8;stroke-width:2.2}#dsfig-u2-02 .n.rb-b{fill:#16181D;stroke:#16181D}#dsfig-u2-02 .n.rb-r{fill:#BD3227;stroke:#BD3227}#dsfig-u2-02 text{font-family:"JetBrains Mono",ui-monospace,Menlo,Consolas,monospace;font-size:13px}#dsfig-u2-02 .t{fill:#16181D;font-weight:500}#dsfig-u2-02 .t.inv{fill:#FFFFFF;font-weight:700}#dsfig-u2-02 .kd{stroke:#16181D;stroke-width:1.2}#dsfig-u2-02 .dot{fill:#16181D}#dsfig-u2-02 .ann{fill:#2340B8;font-size:11px;font-weight:700}#dsfig-u2-02 .lbl{fill:#6F7787;font-family:system-ui,-apple-system,sans-serif;font-size:12px;font-weight:700}#dsfig-u2-02 .ptr{fill:#2340B8;font-size:12px;font-weight:700}#dsfig-u2-02 .ah{fill:#454C5A}#dsfig-u2-02 .ah.hi{fill:#2340B8}#dsfig-u2-02 .wl rect{fill:#FFFFFF;stroke:#DCE0E7}#dsfig-u2-02 .wl .t{font-size:12px;font-weight:700}#dsfig-u2-02 .wl.hi rect{fill:#2340B8;stroke:#2340B8}#dsfig-u2-02 .wl.hi .t{fill:#FFFFFF}html.dark #dsfig-u2-02 .e{stroke:#B1B7C3}html.dark #dsfig-u2-02 .e.hi{stroke:#8FA3FF}html.dark #dsfig-u2-02 .n{fill:#161920;stroke:#E6E8ED}html.dark #dsfig-u2-02 .n.hi{fill:#1E2748;stroke:#8FA3FF}html.dark #dsfig-u2-02 .n.rb-b{fill:#E6E8ED;stroke:#E6E8ED}html.dark #dsfig-u2-02 .n.rb-r{fill:#FF7E71;stroke:#FF7E71}html.dark #dsfig-u2-02 .t{fill:#E6E8ED}html.dark #dsfig-u2-02 .t.inv{fill:#0F1115}html.dark #dsfig-u2-02 .kd{stroke:#E6E8ED}html.dark #dsfig-u2-02 .dot{fill:#E6E8ED}html.dark #dsfig-u2-02 .ann{fill:#8FA3FF}html.dark #dsfig-u2-02 .lbl{fill:#858D9C}html.dark #dsfig-u2-02 .ptr{fill:#8FA3FF}html.dark #dsfig-u2-02 .ah{fill:#B1B7C3}html.dark #dsfig-u2-02 .ah.hi{fill:#8FA3FF}html.dark #dsfig-u2-02 .wl rect{fill:#161920;stroke:#2A2E37}html.dark #dsfig-u2-02 .wl.hi rect{fill:#8FA3FF;stroke:#8FA3FF}html.dark #dsfig-u2-02 .wl.hi .t{fill:#0F1115}</style><defs><marker id="ah2" viewBox="0 0 10 10" refX="9" refY="5" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path class="ah" d="M0,1 L9,5 L0,9 z"/></marker><marker id="ahh2" viewBox="0 0 10 10" refX="9" refY="5" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path class="ah hi" d="M0,1 L9,5 L0,9 z"/></marker></defs><path class="e" d="M57,48.5 L183.8,111.9" marker-end="url(#ah2)"/><path class="e" d="M57,203.5 L183.8,140.1" marker-end="url(#ah2)"/><path class="e" d="M241.5,126 L356,126" marker-end="url(#ah2)"/><g class="wl"><rect x="98.9" y="74" width="54.3" height="18" rx="9"/><text class="t" x="126" y="83" dy=".35em" text-anchor="middle">moving</text></g><g class="wl"><rect x="102.5" y="160" width="47.1" height="18" rx="9"/><text class="t" x="126" y="169" dy=".35em" text-anchor="middle">still</text></g><g class="wl"><rect x="263.7" y="117" width="68.7" height="18" rx="9"/><text class="t" x="298" y="126" dy=".35em" text-anchor="middle">conflict</text></g><circle class="n" cx="40" cy="40" r="18"/><text class="t" x="40" y="40" dy=".35em" text-anchor="middle">Eye</text><circle class="n" cx="40" cy="212" r="18"/><text class="t" x="40" y="212" dy=".35em" text-anchor="middle">Ear</text><rect class="n" x="183.5" y="111" width="57" height="30" rx="15"/><text class="t" x="212" y="126" dy=".35em" text-anchor="middle">Brain</text><rect class="n" x="359" y="111" width="50" height="30" rx="15"/><text class="t" x="384" y="126" dy=".35em" text-anchor="middle">Sick</text></svg><figcaption style="font-size:.82em;opacity:.72;margin-top:.45rem">Eyes report motion, ears report none, conflict causes sickness</figcaption></figure>

Key points.

1. In VR the eyes see the world moving while the inner ear feels no acceleration, and this sensory conflict gives nausea, dizziness, sweating and headache.
2. This condition is called VR sickness or cybersickness, and it is a form of motion sickness caused by the mismatch rather than by real movement.
3. Vection is the feeling of moving when only the scene moves, as when a neighbouring train pulls away and you feel that your own train is moving.
4. Vection is strongest with a wide field of view, fast optical flow and artificial acceleration, such as moving by joystick.
5. Latency between head movement and the display update creates a second mismatch, so the image does not follow the head as the inner ear expects.
6. Low latency, a high and steady frame rate, and accurate head tracking reduce the mismatch.
7. Design remedies include teleport movement, avoiding sudden acceleration, a fixed cockpit or nose reference frame, and narrowing the field of view during turns.
8. Susceptibility differs between users, so sessions should be short at first and the user should be able to stop at any time.

Answer frame. Open with the definition of vection and mismatch; draw the eye-ear-brain diagram; then develop points 1-5 as causes and points 6-7 as remedies; close with the sentence that matching visual and vestibular cues is the goal of comfortable VR.

Pitfall: Vection is an illusion caused by vision, not by real motion; say that the body is still.

Last-minute revision

• Velocity $= dx/dt$; acceleration $= dv/dt$; angular velocity $\omega = d\theta/dt$.
• Velocity estimate from tracker samples: $v \approx (x_2 - x_1)/\Delta t$.
• The body senses acceleration, not constant velocity.
• Vestibular system: three semicircular canals for rotation, two otolith organs (utricle, saccule) for linear acceleration and gravity.
• The vestibulo-ocular reflex moves the eyes opposite to the head to hold the gaze steady.
• Physics loop: $F = ma$, then $v \leftarrow v + a\Delta t$, then $x \leftarrow x + v\Delta t$.
• Collision detection finds the contact and collision response changes the velocities.
• VR runs at about 90 Hz so that latency and jitter stay low.
• Vection is the illusion of self-motion from vision alone.
• VR sickness comes from a visual-vestibular mismatch, reduced by low latency, teleport and a fixed reference frame.

Memory hooks

• Canals = Circles (rotation); Otoliths = Only linear and gravity.
• Eyes move, ears do not: sickness.
• Physics loop order: Force, Acceleration, Velocity, Position (FAVP).
• Vection = Vision-only motion feeling, like the other train pulling away.

Coverage checklist

• Velocities and Accelerations: no past questions.
• The Vestibular System: no past questions.
• Physics in the Virtual World: no past questions.
• Mismatched Motion and Vection: no past questions.