Visualisation,Animanition and Virtuality

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Visualisation,Animanition and Virtuality

• The Physics and Cognition of VR

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Hierarchy of Models
Behaviour
Bio-Mechanics
Physics
Geometry
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Basic Physics Modelling

• Fundamental Laws
• Gravity
• Friction
• Collision Response
• Forward Kinematics
• Particle Systems
• Playing God !!!

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The Fundamental Laws

• Mass (m)
• Mass number of atomic units (not weight)
• Measured in Kilograms
• Forces act on a mass Newtons -gt weight
• Time (t)
• In a virtual environment is related to frame rate
  not real time
• If system slows time slows

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• Position (s)
• X,y,z co-ords in 3D space
• An object is positioned by its centre of mass

For complex masses centre less obvious
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Bounding shapes make easier computation

• To calculate centre of mass of object can use a
  mass for each vertex (n vertices)
• X value sum of x pos mass (from 1 to n)
• divided by sum of masses
• Y value sum of y pos mass (from 1 to n)
• divided by sum of masses

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• Velocity (v)
• Velocity ds/dt
• X pos x pos x velocity (pixels per frame)
• Virtual velocity pixels/second(for a set fps)
  since we are redrawing using a frame rate
• New position old position velocity time

x0 Time t0
x1 x0v0(t2-t1) Time t1
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• Acceleration (a)
• Rate of change of velocity with time

vel
vel
vel
Time -gt
Time -gt
Time -gt
Constant velocity(a 0) Acceleration a
constant Non-constant accel a f(t)
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• Conservation of momentum
• If a ball bounces of a wall and returns at same
  velocity inelastic collision momentum
  conserved
• Momentum transfer
• Usually some energy is absorbed in the form of
  heat and vibration momentum is lost ball
  returns at lower velocity.
• Ignored in VR or game simulations

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Simple Bounce Physics
(vy,-vx)
(-vy,-vx)
(vy,vx)
(-vy,vx)
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Newtons First Law

• An object at rest remains at rest
• An object in motion remains in motion (ie at
  constant velocity) until an exterior force acts
  upon the object

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Modelling Gravity effeects

• Gravity is a result of a distortion of space by a
  large body , but is experienced as a special
  force unique to earth.
• Two cases to consider
• Two or more objects with same relative mass
• One object has much greater mass than other
• F Gm1m2/r2
• Where G is 6.6710-11 Nm/kg2
• And m1, m2 are masses, r is the distance between
  centres

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Modelling Projectile Trajectories
Vix V cosq Viy V sinq
g 9.8 m/s2
T Viy sinq/g
Xhit Vix Viy /g
Vi
q
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Trajectories

Fire a projectile with mass m, at velocity v,
where does it land?
y
q
x
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Friction

• Friction causes deceleration
• Assumed to be a constant deceleration
• Friction on a flat surface is modelled by
  applying a virtual friction
• Each frame the velocity is reduced by a constant
  factor to match to the desired friction (Vnew
  Vold friction)

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Friction

• Usual modelled as frictional force.
• If you try to push a mass in a direction parallel
  to the plane, you will encounter frictional force.

Friction
Push
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Modelling Friction

• Modelling Friction on a flat surface requires a
  constant negative velocity be applied to all
  objects that is proportional to the required
  friction.
• VnewVold-Friction.
• In which case it is necessary to ensure that
  velocity stays positive.

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Friction on an Inclined Plane

• Friction and Gravity work in tandem.

-x
y
q
x
-y
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Friction on an Inclined Plane

• The plane has coefficenets ms and mk for static
  and kinetic cases.
• The equilibrium case is when the sum of the
  forces acting on the body is zero.

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Friction on an Inclined Plane Finding the
Critical Angle

• Firstly we define an xy coordinate system on the
  inclined plane, with x parallel to the plane, and
  the positive part of x in the downward sliding
  direction.
• For the x-axis we know the force of gravity
  pushing the block is mg(sin q).
• The force due to friction is hms.
• The negative sign is because the force acts in
  the opposite direction.

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• Friction on an inclined plane
• Different coefficient of friction for moving and
  static

?s Static ?k Kinetic(moving)
?
?
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Other Physics to consider

• Object-to-object collision (of irregular shaped
  objects)
• Kinematics
• Particulates

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Kinematic Chains

• Solid links connected at movable joints
• Fixed end base
• Movable end tip or end effector
• One degree of freedom (DOF) per joint
• Open chain one fixed end, one movable end
• Closed chain both ends fixed

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Forward and Inverse Kinematics
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Kinematic Redundancy

• End-effector has 6 DoFs
• - (x, y, z) position
• - ( , , ) orientation
• Non-redundant linkage has lt 6 joints (DoFs)
• Redundant linkage has gt 6 joints (DoFs)
• - Human arm has 7 DoFs
• Shoulder 3
• Elbow 1
• Forearm 1
• Wrist 2
• - Redundancy enables multiple solutions

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Inverse Kinematics (IK)

• Non-redundant Linkages
• - Analytical solutions
• Redundant Linkages
• - Many techniques
• Pseudo-inverse (Jacobian)
• Gradient
• Others
• IK Commonly Found in Animation Packages
• - 3D Studio Max

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Iterative solution

• Start at end effector
• Move each joint so that end gets closer to target
• The angle of rotation for each joint is found by
  taking the dot product of the vectors from the
  joint to the current point and from the joint to
  the desired end point. Then taking the arcsin of
  this dot product.
• To find the sign of this angle (ie which
  direction to turn), take the cross product of
  these vectors and checking the sign of the Z
  element of the vector.

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Interaction with virtual Body

• Limitations mean reliance on metaphors for
• object manipulation (grasping and moving)
• locomotion (movement)
• Limitations in haptics mean that restraint on the
  virtual environment exists

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Object Manipulation

• Hand posture may not be tracked - makes grasping
  difficult
• Must establish a point at which union is deemed
  to have taken place
• Moved by repositioning in the scene graph
• Robinett and Holloway 1992

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Object Manuipulation
World
World
Body B
Object O
Body B
Object O
Hand H
Hand H
Object P
Releasing
Object P
Grasping
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Transformations employed in object manipulation

• Calculate relative transformation from hand to
  object MR
• MR (MB.MH)-1.MO.MP
• MB Transformation from body to world co-ords
• MH Transformation from hand to body co-ords
• MO Transformation from Object O to world co-ords
• MP Transformation from Object P to Object O
  co-ords
• After manipulation new local transformation of
  Object Mp is
• Mp MO-1.MB.MH .MR

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Locomotion

• Tracker has a limited range
• Must use locomotion metaphor to move greater
  distances
• Locomotion is on an even plane , virtual terrain
  may not be even
• Collision detection can be employed to raise or
  lower the participant accordingly

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Directions of locomotion
Fly in direction of aim Fly in direction of
pointing Fly in direction of gaze Fly in
direction of torso
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Object Pair Collision Detection

• Vital component of interaction
• Describe Exhaustive Test for when two object
  intersect (process hungry)
• Try to aviod doing exhaustive test igf possible

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Exhaustive Test

• Assume all objects as collection of triangles
  (polygons)
• Object 1 consists of m triangles
• Object 2 consists of n triangles
• Use triangle intersection test to test all
  possible pairs of of intersections
• This requires n.m triangle-triangle tests

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Triangle Intersection Test

• Moller 1997 comparison of triangles A and B
• They do not intersect if all vertices in A lie to
  one side of plane of B and V.V
• Otherwise plane of A intersects plane of B on L
• Find line intersection of L with A (LA) and L
  with B (LB)
• A and B intersect only if LA and LB overlap

LB
B
A
L
LA
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Basic Rejection Tests

• Simplest tests based on distance
• Each scene object has a bounding sphere. Two
  objects cannot overlap if distance between two
  centres is gt than sum of the radii
• Better test id the separating plane test. If a
  plane can be drawn such that all points of one
  object lie on one side and all points of the
  other on the reverse, cannot collide. Key ids to
  find a good separating plane
• Bounding Box range test

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General Collision Detection

• Detecting collision between a set of n objects
  generates n2 possible pairs of objects requiring
  testing for overlap
• Use spatial partitionong to discard as may pairs
  as possible and use object pair collision tests
  on remaining pairs
• Uniform Space Subdivision

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Space Subdivision
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Artificial Intelligence in Virtual Worlds

• AI techniques can be used to control behaviour in
  irtual Environment
• Knowledge instruction Behaviour
• AI agents or cognitive characters can decide on
  its own behaviour during the course of a
  simulation (or Game)
• The behaviour is designed to deal with
  interaction with components of the VE

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Main kinds of interaction

• Interaction with physical world
• Steering and moving objects
• Collision avoidance
• Learned behaviour
• Interaction with other agents(computer or user
  controlled) in the VE
• Rule-based
• Domain specific

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• A cognitive character has its own view of the
  world. An internal model

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Cactus
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Hierarchy of Models
Behaviour
Bio-Mechanics
Physics
Geometry
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Domain Knowledge and Character instruction

• A cognitive character must have a means of
  representing its view of the world. E.g.
• Proximity of objects
• Goals
• Threats
• Position of self
• It must also behave according to its perception.
  Character instruction

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Types of behaviour

• Deterministic or predefined behaviour is
  performed independently of domain knowledge.
• Fall off chair, bump into fixed objects, etc.
• When a character uses domain knowledge to
  determine its own behaviour this is called
  nondeterministic. Optimum response lies between
  random and pre-defined.
• Goal-Setting

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Goal-setting

• Goals are high level directions e.g. go to a
  point, avoid missile etc.
• Character can perform actions which either have
  desirable effects or undesirable effects with
  regard to attaining goals.
• If character is given actions which produce
  desirable effects it can search for the action or
  series of actions that most helps it achieve the
  goal

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Knowledge aquisition

• In order to select the most appropriate action
  the character must be able to sense the state of
  the world. Sensing.
• May also need to know world dynamics. E.g. Door
  opens
• Can be given world dynamics or learn world
  dynamics

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True world Model

• The computer application will have a a
  representation of the world. The real model.
• A character can have its own world view as the
  true model. Not done because
• Inefficient and difficult to achieve
• Unrealistic (e.g. should not be able to see round
  corners)
• Other characters should have different model