Computer Graphics

1
Computer Graphics

• Lecture 10
• 3D Computer Animation (2)
• Lecturer Heather Sayers
• E-mail hm.sayers_at_ulster.ac.uk
• URLhttp//www.infm.ulst.ac.uk/heather

2
Contents

• Dynamics
• Collision Detection
• Broad Phase
• Narrow Phase
• Behavioural animation
• Virtual Reality Modelling Language (VRML)

3
Dynamics

• Dynamics (motion dynamics), is the detailed study
  and modelling of the motion of objects
• This involves modelling the laws of physics,
  representing motion of objects in the real world
• Consider a ball falling from a height and
  bouncing on a surface
• Physicists have developed accurate mathematical
  formulae to describe and predict what happens in
  this situation

4
Dynamics

• For example, knowing the effect of gravity and
  various properties of the ball and the surface,
  it is possible to predict how quickly the ball
  will fall as well as how high and how often it
  will bounce (and what direction the motion will
  take, and when the ball will come to rest etc)
• A ball bouncing on a flat surface is not very
  difficult to predict, but a box bouncing down
  stairs is much more difficult (how far the box
  will bounce, what rotations are involved, which
  edge or corner of the box hits what stair etc)

5
Dynamics

• In setting up the animation, it is necessary to
  define the physical properties of the objects to
  be animated
• One of the most basic properties is mass
• Mass is related to the weight of the objectthe
  weight of an object is the result of gravity
  pulling down on the massiveness of the object
• On Earth, there is a one-to-one relationship
  between weight and mass.in Outer Space, the
  weight of the object would change (though the
  mass remains the same)

6
Dynamics

• A massive object is hard to start moving, and
  difficult to stop once it starts moving
• What makes two objects the same size have
  different masses is related to the density of
  materials from which they are made
• A balsa wood ball is less massive than an iron
  ball, since balsa wood is less dense than iron
• Size does play a role in determining mass, which
  is a function of density and volume (consider a
  small iron ball and a large iron ball)

7
Dynamics

• Another important physical property of objects is
  elasticity
• In motion dynamics, this term does not mean how
  easily the object can be stretched or deformed
  (like an elastic band)
• Elasticity refers to how an object bouncesfor
  example, a glass marble is very elastic, since it
  bounces very high when dropped on, say, a
  concrete floor

8
Dynamics

• Elasticity refers to the amount of energy lost
  when an object makes contact with something else
• Very elastic objects lose very little energy and
  the object bounces a lotinelastic objects lose a
  lot of energy and the object bounces only a
  little
• Most motion dynamic animation systems also
  require the definition of friction created by an
  object
• Friction is a function of how smooth or rough an
  object is (sometimes friction is called
  roughness)
• Static and kinetic friction are defined

9
Dynamics

• Static friction prevents stationary objects from
  sliding down an inclined plane
• If the static friction is very great, the object
  will not slide at all
• Kinetic friction causes moving objects to come to
  a stop
• These two types of friction can be defined
  independently of each other
• For example...

10
Dynamics

• If the static friction of a ball rolling on a
  surface is set to zero, the ball will slide,
  rather than roll along the surface
• At the same time, if the kinetic friction is
  high, the ball will stop quicklyif lowered, the
  ball will come to a stop slowly
• Other major participants in a motion dynamic
  system are gravity and wind

11
Collision Detection

• In a realistic animation system collision
  detection is an important feature
• This can be a very expensive feature to
  implement, since the mathematical calculations
  required are lengthy
• Many systems allow collision detection to be
  turned on or off (sometimes on a per object
  basis)
• In a boundary-representation (b-rep) system
  objects are defined in terms of the geometry
  representing the boundary of the shape

12
Collision Detection

• In such a b-rep system, implementing collision
  detection is very costly.consider two objects
• For accurate collision detection, every surface
  of the animated object must be intersected with
  every surface of the other object (in every
  frame)
• Many systems exploit bounding boxes or bounding
  spheres to simplify the geometry of objects and
  thereby accelerate the collision detection
• The bounding spheres are intersected first to
  determine whether or not the objects are close to
  each otherthen the true geometry can be used if
  necessary

13
Collision Detection

• The standard approach a broad phase followed by
  a narrow phase
• Broad phase finds those pairs of objects that may
  collide it tries to cull away pairs of moving
  objects that cannot possibly collide
• Narrow phase determines the exact collision
  point, if any among the remaining objects
• Many broad phase strategies exist (temporal
  coherence, spatial coherence, bounding volumes)
  most common is bounding volumes

14
Collision Detection

• Time coherence four-dimensional space-time
  bounding volumes are associated with an object
• This is built by sweeping out the 3D, geometric
  bounding volume of the object over the lifetime
  of the moving object
• This can be bounded by a 4D trapezoid for
  simplicity
• The algorithm is based on calculating the
  earliest time that a collision can occur for any
  pair of objects

15
Time Coherence

• No further collision tests are done until this
  time has been reached
• This time is computed for all pairs of objects
• Prior knowledge of the paths of objects is needed
  only suitable for off-line animation (not
  interactive)

16
Spatial Coherence

• Spatial coherence scene space is divided into
  unit cells collisions are checked by examining
  each cell to see if it contains more than one
  object
• Problem best choice of cell size only
  suitable where all objects are similar size
• Alternative approaches are to use a non-uniform
  subdivision structure such as an octree
• To check for collisions, the tree is descended,
  and only those regions containing more than one
  object are examined

17
Spatial Coherence

• The octree eliminates pairs of objects which are
  distant from each other
• Drawback the octree must be rebuilt at every
  step heavy computational load

18
Bounding Volumes

• Bounding boxes most commonly used in broad
  phase collision detection
• 3 types spheres, AABBs (axis aligned), OBBs
  (bounding boxes whose orientation best suits the
  specific object)
• Spheres are easy but may not be a close fit to
  the object, resulting in too many narrow phase
  tests being performed

19
Bounding Volumes

• AABBs also result in low complexity and are
  usually more efficient than spheres, but they
  need updating as the object moves
• OBBs can be precomputed and are defined with
  respect to the object
• Bounding volumes can be further developed into
  bounding volume hierarchies choices here depend
  on the type of tree used (binary, octree) and how
  to deal with updating after object movement

20
Narrow Phase

• This is where broad phase collision detection has
  not seen a negative result
• The technique involves checking the geometries of
  the two objects to determine whether or not a
  collision has taken place
• Algorithm involves 3 tests

21
Narrow Phase

• 1. All the vertices of object A are checked to
  see if they are contained by object B and
  vice-versa
• 2. The edges of A are tested for penetration
  against the faces of B and vice versa
• 3. The case of two identical polyhedra moving
  through each other with faces perfectly aligned
  is tested for this is done by considering the
  centroid of each face of A and using the same
  test as for vertex inclusion
• See diagrams in Watt, page 522
• For interactive systems, collision detection is
  difficult due to the computational demands

22
Behavioural Animation

• Behavioural animation refers to the ability to
  model a system involving living creatures
  (humans, animals, fish, insects etc)
• Such movement goes beyond the laws of physics,
  and therefore requires an additional model to be
  incorporated into an animation system
• Typical elements include the notion of intentions
  and responsesthe attributions of needs, desires
  and the means to satisfy them to an animated
  creature

23
Behavioural Animation

• Such systems can include the modelling of
  creatures by artificial intelligence or expert
  system techniques
• In some cases, distributed AI techniques are
  employed to model groups of creatures such as
  flocks of birds or shoals of fish
• Issues here include how problems are formulated,
  described, allocated and synthesised among the
  grouphow group members communicate and act
  coherently in making decisions, and how
  individual members can reason about their plans
  individually in a group context

24
Behavioural Animation

• Group modelling involves the ability to avoid
  collision with nearby flockmates, match velocity,
  and the modelling of flock centring (attempting
  to stay close to flockmates)
• Other issues include the ability of creatures to
  achieve a high level goal Move from A to B,
  Pick up the pen and then decomposing this goal
  into efficient movement while avoiding objects en
  route

25
Behavioural Animation

• Stimulus response animation (or event animation)
  can be important in this context, where creatures
  respond to some external stimulus in a natural
  way
• .for example, survival instincts of fish when a
  shark comes into view

26
VRML

• Virtual Reality Modelling Language
• Language for describing 3D graphics scenes
• geometry, materials, surface properties
• lights
• cameras
• animation paths
• No specification about rendering
• Internet browser plug-ins availableVRML97 is
  international standardsee specification document
  on www.vrml.org

27
VRML

• All VRML97 files are ascii text files.first line
  must contain VRML V2.0 utf8 header (my italics)
• A number of nodes then describe the scene in
  terms of objects (Shape nodes), cameras
  (Viewpoint nodes), lights (Light nodes) etc
• Each node has a number of fields associated with
  it which typically contain a descriptor and some
  parameters
• A number of example code snippets illustrate.
• VRML files have a .wrl extension (world)

28
VRML

• DirectionalLight
• color 1 1 1
• direction 1 0 0
• This defines a directional light, which is
  assumed to be positioned at infinity, pointing in
  the direction specified above (in the
  x-direction) and with a white colour (R1, G1,
  B1)

29
VRML

• DEF CameraOne Viewpoint
• position 7 7 -90
• orientation 0 1 0 3.14
• This defines a camera position (a viewpoint)
  which the user has called CameraOne (this could
  be any text string)
• The position is in (x, y, z) Cartesian Space
• Orientation is defined by four parameters the
  first three specify the axis of rotation, the
  fourth the angle (in radians) of rotation

30
VRML

• All nodes have default valuesfor example, in the
  Viewpoint node...
• in the default position and orientation, the
  viewer is on the Z-axis looking down the -Z-axis
  toward the origin with X to the right and Y
  straight up
• The code above specifies a rotation (relative) to
  the starting position and orientation) of 180
  degrees about the y-axis
• This points the camera in the desired direction

31
VRML

• Shape
• appearance Appearance
• material Material
• diffuseColor 0 0 1
• geometry Box size 2 2 2
• A Shape node defines geometrythere are two
  sub-nodes specified abovean appearance and a
  geometryeach of these nodes then has a number of
  fields associated with them

32
VRML

• Here we have a box (which is a built-in geometry
  in VRML97) which is scaled by a factor of 2 in x,
  y and z (the default size is one unit in x, y,
  and z)
• Associated with the box is a blue materialthe
  appearance node would also be used to specify
  shininess, transparency and a texture if required
• Note that indentation is used to make the code
  more readable
• Some nodes, such as Shape nodes, take other nodes
  as fieldsothers, such as Material, take a number
  of fields which have specific values

33
Geometry

• Transform
• translation -55 75 -50
• children
• Shape
• appearance Appearance
• material Material
• diffuseColor 0 0 1
• geometry Box size 2 2 2
• Here we see that a Transform node is used to
  position the box in space

34
Texture

• Shape
• appearance Appearance
• texture ImageTexture
• url "wood.jpg"
• geometry IndexedFaceSet
• coord Coordinate
• point -50 0 0, -50 0 -100,50 0 -100,50 0 0
• texCoord TextureCoordinate
• point 0 0, 0 1, 1 1, 1 0
• Here we see a texture associated with a
  boundary-representation of an object..

35
VRML

• the geometry is specified by an IndexedFaceSet
  node which contains four vertices in Cartesian
  space
• This defines a plane with four vertices
• The texture is an image contained in the file
  wood.jpg (note than this is a URL, and so could
  be stored on any accessible website, not just
  locally)
• The TextureCoordinate node defines how the 2D
  texture map is positioned on the plane, vertex by
  vertex a texture space (u,v) to Cartesian space
  (x,y,z) mapping

36
VRML

• We shall now look at how VRML supports animation
  and interaction
• Perhaps the most interesting aspect is the use of
  Sensor nodes, which provide support for
  event-driven animation (stimulus response
  animation)
• Support can be classified as via environmental
  sensors and pointing-device sensors
• Each type of sensor defines when an event is
  generated

37
VRML

• Environmental sensors include Collision,
  Proximity, Time and Visibility
• The ProximitySensor detects when the user
  navigates into a specified region in the world
• This can then cause an event to be generated
  which could, for example, cause a door to be
  automatically opened
• The TimeSensor is a notional clock that has no
  geometry or location associated with it it is
  used to start and stop time-based nodes such as
  interpolators (see later)

38
VRML

• The VisibilitySensor detects when a specific part
  of the world becomes visible to the user
• Again, an event can then be triggered, which
  could for example, cause an audible message to be
  heard Warning you are entering a restricted
  area
• The Collision grouping node detects when the user
  collides with objects in the virtual world, and
  can cause an event (Ouch!)

39
VRML

• Pointing Device Sensors include Anchor, Cylinder,
  Plane, Sphere and Touch sensors
• These detect user pointing events such as the
  user clicking on an object (TouchSensor) or the
  mouse moving over an object (see VRML spec for
  more details)
• These sensors allow a high degree of interaction
  with the virtual environmentfor example the
  notion of teleporting is supportedwhen the user
  clicks on an object the user can be transported
  to another location in the environment (which
  could be in another VRML file on a different
  server, for example)

40
VRML

• Sensor events can be propagated through the scene
  using ROUTE semantics
• Another node which is used is the Interpolator
  node which is used to perform keyframe animation
  for smooth motion
• A number of examples will illustrate these points

41

• DEF animatedObject Transform
• translation 0 0 -20
• children
• Shape
• appearance Appearance
• material Material
• diffuseColor 1 0 0
• geometry Box
• DEF ForwardClick TouchSensor
• DEF ForwardTimeSource TimeSensor cycleInterval
  10.0
• DEF ForwardAnimate PositionInterpolator
• key 0, 1
• keyValue 0 0 -20, 0 0 -120

42
VRML

• This example defines a red box positioned at
  (0,0,-20)
• A TouchSensor is definedthis means that when the
  user clicks on the object an event is
  triggeredwe will see later what happens
• The TimeSensor specifies a cycleInterval of 10
  secondswhen triggered, this will enable some
  animation to occur for a period of 10 seconds
• Finally, the PositionInterpolator is used to
  smoothly interpolate the position of the object
  over the lifetime of the animation (10 seconds)

43
VRML

• The key field of the PositionInterpolator shows
  that there are two key values expected, one at
  the start of the animation (value 0, and one at
  the end, value 1).the values are defined in the
  keyValue field
• The keyValue field then specifies the position of
  the object at the start of the animation
  (0,0,-20), and at the end (0,0,-120)
• When clicked, the object will move (smoothly)
  from (0,0,-20) to (0,0,-120) over 10 seconds

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• ROUTE ForwardClick.touchTime TO
  ForwardTimeSource.startTime
• ROUTE ForwardTimeSource.fraction_changed TO
  ForwardAnimate.set_fraction
• ROUTE ForwardAnimate.value_changed TO
  animatedObject.translation
• ROUTEs are used to propagate the animation from
  node to node
• In this way, when the object is clicked, the
  clock is started, this causes the position of the
  object to be interpolated on each clock tick,
  which in turn causes the object itself to move
• Another example illustrates rotation.

45

• DEF Ball Transform
• rotation 0 0 1 3.14
• Shape geometry Sphere
• DEF RotateClick TouchSensor
• DEF RotateTimeSource TimeSensor
• cycleInterval 100.0
• DEF RotateAnimate OrientationInterpolator
• key 0, .25, .50, 0.75,1.0
• keyValue 0 0 1 0, 0 0 1 0.78, 0 0 1 1.57, 0 0
  1 2.355, 0 0 1 3.14
• ROUTE RotateClick.touchTime TO
  RotateTimeSource.startTime
• ROUTE RotateTimeSource.fraction_changed TO
  RotateAnimate.set_fraction
• ROUTE RotateAnimate.value_changed TO
  Ball.rotation

46
VRML

• In this example we have a sphere with a
  TouchSensor, TimeSensor and OrientationInterpolati
  on node
• The OrientationInterpolation node specifies a
  rotation in radians about the axis specifiedin
  this case the z-axis
• Five key values are defined and the animation
  takes place over 100 seconds
• So the results of the ROUTEs indicate that when
  clicked, the ball will spin 180 degrees about the
  z-axis for 100 seconds

47
Summary

• Motion Dynamics
• mass, elasticity, friction
• gravity, wind
• Collision Detection
• Broad phase
• Narrow phase
• Behavioural Animation
• living creatures
• intentions, responses
• AI techniques
• groups of creatures
• event animation

48
VRML - Summary

• Language for defining highly interactive 3D
  environments, suitable for Web use
• All the usual graphics primitives
  supported.geometry, lights, cameras, textures,
  materials
• Also support for event-driven animationenvironmen
  tal sensors and pointing device sensors
• More details found by looking at the
  specification for VRML97 on www.vrml.org