1. COMP 304 Computer Graphics II
LECTURE 8
MOTION CONTROL – FORWARD KINEMATICS
Dr. Mehmet Gokturk Asst. Prof., Gebze Institute of Technology

2. Some Timeline  The Illusion of Motion
1824, Peter Mark Roget,"Persistence of Vision with Regard to Moving Objects“
a series of images shown in rapid sequence can appear to move fluidly (i.e. a flip book or film projector)
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4. Timeline  Movies (1895) age of movie camera and projector begins
experimentors discover they can stop the crank and restart it again to obtain special effects
(1914) Gertie, Windsor McCay (newspaper cartoonist)
first popular animation
(1928) Steamboat Willie, Disney
an early cartoon w/ sound
cartoons seem plausible as entertainment
(1933) King Kong, Willis O’Brien
(1930’s & 40’s) Golden age of cartoons
Betty Boop, Popeye, Porky Pig, Daffy Duck, Bugs Bunny, Woody Woodpecker, Mighty Mouse, Tom & Jerry
(1937) Snow White, Disney
animated feature film
cost is $1.5M
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5. Timeline  Movies (cont)
(1982) Tron, MAGI
movie with a computer graphics premise
(1984) Last Starfighter
computer graphics was used interchangably with actual models of the spaceship
(1993) Jurassic Park
computer graphics is used to create living creatures that are meant to appear realistic
(1995) Toy Story, Pixar
full-length feature film done entirely with 3D computer animation
(2000) CyberWorld 3D, IMAX
3D IMAX full-length feature film including characters from popular 3D movies such as ANTZ and The Simpsons’ Homer
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6. Conventional Animation Techniques
Drawing on film
Multiple drawings
Rotoscoping (project film of real actors onto drawing paper)
Stop motion animation
Acetate cels, multiple plane cells
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7. Conventional Animation Process
Storyboard
Key frames drawn
Straight ahead vs. pose-to-pose
Intermediate frames filled in (inbetweening)
Trial film is made (called a pencil test)
Pencil test frames transferred to cels
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8. Conventional Animation Process
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9. Role of the Computer In-betweening Disney’s CAPS system
artistic example: Hunger, Peter Foldes 1974
Disney’s CAPS system
scanned artist drawings are read in
"cels" are colored online (broad color palette, exact color matching)
compositing is done online (background, 2D drawings, 3D animation)
3D effects can be created with 2D drawings (e.g. Beauty and the Beast)
used in every film since Beauty & Beast
3D graphical worlds
can experiment more easily with actor position, camera position
can perform more complex camera moves
exchange labor to create drawings with labor to build and animate 3D world
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10. 3D Animation 3D animation is similar to stop motion animation
King Kong (1932)
Flash Gordon (1972)
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11. 3D Animation Stop motion animation (Nightmare Before Christmas)
3D keyframing (Luxo Jr.)
Performance animation and motion capture (Donkey Kong Country)
Which must be done straight-ahead and which can be animated pose-topose?
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12. Keyframing
Key frames mark important visual transitions (extremes of action)
Inbetweening is creation of intermediate frames between the key frames
Can easily be calculated by computer
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13. Temporal Sampling
Film recording takes samples of an image at fixed time intervals
24 frames per second for film
30 frames per second for video
human eye "sees" continuous motion
Sometimes, fewer keyframes are required to describe the motion, especially for “pencil tests” or rough choreography (e.g., Lost World)
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14. Smooth Motion  Passive Physics
No internal energy source and move only when an external force acts on them.
Read for use when:
physical laws encoded
initial conditions specified
Pools of water, clothing, hair, leaves
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15. Smooth Motion  Passive Physics
Clothing (Geri’s Game)
Water (Antz)
“Rigid” body physics (crashing space pods in Phantom Menace)
Geri’s Game, Pixar Animation Studios
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See examples

16. Smooth Motion  Active Physics
User specifies keyframes (start, end, middle)
User specifies constraints (e.g. laws of physics)
System searches for minimum energy motion to accomplish goals
A. Witkin and M. Kass,
“Spacetime Constraints”,
SIGGRAPH ‘88.
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17. Smooth Motion  Active Physics and Simulation
Control an animated character as we would control a robot
behavior is simulated
a "control system" sends proper signals to the character’s "muscles" over time
Mark Raibert’s leg lab at MIT
http ://
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18. Noise Motion We generally don’t want motion to be too smooth
The eye picks up symmetries and smooth curves and interprets them as artificial or fake
By adding noise, we can add texture to smooth motion
K. Perlin, “An Image Synthesizer”,
Computer Graphics, 19(3), July 1985.
Perlin, Improv system
(K. Perlin and A. Goldberg, SIGGRAPH ‘96).
Applets:
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19. Noise Motion
Motion capture (natural noise!)
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20. Camera Path Following
A simple type of animation  everything remains static except the camera (walk throughs or flybys).
The camera  just as any other object as far as orientation and positioning is concerned.
The user needs to construct a path through space for the observer to follow along with orientation information.
Path = key frame positioning + interpolation of the inbetween frames.
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21. Camera Path Following  ways to deal with the view direction (1)
The center of interest can be held constant while observer position is interpolated along a curve
View Direction  Vector between the observer position (POS) and the center of interest (COI)
This is useful when the observer is flying over an environment inspecting a specific location such as a building.
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22. Camera Path Following  ways to deal with the view direction (2)
A path for the center of interest can be constructed, say from a series of buildings in an environment.
Often, the animator will want the center of interest to stay focused on one building for a few frames before it goes to the next building.
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23. Camera Path Following  ways to deal with the view direction (3)
Alternatively, the center of interest can be controlled by other points along the observer path.
For example, observer position for the next frame can be used to determine the view direction for the current frame.
Sometimes this is too jerky. Some nth frame beyond the current frame can be used to produce a smoother view direction.
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24. Camera Path Following  ways to deal with the view direction (4)
The center of interest can also be attached to objects in the animation.
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25. Path following
Have position and orientation interpolation for key framing now
Combining them , get general motions of rigid objects
Add scaling, get stretching/squashing
Path following:
Have keys only for position
how to change orientation “naturally”
Same techniques for camera motion
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26. Orientation along a path
It’s natural to change orientation as things move
Example: looking while walking
Look in the direction one walks
Tedious to specify orientations along the way
Want to get directly from the path
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27. Frenet frame (Moving frame)
At each point on the curve:
Get Tangent vector
Get vector in general curvature direction
In the plane of tangent and curvature vector
Vector orthogonal to the two
Math:
Everything is normalized then
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30. Frenet frame Curvature can be zero along extended parts
Example: straight line
Solution: interpolate boundary frames
Differ only by rotation around the straight line
Zero curvature at a point:
Possible flip (ex. camera flips upside down)
Discontinuities in curvature:
Sudden changes of object orientation
These effects are NOT tolerable
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31. Alternatives Tangent vector is ok for objects
Poor choice for cameras
For cameras: Look at the “center of interest”
Fixed COI: Always look at particular point
Separate path for COI
Can animate this point separately using extra key positions
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32. Alternatives COI (center of interest) travels in front of the camera
COI(s)=P(s+ds)
At the end, along the final tangent vector
Choose several ds, average
Smoothes motion
Trade-off: jerky motion vs. too static view direction
“Up” vector:
In the plane of view vector and global UP vector
Extra offset from this direction
Full key framing
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34. Path Following u = P’(u) x P’’(u) w = P’(u) P’’(u) v = w x u
Frenet Frame
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35. Curvature continuity =0
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36. Look ahead
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37. Define “look-at” vector
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38. Define “up” vector
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43. Kinematics X Dynamics
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44. Kinematics
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45. Kinematics Keyframing requires that the user supply the key frames
For articulated figures, we need a way to define the key frames
There are two ways to pose an articulated character – forward and inverse kinematics
Kinematics is the study of motion without regard to the forces that cause the motion Kinematics
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47. Articulated Models Articulated models:
rigid parts
connected by joints
They can be animated by specifying the joint angles (or other display parameters) as functions of time.
See example animation clips
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48. Some robotics is required !
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51. Drawing Articulated Figures
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52. Static Figure Transformations
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53. Forward Kinematics Control
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54. Example: 2-Link Structure
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55. Forward Kinematics
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56. Forward Kinematics
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57. Forward Kinematics
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58. Forward Kinematics
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59. Forward Kinematics Hierarchical model - joints and links
Joints - rotational or prismatic
Joints - 1, 2, or 3 Degree of Freedom
Links - displayable objects
Pose - setting parameters for all joint DoFs
Pose Vector - a complete set of joint parameters
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61. Forward Kinematics T
data R S
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62. Transformations at the arcs
User modifies
Rotation
(new “pose vector”)
Re-traverse tree
To get new “pose”
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63. Forward Kinematics
Describes the positions of the body parts as a function of the joint angles.
1 DOF: knee
2 DOF: wrist
3 DOF: arm
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64. Joint Representation q
Degree of Freedom
DOF
Joint Limits
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65. Joint Representation Multiple Degrees of Freedom Joint Limits qy w
Degrees of Freedom
Joint Limits
gimbal lock
Axis-angle
quaternions
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66. Joint Representation Noteq y w
Note
User interface representation may not be the same used for internal representation and operations
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68. Drawing Articulated Figure
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72. Denavit and Hartenberg
Standard method of describing relationship of one DOF to next
Used extensively in robotics
Used in some early animation systems
Multiple DOF joints represented by zero-length parameters
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79. Skeleton Hierarchy
Each bone transformation described relative to the parent in the hierarchy:
hips
...
left-leg
r-thigh
r-calf
r-foot
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80. Forward Kinematics
Transformation matrix for a sensor/effecter vs is a matrix composition of all joint transformation between the sensor/effecter and the root of the hierarchy. vs y x z vs vs
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81. Example (1) : Manipulator + 3 Revolute Joints
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82. Example (2) : (1) + Ball-and-Socket Joint
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83. Four link deep appendage with a branch after the second link
The first and third links have two degrees of freedom, the others have one.
The first frame is defined by rotation angles ((0,0),0,[(30,0),-15],[(-30,0),15]
The last frame is defined by rotation angles ((-30,60),-80,[(90,30),-135],[(-90,30),135]
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90. Summary
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