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COMP 304 Computer Graphics II

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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) © M. Gokturk

3 © M. Gokturk

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 © M. Gokturk

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 © M. Gokturk

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 © M. Gokturk

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 © M. Gokturk

8 Conventional Animation Process
© M. Gokturk

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 © M. Gokturk

10 3D Animation 3D animation is similar to stop motion animation
King Kong (1932) Flash Gordon (1972) © M. Gokturk

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? © M. Gokturk

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 © M. Gokturk

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) © M. Gokturk

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 © M. Gokturk

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 © M. Gokturk 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. © M. Gokturk

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 ://www.ai.mit.edu/projects/leglab/ © M. Gokturk

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: © M. Gokturk

19 Noise Motion Motion capture (natural noise!) © M. Gokturk

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. © M. Gokturk

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. © M. Gokturk

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. © M. Gokturk

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. © M. Gokturk

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. © M. Gokturk

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 © M. Gokturk

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 © M. Gokturk

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 © M. Gokturk

28 © M. Gokturk

29 © M. Gokturk

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 © M. Gokturk

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 © M. Gokturk

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 © M. Gokturk

33 © M. Gokturk

34 Path Following u = P’(u) x P’’(u) w = P’(u) P’’(u) v = w x u
Frenet Frame © M. Gokturk

35 Curvature continuity =0 © M. Gokturk

36 Look ahead © M. Gokturk

37 Define “look-at” vector
© M. Gokturk

38 Define “up” vector © M. Gokturk

39 © M. Gokturk

40 © M. Gokturk

41 © M. Gokturk

42 © M. Gokturk

43 Kinematics X Dynamics © M. Gokturk

44 Kinematics © M. Gokturk

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 © M. Gokturk

46 © M. Gokturk

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 © M. Gokturk

48 Some robotics is required !
© M. Gokturk

49 © M. Gokturk

50 © M. Gokturk

51 Drawing Articulated Figures
© M. Gokturk

52 Static Figure Transformations
© M. Gokturk

53 Forward Kinematics Control
© M. Gokturk

54 Example: 2-Link Structure
© M. Gokturk

55 Forward Kinematics © M. Gokturk

56 Forward Kinematics © M. Gokturk

57 Forward Kinematics © M. Gokturk

58 Forward Kinematics © M. Gokturk

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 © M. Gokturk

60 © M. Gokturk

61 Forward Kinematics T data R S © M. Gokturk

62 Transformations at the arcs
User modifies Rotation (new “pose vector”) Re-traverse tree To get new “pose” © M. Gokturk

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 © M. Gokturk

64 Joint Representation q Degree of Freedom DOF Joint Limits © M. Gokturk

65 Joint Representation Multiple Degrees of Freedom Joint Limits q
y w Degrees of Freedom Joint Limits gimbal lock Axis-angle quaternions © M. Gokturk

66 Joint Representation Note
q y w Note User interface representation may not be the same used for internal representation and operations © M. Gokturk

67 © M. Gokturk

68 Drawing Articulated Figure
© M. Gokturk

69 © M. Gokturk

70 © M. Gokturk

71 © M. Gokturk

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 © M. Gokturk

73 © M. Gokturk

74 © M. Gokturk

75 © M. Gokturk

76 © M. Gokturk

77 © M. Gokturk

78 © M. Gokturk

79 Skeleton Hierarchy Each bone transformation described relative to the parent in the hierarchy: hips ... left-leg r-thigh r-calf r-foot © M. Gokturk

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 © M. Gokturk

81 Example (1) : Manipulator + 3 Revolute Joints
© M. Gokturk

82 Example (2) : (1) + Ball-and-Socket Joint
© M. Gokturk

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] © M. Gokturk

84 © M. Gokturk

85 © M. Gokturk

86 © M. Gokturk

87 © M. Gokturk

88 © M. Gokturk

89 © M. Gokturk

90 Summary © M. Gokturk


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