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projects in digital art • animation © 2009 fabio pellacini • 1
animation
projects in digital art • animation © 2009 fabio pellacini • 2
animation
shape specification as a function of time
projects in digital art • animation © 2009 fabio pellacini • 3
how animation works?
• flip very fast a set of fixed images • perceived as motion by our visual system
• how many images per second? – should be above flicker fusion: > 60 Hz – NTSC TV signal: 60 half-frames per second – movies: 24 fps repeated 3 times
projects in digital art • animation © 2009 fabio pellacini • 4
motion blur
• avoid strobing effects (aliasing over time)
[Coo
k et
al.,
1984
]
projects in digital art • animation © 2009 fabio pellacini • 5
principles of animation
• squash-and-stretch
[Las
site
r, 19
87]
projects in digital art • animation © 2009 fabio pellacini • 6
principles of animation
• squash-and-stretch
slow motion
fast motion
fast motion w s.s.
[Las
site
r, 19
87]
projects in digital art • animation © 2009 fabio pellacini • 7
principles of animation
• timing
[Las
site
r, 19
87]
projects in digital art • animation © 2009 fabio pellacini • 8
principles of animation
• anticipation
[Las
site
r, 19
87]
projects in digital art • animation © 2009 fabio pellacini • 9
movie time
luxo jr.
projects in digital art • animation © 2009 fabio pellacini • 10
animation representation
• many ways to represent changes with time
• depends on intent – artistic motion – physically-plausible motion
projects in digital art • animation © 2009 fabio pellacini • 11
animation editing
• different techniques for different processes
• key-framing – describe key poses, interpolate the rest – man-made process: laborious but artistic – good for characters
• procedural animation – motion expressed algorithmically – good for small secondary motion or special effects
• e.g. clock animation
projects in digital art • animation © 2009 fabio pellacini • 12
animation editing
• different techniques for different processes
• motion capture: – reproducing performances – good for character, but requires lots of hand-tuning
• physically-based simulation – assign physical properties – simulate physics – realistic, but difficult to set up and control style
projects in digital art • animation © 2009 fabio pellacini • 13
representing changes
• one frame-at-a-time – inefficient and cumbersome
• key-frame animation – define key poses – interpolate in the middle
projects in digital art • animation © 2009 fabio pellacini • 14
key-frame animation
• used in 2d hand-drawn animation – head animators define key poses – inbetweeners define intermediate poses
• same conceptual framework – animator defines key poses – computer interpolates intermediate poses
projects in digital art • animation © 2009 fabio pellacini • 15
key-frame animation
[Las
site
r, 19
87]
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key-frame interpolation
• how to define interpolating function – choose smooth curve formulation: splines – not controlled by the key-frame themselves
• can only add more keyframes if things go wrong
– acceleration depends on interpolating functions
[Lassiter, 1987]
projects in digital art • animation © 2009 fabio pellacini • 17
key-frame animation
• what to interpolate? – shape are defined by control points
• too many controls for animation purposes
– express deformation with meaningful parameters • deformation: changes in shape
• degrees of freedom – modeling: number of control points – animation: parameters of deformations – ui: parameters of manipulators – use smallest number of degrees of freedom
projects in digital art • animation © 2009 fabio pellacini • 18
key-frame animation visualization
• feedback comes in various forms – animation playback – parameter curve – ghosting
time
valu
e
projects in digital art • animation © 2009 fabio pellacini • 19
inheriting vs. constraining
• hierarchical transformations are inherited – children can completely change their transform – useful as a UI technique to speed up the setup
• sometimes we want to enforce constraints – e.g. feet on the ground – various kinds exists – hard to mix with other animation sources – will not cover in depth
projects in digital art • animation © 2009 fabio pellacini • 20
constraints on hierarchies
• reduce degrees of freedom of child transform
• robot arm example
projects in digital art • animation © 2009 fabio pellacini • 21
constraints on hierarchies
• sliding joints
• rotational joints
projects in digital art • animation © 2009 fabio pellacini • 22
animating a stick-figure/skeleton
• bones do not deform – can be represented by rigid body transformations
• hierarchies can be naturally applied – e.g. hand parented to arm, foot to leg, etc.
• constraints to avoid unrealistic motion – only rotational joints – most rotations have limited angles, e.g. knee
• we have a very good model for stick figure animation!!!
projects in digital art • animation © 2009 fabio pellacini • 23
providing deformation parameters
• kinematics – provide transformation parameters directly – hand-editing
• forward kinematics • inverse kinematics
– motion capture
• dynamics – solve physics equations of motion
projects in digital art • animation © 2009 fabio pellacini • 24
forward kinematics
• artists defines transformation parameters directly
• hierarchical transformations – used for bone structures in character animation
• e.g. skeletons or robots
– hard to define what happens at end of chains • e.g. which angles should the leg be to have the foot touch
the floor? • done by trial and error
projects in digital art • animation © 2009 fabio pellacini • 25
forward kinematics
• position at end of the chain
projects in digital art • animation © 2009 fabio pellacini • 26
inverse kinematics
• specify directly the position at the end of chain – easier to control motion, less trial and error – joints angles solutions by inverting previous eqs.
projects in digital art • animation © 2009 fabio pellacini • 27
inverse kinematics
• more bones results in under-constrained system – infinite number of solutions – which solution to pick? – impose constraints: minimize energy function based
on plausible motion
projects in digital art • animation © 2009 fabio pellacini • 28
inverse kinematics
• or try to capture “styles” – by learning from data sets
[Gro
chow
et
al.,
2004
]
projects in digital art • animation © 2009 fabio pellacini • 29
review: forward kinematics
• top-down method – begin by positioning and rotating parent objects – then position and rotate child objects
• uses a hierarchical linking from parent to child – pivot points define joints between objects
• children inherit the transforms of their parents
projects in digital art • animation © 2009 fabio pellacini • 30
review: inverse kinematics
• bottom-up method – position a goal location for a joint – IK solver determines the transforms for all parents
• uses a hierarchical linking from parent to child – pivot points define joints between objects – joints can be limited by constraining positional and
rotational degrees of freedom
• child transforms affect parents’ ones – depending on goal systems, constraints and defaults
projects in digital art • animation © 2009 fabio pellacini • 31
forward vs. inverse kinematics
• forward kinematics – more laborious approach (needs lots of keyframes) – less setup (since does not require proper joints) – more control over final look
• inverse kinematics – way less work – more setup – a lot less control – new style-based IK systems soon available
projects in digital art • animation © 2009 fabio pellacini • 32
motion capture
• record motion and play it back – how to record: motion capture systems – how to apply motion to digital characters
• motion editing • motion retargeting
projects in digital art • animation © 2009 fabio pellacini • 33
motion capture usage
• heavily in games, a bit in movies – not very expressive, but more high expectation
[© S
ony]
projects in digital art • animation © 2009 fabio pellacini • 34
motion capture systems [©
Ani
maz
oo]
[Pop
ovic
]
mechanical optical
projects in digital art • animation © 2009 fabio pellacini • 35
motion capture editing
• motion capture generates too much raw data – how to edit it? try to fit with lower DOFs models
• motion retargeting – capture from actor A, but apply to actor B – how to do this in a believable manner?
• clean up motion – noise present in data / too little DOFs – how to clean it up?
• often just starting point for manual animation
projects in digital art • animation © 2009 fabio pellacini • 36
kinematics vs. dynamics • kinematics: specify parameters directly • dynamics: solve the equations of motion
– physically based animation
• rigid body dynamics – solve rigid body equations – collision detection – doable in many cases
• more complex cases almost impossible – cannot model physics accurately enough – simply for good-enough solutions
projects in digital art • animation © 2009 fabio pellacini • 37
dynamics
• animation from dynamics is accurate – since we are simulating physics
• at the price of less artistic freedom – cartoon physics anyone?
• control-vs-correctness triage often hard – interests in mixing dynamics with kinematics – open research issue
projects in digital art • animation © 2009 fabio pellacini • 38
dynamics
• simulating simple objects
[Fed
kiw
et
al.]
projects in digital art • animation © 2009 fabio pellacini • 39
dynamics
• simulating complex situations
[Fed
kiw
et
al.]
projects in digital art • animation © 2009 fabio pellacini • 40
dynamics
• simulating complex objects
[Fed
kiw
et
al.]
projects in digital art • animation © 2009 fabio pellacini • 41
dynamics
• simulating complex objects
[Fed
kiw
et
al.]
projects in digital art • animation © 2009 fabio pellacini • 42
controlling dynamics
• basic principle: cheat where you can
[Pop
ovic
et
al.,
2003
]
projects in digital art • animation © 2009 fabio pellacini • 43
movie time
for the birds
projects in digital art • animation © 2009 fabio pellacini • 44
natural phenomena
• often done by physical simulation – looks like computational physics
• simulation domain – choose based on phenomena to define – e.g. smoke uses volumetric adaptive grids – e.g. cloth uses points/springs systems
• simulation algorithms – very different ones depending on simulation domain
• lots of open research
projects in digital art • animation © 2009 fabio pellacini • 45
natural phenomena
[Fed
kiw
et
al.]
projects in digital art • animation © 2009 fabio pellacini • 46
natural phenomena
[Fed
kiw
et
al.]
projects in digital art • animation © 2009 fabio pellacini • 47
natural phenomena
[Fed
kiw
et
al.]
projects in digital art • animation © 2009 fabio pellacini • 48
natural phenomena
[Fed
kiw
et
al.]
projects in digital art • animation © 2009 fabio pellacini • 49
particle systems
• collection of particles – simple, since it is just simulating point dynamics – used heavily in special effects
• complex phenomena represented as point/force collections
– simplest dynamics formulation
• point properties – dynamics: position/velocity/acceleration – varying properties: color/temperature/lifespan – constant properties: mass/lifetime
projects in digital art • animation © 2009 fabio pellacini • 50
particle systems
• for each frame – create new random particles
• where to create? along point/line/surface • artistic control
– delete expired particles • random/lifespan/collision
– update particles based on dynamics – render particles
projects in digital art • animation © 2009 fabio pellacini • 51
particle dynamics
• Newton equation
• find position at time t – given position, velocity and acceleration at time 0 – initial value problem: use Euler method
• more efficient methods exist
projects in digital art • animation © 2009 fabio pellacini • 52
particle systems example
[Ree
ves,
1983
]
projects in digital art • animation © 2009 fabio pellacini • 53
particle systems example
[Ree
ves,
1983
]
projects in digital art • animation © 2009 fabio pellacini • 54
particle systems example
[Ree
ves,
1983
]
projects in digital art • animation © 2009 fabio pellacini • 55
particle systems example
[Ree
ves,
1983
]
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