Computer AnimationComputer Animation

Lecture 10

Computer AnimationComputer Animation Animation creates the illusion of life by showing strobed discrete

images which the human visual system reconstructs into a continuous sequence.

Traditional Animation: Artists paint images onto cels (cellulate panels). Important cels are painted by key-frame artists. The intermediate cels are filled in by inbetweeners. Each cel becomes a single frame in a film (60 frames per second). The process is very time consuming and expensive.

Modelling specifies the geometry of 3D scenes and characters. Rendering determines their visual appearance. Animation determines the evolution over time.

Computer animation controls the position and attributes of all virtual entities (characters, objects, scenery, cameras and lights) over time.

Methods: parameter-based animation, motion capture, physically-based animation.

Parameter-based AnimationParameter-based Animation

Key-framing: Animators specify object parameters (position and orientation) at key

frames representing extremes of action.

Inbetweening: Intermeddiate frames generated by interpolation. Animator can control the path (usually a parametric

curve) and interpolation function.

Animation function: Function mapping time to parametric position. Linear (highly unrealistic) Slow-in Slow-out (smooth acceleration/deceleration)

[+] [-]

Fine control Requires experience

Time consuming

Frustrating

Motion CaptureMotion Capture

Real-world position and orientation of objects (particularly people) can be tracked and applied to computer generated characters.

Track predetermined points (called markers or sensors) on the moving entity in order to reconstruct the event digitally.

Capture systems are optical (cameras+markers), electromagentic (attached magnetic sources + receiver) or electromechanical (exoskeleton measuring bend angles).

Widely used in VFX (e.g. digital extras in “Titanic”).

[+] [-]

Realistic Expensive

Not Re-usable

Physically-based AnimationPhysically-based Animation

Kinematics (object control): Describes the position and velocity of points. Forward example: at time the cube is at . Afterwards it moves with

constant acceleration in direction . Inverse example: find the constant velocity required for a cube to reach

after seconds.

Dynamics (cloth, water, fracture simulation): Considers the physical laws (e.g. Newtonian mechanics, Navier-Stokes

equations) governing kinematics. Forward example: a cube has mass of grams. Gravity acts on the cube. Inverse example: find the force required for a cube to reach after

seconds.

t

pv

p

t

mp t

[+] [-]

Automatic Complicated to build and use

Realistic Computationally expensive

Human Figure AnimationHuman Figure Animation

Virtual Actor The CG representation of a character’s motion and appearance.

Motivation:1. Actor must react in real time (e.g. computer games)

2. Actor’s physical form is difficult to realize in reality (e.g. Jar-Jar Binks)

3. Actor must perform impossible or dangerous actions.

4. Actor is to be placed in a computer generated set (avoids green-screening)

5. Actor is a member of a crowd scene (cheap rent-a-crowd).

6. The real actor is unavailable (e.g. Marilyn Monroe in “Rendezvous A Montreal”).

Problem: We are very good at detecting unrealistic humanoid animation.

Skeletal RepresentationSkeletal Representation

Skeleton: Encodes the degrees of motion freedom.

A set of rigid bones linked by ball (3DOF) and hinge (1DOF) joints

Shoulder blade cannot be represented by a single joint because of sliding action.

Spine has 33 vertebrae (96 DOF) which is unwieldy but, due to movement constraints, can be approximated by 2-3 ball joints.

4914315 Freedom of Degrees Total

Skeletal KinematicsSkeletal Kinematics

Kinematics: From a particular joint configuration calculate the relative position and

orientation of any point on the skeleton.

Terminology: Kinematic link (bone), Kinematic chain (sequence of bones and joints) and

End-effector (last link, e.g. hand or foot).

Solution: Each link has a local co-ordinate system and

is embedded in a space provided by the previous link.

Each joint provides a local rotation and each bone a local translation . Concatenating and gives a local transform .

The transformation of a point on link is found by concatenating all previous transforms in the hierarchy:

iiR

iTiR iT

x jiM

xxx 01jj ...MMMM

Inverse KinematicsInverse Kinematics

Specifying pose using joint angles is difficult.

Animators would prefer to position end-effectors directly.

Problem: Given the position and orientation of an end-effector

Find all such that translates by and rotates by .

Underdetermined non-linear system with many solutions.

Example: a hand has constraints ( and ) and unknowns (clavicle , shoulder , elbow , wrist ).

Solutions: Iterative methods: use small changes in joint angles to iteratively converge

on a correct solution.

Closed form algebraic solutions: only exist for particular simplified cases.

Geometric methods: a prismatic joint solution exists for kinematic chains with only three links.

eT eR

iR MeT eR

6 eT eR 103 3 1 3

Reducing Kinematic FreedomReducing Kinematic Freedom

The degrees of kinematic freedom can be reduced by enforcing “realistic” motion.

Realism rules for human motion:1. Motion tends to be energy minimal (but this doesn’t account for

expressive gestures).

2. Collisions must not occur (muscles and skin surrounding the kinematic bones cannot intersect).

3. Joint limits must be maintained (e.g. elbows don’t bend backwards)

4. Feet in contact with the floor maintain their position unless lifted.

Solutions which obey these realism rules are often even more difficult to find.

Inverse Kinematics ExerciseInverse Kinematics Exercise Given a simple robot arm with the following characteristics:

Two joints, a shoulder joint and an elbow joint. The shoulder joint is connected by a 2-unit length upper arm to the elbow joint, which in turn is connect by a single unit lower arm to the hand.

The joints can rotate only in the -plane. The shoulder joint is attached to a -axis vertical slider, which can

raise or lower the entire robot arm, but is not able to translate it in the -plane.

The initial position of the arm is: shoulder joint (origin with rotation), elbow joint (position with rotation), hand (position )

There is a soft drink can located at position . The robot hand must touch this can. What transformations must the joints undergo to achieve this. Assume a hierarchy of local transformations.

xyz

xy0

)0,0,2( 0)0,0,3(

)1,1,1(

Inverse Kinematics SolutionInverse Kinematics Solution

Cosine Rule:

Shoulder translation:

Shoulder rotation:

Elbow rotation:

)1,0,0(

11.17

89.27coscos

45

222

42112

2221

BC

CBAa

a

aBCCBA cos2222

59.138

41.41coscos

180

212

41212

2221

AC

CABb

b

DynamicsDynamics Simulate skeleton as a set of jointed rigid bodies, each with mass and

intertia, subject to forces arising from muscle action and body collision. Dynamic simulation of human musculature is non-trivial because of

counteracting forces throughout the body. In practice use of kinematics dominates.

Hill’s three component muscle model:1. Contractile elements (muscle fibres)

2. Series elastic element (muscle tendon)

3. Parallel elastic element (connective tissue around fibres)

Energy stored in the parallel element as conctractile element tenses.

Dynamics can provide: Movement which obeys physical properties (gravity, human musculature

and mass distribution). Visual simulation of muscle bulging and skin contraction. Simulation of the behaviour of clothes during movement.

Particle DynamicsParticle Dynamics Energy and Forces

Can be internal (stretch and compression) or external (gravity). Example: stiff spring forces between particles belonging to the same piece

of cloth.

Constraints Particles can be attached to a point or constrained to lie on a plane. The constraints may move over time. Example: a table cloth pinned at a corner.

Collisions Collisions between objects must be detected and a compensating force

calculated. Example: cloth particles interpenetrating the cloth surface are repulsed by

a strong damping force.

Iterative Solutions Given the mass, position, active forces of a set of particles the acceleration

of particles is calculated using an adaptive time-step approach.

Camera Animation: Bullet TimeCamera Animation: Bullet Time

Bullet time effect: the camera rotates while the action remains frozen or unfolds in ultra-slow

motion (12000 frames per second). Employed in “The Matrix”.

Technique: Actor on wire harness performs the action

against a green-screen background. Still 35mm cameras arranged along a curved path

capture the scene. They can be fired sequentially with variable millisecond delays (slow motion) or all at once (frozen time).

The camera position, orientation and focus are pre-visualized in a virtual environment.

Once the scene is shot, morphing software interpolates between images.

Computer-composited backgrounds stitched from photographic images are superimposed.

SummarySummary

Human figure animation is a fundamental challenge in computer animation.

Animation Techniques:

Parameter-based Motion Capture Physically-based

Computer Time

(Machine Hours)

Low

(low level control)

Medium

(marker tracking)

High

(complex simulation)

Human Time

(Man Hours)

Very High

(painstaking)

Medium

(acting the scene)

Low

(specify constraints and external forces)

Expressive Power High

(animator imparted)

High

(expressive acting)

Low

(human emotion not considered)

Realism Medium

(realism difficult to recreate)

High

(data captured from reality)

Med

(only approximate)

Course TimetableCourse Timetable

30 April Video: “Story of Computer Graphics”

2 May Computer Animation

4 May Guest Lecture 1: S. Nirenstein (Phd Student), “Visibility Culling”.

7 May Guest Lecture 2: R. Southern (MSc Student), “Multiresolution Methods”.

9 May Seminar 1: J. Welsh and G. Marshall

11 May Seminar 2: C. Li

15 May Seminar 3: G. Barlow and B. van Swelm

16 May Seminar 4: G. Oberholster and J. Lewis, “BSP Trees”

18 May Seminar 5: R. Neeser and P. Smeddle, “BRDF Lighting”