Computer Animation

1. Computer Animation Lecture 10

2. Computer 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.

3. Parameter-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)

4. Motion 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”).

5. Physically-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.

6. Human Figure Animation • Virtual Actor • The CG representation of a character’s motion and appearance. • Motivation: • Actor must react in real time (e.g. computer games) • Actor’s physical form is difficult to realize in reality (e.g. Jar-Jar Binks) • Actor must perform impossible or dangerous actions. • Actor is to be placed in a computer generated set (avoids green-screening) • Actor is a member of a crowd scene (cheap rent-a-crowd). • The real actor is unavailable (e.g. Marilyn Monroe in “Rendezvous A Montreal”). • Problem: • We are very good at detecting unrealistic humanoid animation.

7. Skeletal 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.

8. Skeletal 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:

9. Inverse 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.

10. Reducing Kinematic Freedom • The degrees of kinematic freedom can be reduced by enforcing “realistic” motion. • Realism rules for human motion: • Motion tends to be energy minimal (but this doesn’t account for expressive gestures). • Collisions must not occur (muscles and skin surrounding the kinematic bones cannot intersect). • Joint limits must be maintained (e.g. elbows don’t bend backwards) • Feet in contact with the floor maintain their position unless lifted. • Solutions which obey these realism rules are often even more difficult to find.

11. Inverse 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.

12. Inverse Kinematics Solution • Cosine Rule: • Shoulder translation: • Shoulder rotation: • Elbow rotation:

13. Dynamics • 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: • Contractile elements (muscle fibres) • Series elastic element (muscle tendon) • 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.

14. Particle 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.

15. Camera 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.

16. Summary • Human figure animation is a fundamental challenge in computer animation. • Animation Techniques:

17. Course 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”