Things that can evolve in the animation:

• objects
• camera
• light sources

Types of animation:

• flip-book
• key-frame

Object Animation
Things that can change for an object:

• position
• orientation (vehicle on the road)
• size (grow or shrink)
• form (morphing)
• color (blushing)
• transparence (fluids)

For a light source:position, orientation, intensity

For the camera:position, look-at point (point of interest), view angle.

Frame

• The effect of motion is obtained by displaying still images (frames) so fast that the eye cannot process them separately.
• Standard frame rate: 24 frames / second.
• Computer screen: 30 - 60 frames / second.
• Real-time animation: the program is capable of displaying the new frames so fast that the viewer sees the action as it happens (games, scientific visualization).
• Frame-by-frame animation: the image is rendered, recorded, and the compiled animation can be projected afterwards (motion picture, cartoons).

Camera Movements

• Still camera: the projection center and plane (pov) are fixed, the image is moving.
• Subjective camera: the projection center and plane are moving. Can be simulated by applying transformations to the entire scene.
• Typical application: the roller coaster animations, first person games.
• Any combination of the two.

• Geometrical scene defined as the state of the system
• state_of_the_system(t + dt) = F(state_of_the_system(t), dt)
• state_of_the_system = F(t)

• Frame-by-Frame (flip-book): compute each frame separately.
• Traditional animation technique.
• Common method in scientific visualization.
• Simulates the behavior of dynamic systems.
• dt small enough to pass from one distinct frame to the next.

• Key-frame animation: compute a number of key frames, then interpolate in between.
• Computer-aided animation.
• Interpolation:
• between object position, achieved by interpolating the object-space transformations, includes interpolating the camera position,
• between the object form: 3D morphing,
• between resulting 2D images : 2D morphing.
• dt much bigger

• Consider one key frame scene (t₁), and the next one scene ( t₂ = t₁ + dt). We want to generate nf frames in between the two key frames.
• We define the frame number i corresponding to the time t₁ + i * dt / nf.
• Linear interpolation:
•  a = i / nf
• scene (t_i) = (1 - a) scene (t₁) + a scene ( t₂)
• Objects move in straight lines.
• C_n interpolation: we want the derivative of order n of the interpolated function to be continuous. Object movements appear smooth.
• Usually C₁ or C₂.

Character Animation

Any animation of a skeleton-based deformable object.

The skeleton devises a hierarchical structure for the object that is usually represented as a scene graph.

Types of character animation:

• direct kinematics
• inverse kinematics
• motion capture
• manual key-framing

Walking

• Alternating the support and swing phases
• The legs and hands are coordinated
• The motion is near periodic
• The need for realism is high

Facial Animation

• Facial expressions, speech.
• Uses different models than the body animation.
• The face is usually represented as a mesh with higher density in regions more likely to move.
• The animation is achieved by mesh deformation.
• Some key points on the figure serve as reference for the movement. These points are moved to achieve an expression and the rest of the mesh adapts to it.