Animation

#comp37111

Overview

• Animation is mostly an extension of modelling where we try to represent a model as a sequence of images which when viewed sequentially gives us a sense of motion.
• Film requires 24 fps, video 30 fps and VR 90 fps.
• Artist driven animation: rigging, skinning and posing
  • Rigging is the process of building such controls.
    • Forward kinematics describes position of body parts as a function of joint angles. Given angles determine end effector
    • Inverse kinematics. Given end effector determine joint angles.
  • Skinning: (Skeleton Subspace Deformation) Inferring how skin deforms with bone transformations.
    • We usually connect a vertex with multiple bones and define the movement as a weighted combination.
      • weights must be non-negative
      • sum over all bones must be unity for every vertex
    • $p_{ij}^{\prime }=T_j{B}_j^{-1}{p}_i$ ; $p_i$ bind pose (rest) $B_j$ bone transformation matrix; $T_j$ transformation matrix
      • $T_j\times B_j^{-1}$ is the relative change between the current pose and the bind pose
• Data driven animation: motion capture
  • records real world and extracts poses as a function of time using optical markers and multiple high speed cameras
  • Retargeting: Marker positions from motion capture must be translated into character controls.
• Procedural animation: describing the motion algorithmically and describing the motion using a small number of parameters
• Fundamental concepts in animation:
  • Squash and Stretch
  • Timing
  • Key Framing (Specify only certain frames and then generate the ones in between, this generation is called tweening)
• Animation is defined using some low dimensional form of control rather than redefining geometry such as joint angles.

Physics Based Animation

• Assign physical properties to objects ex: mass, force, gravity and procedural forces such as wind
• With these properties we then simulate physics by solving equations of motion

1. Particle Systems

• points are generated using emitters
• all points are independent of each other

2. Mass Spring Model

• generalised variant of particle systems
• surface is represented as a set of points which is kept coherent using the forces between neighbouring points
• These could be modelled using Newtonian Mechanics or Euler's Method (approximate at each step)
• Sometimes we add damping to stabilise the solver (for the equations)
• Sometimes there also exists spatial fields, which are predefined external forces acting on particles depending on their location
• Types of forces:
  • Structural Forces: Enforce invariance in the system like distance between two points
  • Internal Deformation Forces
  • External Forces: gravity, friction, air resistance

Simulation

• Rigid Body Simulation:
  • Different from particles in the sense that apart from the location (3 DOF x,y,z for a particle), rigid body simulations act on geometries that also have orientation (6 DOF x,y,z + rotation along the axes).
  • A common approach is to use impulse based collision (based directly on velocity)
  • We also define a rest state for the object at which point we don't simulate any forces between surfaces. (avoids unnecessary vibrations when at rest)
  • Stacking: when you stack rigid bodies on top of each other (duh)
• Deformable Body Simulation:
  • A common approach is to use Finite Element Method (FEM)
    • Convert mesh to tetrahedral (tetrahedralisation) because its the simplest 3D object
    • FEM allows to compute forces to go from deformed to rest shape
• Mass-spring systems can also be used for fracture simulation i.e. if the force passes a threshold the springs break with some propagation to the nearby springs
• Fluid Simulation:
  • Common approach is particle-based fluid simulation solved using Lagrangian methods.
  • Grid-based fluid solution involves analysing the voxels of the bounding box surrounding the fluid. These are modelled using Eulerian methods.
  • Lagrangian + Eulerian = Hybrid Fluid Simulation

Collisions

• geometry of the colliding object is the main factor in choosing which algorithm to use
• It's easy to find intersection points using equations for surfaces (if equation is zero then on surface, less than zero inside surface, ....)
• Collision Response: Model changes in body after collision
• Intersection is usually detected late, i.e. already inside the surface, in this case we usually perform backtracking
• Another method fixing involves project the the object to the closest point on the surface
• Collision detection has complexity $N^2$ for $N$ objects
• Bounding Volumes: find intersection between bounding boxes that contain the objects
  • commonly used AABB (Axis Aligned Bounding Box), Sphere, OBB (Oriented Bounding Box) and k-DOP (k-Discrete Bounding Box)