GAMES101 Lecture 21 - Animation

GAMES101_Lecture_21.pdf

Outline

History
Keyframe Animation
Physical Animation
Kinematics
Rigging

Animation

Bring things to life.

Communication tool
Aesthetic issues often dominate technical issues

An extension of modeling

Represent models as a function of time

Output: A sequence of images that when viewed sequentially provides a sense of motion.

Film: 24 frames per second (usually with motion blur)
Video (in general): 30 fps (usually with motion blur)
Virtual reality: 90 fps

I. History

First Animation (Shahr-e Sukhteh, Iran 3200 BCE)
Phenakistoscope (1831): By showing part of a rotating disk:
First Film (Edward Muybrdige, "Sallie Gardner", 1878): Used as scientific tool rater than for entertainment
First Hand-Drawn Feature-Length (>40 mins) Animation (Disney, "Snow White and the Seven Dwarfs", 1937)
First Digital-Computer-Generated Animation (Ivan Sutherland, "Sketchpad", 1963): Light pen, vector display
Early Computer Animation (Ed Catmull & Frederick Parke, "Computer Animated Faces", 1972)
Digital Dinasours ("Jurassic Park", 1993)
First CG Feature-Length Film (Pixar, "Toy Story", 1995)
- Milestone
- Rasterization only
Computer Animation - 10 Years Ago (Sony Pictures Animation, "Cloudy With a Chance of Meatballs")
Computer Animation - 2019 (Walt Disney Animation Studios, "Frozen 2", 2019)
- Plants, after effects, ...

II. Keyframe Animation

Animator (e.g. lead animator) creates keyframes
Assistant (person or computer) creates in-between frames
- tweening

Keyframe Interpolation

Each frame is seen as a vector of parameter values
- Linear interpolation is usually not good enough
- Splines for smooth/controllable interpolation

III. Physical Simulation

F = m a

Introduction

Δ x = v Δ t + \frac{1}{2} (Δ t)^{2} a

Building the correct physical model leads to correct physical simulation.

Macklin and Müller, Position Based Fluids

Mass Spring System: Example of Modeling a Dynamic System

Mass Spring Rope,
Hair,
Mass Spring Mesh (Cloth)

Spring with Internal Damping

One type of spring-mass system with damping:

f_{a \to b} = k_{s} \frac{(b - a)}{‖ b - a ‖} (‖ b - a ‖ - l)

\begin{matrix} \underset{\begin{matrix} Damping force \\ applied on b \end{matrix}}{\underset{⏟}{f_{b}}} = - k_{d} \underset{\begin{matrix} Relative speed projected \\ to the direction from a to b \end{matrix}}{\underset{⏟}{\frac{b - a}{‖ b - a ‖} \cdot (\dot{b} - \dot{a})}} \cdot \underset{\begin{matrix} Direction from \\ a to b \end{matrix}}{\underset{⏟}{\frac{b - a}{‖ b - a ‖}}} \end{matrix}

$\boldsymbol{a}$ $\boldsymbol{b}$ $\boldsymbol{a}$ ).

In this type of damping, the resistance is proportional to the relative velocity on projected direction.

$k_s$ - stiffness
$l$ - rest length
$\dot{\boldsymbol{b}}$ $\dot{\boldsymbol{a}}$ - velocity
$k_d$ - damping coefficient

Structures from Springs

Behavior is determined by structure linkages
Resistance to shearing and out-of-plane bending.
- Red springs should be much weaker.

Finite Element Method

Particle Systems

Model dynamical systems as collections of large numbers of particles

Dynamical - involving modeling particles described by differential equations.
Each particle's motion is defined by a set of physical (or non-physical) forces
Easy to understand and implement
Scalable: fewer particles for speed, more for higher complexity

Challenges:

May need many particles (e.g., fluids)
May need acceleration structures (e.g. to find nearest particles for interactions)

For each frame in animation

[If needed] Create new particles
Calculate forces on each particles
Update each particle's position and velocity
[If needed] Remove dead particles
Render particles

Examples

Fluid
Flocking
Molecular Dynamics
...

Particle System Forces

Attraction and repulsion forces

Gravity, eletromagenetism, ...
Springs, propulsion, ...

Damping forces

Friction, air drag, viscosity, ...

Collisions

Walls, containers, fixed objects, ...
Dynamic objects, character body parts, ...

Gravitational Attraction

\begin{matrix} (Newton’s Universal Law of Gravitation) & F_{g} = G \frac{m_{1}}{m_{2}} d^{2} \end{matrix}

Gravitational pull between particles
$G = 6.67428 \times 10^{-11} \text{Nm}^2\text{kg}^{-2}$

Simulated Flocking as an ODE

Forward Kinematics

Forward Kinematicsend effector $p$ , given the known joint angles and angular velocities.

Articulated Skeleton

Topology (what's connected to what)
Geometric relations from joints
Tree structure (in absence of loops)

Joint Types

Pin (1D rotation)
Ball (2D rotation)
Prismatic joint (translation)

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Pros

Direct control is convenient
Implementation is straightforward

Cons

Animation may be inconsistent with physics
Time consuming for artists

Inverse Kinematics

Inverse Kinematicsthe position of the end effector $p$ , calculate the variable joint parameters needed to place the end of a kinematic chain, such as a robot manipulator or animation character's skeleton, in a given position and orientation relative to the start of the chain. (Wikipedia)

Multiple solutions in configuration space
Solutions may not always exist

Numerical Solution to general N-Link IK Problem

Choose an initial configuration
Define an error metric (e.g. square of distance between goal and current position)
Compute gradient of error as function of configuration
Apply gradient descent or other optimization procedure

Rigging

Rigging: A set of higher level controls on a character that allow mroe rapid & intuitive modification of pose, deformations, expressions, etc.

Captures all meaningful character changes
Varies from character to character

Expensive to create

Manual effort
Requires bth artistic and technical training

Blend Shapes

Courtesy: Félix Ferrand

Instead of skeleton, interpolate directly between surfaces

Interpolate vertex positions
Splines used to control choice of weights over time

Motion Capture

Motion capture room for ShaqFu

Record real-world performances, extract pose as a functin of time from data collected and apply them to a model.

Optics
Magnetic: Infer position/orientation by sensing magnetic fields
Mechanical: Measure motion directly

Strengths

Can capture large amounts of real data quickly
Realism can be high

Weaknesses

Complex and costly set-ups
Captrued animation may not meet artistic needs, requiring alterations

Facial Motion Capture

Discovery, "Avatar: Motion Capture Mirrors Emotions", https://youtu.be/1wK1Ixr-UmM

Challenge of Facial Animation

Uncanny Valley