Advanced Computer Animation

Group Behaviors

Group Behaviors : Motivation

Many animations require natural-looking behavior from a large number of characters Flock of birds School of fish Crowd of people

What is a flock?

One definition: a group of birds or mammals assembled or herded together

“A flock is simply the result of the interaction between the behaviors of individual birds.”

Why model flocking?

It looks cool Difficult to animate using traditional keyframing

or other techniques Hard to script the path Hard to handle motion constraints Hard to edit motion

Boids!

“boids” comes from “bird-oids” Similar to particle systems, but have orientation Have a geometric shape used for rendering Behavior-based motion

Boid motion

Boids have a local coordinate system The boid itself can move only in one direction (“forward” alon

g its local positive z-axis) The boid steers by rotating about its local x and y axes The boid’s local coordinate system can move and rotate free

ly within world coordinates

Modeling flocking behavior

Modeling flocking behavior Three basic rules, each of which generates an acceleration requ

est

1. Collision AvoidanceAvoid running into other boids or static obstacles

2. Velocity MatchingMatch velocity with nearby flockmates

3. Flock CenteringStay close to nearby flockmates

Flocking – 3 Behaviors (1)

Collision avoidance: avoid collisions with nearby flockmates

Flocking – 3 Behaviors (2)

Velocity matching: attempt to match velocity with nearby flockmates

Flocking – 3 Behaviors (3)

Flock centering: attempt to stay close to nearby flockmates

Flocking Neighborhood

Neighborhood defining the region in which flockmates influence a boids ste

ering characterized by a distance and an angle

• Distance: measured from the center of the boid

• Angle: measured from the boid's direction of flight.

Flockmates outside this local neighborhood are ignored.

Avoiding obstacles (1)

Force field approach Obstacles have a field of repulsion (반발력 ) Boids increasingly repulsed as they approach obstacle

Drawbacks: Approaching a force in exactly the opposite direction Flying alongside a wall

Avoiding obstacles (2)

Steer-to-avoid approach Boid only considers obstacles directly in front of it Finds silhouette edge of obstacle closest to point of eventual

impact A vector is computed that will aim the boid at a point one

body length beyond the silhouette edge

Avoiding Environmental Obstacles

Demo

simulated boid flock avoiding cylindrical obstacles (1986)

Steering Behaviors

Simple behaviors for individuals and pairs: Seek and Flee Pursue and Evade Wander Arrival Obstacle Avoidance Containment Wall Following Path Following Flow Field Following

Combined behaviors and groups: Crowd Path Following Leader Following Unaligned Collision Avoidance Queuing (at a doorway) Flocking (combining: separation, alignment, cohesion)

Reference (Behavior Animation)

http://www.red3d.com/cwr/boids/

Fluid Simulation

Fluid Simulation

Heightfield Fluids A very simple program Physics background Object interaction

Particle Based Fluids Simple particle systems Smoothed Particle Hydrodynamics (SPH)

Offline Fluid Simulation

State of the art is impressive! Typical grid size 2563 cells Linear system with 16 million unknowns! Raytracing (reflection / refraction / caustics) Photorealistic results 10 seconds – 50 minutes per frame!

Reducing Computation Time

Reduce resolution Simple (use same algorithms) Results look blobby and coarse, details disappear

Invent new methods Reduce dimension (e.g. from 3d to 2d) Use different resolutions for physics and appearance Simulate only in interesting, active regions (sleeping) Camera dependent level of detail (LOD) Non-physical animations for specific effects

Solutions

Procedural Water Unbounded surfaces, oceans

Heightfield Fluids Ponds, lakes

Particle Systems Splashing, spray, puddles, smoke

Procedural Animation

Simulate the effect, not the cause [Bridson07], [Yuksel07], [Fournier86], [Hinsinger02]

No limits to creativity E.g. superimpose sine waves

Difficult but not impossible Fluid – scene interaction

Heightfield Fluids

Represent fluid surface as a 2D function u(x,y) Pro: Reduction from 3D to 2D Cons: One value per (x,y) → no breaking waves

Water Rendering

Reflection

Refraction

Caustics: Cheating - Animated texture

a caustic is the envelope of light rays reflected or refracted by a curved surface or object

Particle Based Fluids

Particle systems are simple and fast Without particle-particle interaction

Spray, splashing

With particle-particle interaction Small puddles, blood, runnels Small water accumulations

Simple Particle Systems

Particles store mass, position, velocity, external forces, lifetimes

Integrate

Generated by emitters, deleted when lifetime is exceeded

Particle-Particle Interaction

Particle-Particle Interaction No interaction → decoupled system → fast For n particles O(n2) potential interactions! To reduce to linear complexity O(n)

define interaction cutoff distance h

Smoothed Particle Hydrodynamics (SPH)

Smoothed Particle Hydrodynamics Invented for the simulation of stars [Monaghan92] Often used for real-time fluids in CG [Müller03] Dividing the fluid into a set of discrete "fluid elements". Use scalar kernel function W(r)

• Wi(x) = W(|x-xi|)

Fluid Simulation Demo

www.cs.ubc.ca/~rbridson/fluidsimulation/

Reference (Fluid Simulation)

[Becker07] M. Becker and M. Teschner, Weakly compressible SPH for free surface flows, SCA 07 [Bridson07] R. Bridson et al., Curl noise for procedural fluid flow, Siggraph 07 [Fournier86] A. Fournier and W. T. Reeves. A simple model of ocean waves, SIGGRAPH 86, pages

75–84 [Hinsinger02] D. Hinsinger et al., Interactive Animation of Ocean Waves, In Proceedings of SCA 02 [Jeffrey02] A. Jeffrey, Applied Partial Differential Equations, Academic Press, ISBN 0-12-382252-1 [Monaghan92] J. J. Monaghan, Smoothed particle hydrodynamics. Annual Review of Astronomy an

d Astrophysics, 30:543–574, 1992. [Müller07] M. Müller et al., Screen Space Meshes, SCA 07. [Müller03] M. Müller et al., Particle-Based Fluid Simulation for Interactive Applications, SCA 03, pag

es 154-159. [O’Brien95] J. O’Brien and J. Hodgins, Dynamic simulation of splashing fluids, In Computer Animati

on 95, pages 198–205 [Premoze03] S. Premoze et al., Particle based simulation of fluids, Eurographics 03, pages 401-410 [Teschner03] M. Teschner et al., Optimized Spatial Hashing for Collision Detection of Deformable O

bjects, VMV 03 [Thuerey07] N. Thuerey et al., Real-time Breaking Waves for Shallow Water Simulations Pacfific Gr

aphics 07 [Yuksel07] Cem Yuksel et al., Wave Particles, Siggraph 07

Hair Simulation

Motivation

Hair animation used in movies, games, virtual reality, etc. Important for representing virtual humans

Problem due to complexity Human head has over 100,000 strands of hair Computation time for simulation and rendering is costly

Overview

Hair Modeling [Magnenat-Thalmann, et al. 2000] Hair Rendering

• Hair color, shadows, lighting, transparency, and anti-aliasing Hair Shape Modeling (hairstyle)

• Geometry of the hair – Shape specification• Density, distribution, and orientation of hair

Hair Simulation• Dynamic Simulation• Collision Detection

Hair Modeling

Factors to consider Speed vs. Appearance Short vs. Long Wavy vs. Straight

Movie: Final FantasyVideo Game: Lara Croft - Tomb Raider: Angel of Darkness

Choose hair model based on desired outcome

Hair Simulation

Physics of dynamic simulation Control motion Different styles

Geometric representation of hair Individual strands Wisps Strips

Collision detection and response Hair-Object Interactions Hair-Hair Interactions

(a) hair strip, (b) hair cluster, (c) hair strand

Hair Simulation Demo

http://www.cs.unc.edu/~geom/HSLOD/

References (Hair Simulation)

K. Anjyo, Y. Usami, and T. Kurihara. A simple method for extracting the natural beauty of hair. Computer Graphics, 26(2):111-120, 1992.

T. Kurihara, K. Anjyo, and D. Thalmann. Hair animation with collision detection. In Models and Techniques in Computer Animation, pages 128-38. Springer-Verlag, 1993.

C. K. Koh and Z. Huang. A simple physics model to animate human hair modeled in 2d strips in real time. Proc. of Eurographics Workshop on Animation and Simulation, 2001.

E. Plante, M. Cani, and P. Poulin. A layered wisp model for simulating interactions inside long hair. Proc. of Eurographics Workshop on Animation and Simulation, 2001.

K. Ward, M. C. Lin, J. Lee, S. Fisher, and D. Macri. Modeling hair using level of detail representations. Proc. of Computer Animation and Social Agents, 2003.

K. Ward and M. C. Lin. Adaptive grouping and subdivision for simulating hair dynamics. Proc. of Pacific Graphics, 2003.