Lecture 011

Physics Application

Character Controller

Kinematic Actor: usually player

not affected by physics rules
push other objects
Shapes: capsule, box, convex

Different from other physics, we want the player to slide along the wall as it walks at an angle towards the wall.

We also want the players to be able to move up stairs:

every frame when player walk, tries to increase player $y$ (maybe decrease player height to prevent player cannot walk into a door because the player is too tall)
do physics simulation

We also want the player to move up slopes, but slide down for steep slopes.

When walking on slopes, a real human's walking behavior is drastically different from normal walking. The animation system should take care of that.

Sometimes we need to resize character capsule. We need to do a overlap test before update to avoid insertion inside objects.

For moving platform, we can't use physics engine. We need to do a ray cast to detect which platform the character is standing on.

Not just for character, potentially every moving objects. Objects in elevator will look shaky because there is always a 1-frame difference for object to fall down and push up by elevators.

Ragdoll

Ragdoll: use physics simulation at the end of animation. (usually when character dies)

A character might have more joints than we need for physics simulation. We only pick about 10 joints for ragdoll. Since physics simulation is done on about 10 joints, we need to calculate the rest of joint positions for animation to play. (Animation Re-targeting)

Animation Re-targeting in Ragdoll

Active Joints: position provided by physics simulation.

Leaf Joints: endpoint, controlled solely by animation

Intermediate Joints: calculate and interpolated by animation re-targeting.

Ragdoll need to satisfy joint's constraints (since human joints do not have al degrees of freedom) in order to provide satisfying animation.

Ragdoll can interleave with animation, providing more realistic looking transitions. (e.g. when a conscious human hang on a dynamic object)

Cloth Simulation

Old Methods

Traditional: animated bone

Rigid Body-based Cloth Simulation: bones of cloth are bounded with rigid bodies and constraints solved by physics engine

Pros: cheap, interactive
Cons: undetermined quality, not robust, need good physics engine

Mesh-Based

We separate render mesh with physical mesh for reducing computation complexity.

We set different amount of constaints for each vertex: to prevent penetration to attached body (human characters)

To simulate cloth, we use spring force and dampling on vertices

spring force: elasticity
dampling:
- to take account of friction of cloth's face with air
- to avoid floating point error causing explosion of momentum

$\vec{F}_{\text{net}}^{vertex}(t) = M\vec{g}_{\text{gravity}} + \vec{F}_{\text{wind}} + \vec{F}_{\text{air resistance}}(t) + \sum_{\text{springs } \in v} \left( k_{\text{spring}} \Delta\vec{x}(t) - k_{\text{dampling}}\vec{v}(t) \right) = M\vec{a}(t)$

In cloth simulation, Verlet integration provides more stability and better computational complexity than Euler's Semi-implicit.

Position-based Dynamics

Position-based Dynamics is now commonly used.

Self Collision

Self-collision: when cloth collide with itself or other cloths

Make Cloth Thicker
Use substeps: trade computation with accuracy
Set maximum velocity: so you don't penetrate too far
Contact Constaints and Friction Constraints: apply a force with negative direction

Destruction

When a projectile hit a surface

we create chunk hierarchy assigned by the artist (or automatically generated during compilation by Voronoi Diagram)
we use the assigned "hardness" between connectivity graph
if damage (calculated below) is higher than a threshold, break the connection
generate new triangle mesh by Delaunay Triangulation with new texture and texture coordinate
generate new rigid body for collision

For texture coordinate, we can:

offline generate 3D volume texture and sample from it when things break
online generate 3D volume texture and sample from it when things break

Usually the new rigid body does not collide with other rigid bodies other than the children of original body. This is because for consistency issue, physics simulation might diverge. (e.g. you can't shoot down a wall to hit a player)

$\text{Damage } = \frac{\text{Impulse by Collision}}{\text{Material Hardness}}$