Interactive Sound Rendering

Problems with recorded sounds

difficult to record, repetitiveness, complex interactions

Physical simulation

elastic deformable model, direct simulation infeasible

Modal analysis

each mode represents a resonant mode of vibration, applying impulse excites modes, position of impact determines relative amplitude

1st mode frequency

f0

2nd mode frequency

f1 = 2f0

Higher modes frequencies

fk = kf0

Deformation modeling

vibration of surface generates sound, represent the vibration pattern by a bank of damped oscillators or modes, standard for real

Discretization

an input triangle mesh → a spring

Spring

mass system setup

Ordinary Differential Equation

Kd + Cd’ + Md’’ = f where K = stiffness, C = damping, M = mass

General solution for modal analysis

zi = ciewi+t + c’iewi

State detection

distinguishing between lasting and transient contacts

Lasting contacts

a sequence of impulses, vt ≠ 0

Transient contacts

a single impulse, vpnp < 0 if in contact

Impulse response

zi = ciewi+t + c’iewi

Principle of mode compression

hard to distinguish close frequencies within a specific range

Mode truncation

stop mixing mode when its contribution falls below a prescribed threshold

Quality scaling

give more importance to higher intensity foreground sounds to gracefully adapt to variable time constraints

Limitations of modal analysis

only models the surface, more approximate, can only use linear damping models