Physically Based Sound

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Physically Based Sound

• COMP259 Nikunj Raghuvanshi

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Background

• Producing sounds in an automated manner, just
  like graphics
• Sounds are produced due to surface vibrations
• Sound production occurs at a much smaller spatial
  and temporal scale than most other simulations
• Straight-forward simulation is not feasible

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Previous Approaches

• O'Brien, J. F. et. al., Synthesizing Sounds from
  Physically Based Motion. SIGGRAPH 2001.
• Kees van den Doel et. Al., FoleyAutomatic
  Physically-based Sound Effects for Interactive
  Simulation and Animation. SIGGRAPH 2001.
• O'Brien, J. F., Shen, C., Gatchalian, C. M.,
  "Synthesizing Sounds from Rigid-Body
  Simulations." SCA 2002
• My approach is similar to the last one, but
  differs in that I am using particle systems

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Approach

• Every body has some natural modes of vibration
• Find out these frequencies of vibration of an
  object using physics
• On impact, find how much each mode is excited
  given an external force
• Generate sound by blending these modes based on
  the coefficients calculated above

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Details of method

• Assume a system of particles connected together
  by damped springs
• Suppose the systems rest position is given by a
  vector R0 formed by concatenating the particles
  individual positions
• The forces generated in an object as a result of
  deformation can be linearized about R0
• That is, if R is the change in the position
  vector, then the restoring force can be expressed
  as,

K is a constant matrix which encodes the
restoring force information
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Details of method

• For an undamped system under the action of an
  external force F,
• where M is a diagonal mass matrix

• Assuming that the damping matrix looks like
  (Rayleigh damping)
• we get the following equation

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Details of method

• This equation can be solved analytically
• Suppose K can be diagonalized. That is,
• Here, D is a diagonal matrix and P is an
  invertible square matrix
• Substituting into previous equation, we get,

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Details of method

• Multiplying by P-1 on both sides and introducing
  YP-1R yields
• Since each matrix in the expression is diagonal,
  this is a set of independent differential
  equations which can be solved analytically

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Details of method

• Physical Interpretation A vibrating object (R)
  can be thought of as a set of independent
  oscillators (Y)
• The frequencies of these oscillators are called
  the modes of vibration
• The external force may be though of as exciting
  some modes depending on where it was applied

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Implementation

• LAPACK for Linear Algebra routines
• A simple interactive application capable of
  producing sounds in real-time depending on user
  input
• Can handle arbitrary 1D and 2D particle systems
• The technique can handle arbitrary rigid bodies
  too but has not been programmed into the GUI at
  present

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Project Goals Achieved

• Primary Goal 1D string and harmonics. Done.
• Secondary Goal 2D objects. Done.
• Advanced Goal Rigid Bodies. Partially Done.

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Future Work

• Add support for rigid bodies
• Find out how to model shear and bulk modulus
  using variable spring-constant springs
• Integrate with a rigid-body simulator