利用者:NeXyon/GSoC2011/3D Audio/3D Device
Software 3D Device Design
Here's the signal-flow graph of the audio data:
The calculations how they are done in the specific steps follow, dopper and distance calculation formulars are from the OpenAL 1.1 Specification, the others are derived by me, so might contain errors atm.
Doppler
Input Variables:
- SP = Source Position
- SV = Source Velocity
- LP = Listener Position
- LV = Listener Velocity
- SS = Speed of Sound
- DF = Doppler Factor
Calculations:
<math> \vec{SL} = \vec{LP} - \vec{SP} </math>
<math> vls = \frac{\vec{SL} \cdot \vec{LV}}{|\vec{SL}|} </math>
<math> vss = \frac{\vec{SL} \cdot \vec{SV}}{|\vec{SL}|} </math>
Clamp vls and vss to a maximum of <math> \frac{SS}{DF} </math>
<math> pitch = \frac{SS - DF \cdot vls}{SS - DF \cdot vss} </math>
Pitch
Input Variables:
- SP = Source Pitch
Calculations:
<math> pitch = SP </math>
Distance
Input Variables:
- ref = Reference Distance
- rof = Rolloff Factor
- max = Maximum Distance
- SP = Source Position
- LP = Listener Position
Calculations:
<math> dist = |LP - SP| </math>
Here are three distance models possible with or without clamping.
In case of clamping:
<math> dist = max(min(max, dist), reference) </math>
Inverse Model:
<math> gain = \frac{ref}{ref + rof \cdot (dist - ref)} </math>
Linear Model:
<math> gain = 1- rof \cdot \frac{dist - ref}{max - ref} </math>
Exponential:
<math> gain = \left( \frac{dist}{ref} \right)^{-rof} </math>
Cone
Input Variables:
- SZ = Lookat of the Source
- LP = Listener Position
- SP = Source Position
- in = Inner Cone Angle
- out = Outer Cone Angle
- og = Outer Cone Gain
Calculations:
<math> \vec{LS} = \vec{SP} - \vec{LP} </math>
<math> phi = arccos \left( \frac{\vec{SZ} \cdot \vec{LS}}{|\vec{SZ}| |\vec{LS}|} \right) </math>
<math> t = \frac{phi - in}{out - in} </math>
t is clamped between 0 and 1
<math> gain = 1 + t \cdot (out - 1) </math>
Volume
Input Variables:
- SV = Source Volume
Calculations:
<math> gain = SV </math>
3D-Cue
Input Variables:
- S = Source Position
- N = Listener Up Vector
- C = Listener Position
- Z = Listener Look at Vector
Calculations:
<math> \vec{A} = \vec{S} + \frac{(\vec{C} - \vec{S}) \cdot \vec{N}}{\vec{N}^2} \cdot \vec{N} - \vec{C} </math>
<math> phi = arccos \left( \frac{\vec{Z}\vec{A}}{|\vec{Z}| |\vec{A}|} \right) \cdot sgn( (\vec{N} \times \vec{Z} ) \vec{A} ) </math>
phi is then used to decide which speakers the audio signal is played to.
