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Java 3D API Specification


A P P E N D I X E
Equations




This appendix contains the Java 3D equations for fog, lighting, sound, and texture mapping. Many of the equations use the following symbols:

· Multiplication
Dot product or function operator

E.1 Fog Equations

To be supplied.

E.2 Lighting Equations

The ideal lighting equation is as follows:

Note: If (Li · N) 0, then diffi and speci are set to 0.

Note: For directional lights, atteni is set to 1.

Note: If the vertex is outside the spotlight cone, as defined by the cutoff angle, spoti is set to 0. For directional and point lights, spoti is set to 1.

This is a subset of OpenGL in that the Java 3D ambient and directional lights are not attenuated and only ambient lights contribute to ambient lighting.

The parameters used in the lighting equation are as follows:

E = Eye vector
Ma = Material ambient color
Md = Material diffuse color
Me = Material emissive color
Ms = Material specular color
N = Vertex normal
shin = Material shininess

The per-light values are as follows:

di = Distance from vertex to light
Di = Spotlight direction
expi = Spotlight exponent
Kci = Constant attenuation
Kli = Linear attenuation
Kqi = Quadratic attenuation
Li = Direction from vertex to light
Lci = Light color
Si = Specular half-vector = || (Li + E) ||

Fallbacks and Approximations

E.3 Sound Equations

There are different sets of sound equations, depending on the use of headphones or speakers.

E.3.1 Headphone Playback Equations

For each sound source, Java 3D calculates a separate left and right output signal. Each left and right sound image is made up of the an interaural intensity and an interaural delay. The calculation results are a set of direct and indirect (delayed) sound signals mixed together when sent to the audio playback system left and right transducers.

E.3.1.1 Interaural Time Difference (Delay)

For each point and cone sound source node, the left and right output signals are delayed based on the location of the sound and the orientation of the head. This time difference between these two signals is called the interaural time difference (ITD). This time delay of a particular sound reaching the far ear is affected by the shadow of the listener's head. Java 3d uses an approximation of the ITD using a spherical head model. The interaural path difference is calculated based on the following cases:

The parameters used in the ITD equations are as follows:

= Angle between Vh and Va in radians
De = Distance between ears (interaural distance)
Dh = Distance from interaural center to sound source
Ec = Distance from sound source to ear closest to sound
Ef = Distance from sound source to ear farthest from sound
P = Difference between Paths to right and left ears from source
Va = Vector from center ear forward parallel to Z axis of head coordinates
Vc = Vector from sound source to ear closest to sound
Vf = Vector from sound source to ear farthest from sound
Vh = Vector from center ear to sound source

The time from the sound source to the closest ear is Ec/S, and the time from the sound source to the farthest ear is Ef/S, where S is the region's speed of sound.

E.3.1.2 Interaural Intensity (Gain) Difference

For each active and playing Point and ConeSound source, s, separate calculations for the left and right signal (based on which ear is closest and which is farthest to the source) are combined with non-spatialized BackgroundSound to create a stereo sound image.

Note: For BackgroundSound sources ITD() is an identity function so there is no delay applied to the sample for these sources.
G[l,r] = Gi · Gd[Ec,Ef] · Ga()
Note: For BackgroundSound sources Gd() = Ga() = 1.0. For PointSound sources Ga() = 1.0.
F[l,r] = Fd[Ec,Ef] Fa()
Note: For BackgroundSound sources Fd() and Fa() are identity functions. For PointSound sources Fa() is an identity function.

If the Sound source is on the right side of the head, Ec is used for left G and F calculations and Ef is used for right. Conversely, if the Sound source is on the left side of the head, Ef is used for left calculations and Ec is used for right.

The parameters used in the IID equations are as follows:

= Angle between Vh and Va in radians
d = Distance from sound source to left or right ear (either Ec or Ef)
Ec = Distance from sound source to ear closest to sound from the ITD equation
Ef = Distance from sound source to ear farthest from sound from the ITD equation
Fa = Angular filter from ConeSound definition
Fd = Distance Filter from aural attribute
Ga = Angular Gain attenuation scale factor
Gd = Distance Gain attenuation scale factor
Gi = Initial Gain scale factor
numS = Number of sound sources

E.3.1.3 Doppler Effect Equations

The frequency of sound waves emanating from the source are lowered based on the speed of the source in relation to the listener, and the sound wave length, as follows:

S(f)' = S(f) - [Ds · (Dv/W(f,Dh)]

The parameters used in the Doppler effect equations are as follows:

Dh = Distance from sound source to center ear
Ds = Doppler scale factor (AuralAttribute field)
Dv = Doppler velocity (between the listener and sound source)
f = Frequency
S = Sound source frequency
t = Time
W = Wavelength of sound source based on frequency and distance

E.3.1.4 Reverberation Equations

To be supplied.

E.3.1.5 Filtering Equations

To be supplied.

E.3.2 Speaker Playback Equations

Different speaker playback equations are used, depending on whether the system uses monaural or stereo speakers.

E.3.2.1 Monaural Speaker Output

The equations for headphone playback need only be modified to output a single signal, rather than two signals for left and right transducers. Although there is only one speaker, distance and filter attenuation, Doppler effect, elevation and front and back cues can be distinguished by the listener and should be included in the sound image generated.

E.3.2.2 Stereo Speaker Output

In a two speaker playback system, the signal from one speaker is actually heard by both ears and this affects the spectral balance and interaural intensity and time differences heard by each of the listener's ears. Cross-talk cancellation must be performed on the right and left signal to compensate for the delayed attenuated signal heard by the ear opposite the speaker. Thus a delayed attenuated signal for each of the stereo signals must be added to the output from the equations for headphone playback.

The equations for stereo speaker playback assume that the two speakers are placed symmetrically about the listener (at the same off-axis angle from the viewing axis at an equal distance from the center of the listener's head).

I(t)l' = I(t)l + [D(t) [G(P,) · I(t)r] ]

I(t)r' = I(t)r + [D(t) [G(P,) · I(t)l] ]

The parameters used in the cross-talk equations, expanding on the terms used for the equations for headphone playback, are as follows:

= Angle between vectors from speaker to near and far ears
D = Delay function of signal variant over time
G = Gain attenuation scale factors function taking initial, distance and angular gain scale factors into account
I = Sound image for left and right stereo signals calculated as for headphone output
P = Distance difference between near ear and far ear as defined for ITD, the speaker substituted for the sound source in equation
t = Time

E.4 Texture Mapping Equations

To be supplied.


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Java 3D API Specification


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