spat3d
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## spat3d

spat3d — Positions the input sound in a 3D space and allows moving the sound at k-rate.

## Description

This opcode positions the input sound in a 3D space, with optional simulation of room acoustics, in various output formats. spat3d allows moving the sound at k-rate (this movement is interpolated internally to eliminate "zipper noise" if sr not equal to kr).

## Syntax

    aW, aX, aY, aZ spat3d ain, kX, kY, kZ, idist, ift, imode, imdel, iovr [, istor]

## Initialization

idist -- For modes 0 to 3, idist is the unit circle distance in meters. For mode 4, idist is the distance between microphones.

The following formulas describe amplitude and delay as a function of sound source distance from microphone(s):

amplitude = 1 / (0.1 + distance)

delay = distance / 340 (in seconds)

Distance can be calculated as:

distance = sqrt(iX^2 + iY^2 + iZ^2)

In Mode 4, distance can be calculated as:

distance from left mic = sqrt((iX + idist/2)^2 + iY^2 + iZ^2)
distance from right mic = sqrt((iX - idist/2)^2 + iY^2 + iZ^2)

With spat3d the distance between the sound source and any microphone should be at least (340 * 18) / sr meters. Shorter distances will work, but may produce artifacts in some cases. There is no such limitation for spat3di and spat3dt.

Sudden changes or discontinuities in sound source location can result in pops or clicks. Very fast movement may also degrade quality.

ift -- Function table storing room parameters (for free field spatialization, set it to zero or negative). Table size is 54. The values in the table are:

Room Parameter | Purpose
--- | ---
0 | Early reflection recursion depth (0 is the sound source, 1 is the first reflection etc.) for spat3d and spat3di. The number of echoes for four walls (front, back, right, left) is: N = (2*R + 2) * R. If all six walls are enabled: N = (((4*R + 6)*R + 8)*R) / 3
1 | Late reflection recursion depth (used by spat3dt only). spat3dt skips early reflections and renders echoes up to this level. If early reflection depth is negative, spat3d and spat3di will output zero, while spat3dt will start rendering from the sound source.
2 | imdel for spat3d. Overrides opcode parameter if non-negative.
3 | irlen for spat3dt. Overrides opcode parameter if non-negative.
4 | idist value. Overrides opcode parameter if >= 0.
5 | Random seed (0 - 65535) -1 seeds from current time.
6 - 53 | wall parameters (w = 6: ceil, w = 14: floor, w = 22: front, w = 30: back, w = 38: right, w = 46: left)
w + 0 | Enable reflections from this wall (0: no, 1: yes)
w + 1 | Wall distance from listener (in meters)
w + 2 | Randomization of wall distance (0 - 1) (in units of 1 / (wall distance))
w + 3 | Reflection level (-1 - 1)
w + 4 | Parametric equalizer frequency in Hz.
w + 5 | Parametric equalizer level (1.0: no filtering)
w + 6 | Parametric equalizer Q (0.7071: no resonance)
w + 7 | Parametric equalizer mode (0: peak EQ, 1: low shelf, 2: high shelf)

imode -- Output mode

- 0: B format with W output only (mono)

  aout = aW

- 1: B format with W and Y output (stereo)

  aleft = aW + 0.7071*aY
  aright = aW - 0.7071*aY

- 2: B format with W, X, and Y output (2D). This can be converted to UHJ:

  aWre, aWim hilbert aW
  aXre, aXim hilbert aX
  aYre, aYim hilbert aY
  aWXr = 0.0928*aXre + 0.4699*aWre
  aWXiYr = 0.2550*aXim - 0.1710*aWim + 0.3277*aYre
  aleft = aWXr + aWXiYr
  aright = aWXr - aWXiYr

- 3: B format with all outputs (3D)

- 4: Simulates a pair of microphones (stereo output)

  aW butterlp aW, ifreq ; recommended values for ifreq
  aY butterlp aY, ifreq ; are around 1000 Hz
  aleft = aW + aX
  aright = aY + aZ

Mode 0 is the cheapest to calculate, while mode 4 is the most expensive.

In Mode 4, The optional lowpass filters can change the frequency response depending on direction. For example, if the sound source is located left to the listener then the high frequencies are attenuated in the right channel and slightly increased in the left. This effect can be disabled by not using filters. You can also experiment with other filters (tone etc.) for better effect.

Note that mode 4 is most useful for listening with headphones, and is also more expensive to calculate than the B-format (0 to 3) modes. The idist parameter in this case sets the distance between left and right microphone; for headphones, values between 0.2 - 0.25 are recommended, although higher settings up to 0.4 may be used for wide stereo effects.

More information about B format can be found here: http://www.york.ac.uk/inst/mustech/3d_audio/ambis2.htm

imdel -- Maximum delay time for spat3d in seconds. This has to be longer than the delay time of the latest reflection (depends on room dimensions, sound source distance, and recursion depth; using this formula gives a safe (although somewhat overestimated) value:

imdel = (R + 1) * sqrt(W*W + H*H + D*D) / 340.0

where R is the recursion depth, W, H, and D are the width, height, and depth of the room, respectively).

iovr -- Oversample ratio for spat3d (1 to 8). Setting it higher improves quality at the expense of memory and CPU usage. The recommended value is 2.

istor (optional, default=0) -- Skip initialization if non-zero (default: 0).

## Performance

aW, aX, aY, aZ -- Output signals

| mode 0 | mode 1 | mode 2 | mode 3 | mode 4
--- | --- | --- | --- | --- | ---
aW | W out | W out | W out | W out | left chn / low freq.
aX | 0 | 0 | X out | X out | left chn / high frq.
aY | 0 | Y out | Y out | Y out | right chn / low frq.
aZ | 0 | 0 | 0 | Z out | right chn / high fr.

ain -- Input signal

kX, kY, kZ -- Sound source coordinates (in meters)

If you encounter very slow performance (up to 100 times slower), it may be caused by denormals (this is also true of many other IIR opcodes, including butterlp, pareq, hilbert, and many others). Underflows can be avoided by:

- Using the denorm opcode on ain before spat3d.

- mixing low level DC or noise to the input signal, e.g.

  atmp rnd31 1/1e24, 0, 0

  aW, aX, aY, aZ spa3di ain + atmp, ...

  or

  aW, aX, aY, aZ spa3di ain + 1/1e24, ...

- reducing irlen in the case of spat3dt (which does not have an input signal). A value of about 0.005 is suitable for most uses, although it also depends on EQ settings. If the equalizer is not used, “irlen” can be set to 0.

## Examples

Here is a example of the spat3d opcode that outputs a stereo file. It uses the file spat3d_stereo.csd.

Example 909. Stereo example of the spat3d opcode.

See the sections Real-time Audio and Command Line Flags for more information on using command line flags.

    <CsoundSynthesizer>
    <CsOptions>
    ; Select audio/midi flags here according to platform
    ; Audio out   Audio in    No messages
    -odac           -iadc     -d     ;;;RT audio I/O
    ; For Non-realtime ouput leave only the line below:
    ; -o spat3d_stereo.wav -W ;;; for file output any platform
    </CsOptions>
    <CsInstruments>

    /* Written by Istvan Varga */
    sr      =  48000
    kr      =  1000
    ksmps   =  48
    nchnls  =  2

    /* room parameters */

    idep    =  3    /* early reflection depth       */

    itmp    ftgen   1, 0, 64, -2,                                           \
    		/* depth1, depth2, max delay, IR length, idist, seed */ \
    		idep, 48, -1, 0.01, 0.25, 123,                          \
    		1, 21.982, 0.05, 0.87, 4000.0, 0.6, 0.7, 2, /* ceil  */ \
    		1,  1.753, 0.05, 0.87, 3500.0, 0.5, 0.7, 2, /* floor */ \
    		1, 15.220, 0.05, 0.87, 5000.0, 0.8, 0.7, 2, /* front */ \
    		1,  9.317, 0.05, 0.87, 5000.0, 0.8, 0.7, 2, /* back  */ \
    		1, 17.545, 0.05, 0.87, 5000.0, 0.8, 0.7, 2, /* right */ \
    		1, 12.156, 0.05, 0.87, 5000.0, 0.8, 0.7, 2  /* left  */

    	instr 1

    /* some source signal */

    a1      phasor 150              ; oscillator
    a1      butterbp a1, 500, 200   ; filter
    a1      =  taninv(a1 * 100)
    a2      phasor 3                ; envelope
    a2      mirror 40*a2, -100, 5
    a2      limit a2, 0, 1
    a1      =  a1 * a2 * 9000

    kazim   line 0, 2.5, 360        ; move sound source around
    kdist   line 1, 10, 4           ; distance

    ; convert polar coordinates
    kX      =  sin(kazim * 3.14159 / 180) * kdist
    kY      =  cos(kazim * 3.14159 / 180) * kdist
    kZ      =  0

    a1      =  a1 + 0.000001 * 0.000001     ; avoid underflows

    imode   =  1    ; change this to 3 for 8 spk in a cube,
    		; or 1 for simple stereo

    aW, aX, aY, aZ  spat3d a1, kX, kY, kZ, 1.0, 1, imode, 2, 2

    aW      =  aW * 1.4142

    ; stereo
    ;
    aL     =  aW + aY              /* left                 */
    aR     =  aW - aY              /* right                */

    ; quad (square)
    ;
    ;aFL     =  aW + aX + aY         /* front left           */
    ;aFR     =  aW + aX - aY         /* front right          */
    ;aRL     =  aW - aX + aY         /* rear left            */
    ;aRR     =  aW - aX - aY         /* rear right           */

    ; eight channels (cube)
    ;
    ;aUFL   =  aW + aX + aY + aZ    /* upper front left     */
    ;aUFR   =  aW + aX - aY + aZ    /* upper front right    */
    ;aURL   =  aW - aX + aY + aZ    /* upper rear left      */
    ;aURR   =  aW - aX - aY + aZ    /* upper rear right     */
    ;aLFL   =  aW + aX + aY - aZ    /* lower front left     */
    ;aLFR   =  aW + aX - aY - aZ    /* lower front right    */
    ;aLRL   =  aW - aX + aY - aZ    /* lower rear left      */
    ;aLRR   =  aW - aX - aY - aZ    /* lower rear right     */

    	outs aL, aR

    	endin

    </CsInstruments>
    <CsScore>

    /* Written by Istvan Varga */
    i 1 0 10
    e

    </CsScore>
    </CsoundSynthesizer>

Here is a example of the spat3d opcode that outputs a UHJ file. It uses the file spat3d_UHJ.csd.

Example 910. UHJ example of the spat3d opcode.

    <CsoundSynthesizer>
    <CsOptions>
    ; Select audio/midi flags here according to platform
    ; Audio out   Audio in    No messages
    -odac           -iadc     -d     ;;;RT audio I/O
    ; For Non-realtime ouput leave only the line below:
    ; -o spat3d_UHJ.wav -W ;;; for file output any platform
    </CsOptions>
    <CsInstruments>

    /* Written by Istvan Varga */
    sr	=  48000
    kr	=  750
    ksmps	=  64
    nchnls	=  2

    itmp    ftgen   1, 0, 64, -2,                                           \
    		/* depth1, depth2, max delay, IR length, idist, seed */ \
    		3, 48, -1, 0.01, 0.25, 123,				\
    		1, 21.982, 0.05, 0.87, 4000.0, 0.6, 0.7, 2, /* ceil  */ \
    		1,  1.753, 0.05, 0.87, 3500.0, 0.5, 0.7, 2, /* floor */ \
    		1, 15.220, 0.05, 0.87, 5000.0, 0.8, 0.7, 2, /* front */ \
    		1,  9.317, 0.05, 0.87, 5000.0, 0.8, 0.7, 2, /* back  */ \
    		1, 17.545, 0.05, 0.87, 5000.0, 0.8, 0.7, 2, /* right */ \
    		1, 12.156, 0.05, 0.87, 5000.0, 0.8, 0.7, 2  /* left  */

    	instr 1

    p3	=  p3 + 1.0

    kazim	line 0.0, 4.0, 360.0		; azimuth
    kelev	line 40, p3 - 1.0, -20		; elevation
    kdist	=  2.0				; distance
    ; convert coordinates
    kX	=  kdist * cos(kelev * 0.01745329) * sin(kazim * 0.01745329)
    kY	=  kdist * cos(kelev * 0.01745329) * cos(kazim * 0.01745329)
    kZ	=  kdist * sin(kelev * 0.01745329)

    ; source signal
    a1	phasor 160.0
    a2	delay1 a1
    a1	=  a1 - a2
    kffrq1	port 200.0, 0.8, 12000.0
    affrq	upsamp kffrq1
    affrq	pareq affrq, 5.0, 0.0, 1.0, 2
    kffrq	downsamp affrq
    aenv4	phasor 3.0
    aenv4	limit 2.0 - aenv4 * 8.0, 0.0, 1.0
    a1	butterbp a1 * aenv4, kffrq, 160.0
    aenv	linseg 1.0, p3 - 1.0, 1.0, 0.04, 0.0, 1.0, 0.0
    a_	=  4000000 * a1 * aenv + 0.00000001

    ; spatialize
    a_W, a_X, a_Y, a_Z	spat3d a_, kX, kY, kZ, 1.0, 1, 2, 2.0, 2

    ; convert to UHJ format (stereo)
    aWre, aWim	hilbert a_W
    aXre, aXim	hilbert a_X
    aYre, aYim	hilbert a_Y

    aWXre	=  0.0928*aXre + 0.4699*aWre
    aWXim	=  0.2550*aXim - 0.1710*aWim

    aL	=  aWXre + aWXim + 0.3277*aYre
    aR	=  aWXre - aWXim - 0.3277*aYre

    	outs aL, aR

    	endin

    </CsInstruments>
    <CsScore>

    /* Written by Istvan Varga */
    t 0 60

    i 1 0.0 8.0
    e

    </CsScore>
    </CsoundSynthesizer>

Here is a example of the spat3d opcode that outputs a quadrophonic file. It uses the file spat3d_quad.csd.

Example 911. Quadrophonic example of the spat3d opcode.

    <CsoundSynthesizer>
    <CsOptions>
    ; Select audio/midi flags here according to platform
    ; Audio out   Audio in    No messages
    -odac           -iadc     -d     ;;;RT audio I/O
    ; For Non-realtime ouput leave only the line below:
    ; -o spat3d_quad.wav -W ;;; for file output any platform
    </CsOptions>
    <CsInstruments>

    /* Written by Istvan Varga */
    sr      =  48000
    kr      =  1000
    ksmps   =  48
    nchnls  =  4

    /* room parameters */

    idep    =  3    /* early reflection depth       */

    itmp    ftgen   1, 0, 64, -2,                                           \
    		/* depth1, depth2, max delay, IR length, idist, seed */ \
    		idep, 48, -1, 0.01, 0.25, 123,                          \
    		1, 21.982, 0.05, 0.87, 4000.0, 0.6, 0.7, 2, /* ceil  */ \
    		1,  1.753, 0.05, 0.87, 3500.0, 0.5, 0.7, 2, /* floor */ \
    		1, 15.220, 0.05, 0.87, 5000.0, 0.8, 0.7, 2, /* front */ \
    		1,  9.317, 0.05, 0.87, 5000.0, 0.8, 0.7, 2, /* back  */ \
    		1, 17.545, 0.05, 0.87, 5000.0, 0.8, 0.7, 2, /* right */ \
    		1, 12.156, 0.05, 0.87, 5000.0, 0.8, 0.7, 2  /* left  */

    	instr 1

    /* some source signal */

    a1      phasor 150              ; oscillator
    a1      butterbp a1, 500, 200   ; filter
    a1      =  taninv(a1 * 100)
    a2      phasor 3                ; envelope
    a2      mirror 40*a2, -100, 5
    a2      limit a2, 0, 1
    a1      =  a1 * a2 * 9000

    kazim   line 0, 2.5, 360        ; move sound source around
    kdist   line 1, 10, 4           ; distance

    ; convert polar coordinates
    kX      =  sin(kazim * 3.14159 / 180) * kdist
    kY      =  cos(kazim * 3.14159 / 180) * kdist
    kZ      =  0

    a1      =  a1 + 0.000001 * 0.000001     ; avoid underflows

    imode   =  2    ; change this to 3 for 8 spk in a cube,
    		; or 1 for simple stereo

    aW, aX, aY, aZ  spat3d a1, kX, kY, kZ, 1.0, 1, imode, 2, 2

    aW      =  aW * 1.4142

    ; stereo
    ;
    ;aL     =  aW + aY              /* left                 */
    ;aR     =  aW - aY              /* right                */

    ; quad (square)
    ;
    aFL     =  aW + aX + aY         /* front left           */
    aFR     =  aW + aX - aY         /* front right          */
    aRL     =  aW - aX + aY         /* rear left            */
    aRR     =  aW - aX - aY         /* rear right           */

    ; eight channels (cube)
    ;
    ;aUFL   =  aW + aX + aY + aZ    /* upper front left     */
    ;aUFR   =  aW + aX - aY + aZ    /* upper front right    */
    ;aURL   =  aW - aX + aY + aZ    /* upper rear left      */
    ;aURR   =  aW - aX - aY + aZ    /* upper rear right     */
    ;aLFL   =  aW + aX + aY - aZ    /* lower front left     */
    ;aLFR   =  aW + aX - aY - aZ    /* lower front right    */
    ;aLRL   =  aW - aX + aY - aZ    /* lower rear left      */
    ;aLRR   =  aW - aX - aY - aZ    /* lower rear right     */

    	outq aFL, aFR, aRL, aRR

    	endin

    </CsInstruments>
    <CsScore>

    /* Written by Istvan Varga */
    t 0 60
    i 1 0 10
    e

    </CsScore>
    </CsoundSynthesizer>

## See Also

spat3di, spat3dt

## Credits

Author: Istvan Varga
2001

New in version 4.12

Updated April 2002 by Istvan Varga

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