## bpfcos

bpfcos — Break point function with cosine (easy-in/easy-out) interpolation

## Description

Plugin opcode in emugens.

Break-point function with cosine interpolation. Given an x value and a series of pairs (x, y), it returns the corresponding y value in the half cosine curve defined by the pairs. It works both at i- and k- time

## Syntax

`ky bpfcos kx, kx1, ky1, kx2, ..., kxn, kyn`
`kys[] bpfcos kxs[], kx1, ky1, kx2, ..., kxn, kyn`
`ky bpfcos kx, kxs[], kys[]`
`ky bpfcos kx, ixs[], iys[]`
`ky, kz bpfcos kx, kxs[], kys[], kzs[] `
`ky, kz bpfcos kx, ixs[], iys[], izs[] `

## Performance

kx -- Input value. Can also be an array

kxn, kyn -- Defines a breakpoint. Can be changed at krate, but all kxs must be sorted

The points (kx1, ky1), (kx2, ky2), etc, define a cosine interpolated function. This function is evaluated at point kx. This function extends to both -inf and +inf, so if kx < kx1 then ky = ky1 and the same holds true the other end.

### Array Variants

`kys[] bpfcos kxs[], kx1, ky1, kx2, ..., kxn, kyn`

For each x in kxs, calculate the y value defined by the points (kx1, ky1), ... (kxn, kyn)

`ky bpfcos kx, ixs[], iys[]`

In this variants the points are defined through arrays. ixs contains all the x values, iys contains all the y values

`ky, kz bpfcos kx, kxs[], kys[], kzs[] `

The same as the variant above, but for multidimensional points. Given two curves sharing the same x points, calculate the value at x for both dimensions simultaneously. (see example)

Note x values need to be sorted. Both x and y values can change but x values must stay sorted.

## Examples

Here is an example of the bpfcos opcode. It uses the file bpfcos.csd.

Example 104. Example of the bpfcos opcode.

```<CsoundSynthesizer>
<CsOptions>
-odac
</CsOptions>
<CsInstruments>

; Example for opcode bpfcos

/*

bpf stands for Break Point Function

Given an x value and a series of pairs (x, y), it returns
the corresponding y value in the half cosine curve defined by the
pairs

It works both at i- and k- time

ky     bpfcos kx,    kx0, ky0, kx1, ky1, kx2, ky2, ...
kys[]  bpfcos kxs[], kx0, ky0, kx1, ky1, kx2, ky2, ...
ky     bpfcos kx, kxs[], kys[]
ky, kz bpfcos kx, kxs[], kys[], kzs[]

NB: x values must be ordered (kx0 < kx1 < kx2 etc)

*/
sr = 44100
ksmps = 64
nchnls = 1
0dbfs = 1

instr 1
kx line -1, p3, 2.5
ky bpfcos kx,        \
0,    0,   \
1.01, 10,  \
2,    0.5, \
2.5,  -1
printks "kx: %f   ky: %f \n", 0.1, kx, ky
endin

instr 2
; test i-time
ix = 1.2
iy bpfcos ix, 0,0, 0.5,5, 1,10, 1.5,15, 2,20, 2.5,25, 3,30
print iy
turnoff
endin

instr 3
; bpfcos also works with arrays. For each kx value in kxs,
; calculate the corresponding ky
kxs[] fillarray 0, 0.15, 0.25, 0.35, 0.45, 0.55, 0.6
kys[] bpfcos kxs, 0,0, 0.1,10, 0.2,20, 0.3,30, 0.4,40, 0.5,50
printarray kys, 1, "", "kys="
turnoff
endin

instr 4
; bpfcos is useful to implement envelopes with ease-in/out shape
kpitch bpfcos timeinsts(), 0, 60, 2, 61, 3, 65, 3.5, 60
a0 oscili 0.5, mtof(kpitch)
kenv0 linseg 0, 0.5, 1, p3-1, 1, 0.5, 0
kenv bpfcos kenv0, 0, 0, 0.5, 0.25, 1, 0.7
a0 *= interp(kenv)
outch 1, a0
endin

instr 5
; arrays can also be used to define the points of a break-point-function
; multiple arrays can be used simultaneously
; In this case, we define a line and for each point in the line a
; corresponding pitch (midinote) and amplitude
; NB: kTimes uses absolute times
kTimes[] fillarray    0,  1, 1.5,  2,   3,  5
kPitches[] fillarray 60, 65,  64, 69,  60, 61
kAmps[] fillarray     0,  1, 0.1,  1, 0.1,  1
; play the envelopes at half speed
kpitch, kamp bpfcos timeinsts()*0.5, kTimes, kPitches, kAmps
aout oscili a(kamp), a(mtof:k(kpitch))
; declick
aout *= linsegr(0, 0.1, 1, 0.1, 0)
outch 1, aout
endin

</CsInstruments>
<CsScore>
; i 1 1 3
; i 2 0 -1
; i 3 0 -1
; i 4 0 5
i 5 0 10
e 12
</CsScore>
</CsoundSynthesizer>
```