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]](images/note.png)
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Note |
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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. Play bpfcos.csd
Example 108. 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) See also: bpf, linlin, lincos */ 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>