Sine wave generation playground. Documented things are work in progress, and not guaranteed as proper solutions.

To change frequency of wave, at first, focus on acceleration of time e(x). e(x) goes from 1(current freq.) to K(K-fold freq.). And its integral E(x) is described as "distored time".

n provides easing function as follows:

Finally, formula is defined as follows:

Partially generated sine wave does not ends with end of cycle unless its last arguments is integral multiple of 2 * PI, so must remember its offset value to append next partial wave,

If x is reset zero for each partial wave, in case that the last sine argument A is only provided, offset is described as follows:

Of course, if fmod function is avaiable: offset = fmod(A, 2 * PI)

As above mentioned, sine wave does not always ends with end of cycle, so must adjust last partial wave duration by additional duration. This operation is called "finalize" on this document.

Finalizing algoritm is similar with appending partial wave. In case that the last sine argument A and frequency H are provided, additional duration can be computed as follows:

Authored by Retorillo

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