What equation can perform this type of spline interpolation?

[mikejm]

I have a Reaktor module which can perform pretty nice, smooth spline interpolation like the attachment.

However, the code behind it is quite complex and I'm having trouble understanding how the smooth interpolation you get at the end of the knob (curve position 2) works.

Let's say you have n number of points on a coordinate grid from (0,0) to (1,1) and you are trying to get an equation to interpolate them like this for GUI graphing and data processing (eg. velocity shaping).

What type of equation could this be using? Thanks.

[mikejm]

If it's helpful, I can figure this much out:

- The curve control knob is a cross fade between type 0 (no interpolation), type 1 (linear interpolation), and type 2 ('hifi' interpolation).
- Type 2 (ie. smooth interpolation) is what I want to do.

The guts for the 'hifi' interpolation bits are attached if they make sense to anyone:

General overview:

spline guts 1.PNG

"Interpol" component:

spline guts 2.PNG

"Flo spline" component:

spline guts 3.PNG

"Frac" component:

spline guts 4.PNG

[juha_p]

Maybe based on https://en.wikipedia.org/wiki/Cubic_Her ... Rom_spline or variant as like https://en.wikipedia.org/wiki/Centripet ... Rom_spline