Architect: Few random Qs about generating curves

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Hi.
This is written just in regard of future possibility of Curve generating in Arch (which can be w/ coding, Lua libs etc. pretty cool - in realm of modulation it will allow use heavy weight task (that regularly has to be done outside the DAWs) sort of on fly.))

How is called the form of function looking like on first two pic bellow? – using just time unit (t or u) (ideally in basis functions – so probably smth like B-Splines, NURBS) :borg:
Is it isogeometric analysis – integration of finite element analysis (FEA)?

But mainly, how can I convert - approximate (approximation theory)) :phones: f. e. Cantilevered beam (Euler-Bernoulli beam theory –bottom pic) into just that fnct that use just time or at least some polynomial equation?
(I am not desperate - slowly dig in, but some tiny shiny point light would help)).

BTW: Last two Bicubic B-Spline second degree basis functions (top two pics) are in my DAW bigger (2x and 10x) – I also have no idea how it comes. :x

EDIT: I will get Matlab this week (looks like without some program like this or GNU Octave it is hard to get basic starting idea).
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