Re: Correction for: Interpolating function with two important characteristics

Have a look at cubic bezier interpolation:
http://www.antigrain.com/research/bezier_interpolation/index.html

Nils

<mike@xxxxxxxxxxxxxxxxxxx> schreef in bericht
news:4356396b$1$29558$4fafbaef@xxxxxxxxxxxxxxxxxxxxxx
>
> [sorry, I have to correct myself: I didn't mean first-derivative,
> but second!]
>
> Hello!
> I need an interpolating function Y=Func(Array,X) with these
> characteristics:
>
> 1) Passes through the points.
> 2) At least the SECOND-derivative must be continuos, thus the
> first-derivative must be "smooth", with no abrupt, sudden changes
> in slope.
>
> As far as I know Catmull-Rom doesn't satisfy the 2nd point, and
> many other spline-like functions don't satisfy the 1st point.
>
> Ideally, a third point would be that if the array contains a
> repeating pattern of 0,1,0,-1 then it should produce a sinewave.
> It should produce a sine-like wave also if the repeating pattern
> is e.g. 1,-1 or 0,.707,1,.707,0,-.707,-1,-.707
>
> Is it even mathematically possible? Should I give up? Or what
> should I Google for? :P
>
> PS: yes, I thought too about the Sinc() interpolation.. but how
> long should the window be to give decent ( = ~ 1% error ) results?
> Also, what kind of windowing function should I use? Probably not
> rectangular, I reckon.
>
> It is for generical data, not for audio or video. Generical data may
> mean control data for robotic arms, etc.. I know that B-spline and
> others are used everyday for this task, it was just an example, but
> anyway I'd like this function, when implemented in 2D, to e.g. produce
> a circle if I use 3 points (which if linearly interpolated would make
> a triangle); if I use 4 points (which if linearly interpolated would
> make a square) it should, interpolated, produce a circle too; if I
> use 8 points (which if linearly interpolated would make an octagon)
> it should, interpolated, produce again a circle, etc.. that's why I
> wanted the 1D case to produce sinewaves. I know, that leads me auto-
> magically to sinc() interpolation.. hmm.
>
> Many thanks,
> Mike
>



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