[PD-ot] Peak of 4 point interpolation

[PSPunch]

Hi all,


Reading one of the exercises mentioned in Miller's book, I came across
the fact that 4 point interpolation may introduce values out of boundaries.


------ Excerpt start-------
(p.58)

If a wavetable's contents all fall between -1 and 1 in value, what is
the range of possible outputs of wavetable lookup using 4-point
interpolation?

------ Excerpt end -------

So I tried create a 4 point table
-1 1 1 -1

and fed an index of 1.5

[1.5{
|
[tabread4]

The output is 1.25


I've only taken a rough guess that a curve connecting the 4 points in
the table I mentioned will exceed the range of -1 to 1.

What is the correct answer to this question, and how can it be answered
more mathematically?

--
David Shimamoto