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Convert array to function

From: Marco
Subject: Convert array to function
Date: Fri, 19 Dec 2014 12:36:30 +0100
User-agent: Mutt/1.5.23 (2014-03-12)


I have a problem and assume there's a simple solution. But I neither
know octave nor maths that well. Maybe some of you guys can help

I have a curve that is described as a vector v with n-elements, each
containing a pair:

  v=[0,0; 2,2; 4,2; 6,6; 10,6]

ASCII-art visualised:

  6|           xxxxxxxxx
   |          x
  4|         x
   |        x
  2|   xxxxx
   |  x
   0   2   4   6   8   10

I am only interested in the x-range [0:10] meaning the values below
0 and above 10 can be ignored.

Vector v is given and I have to define a function that evaluates to
the points described by the vector. The points are always connected
by straight lines. So the function should (with the example values
for v as stated above) at point 1 evaluate to 1, at point 2 evaluate
to 2, at point 8 evaluate to 6, etc.

The pairs are not necessarily equally spaced and the number of
elements in v is not constant. (This will be automated and the v is
the input I receive.)

The question: Is there an octave function which I can feed the
vector with pairs (v) and obtain a function which I can evaluate at
any point within the range?

I looked into linear approximation, but that gives me a straight
line through the points and no the required “steps”, thus
introducing a very high error. I also found that polynom or spline
approximation (using splinefit or polyfit) do not yield acceptable
results. Any ideas?

I am happy to provide further information or clarify things if


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