Re: Looking for function (x,y)
- From: "Stephen J. Herschkorn" <sjherschko@xxxxxxxxxxxx>
- Date: Fri, 27 Apr 2007 01:00:23 -0400
Steve555 wrote:
I'm looking for a function similar to y = x from 0 to 1, where (0,0)
and (1,1) are fixed, but with tuneable parameters to give a
symmetrical convex or concave curve in between.
(I'm writing C code to allow the user to shape the output of an
oscillator).
Could this be done with one function, or would I need three (concave,
linear, convex)?
What do you mean by "symmetric"? Do you mean that the graph of f is symmetric with respect to the line x + y = 1? If so, I have two thoughts.
- Pick conic sections passing through (0,0) and (1,1) with an axis lying on the line x + y = 1. You have to make sure that y is a function of x for x in [0,1] for these.
- Consider functions of the form g(x) = +/- [b x (sqrt(2) - x)] ^a where a and b are positive. Rotate the graph 45 degrees. For the resulting graph to determine y as a function of x, (a,b) will be resticted.
In both cases, the linear function does not fit into the suggested form.
--
Stephen J. Herschkorn sjherschko@xxxxxxxxxxxx
Math Tutor on the Internet and in Central New Jersey and Manhattan
.
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