How to interpolate S-shaped curve?

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#329

From: KSZ
Date: Tue, 25 Aug 1992 19:12

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I am wondering if anybody knows how to line-smooth a curve which is S -shaped?
The characteristic of this curve is that y is not single-valued. An example is
a circle.
 
I am interested in cubic spline fitting. My idea is to cut the curve into
pieces and for each piece, do the cubic spline since each piece has single-
valued y. But this doesn't work simply because (1) it is hard to determine
cut points for numeraical data and (2) the left- and right-derivatives of
the middle piece if infinity.
 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 KAIJUN S. ZHAN                          || (613) 990 - 0734 (voice)
 Internet:ksz@vm.nrc.ca                  ||
 Internet:kzhan@sgi1.mathstat.uoguelph.ca|| "Three generates everything".
 Internet:gilwf16@vm.uoguelph.ca         ||
 Bitnet:ksz@nrcvm01                      ||      -- Lao Zhi
 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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From: KSZ@VM.NRC.CA
Subject: How to interpolate S-shaped curve?
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Date: Tue, 25 Aug 92 15:12:22 EDT
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