Re: Optimum spline problem


In article <bzibe.21122$JB.16908@xxxxxxxxxxxxxxxxxxxx>,
John_W_Herman@xxxxxxxxx (John Herman) writes:
>I'm trying to guess a good shape based on very sparce information. I thought
>maybe there might be an optimization approach might allow for an improvement
>in a shape over the "tinker-toy" approach I'm currently using.


if you want to design a curve, much depends on the nature of points.
normally, if you deal with a curve (not a function graph)
you might parametrize with the distances of the interpolating
piecewise linear arc and then interpolate by an ordinary cubic spline or
a spline under tension. selection of the tension parameter is
somewhat arbitrary. minimizing the total curvature makes it a nonlinear
problem . hence anything depends on what you feel is a "nice curve"
taking distances to the end points into account would yield something of minimal
length, a bit similar to the spline under tension?
hth
peter



>
>
>In article <d4iief$ifo$1@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
>spellucci@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (Peter Spellucci) wrote:
>>
>>In article <8tvae.3161$JB.2248@xxxxxxxxxxxxxxxxxxxx>,
>> John_W_Herman@xxxxxxxxx (John Herman) writes:
>> >I have a problem where I am trying to estimate the optimum shape of a line.
>> I
>> >estimates of the radial distance from the end node to each of the other nodes
>>
>> >and the tangent to the the curve at each point except the end node. The
>> nodes
>> >are irregularily spaced but the maximum distance between nodes and the
>> maximum
>> >distance from the end node are known exactly. What approach is best to use
>> >for this problem?
>>
>>it is completely unclear to me what you want to "optimize".
>>the distance to the endpoint: which role should it play here
>>hth
>>peter
.

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