Re: How to calculate two curves equidistant from a given curve?

On Sun, 4 Sep 2005 23:53:02 +0000 (UTC), Timothy Little
<tim-usenet@xxxxxxxxxxxxxxxxxx> wrote:

>Tony wrote:
>> Given parametrized curve of a certain degree (typically a cubic for
>> computer graphics) how does one go about calculating two curves (one
>> for each of two sides) that are always at the same, fixed Euclidean
>> distance from the reference curve, for each parameter value?
>
>In general, this will not be possible. For example, a curve at a
>fixed nonzero distance from y = x^2 is not expressible as a polynomial
>of any finite degree.
>
>
>- Tim

The required curves are parametrizable and there is a simple formula
for the parametrizations based on the parametrization of the original
curve, so calculating the curves is not really a problem.
.

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